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A mechanized horseback riding simulator as an aid to physical therapy
h [electronic resource] /
by Jennifer Lott.
[Tampa, Fla] :
b University of South Florida,
ABSTRACT: Equine-assisted therapy is a nontraditional form of physical therapy that involves riding horses as a form of rehabilitation. Limited access to these riding programs justifies a need to develop a horseback riding simulator capable of simulating the gaits, bend, and collection of the horse. Research involving the development of horseback riding simulators is limited, but the available research does show promising results in the ability to aid in physical therapy. A two-dimensional model and simulation was developed using MATLAB. Using the results from the simulation, a horseback riding simulator was designed, fabricated and tested. The physical simulator was capable of simulating a walk, trot, and canter, bend to the left or right, and collection of the gait. The purpose of the testing of the horseback riding simulator was to evaluate the similarity of the physical simulator to the gaits of the data collected from a real horse. The results from the testing are com pared with the kinematic data from the MATLAB simulation. The biomechanical effect on the hip flexion angle is also evaluated when the system simulates bend and collection of the horse's back. The motion data was collected using a Vicon system. Four cameras were set up to collect the data from the five reflective markers that were placed on the rider. The kinematic results of the horseback riding simulator were compared to the computer simulation using the measurements of the inclination of the ellipse, the major axis of the ellipse, and the frequency. The results from the hip flexion angles shows that the test that simulated bend only results in a significant increase in the hip flexion angle compared to the tests without bend. Simulated collection does not change the hip flexion angles of the rider. Future work on the horseback riding simulator is needed in order to increase the safety so that a person with a disability would be able to use it as part of their physical therapy. A daptive programming of the system is also necessary to make the horseback riding simulator more similar to that of a real horse.
Thesis (M.A.)--University of South Florida, 2006.
Includes bibliographical references.
Text (Electronic thesis) in PDF format.
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Adviser: Rajiv Dubey, Ph.D.
x Mechanical Engineering
t USF Electronic Theses and Dissertations.
4 0 856
A Mechanized Horseback Riding Simulator as an Aid to Physical Therapy by Jennifer Lott A thesis submitted in partial fulfillment of the requirement s 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. Shuh-Jing Ying, Ph.D. Craig Lusk, Ph.D. Date of Approval: July 11, 2006 Keywords: disability, equestrian, hippot herapy, kinematics, rehabilitation Copyright 2006, Jennifer Lott
Acknowledgments Many individuals deserve acknowledgment for their support and assistance throughout the development of this thesis. Dr Dubey, my Major Professor, allowed me to work at my own pace and trusted that I would eventually complete a thesis that was worthwhile. Thank you, Dr. Dubey, for giving me the opportunity to pursue resear ch in an area that I have a passion for and that has the capability of helping so many people. Dr. Ying guided me every step of the way, from my initial concept through the design process and finally to the completion of this thesis. He supported and helped to improve my ideas and made me feel good about what I was doi ng. Dr. Lusk helped break down into manageable pieces the seemingly insurmountabl e amount of work that had to be done. Lisa Payne-Hyslop, my dressage trainer and good friend, brainstormed ideas and offered professional guidance on everything horse related. Lastly, this thesis could not have been completed without the emot ional and financial support of my parents, fa mily, and friends.
i Table of Contents List of Tables ........................................................................................................iii List of Figures .......................................................................................................iv Abstra ct................................................................................................................vi Chapter 1 Â– In troduction.......................................................................................1 1.1 Motiva tion............................................................................................1 1.2 Thesis Ob jectives.................................................................................4 1.3 Thesis Outline......................................................................................5 Chapter 2 Â– Ba ckground.......................................................................................7 2.1 Equine-Assi sted Ther apy.....................................................................7 2.2 Anatomy and Kinemati cs of the Horse...............................................13 2.3 Equine-Assisted Therapy Effects on Children with Cerebral Palsy....24 Chapter 3 Â– Computer M odeling and Simu lation................................................29 3.1 Model and Simula tion Descrip tion.....................................................29 3.2 Position Anal ysis and Resu lts............................................................31 3.3 Velocity Anal ysis and Resu lts............................................................38 3.4 Acceleration Anal ysis and Re sults.....................................................44 Chapter 4 Â– Physical Simulator Design and F abricatio n.....................................49 4.1 Desi gn................................................................................................49 4.2 Fabric ation.........................................................................................54
ii Chapter 5 Â– Motion Anal ysis and Re sults...........................................................58 5.1 Description of the Testing of the Horseback Ridi ng Simulator...........58 5.2 Kinematic Result s..............................................................................61 5.3 Biomechanica l Result s.......................................................................67 Chapter 6 Â– Conclusions and Recomm endations ...............................................69 6.1 Conclu sions .......................................................................................69 6.2 Future Work and Recommendat ions.................................................71 Referenc es.........................................................................................................72 Bibliogr aphy........................................................................................................74 Appendice s.........................................................................................................75 Appendix A Â– Horseback Riding Simulator Sour ce Code........................76 Appendix B Â– Bill of Materials fo r Horseback Riding Simulator................84 Appendix C Â– AutoCAD Drawings of Horseback Riding Simulator..........85
iii List of Tables Table 2-1: Motion Data at the HorseÂ’s Center of Grav ity...................................18 Table 2-2: Range of Motion of the Thoracic Region of the Horse......................22 Table 3-1: Link Lengths of Computer Horse Simulati on....................................30 Table 3-2: Input Function Val ues for Walk, Tr ot, and Ca nter.............................35 Table 5-1: Comparison of the Com puter and Horseback Riding Simulators ....64 Table 5-2: Hip Flexio n Angles Co mparis on ......................................................67 Table B-1: Bill of Mate rials for Si mulator...........................................................84
iv List of Figures Figure 2-1: Ther apeutic Vaul ter..........................................................................9 Figure 2-2: Therapeutic Ri ders Test thei r Balanc e...........................................11 Figure 2-3: Young Bo y Enjoys Hi ppotherapy ....................................................13 Figure 2-4: Anatom y of the Horse.....................................................................14 Figure 2-5: Hoof Sequenc e for Walki ng Horse.................................................15 Figure 2-6: Hoof Sequenc e for Trotti ng Hors e..................................................16 Figure 2-7: Hoof Sequence fo r Horse in Le ft Lead Cant er...............................17 Figure 2-8: Elliptical Mo vement of the Horse at t he Walk, Trot, and Canter.....18 Figure 2-9: Degrees of Motion of Sele cted Intervertebral Joints in Horses.......19 Figure 2-10: Flexi on-Extens ion...........................................................................20 Figure 2-11: Later al Bendi ng..............................................................................20 Figure 2-12: Axia l Rotati on.................................................................................21 Figure 3-1: MATLAB Computer Model of Horseback Ridin g Simulator............29 Figure 3-2: Kinematic Drawing of Horseback Ridin g Simula tor........................31 Figure 3-3: Path of Point P at the Wa lk............................................................36 Figure 3-4: Path of Point P at the Trot..............................................................37 Figure 3-5: Path of Point P at th e Cant er..........................................................37 Figure 3-6: Velocity of Point P at the Wa lk.......................................................41 Figure 3-7: Velocity of Point P at the Tr ot.........................................................42
v Figure 3-8: Velocity of Point P at the Cant er.....................................................42 Figure 3-9: Velocity Magnitudes of Point P.......................................................43 Figure 3-10: Accerleration Magnitudes of Point P ............................................47 Figure 3-11: Fourier Tr ansform Graph of Walk .................................................48 Figure 4-1: Horseba ck Riding Simu lator...........................................................50 Figure 4-2: Flexion-Extension of the Horseback Ridi ng Simula tor....................51 Figure 4-3: Left Bend of t he Horseback Riding Simulato r.................................52 Figure 4-4: Horseback Ridin g Simulator St ructure...........................................54 Figure 4-5: Attachment of Plastic Horse to Simula tor.......................................55 Figure 4-6: Underside of Plasti c Horse.............................................................56 Figure 5-1: Vicon Ca mera Confi guratio n..........................................................59 Figure 5-2: Marker Placement on Rider ............................................................60 Figure 5-3: Fourier Transform Graph of Wa lk...................................................61 Figure 5-4: Horseback Rid ing Simulato r Walk .................................................62 Figure 5-5: Horseback Rid ing Simulato r Trot ...................................................62 Figure 5-6: Horseback Rid ing Simulato r Cant er...............................................63 Figure C-1: AutoCAD Base Detail Drawin g......................................................85 Figure C-2: AutoCAD Suppor t Tube Detail Drawing.........................................86 Figure C-3: AutoCAD Track Detail Drawing .....................................................87 Figure C-4: AutoCAD Cylinde r Joint A Deta il Drawin g.....................................88 Figure C-5: AutoCAD Cylinde r Joint B Deta il Drawin g.....................................89 Figure C-6: AutoCAD Base Cy linder Holder De tail Dra wing.............................90 Figure C-7: AutoCAD S upport Rod Detail Drawing..........................................91
vi A Mechanized Horseback Riding Simulator as an Aid to Physical Therapy Jennifer Lott ABSTRACT Equine-assisted therapy is a nontraditional form of physical therapy that involves riding horses as a form of rehabili tation. Limited access to these riding programs justifies a need to develop a horseback riding simulator capable of simulating the gaits, bend, and collection of the horse. Research involving the development of horseback riding simulators is limited, but the available research does show promising results in the abi lity to aid in physical therapy. A two-dimensional model and simula tion was developed using MATLAB. Using the results from the simulation, a horseback riding simulator was designed, fabricated and tested. The ph ysical simulator was capabl e of simulating a walk, trot, and canter, bend to the left or right, and collection of the gait. The purpose of the testing of the horseback riding simu lator was to evaluate the similarity of the physical simulator to the gaits of t he data collected from a real horse. The results from the testing are compared with the kinemat ic data from the MATLAB simulation. The biomechanical effect on the hip flexion angle is also evaluated when the system simulates bend and coll ection of the horseÂ’s back. The motion data was collected using a Vicon system. Four cameras were set up to collect the data from the five re flective markers that were placed on the
vii rider. The kinematic results of the hor seback riding simulator were compared to the computer simulation using the measurem ents of the inclinatio n of the ellipse, the major axis of the ellips e, and the frequency. The re sults from the hip flexion angles shows that the test that simula ted bend only results in a significant increase in the hip flexion angle compared to the test s without bend. Simulated collection does not change the hip fl exion angles of the rider. Future work on the horseback riding simulator is needed in order to increase the safety so that a person with a disability would be able to use it as part of their physical therapy. Adaptiv e programming of the system is also necessary to make the horseback riding simu lator more similar to that of a real horse.
1 Chapter 1 Â– Introduction 1.1 Motivation Physical therapy exists to try to opt imize a personÂ’s heal th, well-being and quality of life. The num ber of people that can be helped through the aid of physical therapy increases each year as the population with di sabilities or limited function escalates because of an aging population and new technology saving lives of children with birth defects. Wi thout physical therapy to rehabilitate these individuals, recurring injuries may occu r; muscle tone may not fully develop; proper posture may never be seen; the in dividuals may not have the capabilities to perform everyday tasks. For persons wit h disabilities or limited function, there is an extensive list of benefits from ph ysical therapy. While standard physical therapy equipment and proc edures are used to help many people, new types of nontraditional therapies are also being developed to tr y to personalize programs for the greatest individual benefit. Equine-assisted therapy involves riding horses as a form of physical therapy. Therapeutic riding, therapeutic vaulting, an d hippotherapy are three nontraditional forms of physical therapy classified as equine-assisted therapy. Although they are considered nontraditional forms of physical therapy, both the American Occupational Therapy Associat ion and the American Physical Therapy Association recognize the programs as ben eficial to participants and support the
2 programs. Some of the benefits from equine therapeutic ri ding include improved mobility, muscle tone, posture, balance, and self-esteem. Many individuals benefit from these programs including t hose with cerebral palsy, multiple sclerosis, developmental delay, traumatic br ain injury, stroke, au tism, learning or language disabilities, emot ional problems, and behavio ral problems. The North American Riding for t he Handicapped Association (NARHA) certifies equine-assisted therapy programs. Some organizations that support and participate in NARHA incl ude the Muscular Dystroph y Association, Multiple Sclerosis Society, Special Olympics, Spina Bifida Association and United Cerebral Palsy. If research has show n this type of physical therapy to be beneficial and it is recognized and support ed by so many organizations, why arenÂ’t more disabled individuals involv ed? There are many answers to this question including: These programs require donations of time, money, supplies, and equine participants. Many individuals are tentativ e about getting involved with large unpredictable horses. This type of therapy is not o ffered as part of the standard in physical therapy. Each center has to limit the number of indivi duals that can be serviced. Currently there are 692 NA RHA centers helping over 35,000 children and adults reap the benefits of this therapy. Unfo rtunately, there are also thousands on
3 waiting lists that these c enters cannot accommodate. A nd this number continues to increase each year . A horseback riding simulator that could be used as a physical therapy device that simulates the gaits most commonly used during equine-assisted therapy, the walk and trot, w ould be beneficial in involving more individuals with disabilities in these programs. Also it w ould be useful in the initial training program to help the riders over come any fear of the horses. There has been a limited amount of research in developing simulated horseback riding equipment. Youichi Shinom iya et al.  reproduced the walking gait of the horse and evaluated how rea listic the riders felt the walk was. Massaaki Yamaguchi and Nobuhiro Iguc hi  created a horseback riding simulator that was able to reproduce the wa lk, trot, canter of the horse. This simulator also responded to aids from t he rider such as starting and stopping. These two horseback riding simulators only simulated the horse moving in a straight line, not around curves. Patti K oenig and George Bekey at the University of Southern California  created an animated horse that responded to commands given by a rider sitting on a stationary horse-like device. The commands that the animation were capable of were advanced, but the rider was only able to see the results, not feel the results. The forward direction of this res earch is to design a horseback riding simulator where the movements of the simu lator feel realistic when compared to those of a horse, and to allo w the rider more control over the actions of the simulator. Going around a curve, called bending, or asking the horse to shorten or collect its gait changes the kinematics of the horseÂ’s spine and in turn has an
4 effect on the rider. The positive benefits seen from ri ding a real horse may be reproduced more fully on a horseback riding simulator when it is able to replicate the gaits, bend, and collect ion of the horse. A horseback riding simulator that c an replicate the gaits, bend, and collection of the horse can also be used as an initial ev aluation and training for those individuals interested in therapeut ic equine activities. Evaluation and training in a controlled env ironment on a controlled device has many benefits including: Reducing the stress of the people with disa bilities by simulating the activity and allowing them to experi ence what they will feel before having to get on a large, unpredictable animal. Increasing the safety of everyone in volved because the i ndividual can be harnessed into this stationary device. Allowing the people with disabilities to experi ence more than just the walking gait, as in other horseback riding simulators. 1.2 Thesis Objectives There are four main objectives of this research work. These are described below: 1. Model a two-dimensional simulation of a horseback riding simulator using MATLAB. Obtain data from this simula tion relating to position, velocity, and acceleration.
5 2. Design and fabricate a horseback riding simulator, a physical therapy device that replicates the horseÂ’s walk, trot, bend, and collection. 3. Test and evaluate the similarity of the mechanized horseback riding simulator to the gaits of the data colle cted from a real horse. The results from this testing are compared with t he position, velocity, and acceleration data from the MATLAB simulation. 4. Test the biomechanical effect on hip angles when the horse simulates bending and collection of the back. Motion data using cameras are used to collect the data. This device is designed as a prototype, and with fu rther research would be capable of being used in rehabilitation ther apy centers as part of a patientÂ’s standard therapy. The creation of a hors eback riding simulator does not intend to replace the current ther apies used, or phase out th e programs that use real horses. The intent is to make the rehab ilitative effects of the movement of the horse more readily available to those t hat can benefit and to det ermine those that can benefit by performing further research. 1.3 Thesis Outline This work begins with the background and brief history of equine-assisted therapy activities and a de scription of the relevant anatomy and kinematics of the horse in Chapter 2. Also included in Chapter 2 is a de scription of past research and results of persons with disabilities ri ding horse simulators and real horses. Chapter 3 describes the modeling and simulation of the two-dimensional
6 horseback riding simulator using MATLAB. The derivation of the kinematic equations used in the simulati on is explained. This chapter also includes the position, velocity, and acceleration anal ysis from the MATLAB simulation. The design specifications, design and fabricatio n of the horseback riding simulator will be described in Chapter 4. Chapter 5 sh ows the results of the testing done on the horseback riding simulator. Thes e results include comparisons of the horseback riding simulator to a real horse Â’s gaits and the bi omechanical analysis of the riderÂ’s pelvic position while using this device. Conclusions and future recommendations for this research are explained in Chapter 6.
7 Chapter 2 Â– Background 2.1 Equine-Assisted Therapy Equine-assisted therapy, sometimes ca lled equine-facilitated therapy, is a form of physical therapy that involves both riding and interacting with horses. This type of physical therapy using the ho rse has existed for centuries. In the past fifty years, the therapy has becom e much more widespr ead, with hundreds of therapy centers opening, thousands of people participating, and many universities and private firms conducting research studying the benefits of the therapy and seeking to impr ove the therapy. The ex plosion of equine-assisted therapy in the last centur y is often credited to Liz Hartel, whom after being diagnosed with poliomyelitis rehabilitated herself usi ng therapeutic riding and won the Silver Medal for dressage at the 1952 Olympics . The benefits of equine-assi sted therapy are multifac eted. There is the physical aspect, where the participant can experience improved mobility, posture, muscle tone, balance, motor skills and more as a result of the rocking, swaying movement of the horseÂ’s gai t and the coordination requir ed to control the animal. The movement of the horseÂ’s back is transferred to the riderÂ’s pelvis and trunk in a controlled way, and duri ng the walk, the motion transferred to the rider is similar to the walking motion of an able-bodied person. There is also a psychological aspect, a feeling of empowerment, which may come to the
8 participant when riding and interacting with the horse. The participant is riding a higher view and is moving at speeds fa ster than what they would normally experience. Also, the participant has to communicate with the horse, using the appropriate signals so the animal will perfo rm as expected. The height, speed, and necessary communication often results in an invigorating feeling because of the new kinds of stimuli s upplied to the mind through this form of therapy . Equine-assisted therapy is classified in to three areas, therapeutic vaulting, therapeutic riding, and hippotherapy. Therapeutic vaulting combines gymnastics and dance on a moving horse. Professional vaulting is often performed in circuses where the rider attempts daring moves on a horse that is trotting or cantering in a circle. The therapeutic version of vaulting is not as daring or dangerous as what is performed in the circus. Even so, therapeutic vaulting is more commonly used with individuals that have behavioral or emot ional problems rather than ph ysical disabilities. This is because vaulting is a difficult sport that requires strength and balance. Individuals with behavioral or emotional problems benef it from this type of therapy because it requires them to form a bond and to trust the horse while they perform bold maneuvers. The constant re sponse, either positive or negative, from the horse during the vaulting exerci ses is non-judgmental and helps to raise the riderÂ’s self-esteem Therapeutic vaulting is occasionally used as a form of therapy for persons with disabilities. The vaul ting exercises can be performed on a real horse, which could be stationary or moving, or on a plastic horseback. The vaulting surcingle
9 is used in all vaulting activities, ther apeutic and professional, and consists of a padded girth, which ties around the body of the ho rse and two handgrips. Depending on the capabilities a nd extent of the physical di sabilities of the rider, many persons with disabilities are able to learn the basic posit ions of vaulting, and gain the self-esteem and physical benefit s from the activity. Figure 2-1 shows an image of a therapeutic vaul ter being escorted on a horse by a volunteer. Figure 2-1: Therapeutic Vaulter There is not as clear of a distinction between therapeutic riding and hippotherapy as there was a few decades ago. Both t herapies involve riding horses and utilize the benefit of the horseÂ’s motion that is transferred to the
10 riderÂ’s pelvis and trunk. At one time, therap eutic riding was used solely as a form of exercise for the rider on the horse. Now that the therapeutic benefits of horseback riding are proven more scientifical ly, the definition of therapeutic riding has changed. The clear di stinction of these two forms of therapy, however, involves insurance coverage. Hippother apy is considered a type of physical therapy, occupational therapy, or speech t herapy using the horse as a tool and involves a team of therapist s during the riding to achieve the goals of the rider. Insurance plans that cover rehabilitative benefits will cover hippotherapy. This is not the case of therapeutic riding, whic h is not covered by insurance plans because often there is not a licens ed physical therapist on the staff. Therapeutic riding is used to positiv ely contribute to the physical, cognitive, emotional, and behav ioral well-being of people with disabilities through learning how to ride a horse. The rider has an active role in controlling the horse and learns basic to advanced riding skills, depending on their commitment to the sport and their ability to perform. Basic skills that the rider learns involve starting, stopping, and turning the horse. More advanced skills that the rider learns include asking the horse to transition fr om one gait to another, such as from a walk to a trot, or to slow down or s peed up a gait. The way that a rider asks the horse to perform an action is physical or ve rbal and is referred to as an aid. The riderÂ’s position, center of gravity, and aids will dete rmine the response from the horse. Therefore, the rider may need to learn to relax his body, shift his weight in one direction, only pull on one rein, or on ly squeeze with one leg in order to get the desired result. If the rider does not do this, the horse will not respond. Using
11 the horse as a tool, the rider will learn to perfect his coordination, balance, and motor function. Figure 2-2 shows an image of two riders involved in therapeutic riding reaching out to touc h hands while still maintaining their balance on the horse. Figure 2-2: Therapeutic Riders Test their Balance During therapeutic riding, riders oft en are able to experience different types of horseback riding, such as dressage barrel racing, poles, and trail riding. Horse shows promote compet ition among the riders to do their best, while having fun. Improving t he well-being of the rider is always the ultimate goal. The term hippotherapy means treatment wit h the help of the horse. As stated earlier, hippotherapy is cons idered a type of physical therapy, occupational therapy, or speech therapy us ing the horse as a tool and involves a
12 team of therapists during the riding to achieve the goals of the rider. Hippotherapy is the medical approach in equine-assisted therap y. Therapeutic riding is the exercise approach to equi ne-assisted therapy. The team of therapists used in hippotherapy is compos ed of medical professionals including physical therapists, occupat ional therapists, speechlanguage pathologists, and psychologists or psychotherapists. T he goals for the rider may be physical, cognitive behavioral or emotional. As opposed to therapeutic riding, where the rider influences the horse in hippotherapy the horse influences the rider. Specific riding skills are not taught. T he horse is controlled and its speed is regulated by a therapist or a volunteer. The transferred motion from the horse to the rider allows therapists to see how the rider physically responds during different motions. The therapist can therefore regulate the speed, direction, or gait of t he horse in order to get different physical responses. In this wa y, the rider builds a foundation in which the riderÂ’s individual goals are realized. During a hippotherapy session, the therapist may position the rider forwards, backward, supine, pron e, or standing. Each position will have a different affect on the rider and the wa y that their body reacts to the movement of the horse. The therapist may help support the rider by walking next to the horse or by sitting behind the rider on the horse. With severely disabled people, it is often neces sary for the therapist to sit behind the rider and have two or more people suppor ting the sides of the rider from the ground. Figure 2-3 shows an image where a physical therapist adjusts a young boyÂ’s position during a session of hippotherapy.
13 Figure 2-3: Young Boy Enjoys Hippotherapy 2.2 Anatomy and Kinematics of the Horse Each horse is different. The conf ormation or proportions of the horseÂ’s body have a great deal of influence on ho w the horse will move and how this movement will be transmitted to the rider. Different horse sports strive to breed for characteristics that will optimize the hors eÂ’s potential in that particular sport. Although each horse has different c onformation, the f undamental anatomy and gaits are the same. This section will beg in with a review of the basics of the anatomy of the horse. The three basic gaits of the horse will then be described, and an in depth look at the kinematics of the horse and spine will be discussed. The section will conclude with a descripti on of how the movement of the horse influences the rider, and how the rider infl uences the movement of the horse.
14 The basic anatomy of the horse is s hown in Figure 2-4. Some points of interest in this figure are the back and withers, which determines the placement of the saddle, and the girth, where the s addle is cinched about. The poll, crest, croup, and dock connect the vertebral colu mn along the horseÂ’s back. The hind end of the horse, the hock, gaskin, thi gh, stifle, and buttock typically have the largest muscle mass because this area creates the most power during the horseÂ’s movement. Figure 2-4: Anatomy of the Horse The four natural gaits of most breeds of horses are the walk, trot, canter, and gallop. The walk, trot, and canter are described in detail below. The walk is a four beat lateral gait and is the slowest of the four gaits. Four distinct hoof beats can be heard while the horse is wa lking. The sequence that the hooves
15 touch the ground is right hind, right front, left hind, and left front. The sequence that the hooves touch the ground for the walk is shown in Figure 2-5 Figure 2-5: Hoof Sequence for Walking Horse The trot is a two beat diagonal gait. The gait begins with a period of suspension where all four legs are off the ground. Next, a diagon al pairs of legs, the left front and right hind work together, touch the ground at the same time, and then push off at the same time, followed by another period of suspension. The opposite pair of diagonal legs, the right front and left hind, then touch the ground at the same time and push off together. The rider will often rise up and down every other beat, called posting, which us es less energy than sitting the trot and doesnÂ’t affect the natural movement of t he horse as much. Figure 2-6 shows this sequence of diagonal pairs of legs moving t ogether during the trotting of a horse.
16 Figure 2-6: Hoof Sequence for Trotting Horse The canter is a three beat movement and has two possible leads, the right lead and the left lead. The lead refers to which foreleg hits the ground in front. In the left lead canter, the sequence begi ns with the right hind touching the ground while all the other legs are suspe nded. In the second beat, the left hind and right front touch the ground together, a nd the left front touches the ground in the third beat. After the horse pushes of f with its legs, there is a period of suspension. The right lead canter has the same sequence, but begins with the left hind touching the ground followed by the right hind and left front touch the ground simultaneously. The right front woul d then touch the ground in front of the left front and the sequence ends with a period of suspension. The canter creates a rocking motion very comfortabl e to the rider. Figure 2-7 shows the sequence of a horse in a left lead canter.
17 Figure 2-7: Hoof Sequence for Horse in Left Lead Canter As stated at the beginning of this chapter, each horse is different. Modeling the motion of the hor se therefore, is difficult because there is not just one standard motion for the three gaits. Analyzing the motion of the horse normally involves using high-speed phot ography and placing markers at key points on the horse. A trace is then made of the horseÂ’s motion, where movement at constant speed is subtracted out. Averagi ng trace results will result in distinct paths for the horseÂ’s walk, tr ot, and canter. These traces are normally at the center of gravity of the horse when the overall movement of the horse is desired, but can be done on any spot of the horseÂ’s body. Masaaki Yamaguchi and Nobuhiro I guchi analyzed the movement of a horse prior to designing their horseback riding simulator. Traces at the walk, trot, and canter were developed from the motion data that was collected. Table 2-1
18 shows the motion data that was at the horseÂ’s center of gravity at the walk, trot, and canter. The data includes ranges of values for the frequen cy, horizontal and vertical amplitudes, inclination of ellipse, and pitching angle. Table 2-1: Motion Data at the HorseÂ’s Center of Gravity  Walk Trot Canter Frequency (Hz) 1.0 Â– 2.0 2.0 Â– 3.0 1.2 Â– 1.8 Horizontal Amplitude (mm) 20 Â– 50 20 Â– 40 40 Â– 70 Vertical Amplitude (mm) 20 Â– 40 40 Â– 60 60 Â– 110 Inclination of Ellipse (Degrees) 10 Â– 40 90 Â– 100 100 Â– 130 Pitching Angle (Degrees) 6 Â– 9 5 Â– 8 10 14 Using the data in Table 2-1, Yamaguchi and Nobuhiro developed ellipses for each of the three gaits of the horse, the wa lk, trot, and canter. These ellipses are shown in Figure 2-7. All the units listed in this figure ar e in millimeters. With the knowledge of the elliptical motion and frequency of the gaits, a horseback riding simulator can be developed that will simu late these movements. Figure 2-8: Elliptical Movement of the Ho rse at the Walk, Trot and Canter 
19 Since the rider sits on the horseÂ’s back while riding, it is necessary to take a brief look at the anatomy and kinematics of the horseÂ’s spine. Horses have 56 vertebrae extending from thei r poll, through their neck, back, croup, and down to their tail. There are 7 cervical vertebr ae in the neck region from the poll down the crest, 18 thoracic vertebrae in the wither s and back, 6 lumbar vertebrae in the loin, 5 sacral vertebrae in the croup and 20 caudal vertebrae loca ted in the tail of the horse. The degrees of motion s hown in Figure 2-9 relates to the intervertebral motion, or the amount of motion that can occur between two adjacent vertebrae. This motion is very important when discussing how the horseÂ’s motion influences the rider and how the rider can influence the horseÂ’s motion. Figure 2-9: Degrees of Motion of Selected Intervertebral Joints in Horses  The vertebral column of the horse c an rotate in three-dimensions and are described by flexion-extension, lateral bending, and axial rotation. Flexionextension or pitch of the spine allows the neck and back to round or hollow.
20 Lateral bending or yaw of t he spine allows the neck and back to bend to the left or right. Axial rotation or t ilt of the spine allows the vertebral column to twist. Figures 2-10, 2-11, and 2-12 show exam ples of flexion extension, lateral bending, and axial rotation, respectively. Figure 2-10: Flexion-Extension Figure 2-11: Lateral Bending
21 Figure 2-12: Axial Rotation The degree to which the vertebral column can bend in these three ways varies with the region of the vertebral co lumn and the type of rotation. There is also a large variation with individual horses. Like humans, most horses are one sided and are stronger in one direction and capable of stretching more in one direction. These variations are excl uded from most studies, and the average data of a number of horses is used. Th e cervical vertebrae in the head and neck region have the highest range of motion, which allows the horse mobility in order to graze, clean themselves and balance themselves. The caudal vertebrae in the tail region have th e next highest range of motion. The tail needs this mobility in order to allow the horse to swat at bugs that land on their body or to show their mood. Switching the tail back and fort h shows unhappiness and raising their tail high in the air shows exci tement. When developing a horse simulator, these regions are not as important as the thoracic region. Th is is the region where the
22 rider will be able to feel the effect of t he flexion-extension, lateral bending, and axial rotation. In the thoracic region of the vertebr al column, the range of motion varies with the gait that the horse is moving in and the type of rotation of the vertebral column. Marjan Faber et al [8, 9, 10] performed an in vivo study of the threedimensional kinematics of horsesÂ’ vertebr al column that determined the range of motion of the thoracic region. Table 2-2: Range of Motion of the Thoracic Region of the Horse [8, 9, 10] Walk Trot Canter Flexion-Extension 4.2 8.5 2.8 4.9 7.8 12.2 Lateral Bending 2.6 5.3 3.6 4.9 3.1 5.6 Axial Rotation 4.3 11.0 3.1 5.5 6.1 8.5 These results show that a horse has less flexion-extension at a trot than it does at a walk or canter, probably due to the trot bei ng a diagonal gait rather than a lateral gait like the walk and cant er. The lateral bend seen in all three gaits is about equal, showi ng that the gait does not a ffect the amount that the horse can bend laterally. In a walk, t he horse has the greatest range of axial rotation. The range and magnitude of axial rotation at a trot and canter is much smaller than at a walk. The range of motion of the horseÂ’ s vertebral column during flexionextension, lateral bending, and axial rotation has a great influence of the capabilities of the horse in many sports When riding dressage, a type of horse
23 sport, common terms that are heard while in training include Â“collectionÂ”, and Â“bendÂ”. Collection refers to the horse roundi ng and shortening it s entire frame, from the poll to the croup, shifting its weig ht more to its hind end and shortening the length of the stride of the gait. Collection require s a great deal of flexionextension of the vertebral column when done correctly. The humping or rounding of the horseÂ’s back during collection, changes the angle of the riderÂ’s pelvis causing them to sit more on their front seat bones. The movement of the horse will often feel much smoother controlled and balanced. Bending the horse refers to curvi ng the neck and spine around a curve. The horse is trained to bend around pressure from the riderÂ’s leg given at the girth. A correctly bent horse will bend from their poll to their tail evenly. Bending requires both lateral bend and axial rotation of the vertebral co lumn. The riderÂ’s pelvis position and weight needs to be adjusted to accommodate a horse bending. The weight of the rider needs to be slightly to the inside of the curve and the riderÂ’s pelvis needs to follow the same curve that the horseÂ’s pelvis does. This requires the rider to rotate their pel vis so that the side of the pelvis on the outside of the curve is pushe d more forward than the side of the pelvis on the inside of the curve. The riders are required to balance them selves in order to allow the horse to perform collection, bend, and a specific gait A highly trained dressage horse will respond to a slight shift in weight, pull on the rein or squeeze with the leg. The responce may be to speed up, slow down, collect, extend, bend to the right
24 or left, or to just increase the balance or impulsion of t he gait. Even with a horse that is not highly trained, a shift in weight may not signal the horse to do something specific, but may throw it off balance and end up in an undesired result. The rider can influence the horse as much as the horse can influence the rider. The rider influences the horse by givi ng aids that result in specific actions, and the horse influences the rider th rough the motion transmitted through its body to the rider. 2.3 Equine-Assisted Therapy Effect s on Children with Cerebral Palsy Equine-assisted therapy has positive effects, physically, cognitively, behaviorally, and emotionally, on people with disabi lities. This section will focus on the physical improvements that are seen in children with cerebral palsy. Cerebral palsy (CP) is caused by damage or abnormal development in the brain. Symptoms for this disease are normally se en in infancy or ear ly childhood. The physical symptoms exhibit ed may include muscle stiff ness, muscle spasticity, poor muscle tone, uncontrolled movements, and problems with posture, balance, coordination, walking, speec h, and swallowing. The th ree main types of CP are spastic CP, dyskinetic CP, and mixed CP. Spastic CP is the most common form of CP and the defin ing characteristic of this fo rm is increased muscle tone that causes stiff, jerky movements. Dyski netic CP affects the coordination of movements, and mixed CP is a combinat ion of more than one type of CP. Cerebral palsy can be mild to severe, but almost all children with cerebral palsy require some form of therapy. Equi ne-assisted therapy has been proven as an
25 effective therapy to increas e the physical well-being of children with CP, since a large portion of pediatric physical therapy involves children with CP, developing and using a therapy that is effective and that the children enjoy is valuable. Dolores Bertoti  performed one of the first objective clinical analyses on the effectiveness of equine-assisted ther apy for children with CP. Her study focused on measuring postural changes in children with spastic cerebral palsy. She developed a posture assessment scal e, which rated the alignment and symmetry of body parts and control of the muscles around the joints. The children participated in a 10-week hippother apy program, riding twice weekly for one hour. Riding was done while in the pr one, sitting, squatting, standing, and lying positions. The goal of the riding sessions was to reduce spasticity and postural compensations, and to improve the childrenÂ’s movements including trunk control, weight shift, rotation, and isolating movements of the pelvis and shoulders. The horse was directed in circles and up or dow n small grades to challenge the childrenÂ’s balance, strength, and stability. The study showed that the childre nÂ’s posture significantly improved following participation in hippotherapy sessions. The improvements were included increased midlin e head control, decreas ed neck hyperextension, decreased scapular retraction, more dev eloped scapular musculature, improved symmetry at the trunk, decreased latera l trunk flexion, decreased postural scoliosis, decreased exaggerated lumbar lordosis, increased trunk elongation, decreased anterior pelvic tilt, increased alignment of the pelvis and a more erect posture. Other positive benefits that we re observed during the course of this
26 study were improvements in self-confidence, and a decr eased fear of movement and changes in position. John Sterba et al  conducted a study measuring the effects of therapeutic riding on gross motor functi on in children with spastic diplegic, spastic quadriplegic and s pastic hemiplegic CP. The Gross Motor Function Measure (GMFM), an accepted and valid ated way of measuring gross motor function was used to measure the physical e ffect of the therapeutic riding. The children participated in three 6-week sessi ons, for a total of 18 weeks, and rode for one hour per week. Some of the exer cises that the children performed while riding the horses involved reaching for ce rtain parts of the horseÂ’s body while sitting or lying on the horse, holding a stick horizontally with both hands and moving this stick up and down while main taining correct posture, and tossing cones or bags at traffic cones set on the ground. The results of this study showed that after 12 weeks of involvement in the therapeutic riding, there was a significant increase in the GMFM Dimension E, which included walking, r unning and jumping. This in crease remained through the last 6-week session, but dropped slightly six week s following the completion of the therapeutic riding program. The GMFM Dimension E score six weeks after the completion of the progr am was still 2% higher t han before the therapeutic riding program. The total score of t he GMFM had a statis tically significant increase of 7.6% after the completion of the 18 weeks of the program, but returned to pre-riding levels 6 weeks afte r stopping riding. The results from the study do show that therapeutic riding has a positive effect in gross motor function
27 for the participants. Since CP often requires life-long physical therapy, the completion of the therapeutic riding program meant that some of the positive effects that it did have on the gross motor function diminished. Michal Kuczynski and Karina Slonk a  performed a study on the postural stability in children with CP us ing a microprocessor-driven artificial saddle. The artificial saddle provided stim uli that were similar to that of real horseÂ’s movement only at the walk. The dynamics of postural balance were measured quantitatively by stabilogra phy, which computed the centre-ofpressure (COP). COP gives a measurement of the external characteristics of body balance. The testing involved riding on the artificial saddle for 20 minutes twice a week for 3 months. COP measur ements were taken before and after the ride on the artificial saddle. The meas urements involved stand ing on a platform in both the anteroposterior and mediolateral directions. The results of this study showed t hat following the therapy, the children with CP exhibited reduced muscle stiffne ss, and decreased spasticity of the muscles. After single sessions, the pati entsÂ’ ankle stiffness lessened, allowing them to stand more stable wi thout swaying. It was conc luded that the artificial saddle riding contributed to a signifi cant improvement in the postural performance of the children with CP, a nd that this type of treatment is recommended for children with CP. All types of equine-assisted therapy ; therapeutic riding, therapeutic vaulting, and hippotherapy are capable of improving t he physical well-being of children with CP. Increased gross motor function and improved postural stability,
28 show that equine-assisted therapy is a gr eat form of physical therapy for children with CP. Whether it is on a real horse or a simulated hor se, it is the motion that is transferred to the rider that delivers t hese results. Therefore, developing these programs and making them more widely available is inva luable to those children and adults that can benefit from them.
29 Chapter 3 Â– Computer Modeling and Simulation 3.1 Model and Simulation Description A two-dimensional computer model and simulation of a horseback riding device was developed using MATLAB. Figure 3-1 shows the image of the computer model. The links are labeled and lengths of the links are shown in the starting position. Figure 3-1: MATLAB Computer Model of Horseback Riding Simulator
30 The link lengths were chosen to be t he same as the lengths used in the physical horseback riding simulator that will be discussed in Chapter 4. The model is a two-dimensional, tw o degree of freedom system. Link R1 and R5 are the inputs for the system and ch ange length with time. Link R2, R3, R4, and Rp, have constant length. The angles 4 and 5, shown in Figure 3-2, change with time and are dependent on t he link length of R5. Point P is the point of interest of the system, and has a fixed angle of 30 relative to link R4. Point P represents the point where the riderÂ’s hip is, and established the movement that is transmitted from the horseback riding simula tor to the rider. Table 3-1 shows the initial link lengths for the simulation. Table 3-1: Link Lengths of Computer Horse Simulation Link Length (Inches) R1 37.525 R2 22.2875 R3 26.75 R4 22.2875 R5 26.75 The computer model is capable of simu lating the three gaits of the horse, the walk, trot, and canter, by having diffe rent input values and phase shifts for link R1 and link R5. An animation of the horseba ck riding simulator, and the position, velocity and acceleration of point P during the simulation are the outputs. The input values of links R1 and R5 for the simulation were determined based on the kinematics of the walk, trot, and canter discussed in section 2.2.
31 A position, velocity, and acceleration analysis of the system was done in order to calculate the kinem atics of the system. The der ivations of the kinematic equations and results from the MATLAB si mulation will be shown in the following sections of this chapter. The MATLAB code for the simulation may be viewed in Appendix A. 3.2 Position Analysis and Results Figure 3-2 shows the kinematic drawing of the horseback riding simulator. Figure 3-2: Kinematic Drawing of Horseback Riding Simulator A position analysis of the vect or loop that consists of 2r ,3r ,4r and 5r was done in order to determine the unknown angles 4, and 5, as a function of the link lengths. This derivation is shown below.
32 The vectors2r ,3r ,4r and 5r shown in Figure 3-2 create a closed loop and will be used to solve for the angles 4 and 5. 5 4 3 2r r r r (3.2-1) Writing Equation (3.2-1) in complex form yields: 5 4 3 25 4 3 2 i i i ie r e r e r e r (3.2-2) By EulerÂ’s Formula: ) sin( ) cos(x x ii ex (3.2-3) Equation (3.2-3) is substitu tes into Equation (3.2-2). ) ( ) ( ) ( ) (5 5 5 4 4 4 3 3 3 2 2 2is c r is c r is c r is c r (3.2-4) where cos( x) and sin( x) are denoted by cx and sx, respectively. Equation (4) is separated into the real and imaginary components Real: 5 5 4 4 3 3 2 2c r c r c r c r (3.2-5a) Imaginary: 5 5 4 4 3 3 2 2s r s r s r s r (3.2-5b) Known, constant values are substituted in to Equations (3.2-5a) and (3.2-5b). From the design parameters, 2 is 180 and 3 is 90 5 5 4 4 3 2) 2 cos( ) cos( c r c r r r (3.2-6a) 5 5 4 4 3 2) 2 sin( ) sin( s r s r r r (3.2-6b) Equations (3.2-6a) and (3.2-6b) are simplified. 5 5 4 4 2c r c r r (3.2-7a) 5 5 4 4 3s r s r r (3.2-7b)
33 Equations (3.2-7a) and (3.2-7b) are squared to give: 2 5 2 5 2 4 2 4 4 4 2 2 22 c r c r c r r r (3.2-8a) 2 5 2 5 2 4 2 4 4 4 3 2 32 s r s r s r r r (3.2-8b) Equations (3.2-8a) and (3.28b) are added and simplified. 2 5 4 3 4 2 4 2 4 2 3 2 2) ( 2 r s r c r r r r r (3.2-9) Equation (3.2-9) is rearranged. 4 2 4 2 3 2 2 2 5 4 3 4 22 r r r r r s r c r (3.2-10) The right hand side of Equation (3.2-10) is set equal to C. 4 2 5 2 4 2 3 2 22 r r r r r C (3.2-11) Equation (3.2-10) c an now be written as: C s r c r 4 3 4 2 (3.2-12) The following trigonometric identities are substituted into Equation (3.2-12). 2 tan4 u (3.2-13a) 2 2 41 1 cos u u (3.2-13b) 2 41 2 sin u u (3.2-13c) C u u r u u r 2 3 2 2 21 2 1 1 (3.2-14) Equation (3.2-14) is multiplied by 1+u2, to yield:
34 ) 1 ( 2 ) 1 (2 3 2 2u C u r u r (3.2-15) Powers of u are collected. 0 ) ( 2 ) (2 3 2 2 r C u r u r C (3.2-16) The quadratic formula is used to solve Equation (3.2-16). ) ( 2 ) )( ( 4 4 22 2 2 2 3 3r C r C r C r r u (3.2-17) Equation (3.2-17) simplifies to: 2 2 2 2 2 3 3r C r C r r u (3.2-18) Identity (3.2-13a) is substituted in to Equation (3.2-18) to solve for 4. ) ( tan 22 2 2 2 2 3 3 1 4r C r C r r (3.2-19) where C is defined as Equation (3.2-11). Equation (3.2-7a) can be solved for 5. ) ( cos5 4 4 2 1 5r c r r (3.2-20) Once the equations for 4, and 5 were determined, the equations could be included in the computer simulation along with the input functions for r1 and r5 at the walk, trot, and canter. The positive result from Equation (3.2-19) is used in the computer code to calculate angle 4 because since the initial length of r5 is the shortest length that r5 can be, angle 4 can only increase in the positive direction. There is also no concern about the small sens itivity that may occur in Equation (3.2-20) by using the cosine functi on for the angle. The small sensitivity
35 would occur when 5 would approach 0 or 180 The range for 5 in the simulation is between 90 and 92 The input functions for r1 and r5 are changed for each gait and are shown below: r1 = R1 +A1*(1cos(2* *f*time)) r5 = R5+A5*(1-cos(2* *f*time+ ) The different values for the two input f unctions for the walk, trot, and canter are shown in Table 3-2 below. Table 3-2: Input Function Values for Walk, Trot, and Canter Walk Trot Canter R1 37.525 in 37.525 in 37.525 in R5 26.75 in 26.75 in 26.75 in A1 1.14 in 0.725 in 0.41 in A5 1.55 in 1.78 in 2.49 in f 1 cycle/s 2 cycles/s 1.2 cycle/s -37/180 /3 -40/180 For all six of the equat ions listed above, R1 and R5 represent the initial lengths of links r1 and r5. A1, and A5, are the largest incr ease of each link, and these values are added to the function firs t to avoid the link decreasing below its minimum length. Inside the cosine function, the 2 is the period le ngth, the third term is the frequency, f, with units of cycles per second, and the fourth term is the time, which changes through the cycle. The frequency data is taken from Table 2-1. There is a fifth term in the input functions for r5, which is the phase shift, and is used to create the inclinati on of the ellipse for each gait.
36 The result from the position analysis is the path of point P during one cycle at the walk, trot, and canter. Po int P is located at a fixed 30 relative angle to r4, and its horizontal co mponent is 11 inches to t he right of the end of r4. This position represents the point of the hip on a person riding on the simulator. The path of point P at the walk, trot and canter are shown in Figures 3-3, 3-4, and 35, respectively. 33 33.2 33.4 33.6 33.8 34 34.2 34.4 34.6 34.8 4848.54949.55050.5 x-axis (in)y-axis (in) Figure 3-3: Path of Point P at the Walk
37 33 33.2 33.4 33.6 33.8 34 34.2 34.4 34.6 34.8 35 47.84848.248.448.648.84949.249.449.6 x-axis (in)y-axis (in) Figure 3-4: Path of Point P at the Trot 32.5 33 33.5 34 34.5 35 35.5 47.447.647.84848.248.448.648.849 x-axis (in)y-axis (in) Figure 3-5: Path of Point P at the Canter The path of Point P at the walk has a horizontal amplitude of 1.63 inches, a vertical amplitude of 1.5 inches and an inclination of the ellipse of 22 At the trot, the path of Point P has a horizontal amplitude of 1.32 inches, a vertical
38 amplitude of 1.67 inches and an inclination of the ellipse of 135 At the canter, the path of Point P has a hor izontal amplitude of 1.15 in ches, a vertical amplitude of 2.3 inches, and an incli nation of the ellipse of 125 Besides the trot, the inclinations of the ellipse are all within the range given in Table 2-1. The trot is not within the range because of the cons traints of the system. Independent horizontal and vertical motion would be required to create the inclination of the ellipse for the trot. This does not o ccur in the current system because as the length of r5 increases, angle 5 increases since the length of link r4 is constant. This results in link r5 creating both horizontal and vertical motion. 3.3 Velocity Analysis and Results The velocity analysis of the horseback riding simulator was done in a similar manner to that of t he position analysis. A velo city analysis of the vector loop 2r 3r 4r and 5r was done in order to determine the unknowns 4, and 5. This derivation is shown below: The vectors2r 3r 4r and 5r shown in Figure 3-2, create a closed loop and will be used to solve for the angular velocities 4 and 5. 5 4 3 2r r r r (3.3-1) Equation (3.3-1) is written in complex form and yields: 5 4 3 25 4 3 2 i i i ie r e r e r e r (3.3-2) The derivative of Equation (3.3 -2) with respect to time is: 4 4 3 3 2 24 4 4 3 3 3 2 2 2 i i i i i ie dt dr e dt d ir e dt dr e dt d ir e dt dr e dt d ir
39 5 55 5 5 i ie dt dr e dt d ir (3.3-3) From the design parameter s of the mechanism, r2, r3, r4, 2, and 3 are constant. Equation (3.3-3) is simplified. 5 5 45 5 5 4 4 i i ie dt dr e dt d ir e dt d ir (3.3-4) By definition, 4 4 dt d, 5 5 dt d, and 5 5r d t dr Substituting these values into Equation (3.3-4) yields: 5 5 45 5 5 4 4 i i ie r e ir e ir (3.3-5) By EulerÂ’s Formula: ) sin( ) cos(x x ii ex (3.3-6) Equation (3.3-6) is substituted into Equation (3.3-5). ) ( ) ( ) (5 5 5 5 5 5 5 4 4 4 4is c r s ic r s ic r (3.3-7) where cos( x) and sin( x) are denoted by cx and sx, respectively. Equation (3.3-7) is separated into the real and imaginary components. Real: 5 5 5 5 5 4 4 4c r s r s r (3.3-8a) Imaginary: 5 5 5 5 5 4 4 4s r c r c r (3.3-8b) Equations (3.3-8a) and (3.3-8b) are put into matrix form. 5 5 5 5 5 4 5 5 4 4 5 5 4 4s r c r c r c r s r s r (3.3-9) CramerÂ’s rule is used to solve this system of equations.
40 4 is solve for first. 5 5 4 4 5 5 4 4 5 5 5 5 5 5 5 5 4c r c r s r s r c r s r s r c r (3.3-10) Taking the determinate of the top and botto m of Equation (3.3-10) and simplifying yields the solution for 4. ) sin(5 4 4 5 4 r r (3.3-11) Next, 5 is solved for using CramerÂ’s Rule. 5 5 4 4 5 5 4 4 5 5 4 4 5 5 4 4 5c r c r s r s r s r c r c r s r (3.3-12) Taking the determinate of the top and botto m of Equation (3.3-12) and simplifying yields the solution for 5. ) cot(5 4 5 5 5 r r (3.3-13) As was done for the position analysis, after solving for the unknown equations 4 and 5, the computer simulation written in MATLAB could determine the velocity of the system, including the velocity of the point of interest P. The simulation required the rate of change or r1 and r5 with time. These functions were found by taking t he derivates of functions for r1 and r5 with respect to time. The velocity of point P was det ermined by taking the derivative of the x
41 and y components of point P with respect to time. Figures 3-6, 3-7, and 3-8 show the velocity vectors through the path of point P. Figure 3-6: Velocity of Point P at the Walk
42 Figure 3-7: Velocity of Point P at the Trot Figure 3-8: Velocity of Point P at the Canter
43 The velocity of point P is tangential to the path of poi nt P at all points. The black square in the three figures indicate s the start of the cycle at time equal to zero. Figure 3-9 will show a comparison of the magnitude of the velocity of point P at the walk, trot, and cant er through one second. 0 2 4 6 8 10 12 00.10.20.30.22.214.171.124.80.91 Time (Seconds)Speed (inches/second) Walk Trot Canter Figure 3-9: Velocity Magnitudes of Point P The magnitude of the velocity at the walk varies between 3.3 and 6.1 inches per second, at the trot varies between 7.1 and 11.2 inches per second, and at the canter varies bet ween 1.7 and 9.6 inches per second. The greatest variation is in the canter because the ellip se is less round than in the trot or the walk. There is twice as much vertical di splacement as horizont al displacement in
44 the canter, which causes a large variati on in velocity as the simulation changes from going up to going down. Since th e walk is the roundest, the magnitude of the velocity does not change much, resulti ng in the smallest variation. 3.4 Acceleration Analysis and Results The acceleration analysis of the horseback riding simulator was completed in the same manner as the velocity analysis. The ki nematic equations for the unknown angular accelerations, 4 and 5 were determined by the acceleration analysis that follows, beginning with Equation (3.3-4). 5 5 45 5 5 4 4 i i ie dt dr e dt d ir e dt d ir (3.3-4) The derivative of Equation (3.3-4) is taken with respect to time. 4 4 42 4 4 2 4 2 4 4 4 i i ie dt d r e dt d ir e dt d dt dr i 5 5 5 5 55 5 2 5 2 2 5 5 2 5 2 5 5 5 i i i i ie dt d dt dr i e dt r d e dt d r e dt d ir e dt d dt dr i (3.4-1) Equation (3.4-1) is simp lified, given that r4 is constant. 4 42 4 4 2 4 2 4 i ie dt d r e dt d ir 5 5 5 5 55 5 2 5 2 2 5 5 2 5 2 5 5 5 i i i i ie dt d dt dr i e dt r d e dt d r e dt d ir e dt d dt dr i (3.4-2) By definition, 4 4 dt d, 5 5 dt d, 4 2 4 2 d t d, 5 2 5 2 dt d, 5 5r d t dr and 5 2 2 5r d t dr Substituting these values into Equation (3.4-2) yields:
45 5 5 5 5 5 4 45 5 5 2 5 5 5 5 5 5 2 4 4 4 4 i i i i i i ie r i e r e r e ir e r i e r e ir (3.4-3) By EulerÂ’s Formula: ) sin( ) cos(x x ii ex (3.4-4) Equation (3.4-4) is substituted into Equation (3.4-3). ) ( ) (4 4 2 4 4 4 4 4 4is c r s ic r ) ( ) ( ) ( ) ( 25 5 5 5 5 2 5 5 5 5 5 5 5 5 5 5is c r is c r s ic r s ic r (3.4-5) where cos( x) and sin( x) are notated by cx and sx, respectively. Equation (3.4-5) is separated into the real and imaginary components. Real: 5 5 5 2 5 5 5 5 5 5 5 5 4 2 4 4 4 4 42 c r c r s r s r c r s r (3.4-6a) Imaginary: 5 5 5 2 5 5 5 5 5 5 5 5 4 2 4 4 4 4 42 s r s r c r c r s r c r (3.4-6b) Equations (3.4-6a) and (3.4-6b) are put into matrix form. 5 5 5 2 5 5 5 5 5 4 2 4 4 5 5 5 2 5 5 5 5 5 4 2 4 4 5 4 5 5 4 4 5 5 4 42 2 s r s r c r s r c r c r s r c r c r c r s r s r (3.4-7) CramerÂ’s rule can used to solve this system of equations. 4 is solved for first. 5 5 4 4 5 5 4 4 5 5 5 5 5 2 5 5 5 5 5 4 2 4 4 5 5 5 5 5 2 5 5 5 5 5 4 2 4 4 42 2 c r c r s r s r c r s r s r c r s r s r c r c r s r c r (3.4-8) Taking the determinate of the top and bottom of Equat ion (3.4-8) and simplifying yields the solution for 4.
46 ) sin(5 4 4 5 2 5 5 ) 5 4 ( 2 4 4 4 r r r c r (3.4-9) Now 5 is solved for using CramerÂ’s rule. 5 5 4 4 5 5 4 4 5 5 5 2 5 5 5 5 5 4 2 4 4 4 4 5 5 5 2 5 5 5 5 5 4 2 4 4 4 4 52 2 c r c r s r s r s r s r c r s r c r c r c r s r c r s r (3.4-10) Taking the determinate of the top and botto m of Equation (3.4-10) and simplifying yields the solution for 5. ) sin( ) sin( ) sin( ) sin( 25 4 5 5 4 5 5 4 2 5 5 5 4 5 5 2 4 4 5 r r r r r (3.4-11) The second derivate of links r1 and r5 with respect to time were computed in order to complete the simulation. The second derivativ e of the x and y components of point P were also determined in order to calculate the acceleration of the point of interest P. Figure 3-10 shows a graph with the accelerations at point P for all thr ee gaits, the walk, trot, and canter.
47 0 2 4 6 8 10 12 14 00.10.20.30.126.96.36.199.80.91 Time ( Seconds ) Acceleration (ft/s^2) Walk Trot Canter Figure 3-10: Acceleration Magnitudes of Point P The acceleration ranges from 1.7 to 3.2 ft/s2 at the walk, 6.9 to 11.8 ft/s2 at the trot, and 0.4 to 6.1 ft/s^2 at t he canter. The walk has the smoothest acceleration curve, but also moves the s hortest distance at the lowest frequency. The walk, trot, and canter curves are not uniform through a complete cycle. There is slightly lower acceleration at every other valley. The peaks through these curves are also wider then the va lleys. A graph of the Fourier transform showed the fundamental frequency for the system and also a 1st harmonic. The magnitude of the 1st harmonic compared to the magnitude of the fundamental frequency is very small, and therefore does not affect the sine wave much. The affect from the 1st harmonic is seen in the graph for the velocity also, but is more accentuated in the acceleration graph. The graph showing the Fourier Transform
48 for the walk is shown in Figure 3-11. The graphs for the trot, and canter show the same results and theref ore have been omitted. Figure 3-11: Fourier Transform Graph of Walk The small variation of acceleration, only 1.5 ft/s2 difference, would probably not be noticed by a rider. More importantly, a jerk during the second valley of the canter is seen. Again, the change in acceleration is small, so this jerk may not be noticed in a physical simula tor. Depending on the horse that is being ridden, there may be a jerk felt at one point in the canter. The average magnitude of the acceleration is less than a th ird of that of grav ity, so no safety risks concerning high accelerations exist for this simulator.
49 Chapter 4 Â– Physical Simulator Design and Fabrication 4.1 Design The horseback riding simulator was des igned for the purpose of simulating the walk, trot, canter, flexion/extension, a nd lateral bend of th e horse. A device of this kind can be used as a physical therapy device for persons with disabilities or as a training device at riding stables to help riders learn to ride better. This section will include a detailed look at the design of the horseback riding simulation. The following section will descr ibe the fabrication of the simulator. During the development of the concept of the horseback riding simulator, a list of requirements was est ablished. This list included: 1. Replication of the horse Â’s walk, trot and canter. 2. Replication of the horseÂ’s late ral bend to the right and left and flexion/extension. 3. Safety factor of at least two for all components with a rider up to 200 lbs. 4. Safe for a person with a disability to ride. These requirements were evaluated th roughout the design pr ocess, from the initial concept to the completion of the final design of the prototype. The horseback riding simulator consists of the structure, which includes the track, base, and rider s upport bars, two air sprung el ectrically driven linear actuators (PEMRAMs), and the seat for the rider, which is a plastic horseÂ’s back.
50 Detailed AutoCAD drawings with dimens ions are included in Appendix C. The finished design of the horseback riding simulator is shown in Figure 4-1. Figure 4-1: Horseback Riding Simulator The first requirement for the horseback riding simulator is to replicate the horseÂ’s walk, trot, and canter. The si mulator has two degrees of freedom and creates the horseÂ’s moti on in the same manner as the MATLAB computer simulation discussed in Chapter 3. The horizontal and vertical PEMRAMÂ’s change length in a periodic manner and the phase shift between the two PEMRAMs creates the elliptica l motion of the horseÂ’s walk, trot, and canter. The amplitudes of the indi vidual PEMRAMs are set by adju sting the resistance to the amplifiers.
51 The next requirement for the simulator is to replicate the flexion/extension and lateral bend of the horse. These were created by addi ng custom shaped foam to the top and side of the plastic ho rse. The plastic horse without foam simulated a horse with no flexion/extensio n or lateral bend of the back. When the foam was in place, right or left late ral bend and flexion/extension of the back was simulated. Figure 4-2 shows the image of the horse back with the foam simulating flexion-extens ion and Figure 4-3 shows th e image of the horse back with the foam simulating left bend. Figure 4-2: Flexion-Extension of the Horseback Riding Simulator
52 Figure 4-3: Left Bend of the Horseback Riding Simulator A safety factor of at least two for a rider up to 200 lbs is required for the horseback riding simulator. The safety factor of the horseback riding simulator was evaluated by computing the stat ic load analysis of the individual components. Each component is subject ed to a bending, tension, compression, or a combination of the two. The most in fluential stress was used to evaluate the safety of the component. The prototype of the horseback ri ding simulator was grossly over designed. The horizontal rod stabilizes the plastic horseback where the rider will sit. The rod is subjected to a bending stress. Using a uniformly distributed
53 weight of 400 lbs over the 23 inch length of the rod, the maximum displacement and bending stress that the rod is subject ed to is negligible, with a safety factor well over 2. The vertical support tube is subjected to compressive stresses. Using 400 lbs and the area of the tube, the stress is calculated to be 0.4 ksi, which gives a safety factor much gr eater than 2 when compared to the yield stress of 30 ksi of the steel used. This ca lculation is shown in Equation 4.1-1. ksi in lbs A P 4 0 9024 0 4002 (4.1-1) The base of the simulator was made out of st eel to lower the center of gravity of the system in order to eliminate any ti pping effects. The PEMRAMs are capable of moving 220 lbs each. Ad ditional weight can be li fted if air pressure is introduced into the system, but was not necessary with the final design of the simulator. The fourth requirement for the horseba ck riding simulator is that is must be safe for a person with a disability to ride. The simulator that was designed and fabricated is a prototype, and therefore all hazards and dangers of riding the simulator have not been elim inated. Some of the known hazards are listed below. 1. The plastic horse tipping to the si de if the rider loses their balance. 2. Not having full control of the mo vement of the PEMRAMs. When the system is started, the PEMRAMs ext end out to their full capacity to calibrate. The program for the simulato r is then started, but the rider must mount the horse when the simulator is moving.
54 3. There is no external support that the rider can hol d on to or be attached to that will provide additional stability. 4. At least one person must control the simulator while it is being used in order to press the emergency stop butt on if necessary. The rider does not have any control over the simulator. 4.2 Fabrication The structure of the horseback riding simulator includes the track, base, and rider support bars. These ar e labeled in Figure 4-4. Figure 4-4: Horseback Riding Simulator Structure The track is made out of 90 steel angle brackets welded to steel plates. The two tracks have a steel plate welded at the front and back to create a box. The system rides on the track via four v-groove wheels. T he v-groove wheels are self-aligning on the track, eliminati ng any misaligning that may occur with
55 other styles. The horizontal PEMRAM is bol ted to the front plate of the track. This eliminates the need to secure the system to the floor, because since the complete system is bolted together, t he weight will keep it from moving. The base consists of 1 inch steel tubes welded in a rectangle and three reinforcing steel tubes welded across. A 1/8th inch thick steel plate is welded to the top of the base. The base weighs about 100 lbs. The rider support bars include the support tube, support rod, and the vertical PEMRAM. The vertical PEMRAM is attached to the base by a steel bracket. The support tube is a 2-inch squa re tube that is welded to the base as the vertical support. A 1-inch thick r od is used as the horizontal support. The horizontal support tube is attached to t he PEMRAM and to the support tube using clevis joints, which allow the small amount of pivoting motion that is necessary for the simulation. The plastic horse is attached to the horizontal support tube by steel tubes welded together as shown in Figure 4-5. Figure 4-5: Attachment of Plastic Horse to Simulator Two steel bars run parallel to the horiz ontal support rod and three steel bars run perpendicular to the horizontal support r od. The parallel bars have a 90 angle
56 that has been welded to the ends, which bol t to the front and back of the plastic horse. On the underside of the plasti c horse, a wooden platform was attached using epoxy and angle brackets. The wooden platform created a flat surface for the steel bars to sit. This is shown in Figure 4-6. Figure 4-6: Underside of Plastic Horse The fabrication of the horseback riding simulator was kept as simple and inexpensive as possible. The PEMRAMs were taken from a dynamic seat that was already at the University. Steel was used to eliminat e special welding techniques. The brick red paint was applied to reduce rust on the simulator. The
57 system stands alone so that moving it is relatively easy. Improvements on the design are included in Chapter 6.
58 Chapter 5 Â– Motion Analysis and Results 5.1 Description of the Testing of the Horseback Riding Simulator Following the design and f abrication of the horseback riding simulator, testing to evaluate the simulator was performed. The purpose of the testing was to evaluate the similarity of the horseback riding simulator to the gaits of the data collected from a real horse The results from the te sting are compared with the position, velocity, and acceleration dat a from the MATLAB simulation. The biomechanical effect on the hip angle is also evaluated when the system simulates bending and collection of the back. The Vicon system was used to collect t he position, velocity, acceleration, and hip angles of the rider on the horseback riding simulator. Four cameras with infrared lights were set up to collect t he data. A Vicon 612 datastation computer was used to collect and preprocess the dat a from the cameras. A Dell computer took the information from the datasta tion and ran programs using the Vicon Bodybuilder software to anal yze the data. The comput er program was written using the Vicon Bodybuilder software to ca lculate the marker trajectories and the hip angles. Calibration of the system was completed at the beginning of each testing session using a 4-marker calibra tion frame with known distances and a two-marker wand to measure out the co llection volume. Using direct linear transformations, the locations of the ca mera and the marker distances were
59 computed in order to collect the 2-dimensional informati on from each camera into one 3-dimensional set of data. Figure 5-1 shows the set up of two of the cameras. The other two cameras are just off the photo on the right and left hand side. Figure 5-1: Vicon Camera Configuration Five reflective markers were plac ed on the rider. Figure 5-2 shows the placement of the markers on the Anterior Superior Iliac Spine (ASIS), Posterior Superior Iliac Spine (PSIS), sacrum, thi gh, and knee. The ASIS marker is the one that is placed on the hip bone and corresponds to the point P of the computer simulation. T he ASIS, PSIS, and sacrum markers create the pelvis segment and were used alo ng with the knee and thigh po int that created the upper leg segment to determine the hip angle.
60 Figure 5-2: Marker Placement on Rider Four different tests were carried out. These included: 1. Horseback without simula ted bend or collection. 2. Horseback with simula ted collection only. 3. Horseback with simulated left bend only. 4. Horseback with simulated collection and left bend. Eight runs of each of these tests were completed with an av erage data collection time of 9 seconds. The Fourier transforms of each data set was calculated in order to choose the data that would be used. The Fourier transform was used because the data with the least amount of noi se had the best results. Peaks in the graph at all three gaits were seen at 60 Hz, at the fundamental frequency, at the 1st harmonic and 2nd harmonic. Peaks beyond the second harmonic are
61 present, but with magnitudes very low compared to the lower harmonics that these would not affect the motion much. Figure 5-3 shows the Fourier transform graph of the data collected at the walk. The trot and canter graphs are similar, and so are omitted. Note that the noise at 60 Hz is not in cluded in the graph. Figure 5-3: Fourier Transform Graph at Walk 5.2 Kinematic Results The kinematic results from the testing includes the position, velocity, and acceleration of the point of the riderÂ’s right ASIS, or hip. A vi sual inspection of the data was used to determine which gra phs best represented the walk, trot,
62 and canter. As discussed in the previous section, the data for each gait that had the smallest amount of noise as determined from the Fourier transform graph was chosen. Differences in the kinemati cs between the four di fferent tests were not seen. Figures 5-4, 55, and 5-6 show the graph of the pos ition of ASIS for the walk, trot, and canter, respectively. 29 31 33 35 37 39 444648505254 x-axis (in)y-axis (in) Figure 5-4: Horseback Riding Simulator Walk 28 30 32 34 36 38 40 42 40455055 x-axis (in)y-axis (in) Figure 5-5: Horseback Riding Simulator Trot
63 28 30 32 34 36 38 40 42444648505254 x-axis (in)y-axis (in) Figure 5-6: Horseback Riding Simulator Canter The programming capabilities of t he PEMRAMÂ’s movement were limited. The data collected was run on programs that were already available for the system. This frequency, phase shifts and magnitudes were already established in these programs and could not be changed. Two discrete values for the phase shifts were available for the vertical PEMRAM relative to the horizontal PEMRAM. These discrete values for the p hase shifts were only slightly offset. Also, the magnitudes of the PEMRA Ms could not be adjusted. The limitations of the programming capabilities of the system reduced the control over the system. The walk ga it was simulated by using only the horizontal PEMRAM motion. T he trot and canter gaits were simulated using the a program that used both the vertical a nd horizontal PEMRAMs, but with different phase shifts. The largest problem in th e motion that resulted from limited programming capabilities was in chang ing the individual magnitudes of the
64 PEMRAMs. Better motion would be created if it were possible to increase or decrease the magnitudes of the i ndividual PEMRAMs separately. Overall, the riderÂ’s comments on the feel of the gaits as compared to a real horse was promising. The motion was describes as feeling a little large in the canter, but not in the walk. Also, the rider felt that there should be more force exerted in the trot and the canter. Three different measur ements are used to evaluat e the position data of the horseback riding simulator. These me asurements are the in clination of the ellipse, the major axis of the ellipse, and the frequency. Table 5-1 shows these three measurements for the computer simulation and the horseback riding simulator for the three gaits, the walk, trot, and canter. Table 5-1: Comparison of the Computer and Horseback Riding Simulators Inclination of the Ellipse Major Axis Frequency Computer Simulation Walk 22 2.59 Inch 1 Hz Horseback Riding Simulator Walk 5 9.14 Inch 0.5 Hz Computer Simulation Trot 135 2.14 Inch 2 Hz Horseback Riding Simulator Trot 160 8.6 Inch 0.5 Hz Computer Simulation Canter 125 2.86 Inch 1.2 Hz Horseback Riding Simulator Canter 165 10.67 Inch 0.5 Hz
65 Comparing the frequency, length of the ma jor axis of the ellipse, and the inclination of the ellipse between t he computer simulation and the horseback riding simulator shows differences in a ll three measurements. The walk and canter of the horseback riding simulato r have different frequencies from the computer simulation. The horseback riding simulator wa s run at 0.5 Hz during runs for all three gaits. This differenc e in the frequency does not change the feel of the motion, though, and t here is a wide range of fre quencies that a real horse will move. Having a lower frequency for the horseback riding simulator only shows a difference from t he computer simulation, not from the range of frequencies for a real horse. Also, runni ng the horseback riding simulator at a lower frequency was safer for the rider. The length of the major axis is di fferent in the horseback riding simulator and the computer simulation. The lengt h of the major axis for the horseback riding simulator is 352% higher in the walk, 402% in the tr ot, and 373% in the canter compared to the computer simula tion. Although the magnitudes of the horseback riding simulator are larger t han the computer simulation, during the motion testing the rider did not feel that the movements were exaggerated. The magnitudes of the physical simulator c ould be reduced, but the noise from the PEMRAMs is amplified as t he magnitudes are decreased. The inclination of the e llipse is the third measur ement that was used to compare the computer and horse back riding simulators. When the inclination of the ellipse was calcul ated for the three gaits, they were not the same as from the computer simulation. As shown in Ta ble 5-1, the walk did not have enough
66 inclination, and the trot and canter had too much inclinat ion. To improve these values for the horseback riding simula tor, the phase shifts between the two PEMRAMs would have to be adjusted. The velocity and acceleration of the horseback riding simulator was also calculated. The magnitude of the velocity of the walk varied from 1 in/s to 13 in/s, the magnitude of the velocity of the tr ot varied from 1.1 in/s and 23 in/s, and the magnitude of the velocity of the canter varied from 1.3 in/s and 20.8 in/s. Unfortunately because of the noise t hat was apparent in the PEMRAMs the velocity range is much higher. The PEMRAM would stick and slip during the testing which caused inconsistencies in the velocities at the walk, trot, and canter. The acceleration of the horseback ridi ng simulator was also calculated. For the walk, the acceleration ranged from 0 ft/s^2 to 6.5 ft/s^2, for the trot ranged from 0 ft/s^2 to 16.2 ft/s^2, and for t he canter ranged from 0 ft/s^2 to 9.8 ft/s^2. Jerking was felt by the rider and was seen in the data, but the jerking was determined to be from the stick and slip that occurred in the PEMRAMs. Noise that was seen in the graphs for the position of the hip during the walk, trot, and canter is greatly accentuated in the acce leration data. If the noise that was included in the horseback riding simulato r was lessened, the acceleration values would have much less noise, and the ranges would be smaller. But overall, unsafe velocities and acceleration s were not felt by the rider.
67 5.3 Biomechanical Results Biomechanical measurements were also taken during the testing of the horseback riding simulator. Hip angles dur ing the four tests described in section 5.1 were compared. These tests com pared the hip angles when there was no simulated bend or collection, with simula ted bend only, with simulated collection only, and with simula ted bend and collection. Table 5-2 shows the results from the hip angles for the wa lk, trot, and canter. Table 5-2: Hip Flexion Angles Comparison Walk Trot Canter No Bend or Collection 49.5 66.5 36.3 63.1 38.4 66.6 Collection Only 44.1 58.7 37.0 64.6 37.1 66.7 Bend Only 61.2 84.8 57.8 86.1 60.9 86.0 Bend and Collection 54.2 78.9 44.1 79.1 45.9 75.8 The difference between the walk, tr ot, and canter hip flexion angles between the four different tests is minima l. The trot and canter have similar ranges, although the trot r anges are wider than the c anter. The walk has the smallest range of hip flexion angles. There is no hip flexion angle difference between the test without any simulated bend or collection and the test with collection only. The test with the si mulated bend only shows a significant increase in the hip flexion angle compared to the tests without bend. In the walk, the smallest hip flexi on angle increases by 12 in the test with bend only compared to the test without bend or collection. The range of the hip flexion
68 angle also increases by 6.6 This same trend is also seen in the trot and the canter. This shows that adding simula ted collection does not change the hip flexion angles of the rider but adding simulated bend changes the hip flexion angles significantly.
69 Chapter 6 Â– Conclusions and Recommendations 6.1 Conclusions In the past decades, research deali ng with horses has been funded and performed in order to improve the race horse industry. Recently, research dealing with horses has exp anded in all areas, includi ng dressage, jumping, reigning, horse biomechanics, rider biom echanics, and equine-a ssisted therapy. It is unfortunate that with t he expansion of this research, that communities in the United States continue to force horses out. It is for this reason that research involving simulating the horseÂ’s motion is important. It will continue to become harder to have land in and near me tropolitan areas wher e many people with disabilities live, and therefore the expansio n of rehabilitation therapy centers that use horses is not expected to increase as quickly as the number of people that are interested in being involv ed in these programs. A computer model of a horseback riding simulator and a physical horseback riding simulator have been deve loped. The computer model was developed using MATLAB and allo wed the user to choose the gait and the time that the simulator ran for. The resu lts from the comput er simulation was compared with data from a real horse. The physical horseback riding simu lator was designed and fabricated using the same link lengths as the com puter model. The tr ack, frame, rider
70 support bars, and plastic horse seat were designed to work with the PEMRAMs and existing programs. The horseback ridi ng simulator was designed to simulate the walk, trot, canter, bend, and collection of a real horse. Kinematic and biomechanical data was collected duri ng the testing of the horseback riding simulator and was compared to the data from the computer simulation. The results from the horseback riding simulator show that the simulated bend affects the riderÂ’s hip flexion angle si gnificantly more than the simulated collection. This result can be used during the physical therapy treatment of persons with disabilities. During the period when a person with a disability is involved in equine-assisted therapy, the rehabilitation effects will improve their mobility, posture, muscle t one, balance, motor skills. As these effects are seen, the simulated bend can be used to increase the hip flexion angle and hip flexion angle range that the rider will experience. This should result in even greater results from the therapy. The horseback riding simulator is intended to be used as an aid for physical therapy. Clinical st udies involving per sons with disabilities riding the simulator would be necessary to test th e effectiveness of the horseback riding simulator. These clinical studies were not performed because the current horseback riding simulator is a prototype and does not meet the safety criteria that would be necessary. Further develop ment of the simulator to meet this requirement would allow clinical research to be performed.
71 6.2 Future Work and Recommendations More research is needed in the ar ea of equine-assisted therapy. Using a horseback riding simulator it is possible to conduct controlled studies that can quantitatively measure the impr ovement of a rider using th is type of therapy. The prototype of the horseback riding simulato r that was built for this research requires improvement of control of the movement. A graphical user interface created in the programming would eas ily the phase shift, magnitudes, and frequencies of the PEMRAMs to be changed. Also, adding components that give the rider control over the motion that they are feeling would improve using the horseback riding simulator. Rider control could be added by developing a new way to simulate the bend and collection of t he horse. If the rider were able to put pressure with their legs on a specific part of the plastic horse in order to simulate the bend and collection, they would have mo re control over their movement. Also, adding components which would allo w the rider to start and stop the movement is important. There are safety issues to consi der with the horseback riding simulator also. The track and frame have sharp, metal corners that would need to be covered. The rider support bars tend to rotate and unscrew, which tilts the plastic horse. Fixing this problem w ould require welding the bars that are screwed in or having a larger axle at the pivot point of the device. A handle for the rider to hold on to that is more subs tantial than a strap on the saddle is also recommended.
72 References  NARHA, http://www.narha.org/PD Ffiles/2005FactSheet.pdf  Y. Shinomiya, T. Ozawa, Y. Hosaka S. Wang, K. Ishida, and T. Kimura. Â“Development and Physical Training Evaluation of Horseback Riding Therapeutic EquipmentÂ”. Pr oceedings of the 2003 IEEE/ASME International Conference on Advanc ed Intelligent Mechatronics, Kobe, Japan. July 2003, pp. 1239-1243.  Masaaki Yamaguchi and Nobuhiro I guchi. Â“Development of a Horseback Riding SimulatorÂ”. Advanced Robotics, 1992, vol. 6, no. 4, pp. 517-528.  Patti Koenig and George Bekey. Â“G eneration and Control of Lateral Gaits in a Horse-Rider SimulationÂ”. Proceedings of the 1993 IEEE/RSJ International Conference on Intelli gent Robots and Systems, Yokohama, Japan. July 36-30, 1993, pp. 572-579.  Jane I. Tuttle. Â“The Horse as a Me mber of the Ther apeutic TeamÂ”. Rehabilitation Nursing, 1987, vol. 12, no. 6, pp. 334-335.  R. Kijima, M. Kouno, K. Hashimoto, Y. Jiang, T. Aoki, and T. Ojika. Â“Karakuri Horse Riding Therapy Â”. Proceeding s of the 8th International Conference on Rehabilitation Roboti cs (ICORR 2003). D aejeon, Korea. April 2003, pp. 278-281.  Hilary Clayton. Â“The Mysteries of the BackÂ”. February 1999. Dressage Today, pp. 28.  M. Faber, H. Schamhardt, R. van Weer en, C. Johnston, L. Roepstorff, and A. Barneveld. Â“Basic Three-dime nsional Kinematics of the Vertebral Column of Horses Walking on a TreadmillÂ”. American Journal of Veterinary Research, April 2000, vol. 61, no. 4, pp. 399-406.  M. Faber, C. Johnston, H. Schamhardt. R. van W eeren, L. Roepstorff, and A. Barneveld. Â“Basic Three-dime nsional Kinematics of the Vertebral Column of Horses Trotting on a TreadmillÂ”. Americ an Journal of Veterinary Research, May 2001, vol. 62, no. 5, pp. 757-764.
73  M. Faber, C. Johnston, H. Schamhardt, P. van W eeren, L. Roepstorff, and A. Barneveld. Â“Three-di mensional Kinematics of the Equine Spine during CanterÂ”. Equine Veterinary J ournal, 2001, vol. 33, pp. 145-149.  D. Bertoti. Â“Effect of Therapeutic Horseback Rid ing on Posture in Children with Cerebral PalsyÂ”. Physical Ther apy, Oct. 1988, vol. 68, no. 10, pp. 1505-12.  J. Sterba, B. Roger s, A. France, and D. Voke s. Â“Horseback Riding in Children with Cerebral Palsy: E ffect on Gross Motor FunctionÂ”. Developmental Medicine and Child Neurol ogy, May 2002, vo l. 44, no. 5, pp. 301-308.  Michal Kuczynski and Karina Slonka. Â“Influence of Artificial Saddle Riding on Postural Stability in Ch ildren with Cerebral Pal syÂ”. Gait and Posture, 1999, vol. 10, pp. 154-160.
74 Bibliography  Texas Tech Equestrian Center, http://www.asft.ttu. edu/utrc/faq.html.  Easter Acres Miniature Horses, http://home.flash.net/~es tracrs/anatomy.html.  Gary Meregillano. Â“HippotherapyÂ”. Physical Medicine and Rehabilitation Clinics of North America, Nov. 2004, vol. 15, no. 4, pp. 843-854.  WebMD, http://www.emedicineheal th.com/cerebral_palsy/article_em.htm.
76 Appendix A Â– Horseback Riding Simulator Source Code function [Horse_plot] = Horse2(tot_time,gait) % This function will plot a 2-dim ensional model of the horseback riding simulator and graphs. % The input for the function Horse_plot is the total time of the simulation in seconds and the gait, either walk, trot or canter that should be simulated. % The gait can be specified by: % Walk = 1 % Trot = 2 % Canter = 3 % Written by Jennifer Lott on January 20, 2006. % Revised on February 11, 2006 in or der to update equations for Theta_4 and Theta_5. % Updated on May 22, 2006 to change the input functions and add velocity and acceleration graphs. __________________________ ________________________ ______________ % This will be the time intervals used dt = 0.01; % Total number of steps that the simulation will go through Steps = (tot_time/dt); % Initialize the length of r1 r1 = 37.525; % Initialize the velocity of r1 dr1_dt = 0; % Initialize the acceleration of r1 d2r1_dt2 = 0; % Given the value of the length of r2 r2 = 22.2875; % Given the value of the length of r3 r3 = 26.75; % Given the value of the length of r4 r4 = 22.2875; % Initialize the length of r5 r5 = 26.75; % Initialize the velocity of r5 dr5_dt = 0; % Initialize the acceleration of r5
77 Appendix A (Continued) d2r5_dt2 = 0; % Given the value of the angle delta delta = 30*pi/180; % Given the value of the length of rp rp = 11/cos(delta); % Initialize the time time = 0; % The initial value of r1 is needed for the input functions R1 = r1; % The initial value of r5 is needed for the input functions R5 = r5; % Simplification for the equation that is solved for the position of Theta_4 C = (r2^2+r3^2+r4^2-r5^2)/(2*r4); % Equations for theta_4 and theta_5 Theta_4 = 2*atan((-r3+sqrt(r3^2+r2^2-C^2))/(C+r2)); Theta_5 = acos((-r2+r4*cos(Theta_4))/r5); % Equations for omega_4 and omega_5 Omega_4 = -dr5_dt/(r4*sin (Theta_4-Theta_5)); Omega_5 = -dr5_dt/r5*co t(Theta_4-Theta_5); % Equations for alpha_4 and alpha_5 Alpha_4 = (-r4*Omega_4^2*cos( Theta_4-Theta_5)+r5*Omega_5^2d2r5_dt2)/(r4*sin(Theta_4-Theta_5)); Alpha_5 = (-r4*Omega_4^2-2* dr5_dt*Omega_5*sin(Theta_4Theta_5)+r5*Omega_5^2*si n(Theta_4+Theta_5)d2r5_dt2*sin(Theta_4+Theta_5))/ (r5*sin(Theta_4-Theta_5)); % These values are initialized for t he plots of these changing values plot_r1 = r1; plot_r5 = r5; plot_Theta_4 = Theta_4; plot_Theta_5 = Theta_5; plot_p = [r1+rp*cos(Theta_4+delta ),r3+rp*sin(Theta_4+delta)]; plot_dp_dt = [dr1_dtrp*Omega_4*sin(Theta_4+delta),rp *Omega_4*cos(Theta_4+delta)]; plot_d2p_dt2 = [d2r1_dt2(rp*Omega_4^2*cos(Theta_4+delta)+rp*Al pha_4*sin(Theta_4+delta)),Alpha_4*rp *cos(Theta_4+delta)-Omega_4^2*rp*sin(Theta_4+delta)]; plot_dr1_dt = dr1_dt; plot_dr5_dt = dr5_dt;
78 Appendix A (Continued) plot_d2r1_dt2 = d2r1_dt2; plot_d2r5_dt2 = d2r5_dt2; % Loop to animate simulation for LOOP = 0:Steps-1 % Clear the graph for t he animation of the simulation clf; % Establish the x axis of the first link r1 fa = [0,r1]; % Establish the y axis of the first link r1 fb = [0,0]; % Establish the x axis of the second link r2 (Constant length) fc = [r1,r1+r2]; % Establish the y axis of the second link r2 (Constant length) fd = [0,0]; % Establish the x axis of t he third link r3 (Constant length) fe = [r1,r1]; % Establish the y axis of t he third link r3 (Constant length) ff = [0,r3]; % Establish the x axis of t he fourth link r4 (Constant length) fg = [r1,r1+r2-r5*sin(Theta_5-(pi/2))]; % Establish the y axis of t he fourth link r4 (Constant length) fh = [r3,r5*cos(Theta_5-(p i/2))]; % Establish the x axis of the fifth link r5 fi = [r1+r2,r1+r2-r5* sin(Theta_5-(pi/2))]; % Establish the y axis of the fifth link r5 fj = [0,r5*cos(Theta_5-(pi/2))]; % Establish the x axis of rp (Constant length) fk = [r1,r1+r p*cos(Theta_4+delta)]; % Establish the y axis of rp (Constant length) fl = [r3,r3+rp*sin(Theta_4+delta)]; % Figure(1) is the animation of t he position of the horse riding simulator figure(1) plot(fa,fb,'-k+',fc,fd,' -k+',fe,ff,'-k+',fg,fh,'-k+',fi,fj,'-k +',fk,fl,'-k+','LineWidth',4) grid off axis([-1 70 -0.5 40]) title( 'Horse Simulation') xlabel('x axis (in)','FontSize',12) ylabel('y ax is (in)','FontSize',12) hold on pause(0.01)
79 Appendix A (Continued) % Update the current time time = time + dt; if gait == 1 % Input functions for WALK % Input position function for r1 r1 = R1+0.8496* 1.34-0.8496*1.34*cos(2*pi*1*time); % Input ve locity function for r1 dr1_dt = 2.2769*pi*sin(2*pi*1*time); % Input acceleration function r1 d2r1_dt2 = 4. 5539*pi^2*cos(2*pi*1*time); % Input position function for r5 r5 = R5+0.6209*2.50.6209*2.5*cos(2*pi*1 *time-37*pi/180); % Input ve locity function for r5 dr5_dt = 3.1045*pi *sin(2*pi*1*time-37*pi/180); % Input a cceleration function for r5 d2r5_dt2 = 6.209*p i^2*cos(2*pi*1*time-37*pi/180); elseif gait == 2 % Input functions for TROT % Input position function for r1 r1 = R1+0.6594* 1.1-0.6594*1.1*cos(2*pi*2*time); % Input ve locity function for r1 dr1_dt = 2.90136*pi*sin(2*pi*2*time); % Input acceleration function r1 d2r1_dt2 = 11. 6054*pi^2*cos(2*pi*2*time); % Input position function for r5 r5 = R5+0.8366*2.1250.8366*2.125*cos(2*pi*2*time-pi/3); % Input ve locity function for r5 dr5_dt = 7.11* pi*sin(2*pi*2*time-pi/3); % Input a cceleration function for r5 d2r5_dt2 = 28.44 *pi^2*cos(2*pi*2*time-pi/3); elseif gait == 3 % Input functions for CANTER % Input position function for r1 r1 = R1+0.6157/1. 5-0.6157/1.5*cos(2*pi*1.2*time); % Input ve locity function for r1 dr1_dt = 0.98512*pi*sin(2*pi*1.2*time); % Input acceleration function r1 d2r1_dt2 = 2.364 3*pi^2*cos(2*pi*1.2*time);
80 Appendix A (Continued) % Input position function for r5 r5 = R5+2.3228/2*21.244*2*cos(2*pi*1.2*time-40*pi/180); % Input ve locity function for r5 dr5_dt = 5.9712*pi *sin(2*pi*1.2*time-40*pi/180); % Input a cceleration function for r5 d2r5_dt2 = 14.331*pi ^2*cos(2*pi*1.2*time-40*pi/180); end % Simplification for the equation that is solved for Theta_4 C = (r2^2+r3^ 2+r4^2-r5^2)/(2*r4); % Position equatio ns for theta_4 and theta_5 Theta_4 = 2*atan((-r3+sqr t(r3^2+r2^2-C^2))/(C+r2)); Theta_5 = acos((-r2 +r4*cos(Theta_4))/r5); % Equations for omega_4 and omega_5 Omega_4 = -dr5_dt/(r4 *sin(Theta_4-Theta_5)); Omega_5 = -dr5_dt/r 5*cot(Theta_4-Theta_5); % Equations for alpha_4 and alpha_5 Alpha_4 = (-r4*Omega_4^2* cos(Theta_4-Theta_5)+r5*Omega_5^2d2r5_dt2)/(r4*sin(Theta_4-Theta_5)); Alpha_5 = (-r4*Omega_4^ 2-2*dr5_dt*Omega_5*sin(Theta_4Theta_5)+r5*Omega_5^2*si n(Theta_4+Theta_5)d2r5_dt2*sin(Theta_4+Theta_5))/ (r5*sin(Theta_4-Theta_5)); % This will add the r1 values for the plot of r1 plot_r1 = [plot_r1;r1']; % This will add the r5 values for the plot of r5 plot_r5 = [plo t_r5;r5']; % This will add the Theta_4 values for the plot of Theta_4 plot_Theta_4 = [plot_Theta_4;Theta_4']; % This will add the Theta_5 values for the plot of Theta_5 plot_Theta_5 = [plot_Theta_5;Theta_5']; % This will add the point p values for the plot of point p plot_p = [plot_p;fk(2),fl(2)]; % This will add the point dp_d t values for the plot of dp_dt plot_dp_dt = [plot_dp_dt;dr1_dtrp*Omega_4*sin(Theta_4+delta),rp *Omega_4*cos(Theta_4+delta)]; % This will add the point d2p_dt 2 values for the plot of d2p_dt2 plot_d2p_dt2 = [plot_d2p_dt2;d2r1_dt2(rp*Omega_4^2*cos(Theta_4+delta)+rp*A lpha_4*sin(Theta_4+delta)),Alpha_4*rp *cos(Theta_4+delta)-Omega_4^2*rp*sin(Theta_4+delta)]; % This will add the dr1_dt values for the plot of dr1_dt plot_dr1_dt = [plot_dr1_dt;dr1_dt']; % This will add the dr5_dt values for the plot of dr5_dt plot_dr5_dt = [plot_dr5_dt;dr5_dt'];
81 Appendix A (Continued) % This will add the d2r1_dt2 val ues for the plot of d2r1_dt2 plot_d2r1_dt2 = [plot_d2r1_dt2;d2r1_dt2']; % This will add the d2r5_dt2 values for the plot of d2r5_dt2 plot_d2r5_dt2 = [plot_d2r5_dt2;d2r5_dt2']; % if LOOP==-1 if LOOP==Steps-1 hold on pause(1) figure(2); plot(p lot_r1,'LineWidth',2) title( 'Link r_1 vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('inches','FontSize',12) pause(0.5) figure(3); plot(p lot_r5,'LineWidth',2) title( 'Link r_5 vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('inches','FontSize',12) pause(0.5) figure(4); plot(plot_Theta_4,'LineWidth',2) titl e('Theta_4 vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('rad','FontSize',12) pause(0.5) figure(5); plot(plot_Theta_5,'LineWidth',2) titl e('Theta_5 vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('rad','FontSize',12) pause(0.5) figure(6); plot(plot_dr1_dt,'LineWidth',2) title( 'dr_1/dt vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('inches/Seconds','FontSize',12) pause(0.5)
82 Appendix A (Continued) figure(7); plot(plot_dr5_dt,'LineWidth',2) title( 'dr_5/dt vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('inches/Seconds','FontSize',12) pause(0.5) figure(8); plot(plo t_d2r1_dt2,'LineWidth',2) title('d ^2r_1/dt^2 vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('inches/Seconds','FontSize',12) pause(0.5) figure(9); plot(plo t_d2r5_dt2,'LineWidth',2) title('d ^2r_5/dt^2 vs. Time') xlabel('Time (Seconds*100)','FontSize',12) ylabel('inches/Seconds','FontSize',12) pause(0.5) plot_dp_dt plot_d2p_dt2 for rp_loop = 1:Steps figure(10); plot (plot_p(rp_loop,1),plot_p(rp_l oop,2),'k+','LineWidth',4) grid off axis('square') titl e('Position of Point p') xlabel(' x axis (in)','FontSize',12) ylabel ('y axis (in)','FontSize',12) hold on end for rp_vel = 2:10:Steps figure(11); scale = 0.1; axis('square') quiver(plot_p(rp_vel,1),plot_p(rp_vel,2), plot_dp_dt(rp_vel,1),plot_dp_dt(rp_vel,2), scale,'k') xlabel(' x axis (in)','FontSize',12) ylabel ('y axis (in)','FontSize',12)
83 Appendix A (Continued) grid off hold on end end end
84 Appendix B Â– Bill of Material s for Horseback Riding Simulator Table B-1: Bill of Materials for Simulator
85 Appendix C Â– AutoCAD Drawings of Horseback Riding Simulator Figure C-1: AutoCAD Base Detail Drawing
86 Appendix C (Continued) Figure C-2: AutoCAD Support Tube Detail Drawing
87 Appendix C (Continued) Figure C-3: AutoCAD Track Detail Drawing
88 Appendix C (Continued) Figure C-4: AutoCAD Cylinder Joint A Detail Drawing
89 Appendix C (Continued) Figure C-5: AutoCAD Cylinder Joint B Detail Drawing
90 Appendix C (Continued) Figure C-6: AutoCAD Base Cylinder Holder Detail Drawing
91 Appendix C (Continued) Figure C-7: AutoCAD Support Rod Detail Drawing