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Kinematic analysis and evaluation of wheelchair mounted robotic arms

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Title:
Kinematic analysis and evaluation of wheelchair mounted robotic arms
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English
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McCaffrey, Edward Jacob
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Subjects / Keywords:
manipulator
assistive
workstation
mobile
design
Dissertations, Academic -- Mechanical Engineering -- Masters -- USF   ( lcsh )
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government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Summary:
ABSTRACT: The goal of this thesis is the kinematic analysis and evaluation of wheelchair mounted robotic arms. More specifically, to address the kinematics of the wheelchair mounted robotic arm (WMRA) with respect to its ability to reach positions commonly required by an assistive device in activities of daily living (ADL). A robotic manipulator attached to a power wheelchair could enhance the manipulation functions of an individual with a disability. In this thesis, a procedure is developed for the kinematic analysis and evaluation of a wheelchair mounted robotic arm. In addition to developing the analytical procedure, the manipulator is evaluated, and design recommendations and insights are obtained. At this time there exist both commercially-available and industrial wheelchair mountable robotic manipulators. The commercially-available manipulators (of which two will be addressed in this research) have been designed specifically for use in rehabilitation robotics. In contrast, industrial robotic manipulators are designed for speed, precision, and endurance. These traits are not required in assistive robots and can actually be dangerous to the operator if mounted onto a wheelchair. Manipulators to be used as WMRAs must be designed specifically for assistive functions in order to be utilized as a wheelchair mounted robotic arm. In an effort to evaluate two commercial manipulators, the procedure for kinematic analysis is applied to each manipulator. Design recommendations with regard to each device are obtained. This method will benefit the researchers by providing a standardized procedure for kinematic analysis of WMRAs that is capable of evaluating independent designs.
Thesis:
Thesis (M.S.M.E.)--University of South Florida, 2003.
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Includes bibliographical references.
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by Edward Jacob McCaffrey.
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Title from PDF of title page.
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Document formatted into pages; contains 120 pages.

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aleph - 001447454
oclc - 54068520
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usfldc handle - e14.195
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Kinematic Analysis and Evaluation of Wheelchair Mounted Robotic Arms by Edward Jacob McCaffrey A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Rajiv Dubey, Ph.D. Glen Besterfield, Ph.D. Thomas Eason, Ph.D. Date of Approval: November 13, 2003 Keywords: manipulator, assistive, workstation, mobile, design Copyright 2003 Edward Jacob McCaffrey

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i Table of Contents List of Tables…….............................................................................................................ii i List of Figures……............................................................................................................iv Abstract……………..........................................................................................................vi Chapter One Introduction.........................................................................................1 1.1 Motivation...........................................................................................................1 1.2 Objectives...........................................................................................................2 Chapter Two Background.........................................................................................3 2.1 History of Rehabilitation Robotics.....................................................................3 2.2 Workstation-Based Systems...............................................................................4 2.3 Mobile Systems...................................................................................................9 2.4 Integrated Robotic Systems..............................................................................10 2.5 Research WMRAs............................................................................................12 2.5.1 Rear Mount...............................................................................................14 2.6 Commercially Available WMRAs....................................................................15 2.6.1 The Manus ................................................................................................15 2.6.1.1 Front Mount.........................................................................................16 2.6.1.2 Closed Loop Control............................................................................17 2.6.2 The Raptor ................................................................................................18 2.6.2.1 Side Mount...........................................................................................19 2.6.2.2 Open Loop Control..............................................................................20 Chapter Three Procedure for Kinematic Analysis....................................................21 3.1 Determination of Workspace............................................................................21 3.2 Denavit Hartenberg Parameters......................................................................24 3.3 Jacobian Matrix.................................................................................................27 3.4 Manipulability Ellipsoid...................................................................................29 3.5 Inverse Kinematic Program..............................................................................32 3.6 Procedure for Analysis......................................................................................35 Chapter Four Analysis Results................................................................................36 4.1 Evaluation of the Manus :..................................................................................36 4.1.1 Vertical Planes..........................................................................................42 4.1.2 Horizontal Planes......................................................................................49 4.2 Evaluation of the Raptor ...................................................................................58 4.2.1 Vertical Planes..........................................................................................62 4.2.2 Horizontal Planes......................................................................................69 Chapter Five Design Insigh ts and Recommendations............................................79 5.1 Design Insights..................................................................................................79

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ii 5.2 Design Recommendations................................................................................81 5.2.1 Rail Mounted Manipulator........................................................................82 5.2.2 Reconfigurable Manipulator.....................................................................83 Chapter Six Summary and Future Work...............................................................84 6.1 Design Recommendations and Insights............................................................84 6.2 Future Work......................................................................................................85 References………….........................................................................................................87 Appendices………............................................................................................................90 Appendix A: Manipulability Data................................................................................91 Appendix B: Inverse Kinematic Program...................................................................102

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iii List of Tables Table 4.1 : D-H Parameters for Manus .............................................................................38 Table 4.2 : Data for x = 27.54.........................................................................................43 Table 4.3 : Data for x = 14.04.........................................................................................44 Table 4.4 : Data for x = 6.75...........................................................................................45 Table 4.5 : Data for x = 0.54...........................................................................................46 Table 4.6 : Data for Manus x = 0....................................................................................47 Table 4.7 : Data for Manus at x = -4...............................................................................48 Table 4.8 : Data for Manus at z = 24.18.........................................................................49 Table 4.9 : Data for Manus at z = 18.2...........................................................................50 Table 4.10 : Data for Manus at z = 6.18.........................................................................51 Table 4.11 : Data for Manus at z=-0.8............................................................................52 Table 4.12 : Data for Manus at z = -5.82........................................................................53 Table 4.13 : Data for Manus at z = -13.8........................................................................54 Table 4.14 : Data for Manus at z = -22.8........................................................................55 Table 4.15 : Data for Manus at z = -29.8........................................................................56 Table 4.16 : Qualitative Summary of Manus Effectiveness.............................................57 Table 4.17 : Raptor D-H Parameters................................................................................60 Table 4.18 : Data for Raptor at x = 27.54.......................................................................64 Table 4.19 : Data for Raptor at x = 14.04.......................................................................65 Table 4.20 : Data for Raptor at x = 6.75.........................................................................66 Table 4.21 : Data for Raptor at x = 0.54.........................................................................67 Table 4.22 : Data for Raptor at x = 0..............................................................................68 Table 4.23 : Data for Raptor at x = -4.............................................................................69 Table 4.24 : Data for Raptor z = 24.18...........................................................................70 Table 4.25 : Data for Raptor z = 18.2.............................................................................71 Table 4.26 : Data for Raptor z= 6.18..............................................................................72 Table 4.27 : Data for Raptor z = -0.8..............................................................................73 Table 4.28 : Data for Raptor z = -5.82............................................................................74 Table 4.29 : Data for Raptor z = -13.8............................................................................75 Table 4.30 : Data for z = -22.8........................................................................................76 Table 4.31 : Data for Raptor at z = -29.8........................................................................77 Table 4.32 : Qualitative Summary of Raptor Effectiveness.............................................77

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iv List of Figures Figure 2.1 : Puma 250 Arm.................................................................................................4 Figure 2.2 : Handy-1........................................................................................................... 5 Figure 2.3 : RAID Workstation..........................................................................................7 Figure 2.4 : Robot Assistive Device...................................................................................8 Figure 2.5 : ProVAR System..............................................................................................8 Figure 2.6 : MoVAR...........................................................................................................9 Figure 2.7 : MoVAID.......................................................................................................10 Figure 2.8 : FRIEND Robotic System..............................................................................11 Figure 2.9 : TAURO Robotic System...............................................................................12 Figure 2.10 : Weston Arm................................................................................................13 Figure 2.11 : Asimov Arm................................................................................................14 Figure 2.12 : Manus Arm..................................................................................................16 Figure 2.13 : Manus Joystick Controller...........................................................................18 Figure 2.14 : Manus Keyboard Controller........................................................................18 Figure 2.15 : Raptor Arm..................................................................................................19 Figure 3.1 : Workspace Horizontal Planes.......................................................................22 Figure 3.2 : Workspace Vertical Planes............................................................................23 Figure 3.3 : Workspace Vertical Planes............................................................................24 Figure 3.4 : D-H Parameter Link Parameters...................................................................26 Figure 3.5 : Manipulability Ellipsoid................................................................................31 Figure 3.6 : Program Flowchart........................................................................................34 Figure 4.1 : Manus Reference Frames..............................................................................37 Figure 4.2 : Representation of th e Manipulability Measure.............................................42 Figure 4.3 : Manus y-z Plane @ x = 27.54".....................................................................43 Figure 4.4 : Manus y-z Plane @ x = 14.04".....................................................................44 Figure 4.5 : Manus y-z Plane @ x = 6.75".......................................................................45 Figure 4.6 : Manus y-z Plane @ x = 0.54".......................................................................46 Figure 4.7 : Manus y-z Plane @ x = 0............................................................................47 Figure 4.8 : Manus y-z Plane @ x = -4"...........................................................................48 Figure 4.9 : Manus x-y Plane @ z = 24.18.....................................................................49 Figure 4.10 : Manus x-y Plane @ z = 18.2.....................................................................50 Figure 4.11 : Manus x-y Plane @ z = 6.18.....................................................................51 Figure 4.12 : Manus x-y Plane @ z = -0.8......................................................................52 Figure 4.13 : Manus x-y Plane @ z = -5.82....................................................................53 Figure 4.14 : Manus x-y Plane @ z = -13.8....................................................................54 Figure 4.15 : Manus x-y Plane @ z = 22.8...................................................................55

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v Figure 4.16 : Manus x-y Plane @ z = 29.8”...................................................................56 Figure 4.17 : Raptor Reference Frames............................................................................59 Figure 4.18 : Raptor y-z Plane @ x = 27.54”...................................................................64 Figure 4.19 : Raptor y-z Plane @ x = 14.04”...................................................................65 Figure 4.20 : Raptor y-z Plane @ x = 6.75”.....................................................................66 Figure 4.21 : Raptor y-z Plane @ x = 0.54”.....................................................................67 Figure 4.22 : Raptor y-z Plane @ x = 0”..........................................................................68 Figure 4.23 : Raptor y-z Plane @ x = -4”.........................................................................69 Figure 4.24 : Raptor x-y Plane @ z = 24.18”...................................................................70 Figure 4.25 : Raptor x-y Plane @ z = 18.2”.....................................................................71 Figure 4.26 : Raptor x-y Plane @ z = 6.18”.....................................................................72 Figure 4.27 : Raptor x-y Plane @ z = -0.8........................................................................73 Figure 4.28 : Raptor x-y Plane @ z = 5.82”...................................................................74 Figure 4.29 : Raptor x-y Plane @ z = 13.8”...................................................................75 Figure 4.30 : Raptor x-y Plane @ z = 22.8”...................................................................76 Figure 4.31 : Raptor x-y Plane @ z = -29.8”....................................................................77

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vi Kinematic Analysis and Evaluation of Wheelchair Mounted Robotic Arms Edward Jacob McCaffrey ABSTRACT The goal of this thesis is the kinematic analysis and evaluation of wheelchair mounted robotic arms. More specifically, to address the kinematics of the wheelchair mounted robotic arm (WMRA) with respect to its ability to reach positions commonly required by an assistive device in act ivities of daily living (ADL). A robotic manipulator attached to a power wheelchair could enhance the manipulation functions of an individual with a disability. In this thesis, a procedure is developed for the kinematic analysis and evaluation of a wheelch air mounted robotic arm. In addition to developing the analytical procedure, the manipulator is evaluated, and design recommendations and insights are obtained. At this time there exist both commerci ally-available and industrial wheelchair mountable robotic manipulators. The commerci ally-available manipulators (of which two will be addressed in this research) have been designed specifically for use in rehabilitation robotics. In contrast, industria l robotic manipulators ar e designed for speed, precision, and endurance. These traits are not re quired in assistive robots and can actually be dangerous to the operator if mounted onto a wheelchair. Manipulators to be used as WMRAs must be designed specifically for assistive functions in order to be utilized as a wheelchair mounted robotic arm. In an effort to evaluate two commercial manipulators, the procedure for kinematic analysis is applied to each manipulator. Design recommenda tions with regard to each device are obtained. This method will benefit th e researchers by providing a standardized

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vii procedure for kinematic analysis of WMRAs that is capable of evaluating independent designs.

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1 Chapter One Introduction 1.1 Motivation A wheelchair mounted robotic arm can enhance the manipulability functions of people with disabilities. To be tter understand the effectiveness of a robotic arm, it must be analyzed with respect to its kinema tics and the workspace in which it operates. Kinematics is defined as the relationship between the positions, velocities, and accelerations of the links of a robotic arm. Data from the US Census Bureau St atistical Brief of 1993 showed that over 34 million Americans had difficulty performing functional activities1. Of this number, over 24 million were considered to have severe disabilities. Every year more and more people become disabled in a way which minimizes th eir use of upper extremities. These can be motor dysfunctions due to accidents, disease, or genetic predispositions. The field of Rehabilitation Robotics ha s been created in an attempt to increase the quality of life and to assist in activities of daily living. Rehabilitation Robotics addresses assistive technologies as well as the traditiona l definition of rehabilitation: increasing or expanding the individuals mental, physical, or sensory capabilities. The primary focus of Rehabilitation Engineering2 and robotics is to increase the quality of life of individuals through increasing functional independence and decreasing the costs associated with the assistance required by the individual. Robotic aids used in these applications vary from advanced limb orthosis to robotic arms. These devices can help in ev eryday activities for persons with severe physical disabilities limiting their ability to manipulate objects by reducing their dependency on caregivers.

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2 In the case of spinal injury or dysfunc tion, these aids are mo st appropriate for individuals with spinal deficiencies ra nging from cervical spine vertebrae 3 through cervical spine vertebrae 5. Below the cervical spine vertebrae 5, individuals often can be served with simpler, more traditional assis tive technology. Spinal fractures above cervical spine vertebrae 3 often require other medical necessities such as a respirator and daily attendants, thereby minimizing the need for assistive devices Individuals with neuromuscular deficiencies such as muscular sclerosis can benef it from these robotic devices. Individuals that require mobility assist devices such as a power wheelchair can benefit from various robotic devices because the power wheelchair provides a platform with which to mount the device as well as a power supply, using the wheelchair’s batteries. There have been several attempts in the past to create commercially-viable wheelchair mounted robotic arms. Currently there are only two comm ercially available WMRAs available, the Manus (Exact Dynamics, Inc., Netherlands) and the Raptor (Applied Resources, Inc, NJ USA). 1.2 Objectives The focus of this thesis is to analyze and evaluate WMRAs. To complete the analysis, an analytic procedure must be designed to systematically study the effectiveness of WMRAs. The procedure is executed and the mani pulator is then evaluated using criteria specific to rehabilitation applications. A completed evaluati on can provide design recommendations and possibly insights into design modifications or new manipulator geometries which better fulfill the specific n eeds of a rehabilitation robotic manipulator. The objectives of this thesis are the following: Create a procedure for quantitative kinematic analysis Evaluate the Manus and Raptor arm using this procedure Obtain design recommendations a nd insights based on the evaluation

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3 Chapter Two Background 2.1 History of Rehabilitation Robotics There have been various attempts over the years to create robotic assistants for individuals with various levels of disabilities. For over 30 years, research has progressed in the field with only partial commercial su ccess. An early attempt at telemanipulators was done at the Case Institute of Technol ogy during the early 1960s. The Case system3 was a floor-mounted, powered exoskeleton. It was controlled by an operator who wore a head-mounted light source which triggered ligh t sensors in the environment. By looking at specific points in the room, the operator co uld trigger the light sensors and initiate one of several preprogrammed gestures whic h were stored on magnetic tape. A later development allowed for Cartesian movement and direct control of individual joints along with myoelectric signals for velocity control. One of the first attempts at rehabilita tion robotics included the Rancho Golden arm 4 designed in 1969 at Rancho Los Amigos Hospital in Downy, California. The arm was an electrically-driven 6 Degree Of Freed om (DOF) robotic arm which mounted to a powered wheelchair and was cont rolled at the joint level by an array of tongue-operated switches. Further discussions on the topic of the controllability of the arm commented on both successes and failures of the design. The successes with the project can be attributed to the important role that proprioceptive fee dback plays in the control of a persons own extremities5. These pioneering research projects provided a framework for future development. Assistive robotics can be grouped into one of three categories: Workstation robots which operate in stat ionary, well-structured environments Mobile assistive robots whic h travel about the room a nd have a manipulator arm

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4 Wheelchair mounted robotic arms whic h mount a manipulator arm onto the individual’s wheelchair to provi de assistance throughout the day 2.2 Workstation-Based Systems The very first rehabilitation robotics a pplications focused on using commerciallyavailable industrial manipulator s and modifying them for rehabilitation applications. An example of these manipulators is the PUMA 250 shown in Figure 2.1. A factor which limits the use of industrial robotic arms in rehabilitation is the basic difference in operational requirements. Industrial arms ar e designed to work at high speed in an environment where there are no humans. This reason alone would limit their use for reasons of safety of the operator. For app lications in a human-intensive workspace, assistive robotic arms need to be mechanically limited to low velocity and accelerations. A more modern version of this workst ation approach is the RAID (Robotic Assistance in Daily Living) system which w ill be discussed in more detail later. Figure 2.1 : Puma 250 Arm The Robotic Aid Project6 was an attempt to create a system for users with quadriplegia. The project was an integration of a PUMA 250 industrial manipulator arm, microprocessor, multi-line monochrome disp lay and speech synthesis and recognition systems. Limitations with the speech-rec ognition systems and computational power of

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5 the day restricted the success of the program The processing ability of the contemporary computers did not allow for real-time reverse kinematics of the arm. This limited the arm to merely replaying preprogrammed actions Individual joints of the arm could be manipulated but coordinated, real-time mu lti-joint maneuvers were impossible. As more application-specific robotic arms and computers with increased computational power became available, arms with controllers could now be mounted onto mobile platforms. At first these syst ems were simply rolling bases which then increased in complexity and degrees of fr eedom to include powered mobile robots. Handy-17 is a robotic arm mounted to a non-pow ered wheeled base to assist in very specific activities of daily living (ADL ). Handy-1 was developed in 1988 to provide persons with severe disabilities assistance at mealtimes. Since its initial introduction the unit has expanded capabilities and is now capab le of providing assistance in a broader number of activities of daily living (ADL). Handy-1 is cap able of assisting individuals with personal hygiene, eating and drinking, and the application of make-up. During user trials, women specifically asked if the unit would be capable of applying cosmetic products. Shortly after the tria l, the design was upgraded w ith a new tray and gripper accessory. Each ADL task has a specific tray to accomplish its goal. Handy-1 is shown in Figure 2.2 and is based on a 5 DOF light ly modified industrial manipulator. Figure 2.2 : Handy-1 In the feeding mode the ope rator controls the robot thr ough an interface that uses lights which move across the available food tr ays, and a button that selects the item

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6 desired. Once the button is pre ssed, the robot scoops up the sele cted food and brings it to a predetermined place near the operator’s m outh. Once the user has consumed the food, the operator presses the button again and the robot returns to the food selection mode. This process is repeated until the operator is finished. This assistive device does not eliminate the need for a personal assistant but allows for individuals to have an increased leve l of self-sufficiency. In user trials almost invariably all the users believed the device to significantly increase their quality of life. An advancement of the technology of Handy-1 is being explored with the Robotic Aid to Independent Living8 (RAIL) project. RAIL improve s upon the Handy-1 design by incorporating a new controller for better mani pulator control, a 3D simulation tool for modeling virtual scenarios and attachment of sensors to assist set up and position error determination. The Wessex robot 9(Bath Institute of Medical Engi neering) is a trolley-mounted mobile robot of modified SCARA geometr y. A SCARA arm has two revolute joints in the horizontal plane, allowing it to reach any point within a horizontal planar workspace defined by two concentric circles. In modifi ed SCARA configuration, most of the joints operate in the horizontal plane. All vertical movement is achieved through the use of a single vertical actuator. The Wessex robot suffered from several design shortcomings. One example was its limited manipulator reach. The manipulat or was designed to grasp only items on a tabletop. Because of this limitation, it was unable to pickup items off the ground. The trolley was not powered and was pushed in to location by the daily assistant. In user trials the operator felt limited by the number of programs which it could store and that the trolley was not powered. The user felt that if the trolley were able to be driven by remote control it c ould be used to retrieve or manipulate objects within the same room. This could allow the user to adjust the thermostat or retrieve a drink from an attached kitchen. The RAID workstation10 shown in Figure 2.3 was designed to be a workstation assistive robot system. It is comprised of a 6 DOF robotic arm mounted onto a linear

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7 track in a well-controlled envir onment. In the figure the mani pulator can be seen near the top of the shelf in the center of the cabinet. Figure 2.3 : RAID Workstation The RAID system provides benefits that ar e enhanced by the formal structure provided by a workstation environment. This orga nization allows the manipulator arm to repeatedly move and acquire items need ed by the operator using preprogrammed functions and routines. At this time the RAID system is currently under evaluation in Europe. The Robotic Assistive Device11 shown in Figure 2.4, is a robotic arm currently under development by the Neil Squire Foundation in Vancouver, Canada. The RAD is a 6 DOF workspace mountable manipulator that uses a serial port computer interface. The manipulator is controlled through a graphica l user interface (GUI) utilizing icons to symbolize predefined tasks. The system consist of several modules which when combined create an arm with a cylindrical r each of approximately 55” and a height of 110”. The arm can be mounted on various surfaces and has good repeatability at 0.12” and relatively large payload capacity of 9.5 lbs. Most reha bilitation specific manipulators have maximum payloads of 5 pounds or less.

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8 Figure 2.4 : Robot Assistive Device The ProVAR 12(Stanford, CA) is a system based on a Puma 260 robotic arm designed to operate in a voc ational environment. The Pr oVAR manipulator shown in Figure 2.5 is the next generation of the De VAR system and expands upon the previous research by reducing operating costs and increasing overall usefulness. Figure 2.5 : ProVAR System The ProVAR system uses a web-base d virtual environment to model the functionality of the manipulator. In this way the operator can examine potential arm movements for a given task, and if the si mulation is successful, the action can be

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9 initiated. In this way, the actions of the arm and its interactions within its workspace can be seen before any action is taken. The primary goals for ProVAR are more functionality per dollar, easier operator control, and hi gher system reliability compared with the previous generation of vo cational assistive robots. 2.3 Mobile Systems Mobile systems are capable of assisti ng individuals with disabilities. These systems include a mobile base, various sensor s and a manipulator arm. An early version of one such system is the M obile Vocational Assistant Robot13 (MoVAR). MoVAR, shown in Figure 2.6, utilizes an omni-directi onal mobile platform mounting a PUMA-250 robotic arm as well as several sensors incl uding a remote viewing camera, force and gripper proximity sensors. Figure 2.6 : MoVAR MoVAID is an advanced version of the MoVAR system, designed specifically for home use. MoVAID improves upon the previous model by applying the lessons learned in laboratory testi ng to assist in comm on tasks around the home such as cleaning and food preparation. MoVAID inco rporates a variety of sens ing devices both mounted to the manipulator and the base. In Figure 2.7 MoVAID can be s een along with the various

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10 sensors that are located on the manipulator ar m. Sensors mounted to the first link of the arm include a pair of cameras used for stereo vision and a laser loca lization system used in task execution. The MoVAID system uses active beacons pos itioned within the room that provide reference data to determine its location and or ientation. In addition to position detection, the unit also has ultrasonic range detectors a nd an active bumper that disables the device should an impact occur. Figure 2.7 : MoVAID The robotic arm used by MoVAID has 8 DOF and a three-fingered gripper with two degrees of freedom. The gripper was orig inally designed as a prosthetic device specifically to have excellent dexterity. Th e increased agility pr ovided by the gripper over more traditional end-effectors allows MoVAID to be very effective in the unstructured home environment. 2.4 Integrated Robotic Systems Research is being conducted on robotic as sistive devices with increased autonomy and some artificial intelligence. This increa sed integration of robotic arms and other

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11 sensors has led to some increasingly capab le designs. Although still in development, these designs offer even greater potentia l as assistive devices for the future. The FRIEND14 robotic system is a Manus arm mounted onto a wheelchair and integrated with stereo visi on, dedicated computer control, and specialized software. Besides programming with a keypad or joys tick, the FRIEND system, shown in Figure 2.8, is capable of being programmed via a haptic interface glove. The haptic glove allows the operator / programmer to feel what the robot feels through feedback to the user. A Haptic glove is put on and the action, such as pouring a glass, is completed and stored into the computer for future use. The action can then be replayed at a later time as a predefined user function. The operator may also control the arm through verbal commands using an integrated vo ice recognition system. Figure 2.8 : FRIEND Robotic System Another design is the TAURO. The TAURO is an integrated robotic system using off-the-shelf components such as a power wheelchair, Manus manipulator, ultrasonic sensors, camera and computers. TAURO is a mobile service robot being developed for inspection, stocktaking and documentation ta sks in indoor environments. The TAURO system integrates the movement of the wheel chair and the operati on of the manipulator.

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12 In this way if the goal is out of reach of the manipulator, the wheelchair will move on a path toward the goal until the manipulator can reach its goal. This coordinated control is a significant advance in the use of WMRAs. Although not specifically designed for rehabilitation robotics tasks, it would be readily adaptable to the task. The TAURO system can be seen in Figure 2.9. Figure 2.9 : TAURO Robotic System 2.5 Research WMRAs Wheelchair mounted robotic arms (WMRAs) Combining the idea of a workstation a nd a mobile robot, a WMRA mounts a manipulator arm onto a power wheelchair. In the past, industrial manipulators have been too large and heavy to be mounted onto a pow er wheelchair. An industrial manipulator mounted onto the wheelchair would have exce ssively hindered the operator’s ability to maneuver the chair through doors and hallways. More recently, manipulator arms have been specifically designed to be used as WMRAs. Currently there are two production wheelch air mounted robotic arms (WMRAs) : the Manus, manufactured by Exact Dynamics, and the Raptor manufactured by Applied Resources. Some WMRAs under development are the Helping Hand (USA), Weston Arm (UK), and the Asimov (Sweden).

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13 Helping Hand system15 (Kinetic Rehabilitation Instruments, Hanover Massachusetts) is a 5DOF robotic arm being de veloped for commercial use. Its design is modular in nature and can be mounted to th e side of a power wheelchair. The Helping Hand operates by joint control and is manipulat ed by using switches to control individual joints. The Weston robotic arm (Bath Institute of Medical Engineering) utilizes a vertical actuator mounted to a wheelchair with the main rotary joints (shoulde r, elbow, and wrist) constrained to move in the horizontal plane. This is the continuation of the trolley mounted Wessex robot arm research. The Weston robotic system shown in Figur e 2.10 is still under development. The Wessex arm is larger than both the Manus and the Raptor designs due to the use of a prismatic first joint. A prismatic joint move s in a linear sliding motion along a track. The other joints of the arm utilize a modified SCARA design as described in the Wessex manipulator. Figure 2.10 : Weston Arm

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14 Another arm currently under development is the Asimov16 The Asimov is a modular manipulator design with the motors and controls distribu ted throughout the arm. A computer rendering of the Asimov is s hown in Figure 2.11. Th e modularity of the design allows for multiple moun ting locations on a wheelchair or stationary application with various workspace geometries. The concept of a modular manipulator ha s several benefits. This provides the opportunity for one manipulator that can be used in either a mobile or workstation environment. Different link geometries can be explored to creat e the optimum design for any given application. Asimov models have been shown with all three possible mounting positions: front, side and rear. Without physical m odels to test the efficacy of the design, it is unknown how well the design would inte grate into real-world applications. Figure 2.11 : Asimov Arm 2.5.1 Rear Mount Several design considerations must be me t before deciding on where, on a power wheelchair, to mount a robotic arm. The foremo st design consideration is the safety of the operator17. The mount must be sturdy and rigid and not compromise the structural integrity or the functionality of the chair in any way. Next the robotic arm must be

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15 mounted in such a way that it has a minimum footprint outside the footprint of the chair itself. One of the potential benefits of a rear-m ounted arm is that it will not increase the width of the wheelchair when not in use. Assuming that the arm is capable of being stowed behind the wheelchair, the arm would not create a distraction for individuals interacting with the person. Additionally, a rear-mounted arm would not be a physical obstruction during transfer into and out of the wheelchair. Rear-mounted robotic arms have drawback s caused specifica lly by the mounting location. In order for a manipulator to reach to the front of the wheelchair the manipulator must have longer link lengths than a fr ontor side-mounted design. The longer link lengths required by the dorsa l (rear) mount require greater torque from the motors and increased loads on the bearings. At this time there are no commercially available WMRAs that are mounted to the rear of the wheel chair. It should be noted that there is an optional rear mounting bracket available for the Raptor but this eliminates most of the ability of the arm to reach dire ctly in front of the chair. 2.6 Commercially Available WMRAs 2.6.1 The Manus The Manus manipulator arm is a fully de terministic manipulator. A fully deterministic arm can be programmed in a manner comparable to industrial robotic manipulators. At any time the joint angles are known by the contro ller and the exact gripper position is known. The Manus has been under development since the mid 1980’s and entered into production in th e early 1990’s. A picture of the Manus mounted onto a Permobil Max90 wheelchair is shown in Figure 2.12.

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16 Figure 2.12 : Manus Arm 2.6.1.1 Front Mount There are several possible mounting locations for a WMRA18. The mount may be in the front, side or rear of the wheelchair. The Manus utilizes a front mounting location to the left of the operator’s left knee. The fi rst joint of the arm rotates about the z-axis (floor to ceiling) and is located approximately two inches above the level of the arm rest of the power wheelchair. This location allo ws for good manipulation of objects that are above the plane of the wheelchair seat, and mo st importantly the operator’s face and lap. The front mount offers greater access to the operator’s immediate working environment. The lap, tray top on armrests, a nd the mouth location can all be considered the immediate environment of the operator. Manipulation of objects in these areas is optimized with this mounting location. The high mounting position near the knee allows for good access to high objects such as items on shelves or operating doors on high cabinets. Objects in front of the ch air are also readily manipulated. Additionally, the front mounting of the robotic arm provides excellent accessibility to high shelves and allows the execution of various activities of daily living. The front mount for a WMRA has limita tions. Users have commented the front mounting makes the manipulator arm obtrusive and can create uncomfortable social

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17 tensions with people unfamiliar with robotic technology. This was noted as a hindrance in long-term Manus trials19. The mounting location also limited the ability of the operator to put their legs under desks, tables, and sinks in clinical evaluations. 19 2.6.1.2 Closed Loop Control The Manus manipulator is controlled by a joys tick and a keypad. The joystick is used to manually operate the mani pulator is shown in Figure 2.13. Manus can also perform coordinated control of multiple join ts with preprogramme d gestures using the 16button keypad shown in Figure 2.14. Gestures can be taught to the Manus and stored for future use via the keypad. With the use of the two input devices the operator can run pre-programmed routines or directly c ontrol the manipulator in real time. The controller converts th e inputs from an input device into a signal which directly controls the robotic ar m. There may be a direct or indirect link between the input device and the output signal. This control may be a simple proportiona l control or a more complex method where input position is converted into arm velocity output. Closed loop systems are commonly used in industrial robotics. These systems permit accurate repeated motions of robotic manipulators to accomplish specific tasks within a manufacturing cell. A manufacturing cell is a highly structured environment which permits high productivity by eliminating positioning variances. Rehabilitation workstations are very simila r to the workspace originally used by industrial robotic arms. A closed loop syst em is useful in re habilitation robotics applications by allowing pre-programmed actions and maneuvers. Pre-programmed gestures can be as simple or as complicated as required to accomplish a specific task. Closed loop control also allows further integration of the arm into more complicated and intelligent systems which can assist the operator. The MANUS system is a version of a closed loop system. The downside to closed loop systems is th eir higher initial cost The drive motors for the links must have encoders or some other form of feedback to send to the controller. Often the increased productivit y, programmability, and system interoperability of a

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18 closed loop system can compensate for this increased initial cost by offering more “bang for the buck”. Figure 2.13 : Manus Joystick Controller Figure 2.14 : Manus Keyboard Controller 2.6.2 The Raptor Another production WMRA is the Raptor [Applied Resources, Inc.], which mounts the robotic arm to the right side of the wheelchair. This manipulator has four degrees of freedom plus a planar gripper a nd can be seen mounted to a power wheelchair in Figure 2.15. The arm is directly controlled by the user by either a joystick or 10-button controller. Because the Raptor does not have encoders to provide feedback to the controller, the manipulator cannot be pre-progr ammed in the fashion of industrial robots. This compromise was done to minimize overall system cost and make the product more readily available to the public. The simplicity of the Raptor arm and its controller allows it to be one-half the cost of the Manus arm.

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19 Figure 2.15 : Raptor Arm 2.6.2.1 Side Mount The Raptor is a side-mounted arm. The primary joint motor of the Raptor is an exposed gear motor which must be mounted onto the frame under the seat of the wheelchair. In the specific a pplication that was used, the mo tor is positioned slightly in front of the operator’s waist. The Raptor side-mount is partially hidden underneath the chair. When the arm is not in use, the Raptor arm can be stowed relatively inconspicuously. Similar in design to front-mounted mani pulators, the side-mounted manipulators also have drawbacks. One significant proble m with a side-mount robotic arm is that it increases the width of the power wheelchair. With the side-mount located lower than the armrest (under the wheelchair), the arm will alwa ys add at least the width of the first link to the width of the wheelchair. This makes it even more difficult to for the operator to maneuver through doorways and tight hallways9. This exacerbates mobility problems already encountered with power wheelchairs. The side mount requires longer link lengths than a front mounted arm, to allow for manipulation of objects in front of the power wheelchair. These increased link lengths require larger and more powerful motors and gear-heads to move a nd stabilize the links’

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20 actuation. These factors often increase the wei ght and cost of designing arms for this application. The Raptor link geometry cannot be cha nged for specific applications. 2.6.2.2 Open Loop Control An open loop controller places a human directly in the loop of controlling the arm. The operator continuously directs the arm into its final position. This type of system is inherently tolerant of positioning errors from a variety of causes. These errors may be specific to the robotic device such as play in the motors, gears, bearings or compliance within the links due to loading or environmen tal conditions such as thermal effects, wind, and movement of the base with respect to the reference frame. The open loop controller can correct for various types of positioning error because the operator continuously updates its position or the arm during the manipulation. The operator indirectly considers the sum of all the errors and moves the arm according to the actual perceived position of the end-effector. Robotic arms with open loop control requ ire higher levels of concentration and eye-hand coordination from the operator than closed loop systems. This may be more taxing for the operator and can limit the use of the assistive robotic device. Open loop systems are unable to make precisely reproducible motions. A robotic system using an open loop c ontroller may be much simpler by not requiring encoders to determine position or comp lex controllers. This trade-off allows for a cost-effective design. The Raptor exclusively employs an open loop control scheme. Typically these open loop controllers are driven one joint at a time in order to simplify the controller.

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21 Chapter Three Procedure for Kinematic Analysis 3.1 Determination of Workspace A workspace has been chosen which reflects specific requirements of individuals with disabilities20 21 22. Horizontal planes (x-y) were chosen with re spect to the floor as the vertical axis z = 0. The origin of the user-coordinate system is 31.8 above the floor and all values given are referenced above the floor. A value of 2 above a given plane was required in order to give room for the manipulator to reach an obj ect. The value in parenthesis is the z-axis height with respect to the us er coordinate system (farthes t forward-most point between the armrests) can be seen in Figure 3.1. 1. Small objects on the floor: 2 (-29.8) 2. Larger light objects on the floor: 9 (-22.8) 3. Height of electric socket: 18 (-13.8) 4. Low coffee table: 26 (-5.82) 5. Height of standard table and door knob: 31 (-0.8) 6. Kitchen counter top: 38 (6.18) 7. Wall-mounted light switch: 50 (18.2) 8. Low shelf above kitchen counter top 56 (24.18)

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22 -29.8” -22.8” -13.8” -5.82” -0.8” 6.18” 18.2” 24.18” Figure 3.1 : Workspace Horizontal Planes There are three horizontal lines that are al so used in determining the manipulability measure. These are slightly above the lap of the operator and move from the upper tip of the wheelchairs armrests. These would be (0, y, 0) Intersecting each of these horizontal (x-y) planes are vertical planes (y-z) which reflect objects directly on axis with the wheel chair (as if the operato r was driving straight forward). These are distances in front of th e operator based on the frame reference that the top-most intersection of the tip of the arm rest is the origin. The distances are in the x axis of the user coordinate system (farthest forward-most point between the armrests) can be seen in Figure 3.2. Starting from the farthest point and work ing toward the operator is described as follows.

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23 1. 2” in front of the footrest of the pow er wheelchair 27.54”. This is the primary reference x-z plane. 2. 14.04” in front of the operator. This is 13.5” behind the first x-z plane. 3. 6.75” in front of the operator. This is half the distance of the 13.5” grid. 4. 0.54” is front of the operator. This is 13.5” behind the second x-z plane. 5. The x-z plane at the origin of the user reference plane. 6. The x-z plane that reflects the mouth of the operator. 4” behind the origin. 6.75” 14.04” 27.54” -4” 0” 0.54” Figure 3.2 : Workspace Vertical Planes Finally to create the individual points a third plane (x-z) is defined. The plane located at the origin separates the chai r into two lateral halves a nd is shown in Figure 3.3. The wheelchair used for the analysis is 27” wide including the width of the drive wheels. The y axis in the user frame of reference is positive moving from the body to the right hand extended out along the arm. 1. The plane intersecting the origin. 2. 13.5” from the origin toward the mounted arm.

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24 3. 23.5” from the origin toward the mounted arm. This represents the 10” from the outermost edge of the wheels. 23.5” 0” 13.5” Figure 3.3 : Workspace Vertical Planes 3.2 Denavit Hartenberg Parameters The Denavit Hartenberg parameters23 are a method of analyzing robotic manipulators that was first introduced in 1955. This technique allows robotics researchers an approach to standardize robotics nomen clature and to create an easy method to consider link arrangements in robotic manipulators. Each joint angle is analyzed separately with links separati ng each joint. A li nk is defined only as a rigid body that maintains a relationship between two adjacent jo int axes within a manipulator. Joints in robotic mechanisms may be single dimensional such as rotational (re volute) or prismatic (linear extension). Of the two previous joint types the revolute joint is by far the most common. Multidimensional (two and three dimension) joints could be cylindrical, screw, planar, or spherical. Due to the increased comp lexity of these types of joints they are not used as often as revolute or prismatic joints. When analyzing a joint of n dimensions with

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25 the Denavit-Hartenberg (D-H) parameter method the joint is broken into n joints with one degree of freedom connected to n-1 links of zero links. The Denavit-Hartenberg rules provide a guide for locating c oordinate systems on each link of a multi-link kinematic chain. By following the D-H rules, the homogeneous transformations between adjacent links are de fined. In order to use the D-H parameter method the parameters must be properly us ed. There are four pa rameters used in manipulator analysis. Three are fixed and ar e purely geometric these are the link twist, the link length, and the last is the link offset. The final parameter is variable and it is the joint angle. Within the nomenclature variable i refer to the link number. The link length (a i-1) is the length of a line that is mutually orthogonal to the previous joint axis (i-1) and the ne xt joint axis (i). The link twist ( defines the relative location of the two joint axis. The link twist is determined by creating a plane which is normal to the previously mentione d mutually perpendicula r line and projection of both axes onto this plane. The angle meas ured from link i-1 and link i (using a right hand rule for angle determination) is the link twist. The third parameter is link offset (di) which is the distance along the common axis from one link to the following link. The final parameter is the joint angle ( The Figure 3.4 shows the relationships be tween link number (i), link length (a i-1), link twist ( link offset (di), and joint angle (

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26 Figure 3.4 : D-H Parameter Link Parameters The Link Transformation equation relates all of the D-H parameters together. It can be seen that each parameter is used once and in a specific order within the link transformation equation. This equation show n below and contain two rotations and two translations in a specific orde r. The first rotation is done about the x axis by the amount of the link twist ( next there is a translation about the x axis by an amount of the link length (a i-1) Equation 3.1 Equation 3.1 relates the order with which the rotation and translations must be accomplished in order to use the D-H parameter table is shown in. Equation 3.2

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27 The individual link transformations can be determined by using D-H parameters and Equation 3.2. 3.3 Jacobian Matrix The Jacobian is a multidimensional form of the derivative. Because we are working with a three degree of freedom mani pulator there are three separate equations that define the positional ma trix (forward kinematics). Let us consider that we ha ve three functions, each comp rised of thre e independent variables. This is equivalent to the three posi tion vectors that are all functions of the three joint angles. In our case the y variables repr esent position and the x variables represent the joint angles. The functions fn are shown in Equation 3.3 re present the pos ition vector from within the final transforma tion matrix of the manipulator. y= f(x, x, x)33 123y= f(x, x, x)11 123y= f(x, x, x)22 123 Equation 3.3 These functions can also be expresse d in vector notation by Equation 3.4. Y = F(X) Equation 3.4 Using the chain rule and differentiating we can determine the differentials of yi as a function of xj the previous function is shown in Equation 3.5.

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28 y= 1 x3f1x3+ x1f1x1 x2f1x2+y= 3 x3f3x3+ x1f3x1 x2f3x2+y= 2 x3f2x3+ x1f2x1 x2f2x2+ Equation 3.5 To simply the previous equation we can ag ain place it into vector notation in Equation 3.6. Y = X FX Equation 3.6 This equation is a 3 x 3 matrix and is referred to as the Jacobian. It should be noted that if the functions f1(X) through f3(X) are nonlinear then their part ial derivatives are a function of xi. This equation can then be shown in Equation 3.7 Y = J(X) X Equation 3.7 Finally by dividing by the differential time element the Jacobian becomes a method of mapping velocities in X to velocities in Y. Y = J(X) X Equation 3.8 J(X) is a linear transformation that change s with time. Hence the Jacobian shown in Equation 3.8 is a time-varyi ng linear transformation. The use of the Jacobian in Robotics relates joint velocities to Cartesian velocity at the tip of the gripper. In a Jacobian matrix the number of rows indicate the number of

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29 degrees of freedom in the Cartesian space be ing considered and the number of columns equals the number of joints in the manipulator arm. It should be noted that there is an instantaneous linear re lationship between joint angle rate s and manipulator tip velocities. This relationship is used in the determination of joint angles from positional input is applied in the inverse kinematic program used to determine joint angles from positional input arguments. The relationship between joint velocity and Cartesian manipulator tip velocities in Equation 3.9 relies on the requirement that the Jacobian velocity be invertible. A matrix that is singular is not invertible. In order for the Jacobian to be used in this application it must be non-singular and thus invertible. J ( -1 Equation 3.9 Most manipulators have values for their joint angles where the Jacobian becomes singular. These points are referred to as singular ities of the mechanism or often shorted to singularities. All robotic mani pulators have singularities at the limit of their workspace. Additionally there are singulariti es within the workspace of manipulators as well. These are referred to as internal singularities. From this we can see that there exist two types of singularities: Workspace boundary singularities occur when the manipulator is fully extended or folded upon itself so that the end effect or is sufficiently near the boundary of the workspace. The other type of singularity is a Workspace interior singularity. These are usually away from the workspace boundary but generally occur where two or more joint axes line up. At a singularity the manipulator looses one or more de grees of freedom in Cartesian space making the movement of the end effector impossible. 3.4 Manipulability Ellipsoid A concept known as the manipulability ellipso id will be introduced as well as the volume of the ellipsoid the manipulability meas ure. In the end a to tal evaluation of any

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30 manipulator system would require the analysis of many factors such as the volume of the workspace, ease of use, speed, precision and accuracy etc. The manipulability measure is the absolute value of the determinate of the Jacobian matrix of the positional sub-matrix of the final transformation matrix of the manipulators arm reference frame. We will consider a manipulator with three degrees of freedom. This is the case with both manipulators being studied. The thre e joint variables will be denoted as a 3x1 vector and describe the position of the end effector. The kinematic relation between q and r is shown in Equation 3.10. r = f (q)r Equation 3.10 The relation between the velocity vector v corresponding to r and the joint velocity is shown in Equation 3.11. v = J ( q q Equation 3.11 where J(q) is the Jacobian matrix in Equation 3.11 If we consider the set of all possible joint velocities and the resultant end effector velocities q (q + q + q)1 2 3222 = Equation 3.12 In the Equation 3.12, the value to the left of the equation, must be less than or equal to unity. This is the manipulability ellipsoid w ith the major axis of the ellipsoid being the

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31 vector which will allow for the greatest end effector velocity and the minor axis of the ellipsoid will be vector whic h gives the lowest possible end effector velocity. In the case being analyzed the manipulability ellipsoid wi ll have three axes. In manipulators with m links the manipulability elli psoid will have m axes. Figure 3.5 : Manipulability Ellipsoid In the special case where all the ellipsoid axes are equal the ellipsoid will actually be spherical. At the special case where the manipulability ellipsoid is spherical the end effector can move in any direction with the same maximum velocity. The larger the size of the ellipsoid the faster the end effector can move. One possible method of analysis is to de termine the volume of the ellipsoid. This is computationally straight forwar d and is defined in Equation 3.13 by cmw where: w = 2 m / 2/[2 4 6 (m-2) m] if m is odd c =m 2(2 )(m-1)/2/[1 3 5 (m-2) m] if m is even { Equation 3.13 The value of cm is constant when m is fixed. This is the case, m = 3, with the manipulators being studied. Because the value of cm is constant we can see that the

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32 volume of the ellipsoid is proportional to the value of w We refer to w as the manipulability measure. The manipulability meas ure has specific properties that allow us to define it readily from the Jacobian and know n joint angles. First in the broadest sense the manipulability measure show n is shown in Equation 3.14: w = det J(q) J(q)T Equation 3.14 And more specifically to our application where the manipulator is non-redundant the previous equation reduces to Equation 3.15. w = det J(q) Equation 3.15 This shows that at a singular configuration the value of w approaches or equals zero. Hence the value of the manipulability measure, which is the volume of the manipulability ellipsoid, will be equal to the determinate of the Jacobian. 3.5 Inverse Kinematic Program A method for determining the joint angles of each robot arm was required in order to determine the manipulability measure and to verify it within the solid model in Solid WORKS. An overview of the program and th e methods required to operate its subroutines is as follows. In essence, the manipulability measure is the absolute value of the determinate of the Jacobian matrix of the positional sub-matr ix of the final transformation matrix of the manipulators arm reference frames. It is this value that is used as the main

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33 The Jacobian matrix is derived from the 1x3 positional matrix within the final transformation matrix of the arm. The tran sformation matrix is created through the judicious application of the DH-parame ters using the appropriate formulae. One challenge is to determine the joint angles of the robotic arm for a given point in 3-D space. This requires the use of a method of reverse kinematics. The reverse kinematics of the robotic arms was determined with a program in MatLAB. The program shown in Figure 3.6 uses the Jacobian matrix in a numerical methods approach subdividing the positional difference from the start position of the gripper and the desired goal position into se veral discrete goals. These discrete goal positions were entered sequentially entered into the Jacobian. The output of the Jacobian is a matrix c ontaining the incremental change of joint angles required to obtain th e new position. The joint angl e change is added to the previous joint angle and this new value is input into the forward kinematics of the transformation matrix. The actual position is compared to the desired discrete position and if it is below an error value than the next position is computed. If the error is too great the final error position is subtracted fr om the desired position and recomputed into the Jacobian and the pr ocess repeats the loop. In the inverse kinematic solution there are four subroutines along with the main program. The subroutines are called by the ma in program to execute additional steps.

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34 Figure 3.6 : Program Flowchart Read Initials (thetas (1,2,3)) Define number of steps Set tolerance (z,y,z) Set manipulability threshold Get final position [x;y;z;] Calculate Initial Position [x;y;z] From given Thetas (1,2,3) Initialize Current State Initial Position [x;y;z;] Initial Thetas ( 1,2,3 ) Calculate waypoints on straight line path = the plan Set the waypoint position goal Attempt an arm move Move arm toward goal attempt Is position approaching a singularity? Is new position goal within tolerance? Is this the last point in the plan? Display results Show points Show angles Finish START robot.m no no y es no y es y es

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35 The main program is called robot.m and is a MatLAB file which has been extensively commented for ease in comprehe nsion. The code for robot.m and the five subroutines that it ca lls upon can be found in the Appendix B. The subroutines are listed in the order that they are called upon. 3.6 Procedure for Analysis The evaluation of WMRAs will encompass th ree steps. First is the creation of a procedure for the kinematic analysis of any robotic arm. Second is the evaluation of two commercially availa ble manipulators ( Manus and Raptor ). And third are the design recommendations or insights gained from the second step. In order to create a procedure for the kinema tic analysis of WMRAs it is necessary to separate the process into a series of steps. More specifically the procedure followed these steps: 1. Create a Denavit Hartenberg parameter table and transformation matrices for the manipulator to be measured. 2. Create link transformations for the manipulator. 3. Determine the Jacobian Matrix for the manipulator. 4. Model the manipulator and a generi c power wheelchair in Solid WORKS so that angle and joint relationshi ps can be shown graphically. 5. Pick a series of points (grid) surrou nding the wheelchair / arm assembly. These points have specific applications in rehabilitation engineering. 6. Create a computer program us ing a numerical methods approach to determine the joint angles of the arm for a given point in the workspace. The joint angles are then used to determine the manipulabili ty of the arm for the given point. 7. Plot and compare the normalized manipulability measures for each arm. Verify that the joint angle provided by the i nverse kinematics program correspond to positions in the model space.

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36 Chapter Four Analysis Results 4.1 Evaluation of the Manus : This is the analysis of the Manus system. An operating unit was not available to test directly. Therefore, speci fications from the ma nufacturer, technical illustrations and photographs of the system were used to create the solid model. It was reproduced as faithfully as possible with the provided information. The figure below shows the frames of reference for the power wheelchair and the Manus The Manus in Figure 4.1 is shown in its fully lowered position. This position was chosen because it allows the manipulator access to the floor. It is possible that the manipulability measures would be higher when reaching into cabinets if the Z-lift mechanism were used. The reference frames are important in understanding the relationships shown in the D-H Parameter tables.

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37 ZuZ3ZGZ0,1XuX3 X GX0,1Y2X2 Figure 4.1 : Manus Reference Frames The transformations for each joint with re spect to the previous joint are shown below. The nomenclature for each matrix is as follows. T Transformation Matrix wrt With Respect To Number (pre & post) Corresponds to the frame of reference

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38 The D-H Parameters for the Manus with 3 DOF are outlined in Table 4.1. The table shows the relationships between link number (i), link twist ( link length (a i-1), link offset (di), and joint angle ( Table 4.1 : D-H Parameters for Manus i ai-1 di 1 0 0 0 2 -90 0 0 3 0 15.75 9.20 4 0 18.77 -3.94 0 Figure 4.1 is used to create the D-H Parameters shown in Table 4.1. These parameters are entered into Equation 3.2 to achieve each respective frame transformation. The transformation matrix which relates frame 1 with respect to frame 0 is shown in Equation 4.1 T1wrt0 cos 1 sin 10 0 sin 1 cos 10 0 0 0 1 0 0 0 0 1 Equation 4.1 The transformation matrix which relates frame 2 with respect to frame 1 is shown in the Equation 4.2. T2wrt1 sin 2 0 cos 20 cos 2 0 sin 2 0 0 1 0 0 0 0 0 1 Equation 4.2 The transformation matrix which relates frame 3 with respect to frame 2 is shown in the Equation 4.3.

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39cos 3 sin 30 0 sin 3 cos 30 0 0 0 1 0 15.75 0 9.20 1 3 Equation 4.3 The transformation matrix which relates fram e G, or the frame of the gripper, with respect to frame 3 is shown in Equation 4.4. TGwrt3 1 0 0 0 0 1 0 0 0 0 1 0 18.77 0 3.94 1 Equation 4.4 A user frame {U} is created to reflect a frame with correlation to the user. Equation 4.5 below shows the transformation matrix which defines the translational relationship between frame 0 {0} with respect to the user frame {U}. T0wrtU 1 0 0 0 0 1 0 0 0 0 1 0 15.04 9.97 1.74 1 Equation 4.5 The transformation matrices are multiplied t ogether (Equation 4.6) to give the transform relating the end gripper position wi th respect to the user frame. T0wrtU*T1wrt0*T2wrt1*T3wrt2*TGwrt3 = TGwrtU Equation 4.6 The final transformational matrix is show n in Equation 4.7. Due to the size of the transformation matrix and the constraints of page formatting, the matrix has been separated into columns one and two:

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40cos 1sin 2 cos 3 cos 1cos 2 sin 3 sin 1sin 2 cos 3 sin 1cos 2 sin 3 cos 2cos 3 sin 2sin 3 0 cos 1 sin 2 sin 3 cos 1 cos 2 cos 3 sin 1 sin 2 sin 3 sin 1cos 2 cos 3 cos 2 sin 3 sin 2cos 3 0 Equation 4.7 and then columns three and four: sin 1 cos 10 0 1877cos 1 sin 2 cos 3 1877cos 1 cos 2 sin 3 1504 526sin 1 1575cos 1 sin 2 1877sin 1 sin 2 cos 3 1877sin 1 cos 2 sin 3 997 526cos 1 1575sin 1 sin 2 1877cos 2 cos 3 1877sin 2 sin 3 174 1575cos 2 1 The position vector, a 3x1 matrix, is the first three rows of the final column of the final transformational matrix and is shown in Equation 4.8. This matrix is also the forward kinematic matrix. When the three join t angles are computed, the result is the position of the gripper in space with respect to the user frame {U}. From the forward kinematic matrix we can compute the Jacobian Matrix the partial derivative of the positional matrix. 18.77cos 1 sin 2 cos 3 18.77cos 1 cos 2 sin 3 15.04 5.26sin 1 15.75cos 1 sin 2 18.77sin 1 sin 2 cos 3 18.77sin 1 cos 2 sin 3 9.97 5.26cos 1 15.75sin 1 sin 2 18.77cos 2 cos 3 18.77sin 2 sin 3 1.74 15.75cos 2 Equation 4.8 Equation 4.9 below is the Jacobian of the Manus The matrix has been separated into three columns and is shown seque ntially for ease of viewing. Column 1: -18.77*sin(t1)*sin(t2)*cos(t3)-18.77*sin(t1)*co s(t2)*sin(t3)-5.26*cos(t1)-15.75*sin(t1)*sin(t2) 18.77*cos(t1)*sin(t2)*cos(t3)+18.77 *cos(t1)*cos(t2)*sin(t3)-5.26*sin(t1)+15.75*cos(t1)*sin(t2) 0 Equation 4.9

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41 Column 2: 18.77*cos(t1)*cos(t2)*cos(t3)-18.77*cos(t1)* sin(t2)*sin(t3)+15.75*cos(t1)*cos(t2) 18.77*sin(t1)*cos(t2)*cos(t3)-18.77*sin(t1)*sin(t2)*sin(t3)+15.75*sin(t1)*cos(t2) -18.77*sin(t2)*cos(t3)-18.77*c os(t2)*sin(t3)-15.75*sin(t2) Column 3: -18.77*cos(t1)*sin(t2)*sin(t3)+ 18.77*cos(t1)*cos(t2)*cos(t3) -18.77*sin(t1)*sin(t2)*sin(t3)+18.77*sin(t1)*cos(t2)*cos(t3) -18.77*cos(t2)*sin(t3)-1 8.77*sin(t2)*cos(t3) Values for the manipulability measure are plotted in both horizo ntal and vertical planes. The grid density in the analyzed work space is greater in the z axis, which gives a greater number of points with which to observe trends and changes of the manipulability measure. There are four vertical axes and eight horizontal axes.

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42 4.1.1 Vertical Planes In robotics, the term approach is used to describe reaching a point in space without regard for gripper orient ation. In this th esis, the term approach and also access will be used in a similar fashion, indicating that the arm is capable of reaching that specific point, or in broader terms, the area spec ified. In order for a point to be defined as having access, it must have a manipulability measure of at least 100. The maximum value of the manipulability measure in the da ta set was 7084.4 at point [-4, -6.75, 13.5]. Because of the 3-dimensional nature of the data to be diagrammed, a method for representing the relative value of the manipulability measure and a qualitative determination are shown in Figure 4.2. The si ze and color of the spheres are used to represent the manipulability measure as a percentage of the maximum manipulability measure computed. 81 100% Excellent 61 80% Very Good 41 60% Good 21 40% Limited 01 20% Very Limited > 1% UndeterminedManipulability Measure Figure 4.2 : Representation of the Manipulability Measure Figure 4.3 through Figure 4.6 show th e manipulability measures of the Manus for vertical planes within the defined workspace. The Manus arm offered very good access to low cabinets and shelves in front of and to the far left corner of the worksp ace that has been defined. In Figure 4.3 the manipulability measure remained very good throughout the z-axis in this far left corner of the operator’s workspace. A significant limitation was the very limited ability to grab

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43 objects from the floor directly in front of th e operator’s feet. The area of highest agility would be at least partially obscured by the robot base. Figure 4.3 : Manus y-z Plane @ x = 27.54" Table 4.2 : Data for x = 27.54” x y z n 27.54 0 24.18 0.64 27.54 13.5 24.18 0.52 27.54 23.5 24.18 0.72 27.54 0 18.2 0.65 27.54 13.5 18.2 0.49 27.54 23.5 18.2 0.77 27.54 0 6.18 0.53 27.54 13.5 6.18 0.35 27.54 23.5 6.18 0.69 27.54 0 -0.8 0.52 27.54 13.5 -0.8 0.33 27.54 23.5 -0.8 0.68 27.54 0 -5.82 0.56 27.54 13.5 -5.82 0.38 27.54 23.5 -5.82 0.71 27.54 0 -13.8 0.64 27.54 13.5 -13.8 0.48 27.54 23.5 -13.8 0.77 27.54 0 -22.8 0.61 27.54 13.5 -22.8 0.50 27.54 23.5 -22.8 0.66 27.54 0 -29.8 0.00 27.54 13.5 -29.8 0.22 27.54 23.5 -29.8 0.00 As the yz plane approaches the ma nipulator base, a si ngularity creates a limitation of movement near the first rotational axis as shown in Figure 4.4. At the line of data points shown in Figure 4.4 that sati sfy y = 13.5” and y-z plane x = 14.04”, the manipulability measure becomes very low. With the threshold that was used for the program, these points were defined as unobtainable.

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44 Figure 4.4 : Manus y-z Plane @ x = 14.04" Table 4.3 : Data for x = 14.04” x y z n 14.04 0 24.18 0.37 14.04 13.5 24.18 0.00 14.04 23.5 24.18 0.54 14.04 0 18.2 0.34 14.04 13.5 18.2 0.00 14.04 23.5 18.2 0.52 14.04 0 6.18 0.19 14.04 13.5 6.18 0.00 14.04 23.5 6.18 0.38 14.04 0 -0.8 0.18 14.04 13.5 -0.8 0.00 14.04 23.5 -0.8 0.37 14.04 0 -5.82 0.23 14.04 13.5 -5.82 0.00 14.04 23.5 -5.82 0.41 14.04 0 -13.8 0.33 14.04 13.5 -13.8 0.00 14.04 23.5 -13.8 0.51 14.04 0 -22.8 0.37 14.04 13.5 -22.8 0.00 14.04 23.5 -22.8 0.53 14.04 0 -29.8 0.23 14.04 13.5 -29.8 0.00 14.04 23.5 -29.8 0.20 The Manus arm as shown in Figure 4.5 has very good access to objects along the side of the chair at the verti cal plane of x = 6.75”. The only li mitation to this side reach is approaching low objects on the floor. It should also be noted that the effect of the singularity shown in Figure 4.4 has not been completely elim inated. At the vertical line on the yz plane at y = 13.5, the manipulability measure is very low from coffee table (z = -5.82”) to kitchen countertop (z = 6.18”).

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45 Figure 4.5 : Manus y-z Plane @ x = 6.75" Table 4.4 : Data for x = 6.75” x y z n 6.75 0 6.18 0.35 6.75 13.5 6.18 0.14 6.75 23.5 6.18 0.51 6.75 0 24.18 0.52 6.75 13.5 24.18 0.32 6.75 23.5 24.18 0.64 6.75 0 18.2 0.49 6.75 13.5 18.2 0.28 6.75 23.5 18.2 0.64 6.75 0 -0.8 0.33 6.75 13.5 -0.8 0.13 6.75 23.5 -0.8 0.51 6.75 0 -5.82 0.37 6.75 13.5 -5.82 0.18 6.75 23.5 -5.82 0.55 6.75 0 -13.8 0.47 6.75 13.5 -13.8 0.27 6.75 23.5 -13.8 0.64 6.75 0 -22.8 0.50 6.75 13.5 -22.8 0.32 6.75 23.5 -22.8 0.61 6.75 0 -29.8 0.25 6.75 13.5 -29.8 0.21 6.75 23.5 -29.8 0.00 Access to high shelves and counters incr eased as the operator approached them from the left side. Values of the manipulab ility measure in Figure 4.6 were near optimum for reaching objects when the operator aligned th e goal parallel to the se at of the chair at the yz plane of x = 0.54”. It can also be s een in the following figur es that the measure was near maximum between the valu es of x from 0” to -4”.

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46 Figure 4.6 : Manus y-z Plane @ x = 0.54" Table 4.5 : Data for x = 0.54” x y z n 0.54 0 24.18 0.70 0.54 13.5 24.18 0.60 0.54 23.5 24.18 0.75 0.54 0 18.2 0.73 0.54 13.5 18.2 0.59 0.54 23.5 18.2 0.83 0.54 0 6.18 0.63 0.54 13.5 6.18 0.46 0.54 23.5 6.18 0.78 0.54 0 -0.8 0.62 0.54 13.5 -0.8 0.45 0.54 23.5 -0.8 0.77 0.54 0 -5.82 0.66 0.54 13.5 -5.82 0.49 0.54 23.5 -5.82 0.79 0.54 0 -13.8 0.72 0.54 13.5 -13.8 0.58 0.54 23.5 -13.8 0.83 0.54 0 -22.8 0.65 0.54 13.5 -22.8 0.57 0.54 23.5 -22.8 0.66 0.54 0 -29.8 0.00 0.54 13.5 -29.8 0.12 0.54 23.5 -29.8 0.00 Access to the mouth was at maximum va lues and actually increased as the arm moved past the mouth position [-4, 0, 13.5] in Figure 4.7 toward the opposite side of the chair. The arm has very good access to the area directly in front of the chest of the operator. It is interesting to note that the Manus arm is capable of reaching across the centerline of the wheelchair to manipulate object s. In fact, in regions directly around the operator, the manipulability measure actually rises to a maximum value 6.75” past the centerline of the wheelchair.

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47 Figure 4.7 : Manus y-z Plane @ x = 0” Table 4.6 : Data for Manus x = 0” x y z n 0 -6.75 16.5 0.94 0 -4 16.5 0.87 0 0 16.5 0.75 0 4 16.5 0.65 0 6.75 16.5 0.60 0 13.5 16.5 0.61 0 23.5 16.5 0.85 0 -6.75 13.5 0.96 0 -4 13.5 0.86 0 0 13.5 0.73 0 4 13.5 0.62 0 6.75 13.5 0.57 0 13.5 13.5 0.58 0 23.5 13.5 0.85 0 -6.75 0 0.94 0 -4 0 0.82 0 0 0 0.65 0 4 0 0.53 0 6.75 0 0.48 0 13.5 0 0.48 0 23.5 0 0.80 The maximum manipulability measure for the Manus manipulator was found at [4, -6.75, 13.5] in Figure 4.8. These values were determined through discrete analysis and are not necessarily a global maximum. Th e measure is increasing, moving from x = 0 through x = -4 to x = -6.75, where the last data point was on the z = 13.5” height. The Manus has excellent manipulability measures at the vertical plane (x = -4”) at or near the height of the mouth (z = 13.5” to 16.5”) of the operator. The Manus provides excellent manipulator use when feeding and completing tasks that are at or about the mouth of the operator.

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48 Figure 4.8 : Manus y-z Plane @ x = -4" Table 4.7 : Data for Manus at x = -4” x y z n -4 -6.75 13.5 1.00 -4 -4 13.5 0.95 -4 0 13.5 0.87 -4 4 13.5 0.80 -4 6.75 13.5 0.76 -4 13.5 13.5 0.76 -4 23.5 13.5 0.95 -4 -6.75 16.5 0.95 -4 -4 16.5 0.93 -4 0 16.5 0.86 -4 4 16.5 0.80 -4 6.75 16.5 0.77 -4 13.5 16.5 0.77 -4 23.5 16.5 0.92

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49 4.1.2 Horizontal Planes Approaching the analysis from horizontal slices better fit the requirements for designing a manipulator as an assistive device Most objects rest on horizontal surfaces that have standard heights above ground level. An example is the standard desk height or the height of a light switch or a door handle. These horizontal slices through the worksp ace also help to reflect the importance of wheelchair orientation for reaching a goa l with a WMRA. A manipulator with very little access in one orientation but excellent access in another may require that the operator approach the goal with a di fferent bearing to achieve the goal. Starting at the top or highe st defined plane, Figure 4.9 shows that for access to low kitchen cabinet shelves, the Manus has very good manipulability measures directly to the front and to the side of the chair. The overall average of normalized mani pulability is good at 0.53. The closer the goal is to the first rotational axis, the lo wer the manipulability measure will be. This remains constant throughout al l of the horizontal planes. Figure 4.9 : Manus x-y Plane @ z = 24.18” Table 4.8 : Data for Manus at z = 24.18” x y z n 27.54 0 24.18 0.64 27.54 13.5 24.18 0.52 27.54 23.5 24.18 0.72 14.04 0 24.18 0.37 14.04 13.5 24.18 0.00 14.04 23.5 24.18 0.54 6.75 0 24.18 0.52 6.75 13.5 24.18 0.32 6.75 23.5 24.18 0.64 0.54 0 24.18 0.70 0.54 13.5 24.18 0.60 0.54 23.5 24.18 0.75 In Figure 4.10 the horizontal plane of a light switch (z=18.2”) can be seen.

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50 When attempting to operate a light switch, the optimum approach is from the side because the n value directly to the side of the operator is excellent (0.83). The manipulability measure is still very good in the far front of the operato r and to the far left corner of the workspace. The average nvalue for this plane is good at 0.53. Access to the inside the perimeter of the workspace are limited. Figure 4.10 : Manus x-y Plane @ z = 18.2” Table 4.9 : Data for Manus at z = 18.2” x y z n 27.54 0 18.2 0.65 27.54 13.5 18.2 0.49 27.54 23.5 18.2 0.77 14.04 0 18.2 0.34 14.04 13.5 18.2 0.00 14.04 23.5 18.2 0.52 6.75 0 18.2 0.49 6.75 13.5 18.2 0.28 6.75 23.5 18.2 0.64 0.54 0 18.2 0.73 0.54 13.5 18.2 0.59 0.54 23.5 18.2 0.83 At the kitchen countertop le vel, Figure 4.11, the manipulat or’s effectiveness drops significantly. This is due in part to the pl ane being observed having very little vertical separation from the plane that the first link rotates along. This would make the manipulability measure reach low values in the horizontal pl ane of z = 1.74”. Because the planes of the countertop (z = 6.16” Figure 4.11) and desktop / door handle (z = 0.8” Figure 4.12) are close to this pl ane, they have very similar values for the manipulability measure. The average n -value for the plane is good at 0.42. The highest n -value on this plane is to the left of the ope rator. Accessibility of objects within the workspace are best when attempted close to the operator, such as at x = 0.54 compared to any other yz-plane.

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51 Figure 4.11 : Manus x-y Plane @ z = 6.18” Table 4.10 : Data for Manus at z = 6.18” x y z n 27.54 0 6.18 0.53 27.54 13.5 6.18 0.35 27.54 23.5 6.18 0.69 14.04 0 6.18 0.19 14.04 13.5 6.18 0.00 14.04 23.5 6.18 0.38 6.75 0 6.18 0.35 6.75 13.5 6.18 0.14 6.75 23.5 6.18 0.51 0.54 0 6.18 0.63 0.54 13.5 6.18 0.46 0.54 23.5 6.18 0.78 The Manus arm manipulability at the height of a table or door knob is shown in Figure 4.12. At this plane the interior regions of the plane have very limited accessibility. At the outer corners of the workspace the ar m has good or better access to objects with the maximum manipulability, for this pl ane, to the left of the operator. The average n-value for the plane is 0.41 and is the poorest average plane value with the exception of lowest pl ane. This plane is marginally good on the qualitative scale.

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52 Figure 4.12 : Manus x-y Plane @ z = -0.8” Table 4.11 : Data for Manus at z=-0.8” x y z n 27.54 0 -0.8 0.52 27.54 13.5 -0.8 0.33 27.54 23.5 -0.8 0.68 14.04 0 -0.8 0.18 14.04 13.5 -0.8 0.00 14.04 23.5 -0.8 0.37 6.75 0 -0.8 0.33 6.75 13.5 -0.8 0.13 6.75 23.5 -0.8 0.51 0.54 0 -0.8 0.62 0.54 13.5 -0.8 0.45 0.54 23.5 -0.8 0.77 Manus arm at the height of a coffee table is shown in Figure 4.13. Access to an object to the side of the opera tor is good and has its highest va lue of n (0.79) left of the operator’s hand (0.54, 23.5, -5.82). The average n -value for this plane is good at 0.44. The arm has lower accessibility near the centerline of the wh eelchair (y = 0) compared with the outer edge of the workspace (y = 23.5).

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53 Figure 4.13 : Manus x-y Plane @ z = -5.82” Table 4.12 : Data for Manus at z = -5.82” x y z n 27.54 0 -5.82 0.56 27.54 13.5 -5.82 0.38 27.54 23.5 -5.82 0.71 14.04 0 -5.82 0.23 14.04 13.5 -5.82 0.00 14.04 23.5 -5.82 0.41 6.75 0 -5.82 0.37 6.75 13.5 -5.82 0.18 6.75 23.5 -5.82 0.55 0.54 0 -5.82 0.66 0.54 13.5 -5.82 0.49 0.54 23.5 -5.82 0.79 Closer to the ground, the measure begins to rise and access to an electric socket (z = -13.8” Figure 4.14) is ex cellent to the side of the chair an d still very high in front of the wheelchair. It can be noted here that this is the lowest pl ane that still has good or better qualitative rating. The average n -value for this plane is good at 0.5 2 but the range of manipulability measures within this plane is larger than other planes. The lowest reachable n -value is 0.27 and the highest is 0.83.

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54 Figure 4.14 : Manus x-y Plane @ z = -13.8” Table 4.13 : Data for Manus at z = -13.8” x y z n 27.54 0 -13.8 0.64 27.54 13.5 -13.8 0.48 27.54 23.5 -13.8 0.77 14.04 0 -13.8 0.33 14.04 13.5 -13.8 0.00 14.04 23.5 -13.8 0.51 6.75 0 -13.8 0.47 6.75 13.5 -13.8 0.27 6.75 23.5 -13.8 0.64 0.54 0 -13.8 0.72 0.54 13.5 -13.8 0.58 0.54 23.5 -13.8 0.83 For tall objects on the ground, accessibility is very good directly to the front of and to the sides of the wheelchair. Reaching this plane is best from the side of the wheelchair with the average value along the right side of the plane being 0.62. Overall the plane has a good average n -value of 0.50.

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55 Figure 4.15 : Manus x-y Plane @ z = 22.8” Table 4.14 : Data for Manus at z = -22.8” x y z n 27.54 0 -22.8 0.61 27.54 13.5 -22.8 0.50 27.54 23.5 -22.8 0.66 14.04 0 -22.8 0.37 14.04 13.5 -22.8 0.00 14.04 23.5 -22.8 0.53 6.75 0 -22.8 0.50 6.75 13.5 -22.8 0.32 6.75 23.5 -22.8 0.61 0.54 0 -22.8 0.65 0.54 13.5 -22.8 0.57 0.54 23.5 -22.8 0.66 Objects low to the ground, shown in Figur e 4.16, are at the lo wer limit of the reach of the Manus manipulator. The arm is not capable of reaching objects in the far corners of the workspace on the horizont al plane at z = -29.8”. The average n -value for all the points on the plane is 0.10. This m eans that the manipulator has very limited access to the plane. It is interesting to note that regi ons where the arm traditionally has lower manipulability measures are the areas that ha ve the highest measures at z = -29.8”. These zones are the vertical lines that shar e the points (27.54, 13.5, z) and (14.04, 23.5, z).

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56 Figure 4.16 : Manus x-y Plane @ z = 29.8” Table 4.15 : Data for Manus at z = -29.8” x y z n 27.54 0 -29.8 0.00 27.54 13.5 -29.8 0.22 27.54 23.5 -29.8 0.00 14.04 0 -29.8 0.23 14.04 13.5 -29.8 0.00 14.04 23.5 -29.8 0.20 6.75 0 -29.8 0.25 6.75 13.5 -29.8 0.21 6.75 23.5 -29.8 0.00 0.54 0 -29.8 0.00 0.54 13.5 -29.8 0.12 0.54 23.5 -29.8 0.00 A summary of effectiveness in reaching ar eas common to activities of daily living (ADL) is shown in Table 4.16. The qualitative assessment is based on the average of the normalized manipulability measure of all po ssible wheelchair orient ations possible to accomplish the task. Six possible qualitative assessments could be given for each task. These qualitative assessments were first show n in Figure 4.2 and are: excellent, very good, good, limited, very limited, and undefined or unreachable. For example, an object can be picked off the ground from in front of the wheelchair as well as along the side. The aver age of all the recorded values for the normalized manipulability measure ( n ) along the entire perimeter of the wheelchair at the plane of the specific activity of daily living is sh own in the second column of Table 4.16. Each row involved only one horizontal plane except for picking up objects on the ground and access to mouth. For the ADL “Pickup off Ground” the average value for the perimeter of the chair was taken for the two lowest planes (z = 22.8” and z = -29.8”). The ADL “Access to mouth” took the average of three points on two vertical planes x = 0” and x = -4”. Because head position may not be perfectly in the centerline of the wheelchair points, y = 4”, 0”, -4 ” were averaged at both he ad heights (z = 13.5” and z = 16.5”).

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57 The method used for determining the quali tative efficacy of a manipulator is not orientation-specific. In every instance of ADL analysis, there was a wheelchair orientation that would provide a higher normalized manipulability measure than the value listed in Table 4.16. If the operator is given th e ability to maneuver the wheelchair into a specific position for the job, the manipulat or would be able to have a greater manipulability measure for that goal. Table 4.16 : Qualitative Summary of Manus Effectiveness Pick-up off ground 0.33Limited Coffee table 0.57Good Door knob 0.53Good Kitchen countertop 0.54Good Light switch 0.65Very Good Low kitchen shelf 0.64Very Good Reach into lap 0.57Good Access to mouth 0.81Excellent The Manus manipulator provided excellent (0.81) access to th e mouth of the operator. The ability to do tasks above the ki tchen countertop height such as reach a light switch and reach a low kitchen shelf was very good. Reaching from the side of the operator would yield the highest mani pulability measures from the arm. Access to a coffee table and the operator’ s lap were close to very good and had a qualitative rating of good (0.57). The ability to reach a doorknob and a kitchen countertop were both good (0.53 and 0.54 respectively). Finally, the lowest value for the activit ies listed in Table 4.16 was reaching the floor. Access to the floor was limited with a value of 0.33.

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58 4.2 Evaluation of the Raptor The next system to be analyzed is the Raptor Because all power wheelchairs are constructed differently, the moun t used in this application is specific to the chair that was available. Of the two manipulators that were analyzed, only the Raptor was available for direct measurements of the complete system. The power wheelchair that the solid model was created from was a Storm Series “Arrow”. The Raptor motor fit under the chair but there was difficulty finding a satisfactory mounting position with the factory-provided m ounts. To solve the problem, replacement mounting brackets were fabricated from al uminum in order to achieve a level of structural integrity that s howed the overall stiffness of the robotic arm without the mounting adding to positi oning error. With the Raptor manipulator mounted securely, a significant amount (1” 2”) of play c ould be felt at the end effector.

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59 ZuZ2ZGZ3Z0,1XuX2,3,GX0,1 Figure 4.17 : Raptor Reference Frames Figure 4.17 represents the Raptor mounted to a generic power wheelchair along with the corresponding frames of reference (frames 0 to G). Table 4.17 shows the D-H parameter table for the Raptor with 3DOF. This table of D-H parameters, along with Figure 4.17 and Equation 3.2, are used to create the transformation matrix which relates the link i with previous link i-1 These individual transformation matrices for each link are show n after the table of parameters. There is also a row for the fourth link. This link connects the gripper to the third joint. It is purely a translational relation, so the coordinate syst em for the third joint and the gripper have the same orientation.

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60 Table 4.17 : Raptor D-H Parameters i i ai-1 di i 1 0 0 5 2 90 0 27 3 -90 0 0 4 0 15.75 0 0 Inserting the transformation matrices from the DH-Parameter into the table shown in Table 4.17 provides the transformation matr ix that relates frame 1 with respect to frame 0 (Equation 4.10). T1wrt0 cos1 sin10 0 sin1 cos10 0 0 0 1 0 0 0 0 1 Equation 4.10 The transformation matrix which relates frame 2 with respect to frame 1 is shown in Equation 4.11. T2wrt1 sin2 0 cos20 cos2 0 sin20 0 1 0 0 0 27 0 1 Equation 4.11 The transformation matrix which relates frame 3 with respect to frame 2 is shown in Equation 3.9 the Equation below. T3wrt2 cos3 0 sin30 sin3 0 cos30 0 10 0 0 0 0 1 Equation 4.12

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61 The transformation matrix which relates fram e G, or the frame of the gripper, with respect to frame 3 is shown in Equation 4.13. TGwrt3 1 0 0 0 0 1 0 0 0 0 1 0 18.38 0 0 1 Equation 4.13 It is necessary to work with a frame that has correlation to the user, therefore a user frame must be created. Equation 4.14 shows the transformation matrix which defines the translational relationship between frame 0 with respect to the user frame. T0wrtU 1 0 0 0 0 0 1 0 0 10 0 6.30 13.4616.161 Equation 4.14 Concatenation of the transformation matrices is shown in Equation 4.15, to give the transform relating the end gripper position with respect to the user frame. This will be the complete transformation matrix. T0wrtU*T1wrt0*T2wrt1*T3wrt2*TGwrt3 = TGwrtU Equation 4.15 The final transformational matrix is shown in Equation 4.16 the figure below. cos 1 sin 2 cos 3 sin 1 sin 3 cos 2 cos 3sin 1sin 2cos 3cos 1sin 3 0 cos 1 sin 2 sin 3 sin 1 cos 3 cos 2sin 3sin 1 sin 2sin 3cos 1cos 3 0 cos 1 cos 2 sin 2 sin 1 cos 20 18.38 cos 1 sin 2 cos 3 18.38 sin 1 sin 3 6.30 27sin 1 18.38 cos 2cos 313.46 18.38 sin 1sin 2cos 318.38 cos 1sin 316.16 27 cos 1 1 Equation 4.16 The position vector, a 3x1 matrix, is the first three rows of the final column of the final transformational matrix and is shown in the figure below. This matrix is also known

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62 as the forward kinematic matrix. When the thr ee joint angles are input, the result is the position vector (Equation 4.17) of the gri pper with respect to the user frame. 18.38cos 1 sin 2 cos 3 18.38sin 1 sin 3 6.30 27sin 1 18.38 cos 2 cos 3 13.46 18.38sin 1 sin 2 cos 3 18.38cos 1 sin 3 16.16 27cos 1 Equation 4.17 From the forward kinematic matrix we can compute the Jacobian Matrix the partial derivatives of the positional matrix as shown Equation 4.18. Due to the size of the Jacobian, the matrix will be di splayed one column at a time. Column 1: -18.38*sin(t1)*sin(t2)*cos(t3) -18.38(t1)*sin(t3)-27*cos(t1) 0 18.38*cos(t1)*sin(t2)*cos(t3)-18.38*sin(t1)*sin(t3)-27*sin(t1) Equation 4.18 Column 2: 18.38*cos(t1)*cos(t2)*cos(t3) 18.38*sin(t2)*cos(t3) 18.38*sin(t1)*cos(t2)*cos(t3) Column 3: -18.38*cos(t1)*sin(t2)*sin (t3)-18.38*sin(t1)*cos(t3) 18.38*cos(t2)*sin(t3) -18.38*sin(t1)*sin(t2)*sin(t3)+18.38*cos(t1)*cos(t3) 4.2.1 Vertical Planes The following figures show the ma nipulability measures for the Raptor arm as mounted on the Arrow Storm Series power wheelchair. After all data points were collected, the maximum manipulability measure for the Raptor was found to be 9121.0 at the point [-4,-13.5,16.5]. Comments regarding the data:

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63 As shown in Figure 4.18, the Raptor is incapable of reaching objects on a high shelf. At this distance of 27.54” in front of th e user frame, operati ng a light switch is only possible when directly in line with the plane of the first link’s rotation (xz plane where y = -13.5”), which also is the plane that ha s maximum manipulability measure values. The Raptor has very good manipulability from the ground to the height of a low coffee table (z = 5.82”) and still has good manipulability at the height of a standard table (z = 0.8”). At this distance from the user frame, th e arm is not capable of reaching objects on a low shelf (z = 24.18). A light switch can only be manipulated di rectly along a lateral line of y = -13.5”.

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64 Figure 4.18 : Raptor y-z Plane @ x = 27.54” Table 4.18 : Data for Raptor at x = 27.54” x y z n 27.54 0 -29.8 0.46 27.54 -13.5 -29.8 0.93 27.54 -23.5 -29.8 0.70 27.54 0 -22.8 0.58 27.54 -13.5 -22.8 0.98 27.54 -23.5 -22.8 0.79 27.54 0 -13.8 0.60 27.54 -13.5 -13.8 0.99 27.54 -23.5 -13.8 0.80 27.54 0 -5.82 0.53 27.54 -13.5 -5.82 0.97 27.54 -23.5 -5.82 0.76 27.54 0 -0.8 0.40 27.54 -13.5 -0.8 0.90 27.54 -23.5 -0.8 0.66 27.54 0 6.18 0.00 27.54 -13.5 6.18 0.66 27.54 -23.5 6.18 0.35 27.54 0 18.2 0.00 27.54 -13.5 18.2 0.24 27.54 -23.5 18.2 0.00 27.54 0 24.18 0.00 27.54 -13.5 24.18 0.00 27.54 -23.5 24.18 0.00 From Figure 4.19 it can be seen that the ability of the Raptor manipulator to reach low kitchen cabinet shelves is very limited. At this distance (x = 14.04”) the operato r would have to position his/her feet approximately 20” under a countertop. This is not possible with some kitchen designs2. At this distance, accessibility of objects on ta bles and countertops is excellent from the front. Access to all levels except for the low shelf is very good from the side.

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65 Figure 4.19 : Raptor y-z Plane @ x = 14.04” Table 4.19 : Data for Raptor at x = 14.04” x y z n 14.04 0 -29.8 0.59 14.04 -13.5 -29.8 0.78 14.04 -23.5 -29.8 0.70 14.04 0 -22.8 0.48 14.04 -13.5 -22.8 0.62 14.04 -23.5 -22.8 0.57 14.04 0 -13.8 0.44 14.04 -13.5 -13.8 0.57 14.04 -23.5 -13.8 0.53 14.04 0 -5.82 0.53 14.04 -13.5 -5.82 0.70 14.04 -23.5 -5.82 0.63 14.04 0 -0.8 0.62 14.04 -13.5 -0.8 0.82 14.04 -23.5 -0.8 0.73 14.04 0 6.18 0.68 14.04 -13.5 6.18 0.98 14.04 -23.5 6.18 0.83 14.04 0 18.2 0.00 14.04 -13.5 18.2 0.72 14.04 -23.5 18.2 0.42 14.04 0 24.18 0.00 14.04 -13.5 24.18 0.04 14.04 -23.5 24.18 0.00 At the yz-plane where x = 6.75”, shown in Figure 4.20, the Raptor is finally able to reach objects on low shelves with more th an a minimal value. The ability to reach objects to the side of the chair begins to drop off, although it still can reach the ground with a good manipulability measure. Access to th e side at this plane is good but all eight horizontal planes can be reached at this distance from the operator. This is the only vertical plane that offers this ability to reach all horizontal planes with the Raptor

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66 Figure 4.20 : Raptor y-z Plane @ x = 6.75” Table 4.20 : Data for Raptor at x = 6.75” x y z n 6.75 0 -29.8 0.36 6.75 -13.5 -29.8 0.49 6.75 -23.5 -29.8 0.45 6.75 0 -22.8 0.06 6.75 -13.5 -22.8 0.26 6.75 -23.5 -22.8 0.23 6.75 0 -13.8 0.00 6.75 -13.5 -13.8 0.19 6.75 -23.5 -13.8 0.16 6.75 0 -5.82 0.23 6.75 -13.5 -5.82 0.37 6.75 -23.5 -5.82 0.34 6.75 0 -0.8 0.42 6.75 -13.5 -0.8 0.56 6.75 -23.5 -0.8 0.51 6.75 0 6.18 0.63 6.75 -13.5 6.18 0.84 6.75 -23.5 6.18 0.75 6.75 0 18.2 0.44 6.75 -13.5 18.2 0.92 6.75 -23.5 18.2 0.68 6.75 0 24.18 0.00 6.75 -13.5 24.18 0.46 6.75 -23.5 24.18 0.02 In order to gain the highest manipul ability measure in the low cabinets, the operator will have to approach the cabinet shelf from the side. This yz-plane is represented in Figure 4.21. The m easure at this point is only moderate but this is the highest value available. Access to objects lower than a kitche n counter begins to diminish due to a singularity of the ar m at the height of an elec tric socket (z = 13.8”).

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67 Figure 4.21 : Raptor y-z Plane @ x = 0.54” Table 4.21 : Data for Raptor at x = 0.54” x y z n 0.54 0 -29.8 0.00 0.54 -13.5 -29.8 0.29 0.54 -23.5 -29.8 0.27 0.54 0 -22.8 0.00 0.54 -13.5 -22.8 0.00 0.54 -23.5 -22.8 0.13 0.54 0 -13.8 0.00 0.54 -13.5 -13.8 0.00 0.54 -23.5 -13.8 0.00 0.54 0 -5.82 0.00 0.54 -13.5 -5.82 0.15 0.54 -23.5 -5.82 0.10 0.54 0 -0.8 0.24 0.54 -13.5 -0.8 0.38 0.54 -23.5 -0.8 0.35 0.54 0 6.18 0.55 0.54 -13.5 6.18 0.72 0.54 -23.5 6.18 0.65 0.54 0 18.2 0.55 0.54 -13.5 18.2 0.97 0.54 -23.5 18.2 0.77 0.54 0 24.18 0.00 0.54 -13.5 24.18 0.63 0.54 -23.5 24.18 0.31 The Raptor has its highest manipulability measure at the point [0,-13.5, 16.5] which is shown in Figure 4.22. The ability to manipulate objects is excellent toward the operator’s right side but rapi dly diminishes once the centerline of the arm is reached. Objects slightly above the lap of the operato r have a limited manipulability measure. The manipulator is unable to access an object to th e left of the centerline (y = 0) of the wheelchair. Two of the most important activities of daily living are eating and drinking. Because of the significance of these actions two planes are created specifically to evaluate manipulator effectiveness near the mouth and head (Figure 4.22 and Figure

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68 4.23). The density of the data points is increase d and extends beyond th e centerline of the chair. Both figures show that the manipulabili ty measure is very high toward the outer edge of the defined workspace to both height s (z = 13.5” and z = 16.5”) and is still very good at the operator’s mouth. Figure 4.22 : Raptor y-z Plane @ x = 0” Table 4.22 : Data for Raptor at x = 0” x y z n 0 6.75 0 0.00 0 4 0 0.00 0 0 0 0.28 0 -4 0 0.38 0 -6.75 0 0.40 0 -13.5 0 0.40 0 -23.5 0 0.38 0 6.75 13.5 0.00 0 4 13.5 0.27 0 0 13.5 0.68 0 -4 13.5 0.85 0 -6.75 13.5 0.92 0 -13.5 13.5 0.98 0 -23.5 13.5 0.84 0 6.75 16.5 0.00 0 4 16.5 0.00 0 0 16.5 0.63 0 -4 16.5 0.84 0 -6.75 16.5 0.92 0 -13.5 16.5 1.00 0 -23.5 16.5 0.82

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69 Figure 4.23 : Raptor y-z Plane @ x = -4” Table 4.23 : Data for Raptor at x = -4” x y z n -4 6.75 13.5 0.00 -4 4 13.5 0.28 -4 0 13.5 0.68 -4 -4 13.5 0.84 -4 -6.75 13.5 0.91 -4 -13.5 13.5 0.97 -4 -23.5 13.5 0.83 -4 6.75 16.5 0.00 -4 4 16.5 0.01 -4 0 16.5 0.64 -4 -4 16.5 0.85 -4 -6.75 16.5 0.93 -4 -13.5 16.5 1.00 -4 -23.5 16.5 0.83 4.2.2 Horizontal Planes Starting from the plane of a low kitchen shelf, Figure 4.24 shows that the Raptor is able to reach objects from the side of the wheelchair directly to the right of the operator. Although these points can be reached, the access to them is minimal. The average n-value of the horizon tal plane is very limited at 0.12.

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70 Figure 4.24 : Raptor x-y Plane @ z = 24.18” Table 4.24 : Data for Raptor z = 24.18” x y z n 27.54 0 24.18 0.00 27.54 -13.5 24.18 0.00 27.54 -23.5 24.18 0.00 14.04 0 24.18 0.00 14.04 -13.5 24.18 0.04 14.04 -23.5 24.18 0.00 6.75 0 24.18 0.00 6.75 -13.5 24.18 0.46 6.75 -23.5 24.18 0.02 0.54 0 24.18 0.00 0.54 -13.5 24.18 0.63 0.54 -23.5 24.18 0.31 At the level of a wall-mounted light sw itch the manipulability measure increases compared to the highest plane. The gripper is able to reach a light switch both from directly in front of the arm and to the side of the chair. Access to objects to the side of the operator is good. This would be the preferred wheelchair orie ntation when attempting to actuate a light switch. Figure 4.25 shows that access to the light sw itch directly in front of the arm is limited, while along the side of the chair the manipulability measures are very good. The average n-value for this plane is good at 0.48.

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71 Figure 4.25 : Raptor x-y Plane @ z = 18.2” Table 4.25 : Data for Raptor z = 18.2” x y z n 27.54 0 18.2 0.00 27.54 -13.5 18.2 0.24 27.54 -23.5 18.2 0.00 14.04 0 18.2 0.00 14.04 -13.5 18.2 0.72 14.04 -23.5 18.2 0.42 6.75 0 18.2 0.44 6.75 -13.5 18.2 0.92 6.75 -23.5 18.2 0.68 0.54 0 18.2 0.55 0.54 -13.5 18.2 0.97 0.54 -23.5 18.2 0.77 At kitchen countertop level (Figure 4.26) the Raptor has very good to excellent access to the sides of the chair, while access to the front of th e chair is moderate. At this point, the gripper is unable to reach di rectly in front of the operator. Access to objects to the side of the wheel chair is very good to excellent. This is the highest plane that the manipulator can reac h an object in the far right corner of the workspace. Overall the plane has the highest averag e manipulability measures of all the horizontal planes analyzed at 0.64 with a very good qualitativ e assessment. This is the maximum average n-value for any horizontal plane.

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72 Figure 4.26 : Raptor x-y Plane @ z = 6.18” Table 4.26 : Data for Raptor z= 6.18” x y z n 27.54 0 6.18 0.00 27.54 -13.5 6.18 0.66 27.54 -23.5 6.18 0.35 14.04 0 6.18 0.68 14.04 -13.5 6.18 0.98 14.04 -23.5 6.18 0.83 6.75 0 6.18 0.63 6.75 -13.5 6.18 0.84 6.75 -23.5 6.18 0.75 0.54 0 6.18 0.55 0.54 -13.5 6.18 0.72 0.54 -23.5 6.18 0.65 The Raptor is able to reach objects directly in front of the operator at the height of a standard table (Figure 4.27). At this elev ation and below, the manipulator has limited access to objects directly in front of the opera tor and the manipulator is able to access all twelve points in the workspace. This is the only plane above the seat of the wheelchair that this occurs. To open a door the operator would have a greatest chance for success by approaching the door directly in front of the manipulator (y = -13.5”). The average nvalue for this plane is good at 0.55. Manipulability is at its highest level on this plane at x = 27.54 and decreases steadily as you approach x = 0.54 ex cept for the x-z plane at y = 0.

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73 Figure 4.27 : Raptor x-y Plane @ z = -0.8 Table 4.27 : Data for Raptor z = -0.8” x y z n 27.54 0 -0.8 0.40 27.54 -13.5 -0.8 0.90 27.54 -23.5 -0.8 0.66 14.04 0 -0.8 0.62 14.04 -13.5 -0.8 0.82 14.04 -23.5 -0.8 0.73 6.75 0 -0.8 0.42 6.75 -13.5 -0.8 0.56 6.75 -23.5 -0.8 0.51 0.54 0 -0.8 0.24 0.54 -13.5 -0.8 0.38 0.54 -23.5 -0.8 0.35 At the height of a coffee table (Figure 4.28) access to all points in front of the operator is good to excellent. The ability to reach objects to the side of the operator continues to decrease. The average n-value of the plane is good at 0.44.

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74 Figure 4.28 : Raptor x-y Plane @ z = 5.82” Table 4.28 : Data for Raptor z = -5.82” x y z n 27.54 0 -5.82 0.53 27.54 -13.5 -5.82 0.97 27.54 -23.5 -5.82 0.76 14.04 0 -5.82 0.53 14.04 -13.5 -5.82 0.70 14.04 -23.5 -5.82 0.63 6.75 0 -5.82 0.23 6.75 -13.5 -5.82 0.37 6.75 -23.5 -5.82 0.34 0.54 0 -5.82 0.00 0.54 -13.5 -5.82 0.15 0.54 -23.5 -5.82 0.10 Access to objects to the side of the chair is at its lowe st point value at z = 13.8” (Figure 4.29). This is due primarily to the li nk geometry, the first li nk is 27” long and the second is 17.5” long, their difference of 9.5” means that the Raptor is incapable reaching objects that are closer than 9.5” to the frame 0 [-6.26, -13.5, -16.18] The average n-value (0.36) for this plane is limited which is the lowest of all the horizontal planes evaluated.

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75 Figure 4.29 : Raptor x-y Plane @ z = 13.8” Table 4.29 : Data for Raptor z = -13.8” x y z n 27.54 0 -13.8 0.60 27.54 -13.5 -13.8 0.99 27.54 -23.5 -13.8 0.80 14.04 0 -13.8 0.44 14.04 -13.5 -13.8 0.57 14.04 -23.5 -13.8 0.53 6.75 0 -13.8 0.00 6.75 -13.5 -13.8 0.19 6.75 -23.5 -13.8 0.16 0.54 0 -13.8 0.00 0.54 -13.5 -13.8 0.00 0.54 -23.5 -13.8 0.00 Near the ground, the manipulab ility measure does not change significantly for high and low objects on the fl oor (Figure 4.30 and Figure 4. 31). Low objects on the floor can be accessed from the front as we ll as the side of the chair. Along the side of the wheelchair the ma nipulability measure drops the farther back the object is and objects directly to the right of the opera tor is very limited. The average n-value for this plane is limited at 0.39.

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76 Figure 4.30 : Raptor x-y Plane @ z = 22.8” Table 4.30 : Data for z = -22.8” x y z n 27.54 0 -22.8 0.58 27.54 -13.5 -22.8 0.98 27.54 -23.5 -22.8 0.79 14.04 0 -22.8 0.48 14.04 -13.5 -22.8 0.62 14.04 -23.5 -22.8 0.57 6.75 0 -22.8 0.06 6.75 -13.5 -22.8 0.26 6.75 -23.5 -22.8 0.23 0.54 0 -22.8 0.00 0.54 -13.5 -22.8 0.00 0.54 -23.5 -22.8 0.13 An interesting note is that there is an apparent horizont al line of symmetry approximately between z = 22.8” and z = 5.82 ”. The true plane of symmetry would be the horizontal plane that the first rotational axis rests (z = 16.18). The average n-value for this plane is good at 0.50 with the highest point within the workspace is at (27.54, -13.5).

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77 Figure 4.31 : Raptor x-y Plane @ z = -29.8” Table 4.31 : Data for Raptor at z = -29.8” x y z n 27.54 0 -29.8 0.46 27.54 -13.5 -29.8 0.93 27.54 -23.5 -29.8 0.70 14.04 0 -29.8 0.59 14.04 -13.5 -29.8 0.78 14.04 -23.5 -29.8 0.70 6.75 0 -29.8 0.36 6.75 -13.5 -29.8 0.49 6.75 -23.5 -29.8 0.45 0.54 0 -29.8 0.00 0.54 -13.5 -29.8 0.29 0.54 -23.5 -29.8 0.27 A summary of the Raptor’s effectiveness in reaching areas common in activities of daily living (ADL) is shown in Table 4.32. This table shows the task, the average manipulability measure of all possible wheelchai r orientations that could achieve the task, and the qualitative assessment. Table 4.32 : Qualitative Summary of Raptor Effectiveness Pick-up off ground 0.57 good Coffee table 0.55 good Door knob 0.59 good Kitchen countertop 0.54 good Light switch 0.35 limited Low kitchen shelf 0.05 very limited Reach into lap 0.31 limited Access to mouth 0.55 good

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78 Overall, the average normalized manipulability measure ( n ) for all the eight tasks in the Table 4.32 is good (0.44). For the tasks that involved reaching onto planes lower than a kitchen countertop oriented from the front or side, the Raptor was close to very good on the qualitative scale (0.54 ~ 0.59). Access to the lap of the operator was limite d (0.31) and the values diminished as the goal moved closer to the operator. Additio nally, the inability of the gripper to reach areas to the opposite of the cen terline of the wheelchair lim ited the effectiveness of the arm in the operator’s lap. Reaching a light switch had limited acces s (0.35). This was due to the low normalized manipulability measures in front of the wheelchair. Access to the side of the operator was very good and as long as this wheelchair orientation was possible, the qualitative accessibility would be very good (0.62). The area least able to be reached is a low kitchen shelf. The Raptor has very limited access and was only able to reach the shelf in two of the six possible outer perimeter data points.

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79 Chapter Five Design Insights and Recommendations 5.1 Design Insights Both of the commercially-available systems analyzed were able to pick up objects from the floor, reach into the operators imme diate workspace, and manipulate objects on cabinets, desks and low tables. In several cases the manipulators are only able to manipulate objects in certain planes from speci fic orientation of the chair. For example, when attempting to retrieve objects off the floor, the Raptor is near its maximum manipulability measure from the front while it is incapable of retrieving an object directly to the right of the user. This would require th e operator to position the chair in a specific orientation before attempting to mani pulate an object with the arm. Additionally, the commercial designs appear to be well thought out, designed and manufactured. Through the analysis of the manipulability measure in a rehabilitationspecific workspace, it has been shown that there are areas of weakness in both designs that can be improved. Several design insight s and recommendations are noted below. The Manus has very low manipulability measur es at or very near the ground and must orient the chair with respect to the object in order to manipulate it. The Manus would be more effective in retr ieving objects from the floor if the mounting base were installed lower on the wheelchair with respect to the floor. The additional height in crease provided by the zaxis lift device would compensate for its lower initial position. The front mounting of the Manus provides excellent access to objects in front and above the operator. The vertical reach of the manipulator is very good even without using the z-axis lift device. All analysis was done with the Z-axis lift in its lowest position.

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80 Given the size of the workspace, the closer the object is to the first axis of rotation of the manipulator, the lower th e manipulability measure will be. Increasing the number of DOF of the mani pulator will allow better access to some internal regions (near singular ities) but this will come at the expense of one or more DOF’s of gripper orientation. Low mounting position and li nk geometry provides the Raptor with very good access to objects low to the ground and items di rectly in front of the wheelchair. The Raptor has very low manipulability when reaching into kitchen cabinets. The side-mount design limits how high that Raptor can be mounted with respect to the floor. Increasing the first link length could allow higher reach. A plane of symmetry exists at a horizontal plane where the first rotational axis rests. This plane of symmetry relates manipulability measures above and below z = 16.26” (user frame). Accessibility on horizontal plan es is still good up to z = 6.18. This is almost twice the distance that the manipulator’s primar y axis of rotation is above the floor. The length of the final link limits the Raptor’s ability to cross the centerline of the wheelchair. Objects on the lap of the ope rator become increasingly difficult to manipulate as one approaches the centerline of the wheelchair. The joint angle range in the third joint reduces the manipulator effectiveness. The arm cannot effectively reach back onto its elf. The arm is not capable of reaching objects near the first joint motor. The closer the goal is to the manipulator’s primary axis of rotation, the lower the manipulability measure. This is magnified by the limited joint angle range in the third revolute joint. The highest manipulability measure for the Raptor for all horizont al planes up to z = -0.8” is at (27.54, -13.5).

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81 5.2 Design Recommendations There is no single mounting location that w ill allow equal potential of manipulability for all activities of daily livi ng. Front mounting of an arm interferes with the user’s ability to maneuver under desks and sinks and is a visual obstruction to social interaction. Side mounting increases the wi dth of the wheelchair, making movement through doors and hallways more difficult. M ounting the arm in the rear of the chair requires longer manipulator link lengths to reach in front of the chair and this increases the loads on the motors and bearings. A single fixed mounting location does not allow access throughout the entire workspace. From the evaluation of the two comme rcial WMRAs, improvements to these commercially-available arms could come in two ways. First would be rail-mounting, allowing for frontand side-locking positions along with a rear-locking position for the manipulator base. In this wa y, the manipulator could bene fit from using the optimum mounting location for completing a specific ADL. There are a variety of uses for a ma nipulator in assistive rehabilitation applications. Additionally, a well-designed r obotic arm could be mounted onto a variety of surfaces and locations if the arm did not have fixed link geometry. In this way, a WMRA could be used in a workstation ap plication with only minor changes to link lengths and controller settings. Commercia lly-available WMRA are designed primarily for mounting onto wheelchairs and are not ea sily used as workstation manipulators. These arms cannot be made to fit a workstati on by the end user. This limits the use of the manipulator and reduces its potential use in a home or office environment. The second enhancement would be to de sign the manipulator as a system of modular joints and link lengths. A modular ma nipulator design would allow the system to be adjusted for various geometries. This would allow the system to be applied to stationary applications as we ll as mobile mounts. The modula rity of the manipulator will apply both to the links and joints as well as the rail track mount.

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82 5.2.1 Rail Mounted Manipulator The first and most novel improvement for a WMRA is a side-mounted railpositioned manipulator base that is capable of multiple base positions while in use. This design uses the concep t of having the manipulator move along a track. This was first developed with DeVAR, an early workstation r obot design. At the time of this research, this mounting track method has not been applied to WMRAs. The base of the manipulator would rest on a detachable track that runs along the side of the chair from the front to the back. The entire shape of the rail would be roughly C-shaped with curved bends at either end. Th e base could then move along this track to three discrete points from which to operate. Additionally, the rail would need to have provisions for quick release, f acilitating ease of tr ansfer to and from the wheelchair. There would be three positions for the base of the manipulator. The first would be in front of the chair and would allow access to objects in front and center of the operator, the second position would be a side mount that is slightly behind the yz plane of the operator which would allow for side access a nd for feeding, the final position is a stow position which would allow the arm to be folded away when not in use. The front lock location would be analogous to the Manus mount while the second lock location would be near the Raptor position. Link geometries would be critical for th e success of the desig n. There would need to be a compromise in the link geometry between the requirements for each base position. Each base position would have specific li nk lengths that would provide optimum workspace for the operator and the final link geometries of the system would be a compromise between the two sub-systems requirements. It may also be beneficial for the track to have a 90-degree twist in the track. In the side-mount location, the arm has its first rotational axis in the y direction and the frontmount location has a first rotational axis in the z direction. This change in the first rotational axis may pose too significant a rest riction on the link le ngth geometries. The optimum link geometries for each base position may actually compete against each other, making the final compromise manipu lator unacceptably inefficient.

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83 The design provision of a track-mounted manipulator arm would allow for the user to move under desks and still use the ma nipulator arm in the side mount mode or move through doors and confined areas with th e manipulator arm, stowed in the rear position, folded up safely behind the wheelchair. 5.2.2 Reconfigurable Manipulator The other design recommendation for the manipulator is that it be reconfigurable, modular, and aesthetically plea sing to the user. Reconfigurab ility would be a beneficial aspect for the robotic arm b ecause the real world cannot be rearranged so that a fixed manipulator can be more efficient. Often it is not possible to mount a manipulator in the optimum location for its intended task. This was the case with the mounting of the Raptor arm. The power wheelchair’s structure did not allow the motor to be affixed as high as necessary for an optim um mounting location. Individual arm link lengths can be modified to create a robotic arm workspace that matches actual workspace requirements. Because both power wheelchairs and workspaces vary in size and construction, a modular approach to link lengths design and joint construction should be utilized. This m odularity would allow the installer to custom tailor the links to better fit the mounting location. Modularity is addressed through the use of easily-altered revolute joints which allow for changes to the number of degrees of freedom in the arm with only simple change of components. Thus the arm can be designed around the user’s requirements and not vice versa. Controller design would inco rporate configuration changes and compute inverse kinematics of the revised design. Finally, a design that can be used in seve ral applications would provide a greater function per dollar by allowing one general manipulator to serve multiple roles. A reconfigurable modular manipulator could be mounted on a wheelchair, mobile base, or within a workstation. The increased functi onality of the arm could allow for improved market share. The potential benefit from th e higher production rates would be a decrease in cost of the manipulator.

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84 Chapter Six Summary and Future Work There has been significant progress in bringing commercially-viable WMRAs into the marketplace in the past 30 years. Of these devices, the Manus arm has seen the most development, though mostly in Europe. Th ere is still much progr ess to be made in order to minimize user effort and reduce ope rator fatigue. Over the operational life of WMRAs they are cost-effective yet their high in itial cost has been a prohibitive barrier for many users. 6.1 Design Recommendations and Insights Link lengths need to be kept as short as possible to reduce dynamic loads. While longer links allow for greater values of ma nipulability measure, they require greater encoder precision to achieve the same level of precision as a shorter link. Mounting the arm closer to the ground bi ases the arms ability to manipulating objects close to the ground, desks and counter tops. While a rear mount would solve the problems of increased chair width and visual obstruction, it can cause further difficulties with link geometries. The Raptor design, while very good at manipulating objects in front of the wheelchair, was challenged to reach into the lower cabinet at almost any orientation. The Raptor link geometries could be slightly modi fied to allow access to low cabinets and provide better access across the centerline of the wheelchair. The mounting location of the Manus allowed for excellent access to low shelves and desks but suffered from internal singular ities which limited its ability to manipulate objects close to its base. The internal singularities caused difficulties for the inverse kinematic program to determine the proper join t angles. Often the start point of the arm had to be changed several times in order for the gripper frame to reach the goal.

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85 6.2 Future Work There are both softwareand hardware-bas ed methods to further the work done in this thesis. The software development w ould further the inverse kinematic program (robot.m) and the hardware advancement woul d create virtual manipulators using track mount and modular links. These hard ware models would use both the Manus and Raptor as a baseline for comparison. Modify robot.m to create automatic mesh generation within the workspace. This would determine manipulability measures th roughout the workspace with user-defined grid density. The software program that determined the inverse kinematics of the Manus and Raptor had several limitations. The robot.m program required manual entry of the desired gripper position and c ould only determine one soluti on at a time. A better study of the entire workspace would be achieved with a denser map of the manipulability measures. For each arm, the smallest grid analyzed was 6.21” by 10” by 5.02” with a total number of 131 data points. Integrate the inverse kinematic program with Solid WORKS by creating an interface so that solutions from the inverse kinematic program can be input into Solid WORKS to create real-time simulations of the arm within the workspace. Hardware development would be based on the concept of the rail-mounted multiposition manipulator. The use of both operatin g positions would be fundamental in the analysis because the manipulator should functio n equally in each pos ition and the sum of the manipulability of both positions should be greater than the manipulability of the commercial designs. Although only given a cursory look in this thesis, the use of modular links and joints in a reconfigurable de sign would make a WMRA more ve rsatile so that it could be used in a variety of applications. This flex ibility would allow a production arm to fill more niches and increase the number of un it sales, further decreasing unit cost and increasing availability of the unit. While this thesis has focused solely on a procedure for kinematic analysis and evaluation of manipulators, a ma nipulator is only a series of motors, encoders, gearboxes,

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86 wires, and links without a controller. Contro ller design is a vital consideration when designing a complete robotic manipulator system. The greatest gains for robotic manipulators in rehabilitation applications wi ll come from advanced controllers that are easily programmed and operated.

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87 References 1US Census Bureau (1993). Americans with Disabilities. Statistical Brief SB/94-1, January. 2. R. Cooper: Rehabilitation Engineering Applied to Mobility and Manipulation, Institute of Physics Publishing, ISBN: 0 7503 0343 3. 3.. J.B.Reswick, "The Moon over Dubrovnik -A Tale of Worldwide Impact on Persons with Disabilities," Advances in Exte rnal Control of Human Extremities, 1990. 4.. J.R. Allen, A. Karchak, Jr., E.L. Bontrage r, Design and Fabrication of a Pair of Rancho Anthropomorphic Arms, Technical Re port, The Attending Staff Association of the Rancho Los Amigos Hospital, Inc, 1972. 5. T. Rahman, S. Stroud, R. Ramanathan, M. Alexander, R. Alexander, R. Seliktar, W. Harwin: Consumer Criteria for an Arm Ort hosis, Applied Science and Engineering Laboratories, www95.homepage.villanova.edu/rungun.raman athan/ publications/t_and_d.pdf. 6. H.F. Machiel Van der Loos, Lessons Learned in the Application of Robotics Technology to the Field of Rehabilitation, Proc. IEEE 7. M.J. Topping. The Development of Handy-1, A Robotic System to Assist the Severely Disabled, Proc ICORR 99, 244-249. 8. M. Topping, H. Heck, G. Bolmsjo, D. We ightman: The Development of RAIL (Robotic Aid to Independent Living) Proceedings of the third TIDE Congress. (1998).

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889. M. Hillman, A. Gammie. “The Bath Institut e of Medical Engineering Assistive Robot”. Proc. ICORR ’94, 211-212. 10. J.L. Dallaway, R.D. Jackson: “RAID A Vocational Robotic Workstation”. Proc. ICORR ’92. 11. Robotic Assistive Device, Neil Squire Foundation, http://www.neilsquire.ca /rd/projects/RobotApp.htm 12. N. Katevas (Ed): “Mobile Robotics in Heal th Care Services” IOS Press Amsterdam, 2000, pp. 227-251. 13. H.F.M. Van der Loos, VA/Stanford Rehabilitation Robotics Research and Development Program: “Lessons Learned in the Application of Robotics Technology to the Field of Rehabilitation”. IEEE Trans. Rehabilitation Engineering Vol. 3, No. 1, March, 1995, pp. 46-55. 14. B. Borgerding, O. Ivlev, C. Martens, N. Ruchel: ”FRIEND Functional Robot Arm with Us er Friendly Interface for Disa bled People“. Institute of Automation Technology (IAT) http://www.iat.unibremen.de/Projekte/HTML_e/FRIEND.htm 15. S. Sheredos, B. Taylor, C. Cobb, E. Da nn: “The Helping Hand Electro-Mechanical Arm”. Proc. RESNA ’95, 493-495. 16. G. Bolmsj, M. Olsson, P. Hedenborn, U. Lo rentzon, F. Charnier, H. Nasri: “Modular Robotics Design System Integration of a Robot for Disables People”. 17. H.A. Yanco: "Integrating Robotic Res earch: A Survey of Robotic Wheelchair Development" AAAI Spring Symposium on Integrating Robotic Research Stanford, California, March, 1998.

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8918. P.R. Warner, S.D. Prior: "Investigations into the Design of a Wheelchair-Mounted Rehabilitation Robotic Manipulator", Pro ceedings of the 3rd Cambridge Workshop on Rehabilitation Robotics, Cambridge University, England, April 8 1994. 19. H. Eftring, K. Boschian: “Technical Result s from Manus User Trials”, Proc. ICORR ’99, 136-141. 20. S.D. Prior, P.R. Warner, J.T. Parsons, a nd P. Oettinger: "Desi gn and Development of an Electric Wheelchair Mounted Robotic Arm for Use by People with Physical Disabilities.", Transactions of the IMACS/SICE Interna tional Symposium on Robotics, Mechatronics & Manufacturing Systems, Else vier Science Publishers B.V., ISBN: 0-44489700-3, pp.221-226, July 1993. 21. M. Hillman, K. Hagan, S. Hagan, J. Jepson, R. Orppwood: “A Wheelchair Mounted Assistive Robot”, Proc. ICORR ’99, 86-91. 22. S. Prior: “An Electric Wh eelchair Mounted Robotic Arm A Survey of Potential Users”. Journal of Medical Engineer ing & Technology, B14B:143-154 (1990). 23. J. Craig: “Introduction to Robotics M echanics and Control”, Second Edition, AddisonWesley Publishing, ISBN 0-201-09528-9.

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90 Appendices

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91 Appendix A: Manipulability Data Manus Data from the Inverse kinematics program: x,y,z are the position vector, inputs n is the normalized ma nipulability measure. Manip is the actual manipulability measure; no values for the theta columns indicates that the point was unobtainable desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 14.04 0 -29.8 0.23 -2.2227 2.5172 0.6609 1546.7 14.04 13.5 -29.8 0.00 0 14.04 23.5 -29.8 0.20 1.2464 2.5616 0.3721 1344.2 14.04 0 -22.8 0.37 -2.2235 2.0072 1.4476 2491.4 14.04 13.5 -22.8 0.00 0 14.04 23.5 -22.8 0.53 1.2464 1.9539 1.2999 3562.2 14.04 0 -13.8 0.33 -2.2243 1.4552 2.0769 2197.9 14.04 13.5 -13.8 0.00 0 14.04 23.5 -13.8 0.51 1.2464 1.3794 1.9203 3473.5 14.04 0 -5.82 0.23 -2.2234 0.7967 2.491 1526.9 14.04 13.5 -5.82 0.00 0 14.04 23.5 -5.82 0.41 1.2464 0.7835 2.284 2796 14.04 0 -0.8 0.18 -2.2234 0.19999 2.6498 1190.5 14.04 13.5 -0.8 0.00 0 14.04 23.5 -0.8 0.37 1.2464 0.3467 2.4039 2486.6 14.04 0 6.18 0.19 -2.2234 -0.519 2.6043 1290.4 14.04 13.5 6.18 0.00 0 14.04 23.5 6.18 0.38 1. 2464 -0.1684 2.3711 2574.9 14.04 0 18.2 0.34 -2.2234 -0.6703 2.0199 2271.2 14.04 13.5 18.2 0.00 0 14.04 23.5 18.2 0.52 1. 2464 -0.4019 1.8678 3535.1 14.04 0 24.18 0.37 -2.2234 -0.5335 1.6115 2519.1 14.04 13.5 24.18 0.00 0 14.04 23.5 24.18 0.54 1. 2464 -0.3054 1.4699 3678.2

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92 Appendix A (Continued) Manus data from the inverse kinematics program: desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 6.75 0 -29.8 0.25 3.6017 3.0655 5.7658 1709.9 6.75 13.5 -29.8 0.21 2.1157 3.3018 5.572 1411.7 6.75 23.5 -29.8 0.00 0 6.75 0 -22.8 0.50 -2.6822 1.9595 1.3277 3400.6 6.75 13.5 -22.8 0.32 2.1145 2.034 1.4774 2150.4 6.75 23.5 -22.8 0.61 1.7827 1.9459 1.1789 4090.2 6.75 0 -13.8 0.47 3.5911 1.3889 1.9597 3181.9 6.75 13.5 -13.8 0.27 2.1149 1.4914 2.1138 1849.6 6.75 23.5 -13.8 0.64 1.7827 1.3645 1.8008 4309.2 6.75 0 -5.82 0.37 3.5906 0.7761 2.3309 2503.3 6.75 13.5 -5.82 0.18 2.1157 0.8212 5.5468 1211.9 6.75 23.5 -5.82 0.55 1.7827 0.8093 2.1409 3725.7 6.75 0 -0.8 0.33 3.6007 3.2401 3.8379 2246.7 6.75 13.5 -0.8 0.13 2.1157 3.6571 3.5595 878.2 6.75 23.5 -0.8 0.51 1.7826 3.0423 4.0366 3453.1 6.75 0 6.18 0.35 3.6009 2.6423 3.8725 2338.5 6.75 13.5 6.18 0.14 2.1157 2.7119 3.6114 978.8 6.75 23.5 6.18 0.51 1.7819 2.5687 4.0553 3466.6 6.75 0 18.2 0.49 3.6069 1.694 4.3832 3298.9 6.75 13.5 18.2 0.28 2.1157 1.5904 4.2262 1908.9 6.75 23.5 18.2 0.64 1.7823 1.7173 4.5318 4345.5 6.75 0 24.18 0.52 3.6067 1.3161 4.7835 3483.6 6.75 13.5 24.18 0.32 2.1157 1.2315 4.6385 2156.9 6.75 23.5 24.18 0.64 1.7823 1.3355 4.9287 4319.4

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93 Appendix A (Continued) Manus data from the inverse kinematics program: desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 0.54 0 -29.8 0.00 0 0.54 13.5 -29.8 0.12 2.5426 2.8315 6.0801 829.4 0.54 23.5 -29.8 0.00 0 0.54 0 -22.8 0.65 3.4417 3.1403 5.1939 4366.9 0.54 13.5 -22.8 0.57 2.5428 3.3105 5.0395 3880.3 0.54 23.5 -22.8 0.66 2.1224 2.9872 5.3586 4476.6 0.54 0 -13.8 0.72 3.4417 3.2729 4.5771 4894.2 0.54 13.5 -13.8 0.58 2.5427 3.4566 4.4276 3938.3 0.54 23.5 -13.8 0.83 2.1224 3.1246 4.7186 5627.5 0.54 0 -5.82 0.66 3.4416 3.1534 4.2512 4426.6 0.54 13.5 -5.82 0.49 2.5427 3.3437 4.079 3309.9 0.54 23.5 -5.82 0.79 2.1224 3.016 4.398 5328.9 0.54 0 -0.8 0.62 3.4426 2.9492 4.1506 4176 0.54 13.5 -0.8 0.45 2.5428 3.1103 3.9655 3006.8 0.54 23.5 -0.8 0.77 2.1224 2.8226 4.3109 5182.6 0.54 0 6.18 0.63 3.4424 2.5187 4.1778 4255.1 0.54 13.5 6.18 0.46 2.5428 2.5929 3.998 3104.2 0.54 23.5 6.18 0.78 2.1224 2.4436 4.3368 5246.4 0.54 0 18.2 0.73 3.4423 1.7166 4.6297 4939.4 0.54 13.5 18.2 0.59 2.5427 1.7133 4.4822 4014.5 0.54 23.5 18.2 0.83 2.1224 1.6973 4.7727 5638.9 0.54 0 24.18 0.70 3.4423 1.3326 5.029 4712.8 0.54 13.5 24.18 0.60 2.5427 1.3325 4.8788 4069.4 0.54 23.5 24.18 0.75 2.1224 1.3089 5.1839 5035.1

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94 Appendix A (Continued) Manus data from the inverse kinematics program: desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 0 -6.75 0 0.94 3.7437 2.6441 4.5093 6330.9 0 -4 0 0.82 3.631 2.7441 4.3607 5506.6 0 0 0 0.65 3.4311 2.8739 4.1812 4399.2 0 4 0 0.53 3.1884 2.9772 4.051 3569.8 0 6.75 0 0.48 3.0035 3.0244 3.9956 3221.3 0 13.5 0 0.48 2.5636 3.0203 4.0003 3250.6 0 23.5 0 0.80 2.146 2.7594 4.3389 5376.7 0 -6.75 13.5 0.96 3.7438 1.9343 4.7381 6455.5 0 -4 13.5 0.86 3.631 1.9773 4.5951 5819 0 0 13.5 0.73 3.4312 2.0146 4.4311 4902 0 4 13.5 0.62 3.1888 2.0297 4.3143 4159 0 6.75 13.5 0.57 3.0035 2.0318 4.2699 3861.3 0 13.5 13.5 0.58 2.5636 2.0317 4.2738 3887.7 0 23.5 13.5 0.85 2.146 1.9826 4.5758 5721.1 0 -6.75 16.5 0.94 3.7343 1.7599 4.8583 6329.6 0 -4 16.5 0.87 3.631 1.793 4.7292 5854.8 0 0 16.5 0.75 3.4314 1.8213 4.566 5036.8 0 4 16.5 0.65 3.1888 1.8281 4.456 4360.5 0 6.75 16.5 0.60 3.0035 1.8267 4.4111 4061 0 13.5 16.5 0.61 2.5636 1.8274 4.418 4109.5 0 23.5 16.5 0.85 2.146 1.7973 4.7108 5774.9

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95 Appendix A (Continued) Manus data from the inverse kinematics program: desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip -4 -6.75 13.5 1.00 -2.6301 0.4056 1.3102 7084.4 -4 -4 13.5 0.95 3.5499 1.9044 4.8259 6754.9 -4 0 13.5 0.87 3.3766 1.9576 4.6635 6144.6 -4 4 13.5 0.80 3.1783 1.8014 4.6891 5673.5 -4 6.75 13.5 0.76 3.0326 1.998 4.5107 5367.5 -4 13.5 13.5 0.76 2.6809 1.9972 4.513 5379 -4 23.5 13.5 0.95 2.2967 1.9114 4.8069 6697.7 -4 -6.75 16.5 0.95 -2.6301 0.3921 1.1678 6740.7 -4 -4 16.5 0.93 3.5499 1.7283 4.9618 6584.4 -4 0 16.5 0.86 3.3766 1.7764 4.7974 6126 -4 4 16.5 0.80 3.1783 1.8014 4.6891 5673.5 -4 6.75 16.5 0.77 3.0326 1.8094 4.6459 5462.6 -4 13.5 16.5 0.77 2.6809 1.809 4.648 5472.6 -4 23.5 16.5 0.92 2.2967 1.7345 4.9434 6549

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96 Appendix A (Continued) Raptor data from the inverse kinematics program desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 27.54 0 -29.8 0.46 -1.693 2.5314 0.4655 4173.7 27.54 -13.5 -29.8 0.93 -1.4469 1.5685 0.2696 8474.1 27.54 -23.5 -29.8 0.70 -1.5647 0.9437 0.3764 6387.8 27.54 0 -22.8 0.58 -1.4343 2.4484 0.3109 5283.4 27.54 -13.5 -22.8 0.98 -1.2072 1.5686 0.1236 8982.7 27.54 -23.5 -22.8 0.79 -1.3199 0.9759 0.2267 7172.4 27.54 0 -13.8 0.60 -1.1549 2.434 0.2703 5506.1 27.54 -13.5 -13.8 0.99 -0.9308 1.5686 0.0846 9056.1 27.54 -23.5 -13.8 0.80 -1.0427 0.9813 0.1871 7319.6 27.54 0 -5.82 0.53 -0.9725 2.4783 0.3781 4850.6 27.54 -13.5 -5.82 0.97 -0.7387 1.5686 0.1877 8803.6 27.54 -23.5 -5.82 0.76 -0.8534 0.9638 0.2923 6889.7 27.54 0 -0.8 0.40 -0.9136 2.5776 0.5226 3661 27.54 -13.5 -0.8 0.90 -0.6564 1.5685 0.3222 8206.9 27.54 -23.5 -0.8 0.66 -0.7775 0.9257 0.4314 6013.9 27.54 0 6.18 0.00 0 27.54 -13.5 6.18 0.66 -0.6097 1.5681 0.6209 6034.5 27.54 -23.5 6.18 0.35 -0.7659 0.7255 0.7523 3226.4 27.54 0 18.2 0.00 0 27.54 -13.5 18.2 0.24 -0.4663 1.5664 1.0574 2200.5 27.54 -23.5 18.2 0.00 0 27.54 0 24.18 0.00 0 27.54 -13.5 24.18 0.00 0 27.54 -23.5 24.18 0.00 0

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97 Appendix A (Continued) Raptor data from the inverse kinematics program desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 14.04 0 -29.8 0.59 -1.68 2.4414 -0.2922 5389.7 14.04 -13.5 -29.8 0.78 -1.4375 1.5683 -0.49 7100.6 14.04 -23.5 -29.8 0.70 -1 .5617 0.9426 -0.3781 6374.5 14.04 0 -22.8 0.48 -1.4164 2.5177 -0.4457 4338.6 14.04 -13.5 -22.8 0.62 -1 .1408 1.568 -0.6607 5686.7 14.04 -23.5 -22.8 0.57 -1 .2803 0.8817 -0.5376 5193.9 14.04 0 -13.8 0.44 -0.997 2.5492 -0.4892 3968.5 14.04 -13.5 -13.8 0.57 -0 .7071 1.5679 -0.7108 5238.8 14.04 -23.5 -13.8 0.53 -0 .8531 0.8573 -0.5834 4803.7 14.04 0 -5.82 0.53 -0.6206 2.4775 -0.3766 4861.1 14.04 -13.5 -5.82 0.70 -0 .3628 1.5682 -0.5827 6358.9 14.04 -23.5 -5.82 0.63 -0 .4943 0.9132 -0.4654 5765.2 14.04 0 -0.8 0.62 -0.4458 2.4248 -0.2401 5653.3 14.04 -13.5 -0.8 0.82 -0.2107 1.5684 -0.4338 7509.8 14.04 -23.5 -0.8 0.73 -0.3313 0.9566 -0.3244 6696.7 14.04 0 6.18 0.68 -0.3118 2.3929 0.0273 6204 14.04 -13.5 6.18 0.98 -0.0938 1.5686 -0.1558 8901.6 14.04 -23.5 6.18 0.83 -0.2051 0.992 -0.0537 7613.5 14.04 0 18.2 0.00 0 14.04 -13.5 18.2 0.72 -0.1339 1.5682 0.5603 6544.8 14.04 -23.5 18.2 0.42 -0.2792 0.7875 0.6855 3873.1 14.04 0 24.18 0.00 0 14.04 -13.5 24.18 0.04 -0.3892 1.5594 1.3784 333.4 14.04 -23.5 24.18 0.00 0

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98 Appendix A (Continued) Raptor data from the inverse kinematics program desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 6.75 0 -29.8 0.36 -1.9533 2.6173 -0.5625 3267.4 6.75 -13.5 -29.8 0.49 -1 .6302 1.5677 -0.7979 4446.1 6.75 -23.5 -29.8 0.45 -1.7901 0.8063 -0.6616 4098 6.75 0 -22.8 0.06 -1.9416 3.0336 -0.7428 533.7 6.75 -13.5 -22.8 0.26 -1.3422 1.5666 -1.0329 2394 6.75 -23.5 -22.8 0.23 -1 .5736 0.5819 -0.8592 2137.8 6.75 0 -13.8 0.00 6.75 -13.5 -13.8 0.19 -0 .7349 1.5659 -1.1144 1771.3 6.75 -23.5 -13.8 0.16 -1 .0226 0.4449 -0.9208 1437.6 6.75 0 -5.82 0.23 -0.5673 2.7569 -0.6599 2136.8 6.75 -13.5 -5.82 0.37 -0.1681 1.5672 -0.92 3348 6.75 -23.5 -5.82 0.34 -0.3565 0.7095 -0.767 3080.1 6.75 0 -0.8 0.42 -0.2512 2.5614 -0.5041 3833.5 6.75 -13.5 -0.8 0.56 0.0443 1.5679 -0.7283 5080.6 6.75 -23.5 -0.8 0.51 -0.1041 0.848 -0.5993 4664.3 6.75 0 6.18 0.63 -0.0526 2.4194 -0.2197 5743.3 6.75 -13.5 6.18 0.84 0.1802 1.5684 -0.412 7658.6 6.75 -23.5 6.18 0.75 0.0607 0.9614 -0.3035 6811 6.75 0 18.2 0.44 -0.1134 2.5482 0.4879 3979.6 6.75 -13.5 18.2 0.92 0.1367 1.5685 0.2903 8374 6.75 -23.5 18.2 0.68 0.0174 0.9365 0.3982 6242.3 6.75 0 24.18 0.00 0 6.75 -13.5 24.18 0.46 -0.0151 1.5676 0.8275 4176.8 6.75 -23.5 24.18 0.02 -0.2994 0.0568 0.9933 154.4

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99 Appendix A (Continued) Raptor data from the inverse kinematics program desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 0.54 0 -29.8 0.00 0.54 -13.5 -29.8 0.29 -1 .9646 1.5668 -0.9979 2680.2 0.54 -23.5 -29.8 0.27 -3. 1725 -0.6259 -0.8312 2427.6 0.54 0 -22.8 0.00 0 0.54 -13.5 -22.8 0.00 0 0.54 -23.5 -22.8 0.13 -1 .8579 0.8172 -2.0035 1169.5 0.54 0 -13.8 0.00 0 0.54 -13.5 -13.8 0.00 0 0.54 -23.5 -13.8 0.00 0 0.54 0 -5.82 0.00 0 0.54 -13.5 -5.82 0.15 0.0356 1.5652 -1.1681 1400.9 0.54 -23.5 -5.82 0.10 -0 .3169 0.3155 -0.9587 934.3 0.54 0 -0.8 0.24 -0.0759 2.7438 -0.6529 2229.4 0.54 -13.5 -0.8 0.38 0.3155 1.5672 -0.9108 3428.4 0.54 -23.5 -0.8 0.35 0.1297 0.718 -0.7594 3156.3 0.54 0 6.18 0.55 0.1844 2.4645 -0.3494 5044.8 0.54 -13.5 6.18 0.72 0.4366 1.5682 -0.5526 6608.3 0.54 -23.5 6.18 0.65 0.3077 0.9236 -0.4371 5972.8 0.54 0 18.2 0.55 0.1168 2.4655 0.3515 5031.1 0.54 -13.5 18.2 0.97 0.3477 1.5686 0.1625 8882.5 0.54 -23.5 18.2 0.77 0.2338 0.9689 0.2665 6996.9 0.54 0 24.18 0.00 0 0.54 -13.5 24.18 0.63 0.1953 1.568 0.6584 5706.8 0.54 -23.5 24.18 0.31 0.0305 0.6769 0.7944 2805.5

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100 Appendix A (Continued) Raptor data from the inverse kinematics data desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip 0 6.75 0 0.00 0 0 4 0 0.00 0 0 0 0 0.28 -0.0016 2.7054 -0.6301 2515.7 0 -4 0 0.38 0.2121 2.3509 -0.75 3471.3 0 -6.75 0 0.40 0.2933 2.1308 -0.8131 3650.2 0 -13.5 0 0.40 0.3677 1.5674 -0.8816 3688.5 0 -23.5 0 0.38 0.2091 0.7842 -0.7479 3462.5 0 6.75 13.5 0.00 0 0 4 13.5 0.27 -0.0454 2.8654 0.1593 2424.5 0 0 13.5 0.68 0.2157 2.3931 0.034 6200.1 0 -4 13.5 0.85 0.3358 2.1125 -0.584 7788.9 0 -6.75 13.5 0.92 0.3861 1.9466 -0.1034 8394.4 0 -13.5 13.5 0.98 0.4335 1.5686 -0.1491 8920 0 -23.5 13.5 0.84 0.3223 0.9922 -0.047 7619.8 0 6.75 16.5 0.00 0 0 4 16.5 0.00 0 0 0 16.5 0.63 0.1731 2.4205 0.2242 5724.3 0 -4 16.5 0.84 0.2968 2.1166 0.1304 7664.4 0 -6.75 16.5 0.92 0.3473 1.9459 0.0853 8425.3 0 -13.5 16.5 1.00 0.3944 1.5686 0.0399 9106.8 0 -23.5 16.5 0.82 0.2832 0.9863 0.1419 7454.9

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101 Appendix A (Continued) Raptor data from the inverse kinematics data desired position required angles (radians) x y z n Theta 1 Theta 2 Theta 3 Manip -4 6.75 13.5 0.00 0 -4 4 13.5 0.28 0.1008 2.8484 0.1243 2595.9 -4 0 13.5 0.68 0.3569 2.3925 -0.0007 6211.4 -4 -4 13.5 0.84 0.4837 2.116 -0.123 7681.5 -4 -6.75 13.5 0.91 0.5277 1.9483 -0.1383 8318 -4 -13.5 13.5 0.97 0.5754 1.5686 -0.1842 8815.1 -4 -23.5 13.5 0.83 0.4637 0.9907 -0.0817 7578.5 -4 6.75 16.5 0.00 0 -4 4 16.5 0.01 -0.0647 3.1311 0.3176 86.1 -4 0 16.5 0.64 0.306 2.4121 0.1888 5865 -4 -4 16.5 0.85 0.4284 2.1142 0.0955 7736.5 -4 -6.75 16.5 0.93 0.4787 1.945 0.0506 8468.4 -4 -13.5 16.5 1.00 0.5257 1.5686 0.0052 9121 -4 -23.5 16.5 0.83 0.4149 0.9892 0.1069 7534.7

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102 Appendix B: Inverse Kinematic Program This is a list of all the programs that are called out in the desc ription of the inverse kinematics: robot.m function robot( initial_postion,theta1,theta2,theta3,final_position,steps ) % the robot function is the "main" function of this set of functions % input is the initial arm angles t1, t2, t3, final endeffector position, xyz, and the number of steps to use % set inputs of the initial theta angles in radians % theta1=3.7437; % theta2=2.6441; % theta3=4.5093; theta1=-2.2234; theta2=-.6703; theta3=2.0199; % set the number of steps (resolution) to use from initial to final % steps = input('how many intermediate steps?'); steps=15; % set the tolerance at which the algorithm will loop to before moving on to the next waypoint % this is a position tolerance x,y,z of the edeffector tolerance = [0.001;0.001;0.001];

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103 Appendix B (Continued) % set manip_thres which is where the move_a rm algorithim will break out of the loop if the manipulability becomes too low % this is an indicator of if the arm is moving toward an singularity and keeps it from going into an infinite loop manip_thres = 50; % set the desired final position of the endeffector [x;y;z] final_position = input('final position -eg [5;5;5] = ') %[0;0;0] % Build current_state structure, a structure is used to simplify moving variable data between functions % set the current state as the initial theta and position initial_theta = [theta1 theta2, theta3]; initial_position = find_position(initial_theta); current_state= struct('xyz',{initial_position},'angles',{initial_theta}) % calculate array of waypoints which is a set of points on the line that connects the initial position point to the final point % returns a three dimension waypoint matrix called the_plan disp('calculating plan of attack') the_plan = plot_waypoints(initial_position, final_position, steps); % move the arm, check amount of error, continue with new waypoint if error < tolerance % initialize error = 0 to make a "do loop" like loop % the points array is an array of points traveled to by the arm

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104 Appendix B (Continued) % the angles array is an array of angles traveled to by the arm % set the array to "zeros" for more efficient processing points = zeros(3,steps); angles = zeros(steps,3); % initialize a placeholder variable n for loop counting % n is used to count the number of times the arm move is attempted n = 0; % a for loop from 1 to steps + 1 for i = 1:(steps+1) fprintf('Calculating a waypoint, iteration number %i\n', i) next_position = the_plan(:,:,i); %reset postion error for next loop error = [99;99;99]; % end the for loop if the manipiablilty goes below the manip_thres if ( manip_thres > (abs(manip(current_state.angles))) ) disp('approaching singularity!'); manip_break=1; break; end % loop the move_arm function and update the current_state % if the error is > than the tolerance move_arm and update current_state again while any(error > tolerance) current_state = move_arm(current_state, next_position); error = next_position current_state.xyz; % current_state.xyz

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105 Appendix B (Continued) n = n + 1; % update the points array of points plotted % update the angles array of angles plotted if any(error > tolerance) disp('error, retry move'); end points(:,n) = [current_state.xyz]; angles(n,:,:) = [current_state.angles]; % keep it from becoming an infinite loop % end the for loop if the manipiablilty goes below the manip_thres if ( manip_thres > (abs(manip(current_state.angles))) ) disp('approaching singularity'); manip_break=1; break; end end % end of the while loop end % end of the for loop disp('Waypoints; The steps taken to get from intial to final position') disp('Including all iterative substeps (subloop steps)') % display the points array points

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106 Appendix B (Continued) disp('Waypoint angles; For each of the previous steps') % display the angles array angles %if ( manip_break ) % disp('robot.m stopped calc ulating arm moves due to singularity') %end disp('The Absolute Value of Manipulability which is the') disp('Determinate of the Jacobian for the final position is:') % display the absolute value of the manipulability abs(manip(current_state.angles)) This is the first subroutine called out from robot.m is find_position.m: find_position.m function position = find_position( theta ) % the find_position function takes input of the arm angles and returns the position of the endeffector % set t1,t2,t3 to the current state angles from the input of the structure t1 = theta(1); t2 = theta(2); t3 = theta(3); % the three position equations specific for each robot arm configuration % -----------------RAPTOR -----------------% % x=18.38*cos(t1)*sin(t2)*cos(t3)-18.38*sin(t1)*sin(t3)-6.3-27*sin(t1); % y=-18.38*cos(t2)*cos(t3)-13.46; % z=18.38*sin(t1)*sin(t2)*cos(t3)+18.38*cos(t1)*sin(t3)-16.16+27*cos(t1);

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107 Appendix B (Continued) % -----------------RAPTOR -----------------% % -----------------MANUS ------------------% x=18.77*cos(t1)*sin(t2)*cos(t3)+18.77*cos(t1)*cos(t2)*sin(t3)+15.045.26*sin(t1)+15.75*cos(t1)*sin(t2); y=18.77*sin(t1)*sin(t2)*cos(t3)+18.77*sin(t1)*cos(t2)*sin(t3)+9.97+5.26*cos(t1)+15.75*si n(t1)*sin(t2); z=18.77*cos(t2)*cos(t3)-18.77*sin(t2)*sin(t3)+1.74+15.75*cos(t2); % -----------------MANUS ------------------% % substitute the symbolic variables with the real values and return a xyz position as a matrix subs x y z; position = [x;y;z]; The second called out subrou tine is plot_waypoints.m plot_waypoints.m function plot=plot_waypoints(initial_position, final_position, steps) % sub function to determine all desired points in straight line between inital_pos and final desired %find out what to increment x vector for 'steps' number of steps increment=(final_position-initial_position)/steps; %i know i want to pre allocate some array space to same time x = zeros(3,1,steps); % plot out points x(:,:,1) is initial point % had to use for beginning with 1 due to language constraint

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108 Appendix B (Continued) % actual number of points is steps + 1 for i = 1:(steps+1) plot(:,:,i) = initial_position+(increment*(i-1)); % returns plot, a 3d array end The third subroutine called out is manip.m manip.m function m = manip (theta) % this function here determines the "manipulability" of the robot % input is the arm angles and outputs the determinate of the equation at the given angles % create three symbolic variables used to calculate the jacobian function syms t1 t2 t3 % the three position equations specific for each robot arm configuration % -----------------RAPTOR -----------------% % x=18.38*cos(t1)*sin(t2)*cos(t3)18.38*sin(t1)*sin(t3)-6.3-27*sin(t1); % y=-18.38*cos(t2)*cos(t3)-13.46; % z=18.38*sin(t1)*sin(t2)*cos(t3)+18.38*cos(t1)*sin(t3)-16.16+27*cos(t1); % -----------------RAPTOR -----------------% % -----------------MANUS ------------------% x=18.77*cos(t1)*sin(t2)*cos(t3)+18.77*cos(t1)*cos(t2)*sin(t3)+15.045.26*sin(t1)+15.75*cos(t1)*sin(t2); y=18.77*sin(t1)*sin(t2)*cos(t3)+18.77*sin(t1)*cos(t2)*sin(t3)+9.97+5.26*cos(t1)+15.75*si n(t1)*sin(t2); z=18.77*cos(t2)*cos(t3)-18.77*sin(t2)*sin(t3)+1.74+15.75*cos(t2);

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109 Appendix B (Continued) % -----------------MANUS ------------------% % calculate the jacobian matrix of the position equation J = jacobian([x; y; z], [t1 t2 t3]); % calculate the determinate of the jacobian matrix J = det(J); % prepare to calculate a real number % set the symbolic variables to real numbers, the angles of the arm t1 = theta(1); t2 = theta(2); t3 = theta(3); % substitute the t1,t2,t3 in the equation J and return m m = subs(J); The fourth called out program is move_arm.m move_arm.m function new_state = move_arm(current_state, next_position) % The move_arm function takes input of the current_state structure and the next_position variable % returns the new position of the end effector and the arm angles % calc increment between the current position and the next position increment = next_position current_state.xyz; % calc new theta given the current state angles and the incremental position new_theta = get_theta(current_state.angles, increment); % calc the new position given the newly calculated theta new_position = find_position(new_theta);

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110 Appendix B (Continued) % return the new position and new thetas via a structure new_state = struct('xyz',{new_position},'angles',{new_theta}); The fifth and final called out subroutine is get_theta.m get_theta.m function new_theta=get_theta(theta, increment) % the get_theta function takes input of the robot arm angles and the position increment % outputs a new set of angles which is used to approximate the new position % the jacobian matrix and its inve rse are calculated symbolically syms t1 t2 t3 % the three position equations specific for each robot arm configuration % -----------------RAPTOR -----------------% % x=18.38*cos(t1)*sin(t2)*cos(t3)18.38*sin(t1)*sin(t3)-6.3-27*sin(t1); % y=-18.38*cos(t2)*cos(t3)-13.46; % z=18.38*sin(t1)*sin(t2)*cos(t3)+18.38*cos(t1)*sin(t3)-16.16+27*cos(t1); % -----------------RAPTOR -----------------% % -----------------MANUS ------------------% x=18.77*cos(t1)*sin(t2)*cos(t3)+18.77*cos(t1)*cos(t2)*sin(t3)+15.045.26*sin(t1)+15.75*cos(t1)*sin(t2); y=18.77*sin(t1)*sin(t2)*cos(t3)+18.77*sin(t1)*cos(t2)*sin(t3)+9.97+5.26*cos(t1)+15.75*si n(t1)*sin(t2); z=18.77*cos(t2)*cos(t3)-18.77*sin(t2)*sin(t3)+1.74+15.75*cos(t2); % -----------------MANUS ------------------% % calculating the jacobian

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111 Appendix B (Continued) J = jacobian([x; y; z], [t1 t2 t3]); % calculating the inverse jacobian inverse_jacobian = inv(J); % calculating the delta theta delta_theta=inverse_jacobian*increment; % substituting the current angles into the delta_theta equation t1 = theta(1); t2 = theta(2); t3 = theta(3); % calculating delta_theta delta_theta = subs(delta_theta); % calculate the new theta or the intermediate theta % delta thetas are summed with the current thetas % disp('Waypoint 1 Theta = Original theta + Delta theta') new_theta=[t1+delta_theta(1,1);t2+delta_theta(2,1);t3+delta_theta(3,1)];

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112


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McCaffrey, Edward Jacob.
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Kinematic analysis and evaluation of wheelchair mounted robotic arms
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by Edward Jacob McCaffrey.
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[Tampa, Fla.] :
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2003.
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ABSTRACT: The goal of this thesis is the kinematic analysis and evaluation of wheelchair mounted robotic arms. More specifically, to address the kinematics of the wheelchair mounted robotic arm (WMRA) with respect to its ability to reach positions commonly required by an assistive device in activities of daily living (ADL). A robotic manipulator attached to a power wheelchair could enhance the manipulation functions of an individual with a disability. In this thesis, a procedure is developed for the kinematic analysis and evaluation of a wheelchair mounted robotic arm. In addition to developing the analytical procedure, the manipulator is evaluated, and design recommendations and insights are obtained. At this time there exist both commercially-available and industrial wheelchair mountable robotic manipulators. The commercially-available manipulators (of which two will be addressed in this research) have been designed specifically for use in rehabilitation robotics. In contrast, industrial robotic manipulators are designed for speed, precision, and endurance. These traits are not required in assistive robots and can actually be dangerous to the operator if mounted onto a wheelchair. Manipulators to be used as WMRAs must be designed specifically for assistive functions in order to be utilized as a wheelchair mounted robotic arm. In an effort to evaluate two commercial manipulators, the procedure for kinematic analysis is applied to each manipulator. Design recommendations with regard to each device are obtained. This method will benefit the researchers by providing a standardized procedure for kinematic analysis of WMRAs that is capable of evaluating independent designs.
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