A study of omnidirectional quad-screw-drive configurations for all-terrain locomotion

A study of omnidirectional quad-screw-drive configurations for all-terrain locomotion

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A study of omnidirectional quad-screw-drive configurations for all-terrain locomotion
Freeberg, Jon
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[Tampa, Fla]
University of South Florida
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Dissertations, Academic -- Mechanical Engineering -- Masters -- USF ( lcsh )
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ABSTRACT: Double-screw vehicles have been developed to operate in soft, wet terrains such as marsh, snow, and water. Their exceptional performance in soft and wet terrains is at the expense of performance on rigid terrains such as pavement. Furthermore, turning can be difficult because the method of turning varies depending on the terrain. Therefore, in this study, several different quad-screw-configurations were proposed and tested to improve upon double-screw vehicles. A test-bed was developed which could easily be converted into each quad-screw-configuration for testing on a variety of surfaces (grass, dirt, sand, clay, marsh, snow, gravel, pavement, and water). In addition, a force-vector analysis was performed for each screw-configuration to predict and understand performance in different terrains. From the testing and analysis, the inline-screw configuration was the most versatile because it was omnidirectional on all surfaces but water and pavement. Regardless, it was fully capable of navigating water, both on the surface and submerged, and pavement by rotating about its center.
Thesis (MSME)--University of South Florida, 2010.
Includes bibliographical references.
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by Jon Freeberg.

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A study of omnidirectional quad-screw-drive configurations for all-terrain locomotion
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by Jon Freeberg.
[Tampa, Fla] :
b University of South Florida,
Title from PDF of title page.
Document formatted into pages; contains X pages.
Thesis (MSME)--University of South Florida, 2010.
Includes bibliographical references.
Text (Electronic thesis) in PDF format.
Mode of access: World Wide Web.
System requirements: World Wide Web browser and PDF reader.
3 520
ABSTRACT: Double-screw vehicles have been developed to operate in soft, wet terrains such as marsh, snow, and water. Their exceptional performance in soft and wet terrains is at the expense of performance on rigid terrains such as pavement. Furthermore, turning can be difficult because the method of turning varies depending on the terrain. Therefore, in this study, several different quad-screw-configurations were proposed and tested to improve upon double-screw vehicles. A test-bed was developed which could easily be converted into each quad-screw-configuration for testing on a variety of surfaces (grass, dirt, sand, clay, marsh, snow, gravel, pavement, and water). In addition, a force-vector analysis was performed for each screw-configuration to predict and understand performance in different terrains. From the testing and analysis, the inline-screw configuration was the most versatile because it was omnidirectional on all surfaces but water and pavement. Regardless, it was fully capable of navigating water, both on the surface and submerged, and pavement by rotating about its center.
Advisor: Stuart Wilkinson, Ph.D.
Dissertations, Academic
x Mechanical Engineering
t USF Electronic Theses and Dissertations.
4 856
u http://digital.lib.usf.edu/?e14.4717


A Study of Omnidirectional Quad Screw Drive Configurations for All Terrain Locomotion b y Jon T Freeberg A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Mechanical Engineering Department of Mechanical Engineering College of Engineering University of South Florida Major Professor: Stuart Wilkinson, Ph.D. Craig Lusk, Ph.D. Kyle Reed, Ph.D. Date of Approval: October 2 6 2010 Keywords: Amphibious, Submarine, Robot, Trafficability, Dynamics Copyright 2010 Jon T. Freeberg


i TABLE OF CONTENTS LIST OF TABLES i v LIST OF FIGURES v NOMENCLATURE i x ABSTRACT x CHAPTER 1: BACKGROUND 1 1.1 Fundamentals 1 1.2 History of S crewV ehicles 3 1.3 Applications 5 CHAPTER 2: PREVIOUS RESEARCH 8 2.1 Important S tudies 8 2.2 S crew D esign P arameters 1 1 2.2.1 Helix An gle 1 2 2.2.2 Blade H eight to Drum D iameter R atio 1 2 2.2.3 Number of S tarts 1 3 2.2.4 Lengthto Drum D iameter R atio 1 3 2.2.5 Blade T hickness 1 4 2.2.6 Center of G ravity 1 5 2.3 Trafficability T ests 1 6 2.3. 1 Sand 1 7 2.3.2 Fine G rained S oil 1 8 2.3.3 Snow 20 2.3.4 Water 20 2.3.5 Trafficability T ests S ummary 2 1 CHAPTER 3: THE DOUBLESCREW 2 3 3.1 Capabilities 2 3 3.1.1 CounterR otating S crews 2 5 3.1.2 Co R otating S crews 2 6 3.1.3 Turning 2 7 3.2 Limitations 31 CHAPTER 4: ALTERNATIVE SCREW CONFIGURATIONS 3 4 4.1 Overview 3 4 4.2 Bendable S crew 3 4


ii 4.3 Split Screw 3 6 4.4 Inline Screw 3 9 4.5 Cross Screw and D iamond Screw 4 4 CHAPTER 5: THE TERRAIN TWISTER 4 8 5.1 Description 4 8 5.2 Test Bed C onstruction 4 9 5.3 Test C omparison 51 CHAPTER 6: QUAD SCREW TEST BED CONSTRUCTION 52 6.1 Test Bed F rame 52 6.2 S crewA ssemblies 56 6.3 Wiring and C ontrols 5 7 6.4 Modifications 60 CHAPTER 7: EXPERIMENTS 64 7.1 Experimental G oals 64 7.2 Methodology 65 7.2.1 Test Locations 65 7.2.2 Testing Directions 6 7 7.2.3 Test Setup 6 8 7.3 Test Observations 69 7.3.1 Grass 69 7.3.2 Dirt 71 7.3.3 Marsh 73 7.3.4 Sand 74 7.3.5 Clay 76 7.3.6 Pavement 7 8 7.3.7 Gravel 8 1 7.3.8 Surface of Water 83 7.3.9 Underwater 85 7.3.10 Snow 87 7.3.11 Split Screw Tests 88 7.4 Turning Radius 8 9 7.5 Test Summary 9 2 CHAPTER 8: CONCLUSIONS 99 LIST OF REFERENCES 101 BIBLIOGRAPHY 103 APPENDICES 105 Appendix A : S Diamond Screw Force Vectors 106 Appendix B : S Cross Screw Force Vectors 10 7 Appendix C : Mirrored TestBed Force Vectors 10 8 Appendix D: Terrain Twister Screw Calculations 1 11




iv LIST OF TABLES T able 1: Terrain Twister screw geometry 50 Table 2: Turning diameter and turningratio in marsh 90 Table 3: Quad screw performance matrix 9 2 Table 4: Doublescrew performance matrix 94 Table A1 : Ter rain Twister screw measurements 1 11


v LIST OF FIGURES Figure 1: Riverine Utility Crafts (RUC) speed versus terrain firmness 3 Figure 2: The Fordson Snowmobile 4 Figure 3: A snake like screw robot 5 Figure 4: The Snowbird 6 7 Figure 5: Dr. B.N. Cole working with a model screw vehicle 9 Figure 6: The Marsh Screw Amphibian 10 Figure 7: An illustration of important screw parameters 1 1 Figure 8: The RUCs blade support 1 4 Figure 9: The RUCs center of gravity 1 5 Figure 10: A cone penetrometer 1 7 Figure 11: The MSA buried on pass 36 1 9 Figure 12: The RUC performing a mine sweep test 2 1 Figure 13: Rollingand tractive forces imparted on screws by a soft terrain 2 4 Figure 14: Screws counter rotating on different surfaces 2 6 Figure 15: Screws co rotating in different terrains 2 7 Figure 16: Screws skidturning on soft ground 2 8 Figure 17: The turning radius of hinged screws 30 Figure 18: The minimum turning radius for hinged screws 30 Figure 19: An example of hinged screws 3 3


vi Figure 20: Red and blue halves experiencing alternating tension 3 5 Figure 21: M odes of rotation for a bendable screw 3 6 Figure 22: Top view of the splitscrew layout 3 7 Figure 23: Four symmetric screw rotations for the splitscrew 3 8 Figure 24: A top view of the inline screw 3 9 Figure 25: The turning radius of an inline screw 40 Figure 26: The turning radius of an inline screw superimposed on a hinged screws turning radius 41 Figure 27: Four symmetric screw rotations for the inline screw 42 Figure 28: Reversing the direction of rotation for each symmetric switch pattern results in the opposite direction of locomotion 4 3 Figure 29: Model of the inlinescrew 4 4 Figure 30: Models of the cross screw and diamond screw 4 4 Figure 31: The patented cross screw and diamondscrew configurations 4 6 Figure 32: Four symmetric screw rotations for the diamondscrew 4 6 Figure 33: Four symmetric screw rotations for the cross screw 47 Figure 34: The Terrain Twister screw assembly 49 Figure 35: Right plane, testbed model 5 3 Figure 36: A PVC end cap with the spring for battery contact 5 4 Figure 37: Fro nt plane, testbed model 5 5 Figure 38: Trimetric, test bed model 5 5 Figure 39: A photograph of the testbed 56 Figure 40: The barrier strip wiring 58 Figure 41: The switchbox wiring 59


vii Figure 42: Switch patterns for forward, right and clockwise locomotion 6 0 Figure 43: The author shown alongside the testbed 61 Figure 44: The floating testbed setup 6 2 Figure 45: The inflatable tube used to suspend the testbed 63 Figure 46: An example of the test setup 68 Figure 47: Test setup for grass terrain 7 0 Figure 48: Tracks from the inline screw deviating in dirt 7 2 Figure 49: Tracks in marsh left by the inline screw 7 3 Figure 50: Sand terrain test setup 75 Figure 51: The test setup for clay terrain 76 Figure 52: Inline screw tracks in clay 77 Figure 53: Diamond screw rotation tracks in clay 78 Figure 54: The crossscrew on pavement 79 Figure 55 : Inline screw performance with m inimal tractive force influence such as on pavement 80 Figure 56 : Test setup for gravel terrain 81 Figure 57 : Path from the diamondscrew rotating in gravel 82 Figure 58 : Test setup for the surface of water 84 Figure 5 9 : Inline screw performance with minimal rolling force influence such as on water 85 Figure 6 0 : Underwater view during testing 86 Figure 6 1: Test set up for underwater testing 86 Figure 62 : The test course for snow 87 Figure 63 : The plan and turning diameter 89 Figure 64 : The double screws rotation tracks left in marsh 91


viii Figure 65 : Test bed rotation tracks left in marsh 91 Figure 66 : A graph illustrating the correlation between forward speed and percent slip 9 5 Figure 67 : Longitudinal speeds for the testbed configurations in different terrains 9 6 Figure 68 : The test bed setup for the cross screw and diamondscrew in water 97 Figure 69 : Lat eral speeds for the testbed configurations in different terrains 97 Figure 70 : Rotational speeds for the testbed configurations in different terrains 98 Figure A1 : Four symmetric screw rotations for the S diamondscrew 10 6 Figure B1 : Four symmetric screw rotations for the S cross screw 107 Figure C1 : Four symmetric screw rotations for the mirrored inline screw 108 Figure C2 : Four symmetric screw rotations for the mirrored diamond screw 10 9 Figure C3 : Four symmetric screw rotations for the mirrored c ross screw 110 Figure D1 : The Terrain Twisters major diameter and lead 11 2


ix NOMENCLATURE Symbol Description Units c C enter to center of screws in h Blade height in l Drum length in r Turning radius in D Drum diameter in Dm Screws major diameter in L Screws lead in N Number of blade revolutions non dimensional T Travel distance ft Hinge angle o Helix angle o Acronyms Description C.G. Center of gravity MSA Marsh Screw Amphibian RCI Rating cone index RUC Riverine Utility Craft VCI Vehicle cone index


x A S TUDY OF O MNIDIRECTIONAL QUAD SCREW DRIVE CONFIGURATIONS FOR ALL TERRAIN LOCOMOTION JON T. FREEBERG ABSTRACT Double s crew vehicles have been developed to operate in soft, wet terrains such as marsh, snow, and water. Their exceptional performance in soft and wet terrains is at the expense of performance on rigid terrains such as pavement. Furthermore, turning can be difficu lt because the method of turning varies depending on the terrain. Therefore, in this study, several different quadscrew configurations were proposed and tested to improve up on double screw vehicle s A testbed was developed which could easily be converted into each quad screw configuration for testing on a variety of surfaces (grass, dirt, sand, clay, marsh, snow, gravel, pavement, and water) In addition, a force vector analysis was performed for each screwc onfiguration to predict and understand performance in different terrains. From the testing and analysis, the inline screw configuration was the most versatile because it was omnidirectional o n all surfaces but water and pavement. Regardless, it was fully capable of navi gating water, both on the surface and submerged, and pavement by rotating about its center.


1 CHAPTER 1: BACKGROUND 1.1 Fundamentals Wheeled and tracked vehicles are a proven and effective means of locomotion for a wide range of surfaces. Nonetheless, there are conditions in which both means of locomotion have shortcomings. For instance, both vehicles encounter difficu l ty with marshy environments in which the grounds bearing strength is minimal. In such ex treme off road environments, it can be nearly impossible to prevent the vehicle from sinking and becoming immobilized. In order to understand the degree of effectiveness a wheeled or tracked vehicle will display on a given surface, it is important to understand how it works. Note that while they may have dissimilar performance on a given surface, the underlying principle they use to provide locomotion is the same. Conventional wheeled and tracked vehicles depend up on soil bearing strength for support, and on frictional and cohesive soil shear strength for propulsion. [ 1 ] Clearly, most wheels and tracks provide negligible buoyancy to a vehicle, as is evident in a vehicle sinking in water or a soil of high moisture content. Furthermore, spinning tires on a slippery road demonstrate a wheel


2 or tracks friction al requirement. Finally, wheels that are digging a hole in loose sand underscore the need for cohesive soil shear strength. A novel locomotion concept, which may resolve the shortcomings of wheeled and tracked vehicles, consists of two counterrotating, buoyant screws. The buoyant screw relies on completely different principles for locomotion as compared to a wheeled or tracked vehicle. [ ] the support function is fulfilled by buoyant flotation, rather than by intrinsic soil strength. Propulsion is accomplished by viscous shear and reaction to mass movement of the medium, rather than by friction and cohesion in the soil mass. [ 1 ] Since the s crew provides buoyant flotation, its application extends beyond surfaces of great moisture content to the surface of water itself. However, since the locomotion is generated by mass movement of a medium, it is restricted to nonrigid surfaces. On a solid and rigid surface, such as pavement, the blades rest on the surface and, in turn, operate on the same principle of locomotion as a wheel or track; an exception is ice in which a metal screw is able to carve into i t. Though no specific studies we re available regarding the mechanism for how a screwvehicle works on ice, it has been shown to work. It can be surmised that screwvehicles operate much like an ice skater digging into the ice. Considering the nature of each locomotion system, it is understandabl e that the performances of screw vehicles are nearly the opposite of wheeled and tracked vehicles for different surfaces [ 1 ]. Figure 1 shows the speed of the Riverine Utility Craft screw vehicle The Riverine Utility Craft, or RUC, is a full scale double screw military testbed vehicle. It shows screw vehicle s


3 operate in water and o n soil, but are optimal where conventional vehicles are not. Figure 1 : Riverine Utility Crafts (RUC) speed versus terrain firmness [ 2 ] Note: all values are in generic units. 1.2 History of S crew V ehicles 1804 : A screw steamboat is driven by Colonel John Stevens on New Yorks North River [ 3 ] 1841 : Thomas J Wells patents the buoyant spiral propeller in which the screw provides buoyancy to the vessel [ 1 ] Late 1920s : The Fordson snowmobile is built; demonstrating snow and ice performance [ 3 ]


4 Figure 2 : The Fordson Snowmobile [4 ] 1948 : An amphibious screw tractor is proposed in England by Lt. Col. H.O. Nelson [ 3 ] Early 1950s : A M29C W easel tank is outfitted with screws to replace treads and is tested in Greenland by the US army [ 3 ] 1957 : A German firm demonstrates a screw amphibian at the Hanover exhibition [ 3 ] 1960s : The Russians develop a screwtank to pick up and drop off cosmonauts in heavy snow [5] 1966 : A patent for a ma rsh screw vehicle is awarded to R.G. Schrader [ 3 ] 2001 : The Snowbird 5 fails to cross the Bering Strait due to damage to its pontoon [5] 2002 : The Snowbird 6 is developed and successfully crosses the Bering Strait [5] 2005 : The Tyco Terrain Twister toy is patented [6] 2007 : A snake like, screwrobot is researched [7]


5 Figure 3 : A snake like screw robot [7] 1.3 Applications As discussed in section 1.1, screw vehicles fill an important gap in vehicle performance between the terrainnavigating capabilities of boats and standard wheeled and tracked vehicles. Specifically, in shallow, marshy environments, boats risk damaging the propeller or becoming grounded, whi le wheeled and tracked vehicles perform poorly in saturated ground. Conversely, a screw vehicle performs best in marshy environments [ 7 8 ] Another terrain condition not discussed is snowy ground. Screw vehicles perform well in deep, powdery snow. On the contrary a boat will not operate in snow, while wheeled and tracked vehicles must be specialized for snow in order to perform well Therefore, a vehicle that must cross marshy or snowy surfaces would benefit from screw locomotion An important advantage of a screw vehicle is its capability of traversing a wide rang e of environments without altering the vehicle. Amphibious cars and tanks have been developed, but they typically require a


6 transformation of their locomotion method or vehicle body to go from land to water. In contrast, a buoyant screw can provide flotation and it propels the vehicle aground and afloat. All in all, a screw vehicle can operate on the ocean floor, on top of water, submerged and above the ocean floor, in marshes, snow, sand, dirt, grass, ice and, to a limited extent, pavement. Some exampl es of screw vehicles that have been built in the past include: MudMaster (2009) : T he MudMaster was u sed for bauxite residue production in the alumina refining industry. It was u seful for the alumina industry due to the screw vehicles effectiveness in mud and wet clay [10] Basin cleaning vehicle (BCV) (1999) : T he BCV was d eveloped to crawl along lakebeds to remove sediment Lakebed sediment impedes the percolation process that provides natural filtration to water supplies [1 1] Icy water, oil recovery vehicle (1996) : A n oil recovery vehicle concept was considered by Sintef The concept use d screws to deflect ice and help collect spilled oil. The device was proposed to operate similar to a drum skimmer [12] Snowbird 6 (2002 ) : Th e Snowbird 6 vehicle crossed snowy Alaskan terrain and the Bering Strait using two counterrotating screws [5]


7 Figure 4 : The Snowbird 6 [5] Spiral Track Autonomous Robot (STAR) (1996) : The STAR was a screw robot designed for hostile terrain. Specifically, it was designed for American police and military personnel [13] Terrain Twister (2005) : The Terrain Twister was a toy which use d screws to go over terrains that most toys would not ; including snow and water.


8 C HAPTER 2: PREVIOUS RESEARCH 2.1 Important S tudies The concept of a screw vehicle dates back as early as the 1800s [ 3 ] with the sc rews team boat, and in the 1920s it was first used on land with the Fordson snow tractor [9] More recently, screw vehicles have seen ni che applications, including the Snowbird 6 used to cross the Bering Strait. [5] However the 1960s was the period in which m uch of the rigorous research regarding screw vehicles was performed. Specifically, in the 1960s screw design parameters were developed and screw vehicle trafficability studies were performed. In 1961 a pilot study on screw design was published in England by Dr. B.N Cole [14] and it serves to be an important technical report concerning amphibious screw vehicles. Within Dr. Coles report is a theoretical investigation of screw design parameters such as the blades helix angle and the screw s overall length. His research was for operation in and out of water. In supplement to the theoretical modeling, a scale model was built to compare six sets of left and righthanded screws. These screws were used to reveal how actual data compared with his theoretical calculations. The sets of screws consisted of three 13 inch short screws and three 22.3 inch


9 long screws. Each group of long and short screws consisted of one set of 20o, 30oand 40ohelix angles. The study performed by Dr Cole was an important starting point for the investigation of screwvehicles, but was only a pilot study of a scale model. Furthermore, Dr. Coles research on soil trafficability was limited to highly frictional soils [ 3 ]. Around the same time as Dr. Coles research, Chrysler Corporation Defense Engineering under contrac t with the Advanced Research Projects Agency developed the M arsh Screw Amphibian (MSA) testbed prototype. The MSA was designed to be capable of carrying a payload of half of a ton [ 3 ]. Figure 5 : Dr. B.N. Cole working with a model screw vehicle [14] In the fall of 1961, Chrysler built a 1/8 scale demonstration model of the MSA. The proof of concept was successful and in June of 1962, the Navys Bureau of Ships, or BuShips, directed Chrysler to build a 1/5 scale model to determine screw design parameters. The screw design parameters


10 considered were the optimum lengthto diameter ratio, the height of the screw blade the blade s helix angle, and if 1 2 or 4 starts should be used. In addition, horsepower requirements and the screws slip were investigated on land and water [15] On December 31, 1962 the first full scale model of the MSA was built. From the preliminary testing, 26 inch diameter drums, 32o helix angle blades, and double start blade s were used for the s crews. The screws drum is the portion of the screw that the blade wraps around. It was tested at the Detroit River, Chelsea, Michigan, and Michoud, Louisiana for 100 hours. After the initial tests, BuShips requested Chrysler perform a study on screw parameters in order to optimize water performance. From August to October 1963, the US Army Engineer Waterways Experiment Station, or WES, performed 124 trafficability tests in Louisiana. In the meantime a second MSA was built for snow tests. In February 1964, the second MSA was tested in snow conditions at Houghton, Michigan [15] Figure 6 : The Marsh Screw Amphibian [1].


11 The stud ies on the MSA provided much of the information regarding screw parameters and terrain trafficability used in this thesis In addition, its success led to the development of another screw vehicle program aimed at developing a finalized and practical vehicle. On July 25 1969, the Naval Ship Systems Command requested the US Army Engineer Waterways Experiment Station, or WES, to test Riverine Utility Crafts, or RUCs [9] Similar to the MSAs, the studies on the RUCs were useful in this thesis 2.2 S crew D esign P arameters There are several parameters to consider for a screw design. Some considerations for the screws blade are its helix angle, height, and number of starts. Furthermore, considerations for the screwdrum include its length and diameter. Each of the above parameters have been previously researched in the studies outlined in section 2.1 and are documented in thi s section. Figure 7 : An illustration of important s crew p arameters


12 2.2.1 Helix A ngle. Dr Cole performed tests on screw s comparing helix angles. The helix angles tested were 20o, 30o and 40o and tests were conducted aground and afloat. Chrysler also compared the helix angle o f the blades; including, 30o, 40o and 50o. From Dr. Coles ground experiments, 20o drew the most power from the screws motors and created the greatest amount of ground deformation [14] One benefit of the 20o screw was that it had the best drawbar pull capability. Drawbarpull is a test used to determine the ratio of weight an off ro ad vehicle can tow in comparison to its own weight. In contrast to the 20o screw s, the 40o screw s required the least power but had the greatest amount of slippage [14] The results of Dr. Coles hydrodynamic experiments show that the greater the helix ang le, the greater the axial thrust and driving torque developed [14] They also show that the propulsive efficiency is maximized at 30o. Furthermore, referring back to the ground experiments, it is shown that the vehicle performance gap, as determined by the screw s slippage and power usage, is less between 30o to 40o than it is between 20o to 30o[14] In addition, the drawbar pull is nearly maximized at 30o, with minimal improvement as the helix angle decreases [ 3 ]. Therefore, combining the results of the aground and afloat tests, the optimum helix angle is 30o or slightly larger. In fact, the helix angle chosen for the RUC was 32o [15] 2.2.2 Blade Height to D rum D iameter R atio. In all of Dr Coles tests, a bl ade height to drum diameter ratio of 0.375 was used. He concluded that, from the perspective of propulsive surface area and structural strength of the blades, a ratio of 0.375 was adequate [14] The


13 tests performed by Chrysler included ratios of 0.125, 0 .167 and 0.208 [ 3 ]. The experiments show that increasing the blade s height increases the weight of the failure surface in sand. The increased weight of the failure surface increases the drawbar pull but the effect is minimal [ 3 ]. Chrysler tested blade height in muddy conditions and found that increasing the height reduced effectiveness of the vehicle. In particular, the increased blade height captured more mud and resulted in greater motion resistance [ 3 ]. Overall based off of the blade height to drum diameter ratios tested, 0.125 is the ideal ratio. 2.2.3 Number of S tarts. Not much information is available r egarding the impact of the number of starts for a screw vehicle Nonetheless, Chrysler did perform a study to determine the ideal number of starts Though the study details we re not available, it is apparent that two starts is optimal. The RUC and MSA vehicles each have a design in which there are two starts per screw [ 8 14 ]. Furthermore, Dr. Cole mentions in his research that two starts would be more dynamically balanced than one [14] 2.2.4 Length to D rum Diameter R atio The lengthto drum diameter ratio is an important parameter because it ha s the greatest influence on the drawbarpull capacity compared to the helix angle or blade height [ 3 ]. Unlike the other parameters, the lengthto diameter ratio does not have a monotonic trend of just increasing or decreasing performance as the ratio increases or decreases [ 3 ] Fortunately, when tests were


14 performed in mud and sand, it was determined the optimum ratio was 6 for both mediums [ 3 ]. Another consideration is that increasing the length also increases the number of re volutions of the blade Dr. Cole theorized that increasing the number of re volutions would have an impact on hydrodynamic driving torque and thrust [14] From his tests, Dr. Cole conclude d that longer screw s with more rotations produce much larger driving torque and thrust [14] 2.2.5 Blade T hickness. The performance due to the thickness of the blades i s not explicitly discussed in any available studies. The blades w ere likely made thick enough to withstand the stresses imparted by the weight of the vehicle and terrain interaction. Also, t he material used plays an important role in determining the required structural thickness. It is not entirely evident if there is any importance from the standpoint of performance, but there may be potential impact when on ice. During shock testing of the RUC, the 0.5 in ch blades on a 39 in ch diameter drum, did not fail. However, the screw s cracked from loads imparted by the blades [ 2 ]. In order to reduce stresses, the blade height was reduced and a support was added [ 2 ]. The support brace was added to the side of the blade opposite of the pushed ground when the vehicle was moving forward. Figure 8 : The RUC s blade support [2]


15 2.2.6 Center of G ravity. Although the location of the longitudinal center of gravity, abbreviated as C.G., is not inherently a characteristic of the screw it is still worth mentioning for screw vehicle design. Tests were performed by Chrysler to determine the effects of the location o f the C.G. by placing the C.G. at four locations. The locations selected for the testing were 25% forward of the midpoint, at the midpoint, 12.5% aft of the midpoint, and 25% aft of the midpoint [ 3 ]. Effectiveness of the C.G. location was determined by monitoring the drawbarpull capacity as the slip percentage increased. Typically, as slippage increases, the drawbarpull capacity increases [ 3 ]. However, in sand it was shown that when the C.G. was at the front of the vehicle it began to plow into the sand as slippage increase d [ 3 ] The final results show that the vehicle operates best in sand with the C.G. at the midpoint or a little aft, and when in mud it works best when the C.G. is at the midpoint [ 3 ]. Figure 9 shows that the C.G. is near the midpoint for the RUC. Figure 9 : The RUC s center of gravity [9]


16 2.3 Trafficability T ests In order to understand the performance of off road vehicles, it is important to perform trafficability tests. Trafficability tests are tests performed in a uniform terrain that reveal vehicle to terrain behavior [9] Tests may include maximum straightli ne speed tests, maximum maneuver speed tests, drawbarpull tests, and repetitive pass, or vehicle cone index, tests [9] The tests performed on screw vehicles were meant to determine worstcase operating conditions. As a result, many of the tests resulte d in vehicle immobilization. Maximum straightline speed tests and maximum maneuver speed tests are exactly what their names imply. They test the fastest a vehicle can possibly travel in a straight line or maneuver through an obstacle course. Drawbarpul l tests are used to determine the ratio of weight an off road vehicle can tow in comparison to its own weight, and are among the best tests for determining off road vehicle performance [ 3 ]. Vehicle cone index, or VCI, is a measure of the minimum rating co ne index, or RCI, required for a terrain to support a vehicle for a specified number of passes [9] Typically, 50 passes are specified for the VCI test. The number of passes a VCI is tested at is indicated with a subscript showing the number of passes. Therefore, a 50 pass test is VCI50. The RCI is a measure of soil strength, where a low RCI is a soft soil [9] The value of RCI is found with a tool called a penetrometer.


17 Figure 10 : A c one p enetrometer [9] 2.3.1 Sand. Sand is characterized by a high coefficient of friction and minimal particle cohesion when dry [8] From trafficability tests performed on the MSA it is evident that characteristics of sand work against screw vehicle performance. The RCI of the sand averaged at 95 and ranged from 46 159 during the testing but it was determined that the impact of the RCI was minimal in sand [8] During repetitive pass tests, the MSA displayed difficulty driving straight when unloaded. Furthermore, when it was loaded, it could only make 2 to 3 passes at full throttle [8]. An explanation is when the MSA wa s unloaded the blades may not have dug in as much and skip ped. Alternatively, while loaded the screws may have need ed more power to rotate. When driving slower, the MSA was able to complete 50 passes. The MSA was unique to conventional vehicles because it encounter ed increased difficulty on successive passes after the first pass [8] Conventional vehicles, on the other hand, can make an indefinite number of passes on loose dry sand if they can make the first pass [8] The maximum speed tests showed the MSA travelled slowly in sand with 2.3 mph at the fastest and 1.0 mph at the slowest in full throttle [8] Also, the MSA could not pass any maneuver tests without becoming


18 immobilized. In add ition, the drawbarpull of the MSA was much less than an equivalently powerful tracked vehicle, t he M29C Weasel. The M29C Weasel was considered to display trafficability results that we re standard for tracked vehicles [8] Dr. Coles testing in sand was m ore optimistic than the MSA trafficability tests. During Dr. Coles testing of screw performance, he noted that the screws deformed the ground the most over loose, dry sand [14] However, he added that the ground deformation was not as bad for screws as for conventional wheels [14] He further noted that drawbarpull capacity increased for greater sand compaction and moisture content [14] Tests showed the MSA travelled laterally with ease. Therefore, the difficulty of the MSA in sand was due to its screws. More specifically, the poor performance of a screw vehicle in sand was attributed to the frictional resistance of sand me eting or exceeding the tractive force of the screws [8 ] 2.3.2 Fine G rained S oil. T rafficability tests were performed on the MSA in fine grained soils of varying moisture content and RCI values. The MSA was able to operate in softer terrain with a VCI50 of 5 compared to the M29C Weasel with a VCI50 of 15 [8] The tests showed that the moisture content of the soil played a larger role in performance than the RCI. More importantly, the less friction, the better the MSA performed [8] An example of the importance of reducing friction was the MSA showed improved performance when there was slick grass on the soil [8] The MSA performed better than the M29C Weasel in many of the fine grained soil tests. Nonetheless, due to the demanding nature of trafficability


19 studies, there were several conditions that immobilized the MSA. In soil that was too soft to support the MSA, the carriage bulldozed into the soil. When the carriage bulldo zed into the soil, the tractive force of the screw s was less than the motion resistance from the bulldozing [8] The researc hers noted that if the soil was wetter, the soil c ould have been marshy enough to minimize the bulldozing from the carriage and permit locomotion [8] Another condition that immobilized the MSA was when the soil was sticky, soft, and dry. In sticky, soft and dry soil, the soil adhered to the screw s and prevented the screw s from turning [8] When the same soil was moistened with water, the MSA was able to pass the terrain [8] Figure 11 : The MSA buried on pass 36 [8] Maximum speed tests showed that the MSA went as fast as 5 mph on the softest soil tested with an RCI of 10. When the RCI was as firm as 20, the speed dropped to 2 mph. The MSA was also tested on soil with 3 to 6 inches of water on the surface of the soil, and the vehicle reached speeds of nearly 20 mph [8]


20 The overall performance of the MSA can be simplified to less friction is better, and although soft soil is typically ideal it cannot be generalized as being optimum. For example, soft soil can allow the vehicle to sink and bulldoze. In addition, drawbarpull tests showed maximum pull test values at an RCI of 40, because the soil was firm enough to limit rutting but soft enough to allow blade penetration [8] A potential solution to the first issue is to design a vehicle in which the screws provide sufficient flotation to keep the hull out of the soil. 2.3.3 Snow. The MSA was also tested in deep snow. Based on the results of the fine grain soil testing, snow has ideal characteristics for locomotion The actual report concerning the snow tests could not be obtained, but a paper summarizing the various MSA trafficability tests mentions that the MSA reached speeds of 20 to 25 mph in deep snow [ 1 ]. In comparison to the speeds of 2 to 5 mph in dry soil, it is evident that the MSA performs well in snow. The MSA travelled at approximately 20 mph in mud with a large layer of water, slightly slower than snow, further emphasizing the importance of low friction on the performance of the MSA. 2.3.4 Water. Dr. Cole performed a variety of tests on screws in water. He placed the screw s in four different water depths to observe the differences in torque and thrust. Specifically, he experimented with the screw axis 12 inches below the surface and 3 inches below the surface, the blade tip slightly breaking the surface, and with the screw axis directly at the surface [14] When the depth of immersion was less, the torque and thrust decreased [14] Specifically, when the screw was exposed to air, the torque


21 and thrust significantly dropped [14] C learly, the torque and thrust reached a maximum at the deep immersion condition. With the screw axis submerged 12 inches, the torque and thrust were nearly proportional to the square of the rotational speed of the screw [14] Dr. Cole ran the screw s at speeds of up to 2300 RPM with no cavitation [14] Tests were also performed in water on the MSA. The primary observations made from tests in water were that it was stable in water and responded readily to steering [8] In addition, the maximum speed the MSA travelled a t in water was 5 to 6 mph [8] The speed the MSA travelled at in water was similar to the soft, dry terrain but not as fast as the soft and wet terrain. Figure 12 : The RUC performing a mine sweep test [ 2 ] 2.3.5 Trafficability Tests S ummary. From the testing on the MSA, it was concluded that its performance spectrum was the opposite of wheeled and tracked vehicles. Specifically, the MSA perform ed better in wet and soft soils of low friction in comparison to dry firm friction al soils [ 1 ] They also concluded that it was largely unaffected by vegetation, it work ed well in


22 water and work ed best in mud, excluding sticky mud, of low water content, that is firm enough to walk on. Sticky, dry and firm mud had a tendency to stick t o the screw s enough to seize them up [ 1 ]. Also, it was shown that the screw vehicle should be heavy enough for blade penetration, but not so heavy that the power required to rotate is too large. The trafficability tests discussed provide a detailed account of a screw vehicles performance. However, all of the testing reviewed has been limited to double screw vehicle s Furthermore, after Chryslers MSA testing, they concluded that future tests were desirable for hard ground maneuverability and for improvements in sand [15]


23 CHAPTER 3: THE DOUBLE SCREW 3.1 Capabilities All of the studies discussed thus far were about vehicles with a single pair of opposite handed screws. In this thesis the screw configuration just described is called the double screw, and applies to any vehicle or robot that employs this mode of locomotion. As will be discussed, many more configurations of screws can exist for a screwvehicle, so the names must be kept simple. In this study, three basic mo tions are necessary for a screw vehicle to be considered omni directional. Longitudinal : F orward and backward locomotion Lateral : T ransverse locomotion similar to a crabs locomotion Rotational : L ocomotion that is ideally about the vehicles center. Figure 13 shows the forces imparted on left and righthanded screws by a compliant surface. Specifically, figure 13 shows what is termed tractive and roll ingforce in this study The tractive force is along the screws axis while the roll ing force is directed pe rpendicular to the screws axis Clearly, tractive and rollingforces depend on the direction of rotation and the handedness of the screws blade.


24 A ) B ) C ) D ) Figure 13 : Roll ing and tractive forces imparted on screws by a soft terrain A) Right hand, clockwise B) Left hand clockwise C) Right hand counter clockwise D) Left hand counter clockwise The tractive and rolling forces are what cause locomotion Therefore, the tractive force pushes a screw longitudinally forward or backward. Alternatively, the rolling force produces lateral left and right, locomotion Through different orientations of screws and different directions of screw rotation, a variety of directions of net locomotion are possible. In this study, all of the screws we re assumed to rotate at the same speed. Therefore, all tractive forces were considered equal, and all rolling forces were considered equal. However, the tractive and rolling forces were not necessarily the same The tractive and rollingforces werent always considered the same because the magnitude of each force would vary depending on the helix angle, the friction between the screw and terrain, the


25 depth of penetration of the screws blade, the cohesion of particles within the terrain, and the terrai ns softness. 3.1.1 Counter Rotating S crews. With the double screw longitudinal locomotion is achi eved in water and soft terrain by simply counter rotating the screws at the same speed. On rigid surfaces, excluding ice the screws cannot easily dig into the ground and so the tractive forces that produce forward or backward locomotion are negligible On the contrary, friction and, as a result, rollingforces are sufficient for locomotion on pavement Since rolling forces are friction dependent, on low friction water the rollingforces are negligible compared to the tractive forces F igure 14 show s the forces imposed on a pair of screws and the resulting locomotion It should be noted that by reversing the directions of the counter rotating screws the system moves in the opposite direction.


26 A) B) C) Figure 14 : Screws counter rotating on different surfaces A) Compliant surface B) Rigid surface (small force) C) Water 3.1.2 Co R otating S crews. On paved ground, if both screws are rotated in the same direction and speed, a crablike, lateral locomotion is produced. In contrast to longitudinal locomotion pure lateral locomotion is only possible on paved or other rigid surfaces. The fact that a double screw cannot move longitudinally but can move laterally on pavement is similar to why the opposite is true of a bicycle. When the wheels on a bicycle are counter rotated, no meaningful locomotion is produced. However, forward and backward locomoti on is viable when rotated in the same direction. In both cases the vehicles cannot travel along the axis of rotation and locomotion is only produced when the wheels are moved in the same direction.


27 In soft ground, a double screw vehicle with co rotating s crews will travel in a curved path. The path is more curved in softer soil because the blades interact with the soil more Therefore, pure lateral locomotion does not occur on soil for a double screw Similarly, lateral locomotion is not possible on water with a double screw On water, the rollingforce of the screw is negligible, and the screws produce a net rotational loco motion Figure 15 illustrates how a double screw moves on different surfaces when the screws are turned in the same direction. Again, reversing the direction of the sc rews will move the double screw in the opposite direction. A ) B ) C ) Figure 15 : Screws co rotating in different terrains. A ) Compliant surface B ) Rigid surface C ) Water 3.1.3 Turning. The method and capability of turning depends on the type of ground a double screw is on. When a ground, one method of turning


28 relies upon either not rotating one of the screws or by varying the revolutions per minute (RPMs) between both screws; this m ethod of turning is termed skid turning [9] Skidturning works best on soft, cohesive ground and is nearly impossible in RCIs firmer than 6 [9] Figure 16 shows skid turning by rotating the left s crew. A ) B ) Figure 16 : Screws skidturning on soft ground. A) Left screw rotating clockwise B) Left screw rotating counterclockwise The turning radius for skidturning relies on the resistance to the stationary screw and the amount of tractive force ge nerated by the rotating screw. Therefore, the turning radi us for skidturning on a compliant surface is tighter than in water because the stationary screw has less resistance to hold it in place in water. In addition, skid turning does not work on pavement because it either results in no net locomotion or straig ht, lateral locomotion; the result depends on whether the stationary screw is locked or free to rotate. As discussed in the lateral locomotion section, another method of turning is rotat ing both screws in the same direction and at the same speed. In firm soil, turning the screw s in the same direction causes the vehicle to


29 travel in a wide arc, and this turning is called arc turning [9] In soft cohesive ground, such as marsh, turning the screw s in the same direction causes the vehicle to turn in a much tighter circle and is termed pivotturning [9] During pivot turning the blades dominate the direction in which the vehicle travels and produce a tight pivot [9] Similarly, in water, any lateral locomotion produced by the rotation of the drum s is negligible and the effect of the blade is dominant. Therefore, a double screw will turn approximately about its center on water when the screws are rotated in the same direction. Figure 15 in the co rotation section show s pivotturning, arc turning, and turning in water. Finally, on pavement no combination of screw motions can allow a double screw to turn, except potentially on ice. There were no r esources describing turning capability on ice found Nonetheless, a n exception to the lack of turning capability of a double screw on rigid surfaces is the patented Tyco Terrain Twister, a plastic radio controlled toy The Terrain Twister has the ability to hinge its screws several degrees about the vertical axis of the ir center points. The turning radius of a hing ing, double screw on pavement is given by formula 1 and is shown in figure 17 r c 2 s i n l 2 ( 1 ) Where : r= T urning radius c = C enter to center of screws H inge angle l = D rum length


30 Figure 17 : T he t urning radius of hinged screw s T o, as shown in formula 2 and figure 18 Figure 18 : The m inimum turning radius for hinged screws r c 2 l 2 (2)


31 3.2 Limitations The d ouble screw is capable of moving in many directions and over a wide range of terrains. However, they are not fully omni directional and their locomotion capabilities vary depending on the terrain. This section discusses, in detail, the limitations of the double screw f rom the perspective of omni directional locomotion. A discussion for each limitation is given regarding if it can be remedied with a different configuration of screws. The first limitation of a double screw to consider is its inability to move longitudinally on a rigid surface. Unfortunately, due to the nature of screw locomotion there may be little that can be done to improve longitudinal locomotion on pavement. As will be discussed, a solution is to employ a combination of lateral locomotion and rotati on to overcome rigid obstacles such as pavement. Another limitation of the double screw is the impure lateral movement on all but the most rigid surfaces. Clearly, controlling a vehicle can be cumbersome if it tends to follow an arced path. Furthermore, control issues are exacerbated by the variable nature of the arc. Specifically, a double screw make s a wide arc o n firmer ground but nearly turns about its center on soft soil. As will be discussed, this issue can also be overcome with another configuration of screws. The final limitation of the double screw is rotation. Although turning is possible on all surfaces, the efficacy and method of turning is not consistent for each surface. An ideal system would employ the same method of turning on any surface and always be capable of turning about its center.


32 One of the turning methods discussed was skid turn ing. Skid turning is incapable of turning the vehicle directly about its center point. As a result, skid turn ing requires more space for maneuvering than an ideal turning method Furthermore, the stationary screw is forced to skid or plow across the surface of the ground, thereby reducing turning time and possibly damaging the screw thread. Tests performed on the RUC show that pivot turning is quicker than skid turn ing on soils in which both are possible [9] Turning is possible on hard surfaces by utilizing hinged screws. In the case of the Ter rain Twister, its unique hinged screws allow for steering on hard surfaces, but since the screws d o not hinge 90o, the turning radius is not about its center. Furthermore, the action of hinging the screws takes time and may damage the screws or pavement by scraping the blades along the surface In all, the benefit of hinged screws may be further reduced due to complicated design. In particular, hinged screws require more joints than a nonhinging double screw and require a mechanism, such as an actuator, to perform the hinging motion.


33 Figure 19 : An example of h inged screws Finally, when rotating the screws in the same direction on increasingly soft soils, arc and pivotturning is possible. The degree of arc in the path depends on the helix angle the weight of the vehicle and the softness of the soil The issue of firm soil in which the blades cannot fully dig into the soil, is clear because the turning radius is wide. However, even when the double screw is pivot turning on very soft soil, it does not turn about its center.


34 CHAPTER 4: ALTERNATIVE SCREW CONFIGURATIONS 4.1 Overview Chapters 2 and 3 discussed the issues that the double screw has regarding locomotion on different terrains. Nonetheless, a screw vehicle, in general, likely has the potential to overcome many of the limitations of a double screw Several new screw configurations have been considered prior to building a testbed. This chapter outlines the assumptions and analysis made about each configuration of screw s considered This chapter includes vector analysis for screw configurations of interest. Additional vector analyses are provided in appendices A through C. I n vector analyses in this chapter and appendi ces A through C tractive forces are red arrows as are the moments resulting from those tractive forces ; while the rollingforces are green arrows, as are the moments resulting from the rollingforces Lastly, yellow arrows indicate the net direction of locomotion. 4. 2 Bendable S crew Among the first solutions considered to resolve the limitations of the double screw was the adoption of a bendable screw The concept of the bendable screw was that it c ould be bent to steer the vehicle By bending


35 the ends of the screws toward the vehicle s hull, rotation about the center of the vehicle may be possible F urthermore, by bending the front of both screws either left or right, the vehicle may be able to travel in the direction the screws point to In theory, bendable screw s may be promising from the perspective of turning. However, two bendable screw s alone would not resolve the issue of arced locomotion Furthermore, there we re many complications that could have arisen when developing a bendable screw A known issue was that bending a screw places tension on one side of the screw and compression on the othe r side. When the screw begins rotating, the tension and compression alternates, resulting in cyclical stress. The cyclical tension and compressionstresses imposed on the blades c ould have result ed in failure. Figure 20 : Red and blue halves experienc ing alternating tension. If a material was used that c ould withstand the alternating stresses imposed by bending a rotating screw, another complication would have still exist ed I n order for a bendable screw to work, i t was important that the


36 screw remai n fla t on the ground while it rotated about its center axis. A likely problem was that the screw may rotate about the axis projected through its two endpoints. The result would have be en a screw that rotates similar to a jump rope and with no effect from the blades. In summary, since the best design is the simplest design, the bendable screw was not pursued. Figure 21 : Modes of rotation for a bendable screw 4. 3 S plit S crew Another configurat ion considered for a screw vehicle was one with four screws. Specifically, the screws w ould b e oriented in a box formation in which the front and rearscrews would be axially aligned and the screws on the left and right side would be fixed parallel to each other. The parallel screws would have opposite blade handedness similar to the double screw while the screws directly behind the front screws would have the same blade handedness as those directly in front of them. The configur ation described is essentially the same as the double screw with the freedom to rotate the


37 front and rearscrews independently. Therefore, the screw configuration describe d is called the splitscrew throughout this thesis Figure 22 : Top view of the splitscrew layout From the perspective of skidturn ing, moving forward, backward, and laterally, the splitscrew was presumed to act the same as a vehicle with two screws. I n order to behave exactly like a double screw, the screws in the rear must turn in the same direction and speed as the screws directly in front A s shown in figure 23 B straight lateral locomotion was not co nsidered possible in soft soils The assumed advantage of the splitscrew over the double screw was turning c ould become possible on solid surfaces and i mprove on soft surfaces. Turning was thought to be similar to a tank. When the screws in the front are rotating in the same direction and the screws in the rear are rotating in the other direction, the vehicle c ould possi bly turn about its center on hard and soft surfaces Figure 23 C shows a vecto r analysis of a rotating splitscrew Clearly, the tractive and rolling forces cancel and the moment due to tractive forces cancel leaving the moment due to rolling forces to generate clockwise rotation.


38 In summary, full experimental testing was not carried out on the splitscrew because it showed minimal improvement over the double screw, except that it could rotate about its center. Since i t was critical that a screwconf iguration be developed that could move in a straight, lateral direction on any surface, more configurations were investigated. A) B) C) D) Figure 23 : Four symmetric screw rotations for the splitscrew. A) No locomotion B) Lateral (impure skew motion) C) Rotational D) Longitudinal


39 4. 4 Inline S crew Another configuration utilizing four screws which was conside red was one in which the screws a r e similar to the splitscrew However, each screws handedness alternates As a result, the described screw configuration is unique to the double screw. The refore, the screw configuration described is termed inline quad screw or simply inline screw in this thesis Figure 2 4 : A t op view of the inline screw Figure 2 4 illustrates the inline screw configuration specifically used for the testbed. An alternative inline screw configuration has each left and righthanded screw switched; this screwpattern is termed the mirrored inline screw in this study. Appendix C sho ws the vector analyses for the mirroredinline screw. For the inline screw longitudinal locomotion i s not achieved in the same manner as the double screw or the splitscrew Instead, in order to go forward and backward, the front must be counter rotated and the back must be counter rotated in the opposite direction of the front. To get rotation


40 about the vehicles center, the front screws are rotated in one direction while the rearscrews are rotated in the opposite direction. Similar to the splitscrew, the inline screw can rotate about its center. Furthermore, its turning radius is dictated by the size of the vehicle. The turning radius of the inline screw is given by formula 3 and is shown in figure 2 5 Figure 2 5 : The turning radius of an inline screw. r T r a c k 2 2 W h e e l b a s e 2 2 (3)


41 Figure 26 : The turning radius of an inline screw superimposed on a hinged screws turning radius. A major advantage of the inline screw over the splitscrew was determined to be when attempting lateral locomotion in soft, wet terrain. Since the screws are of opposite direction on the inline screw the front and rearscrews were presumed to attempt to travel in opposing a rced paths The result would be cancelation of both arced paths and the creation of a straight, lateral path. More specifically, all of the moments created by the tractive forces cancel out during lateral motion. Since the inline screw shows promising directions of locomotion, it was chosen to undergo all of the tests in this study.


42 A) B) C) D) Figure 27 : Four symmetric screw rotations for the inline screw. A) Longitudinal B) Lateral C) Rotational D) No locomotion Comparing figure 27 to figure 28 shows that reversing the direction of each screws rotation, for each symmetric switch pattern, results in the inline screw moving in the opposite direction. This is true for all double and quadscrew configurations.


43 A) B) C) D) Figure 28 : Rever sing the direction of rotation for each symmetric switch pattern results in the opposite direction of locomotion. A) Backward B) Left C) Counterclockwise D) No locomotion


44 Figure 29 : Model of the inlinescrew. 4. 5 Cross S crew and D iamond S crew Other interesting screwconfigurations consist of cross and diamond shape s The s crews are located in the same pattern as the inline screw except the sc rews are not inline. The cross shaped configuration is oriented with all four screws pointing to the center of the vehicle, while the diamondshaped configuration has each screw perpendicular to the cross orientation. The described configurations are termed the cross screw and diamond screw, respectively, and can be seen in figure 30 A) B) Figure 30 : M odel s of the cross screw and diamond screw A) Cross screw B) Diamond screw


45 Clearly, the diamond screw and cross screw can also exist for the splitscrew configuration. Figures 32 and 33 show the vector analys es of the crossscrew and diamond screw while appendi ces A and B show the splitscrews crossand diamondshaped vector analysis A review of each vector analysis reveals that the cross screw and diamondscrew are superior to thei r splitscrew counterparts Therefore, the splitscrew s cross and diamondshaped configurations are not tested in this study. Furthermore, for simplicity, the splitscrew s cross and diamondshaped configurations are called the S crossscrew and S diamondscrew Finally, just as there is a mirrored version of the inline screw there are mirrored versions of the diamondscrew and cross screw Only one version of the diamond screw and crossscrew w ere tested. The diamond screw and cross scre w ha d the ir screws in the same order as the inline screw that was tested. Unlike the inline screw proposed here, the crossscrew and diamond screw are not new, but were discovered during a patent search of screwvehicles The order of screws for the diamo nd screw and cross screw in the patent matched the order tested in this study. Since the diamond screw and crossscrew were patented concepts with no evidence of a scientific study, they were tested in all of the same conditions as the inline screw Furthermore, by testing the crossscrew and diamond screw the role s of the tractive and rollingforces were better understood.


46 Figure 3 1 : The patented crossscrew and diamondscrew configurations [16]. A) B) C) D) Figure 32 : Four symmetric screw rotations for the diamondscrew. A) Longitudinal (forward or reverse is indeterminate) B) Lateral C) Rotational D) No locomotion


47 A) B) C) D) Figure 33 : Four symmetric screw rotations for the cross screw. A) Longitudinal B) Lateral (left or right i s indeterminate) C) Rotational D) No locomotion


48 CHAPTER 5: THE TERRAIN TWISTER 5.1 Description The Tyco Terrain Twister is a remote controlled toy that uses two screws to drive. It u s es two DC motors to individually power the screws. These motors are housed in a watertight plastic shell and are located inside the screws. The motors turn a plastic tab, clipped to the inside of the screw, to turn the screw. Each of the Terrain Twisters screw s i s made of two hollow plastic shells that fit around a rod, motor, and Styrofoam. The rods are used to hold the screws and motors in position and they are held in place by forks that attach to both ends of the rods. The forks both mount to the body of the toy which contains all of the electrical and radio signal components. The toy also has gears that rotate the forks so the screws can hinge inward and outward allowing for turning on hard surfaces.


49 Figure 3 4 : The Terrain Twister screw assembly 5.2 Test B ed C onstruction The Tyco Terrain Twister was useful for the quadscrew testbed because it already consisted of screws that work effectively on water, dirt, snow, sand, and to a limited extent, hard surfaces. From the studies reviewed in chapter 2, the screws that came with the Terrain Twister had a geometry that closely matched an ideal screw for most terrains. Table 1 compares the geometry of the Terrain Twister screws to an ideal geometry. The only parame ter that did not closely match the ideal screw geometry was the lengthto drum diameter ratio. Nonetheless, the geometry was acceptable. All of the geometric values for the Terrain Twisters screws are provided in a ppendix D with calculations for the values in T able 1


50 Table 1 : Terrain Twister screw geometry Parameter Terrain Twister Ideal Comments Helix angle (o) 31.03 30 or slightly larger [3,14] Blade height to diameter ratio 0.125 0.125 center diameter measurement [3] Number of helix blade starts 2 2 [3,14] Length to diameter ratio 3.65 6 center diameter measurement [3] Blade thickness (inches) 0.0625 no information on performance impact The Terrain Twister screw was also convenient. The screw already had a motor housed inside it allowing any combination of screw rotations to be performed. Specifically, the individual motors eliminated the need for complicated gearing, belts, or any other transmission system. Also, the screws were lightweight enough to easily float in water with additional buoyancy. Although the Terrain Twi ster was convenient, it was no longer marketed at the time of this study. Therefore, Terrain Twisters were purchased through Ebay, an online auctioning service. The two fork andscrew assem blies were permanently removed from the body of the Terrain Twiste r to mount to the frame of the testbed. Since the testbed use d four screws, two Terrain Twisters were utilized. The Terrain Twister was disassembled so that the forks and screws remained intact. The wires leading from the motors were also kept intact so that they could be used in the wiring of the testbed.


51 5.3 Test C omparison The testing which will be discussed i n chapter 7 sought to understand the advantages and limitations of each quadscrew configuration by observing behavior on different terrains However, in order to make sense of the observations, comparisons were made using a double screw and the quadscrew configurations with identical screws. By testing the double screw in each terrain, it was possible to note if the vehicle behaved in the manners described in previous research. When the double screw operate d as discussed in other papers, it demonstrate d that the screws geometry and scale were appropriate for testing the quad screw configurations


52 CHAPTER 6: QUAD SCREW TEST BED CONSTRUCTION 6.1 Test B ed F rame The frame of the testbed served as a compartment for batteries and a mounting surface for the screw assem blies, the switchbox and other electrical components. Therefore, the material selected for the frame was important. The entire frame of the testbed was made of schedule 40 PVC because it was lightweight, sturdy, hollow, easy to assemble, and readily a vailable. A single piece of 1.25 inch diameter PVC wa s used for the body to house D cell batteries used to power the testbed, and provide appropriate spacing between the screws. The total length of the body piece provide d a 1 inch gap between the ends of each screw. The 1 inch gap exi s ted between the frontand rearscrews when in the inline screw configuration


53 Figure 35 : Right plane test bed model The figure illustrates a 1 inch gap between the screws and 14 inch di s tance between the centers of the front and rear legs A PVC T fitting at the back of the body form ed the connections for the rearlegs and provided a mounting surface for an electrical barrier strip The rearlegs serve d to hold the rearscrew assem blies At the front end of the body piece was a cross fitting made of PVC. The cross fitting wa s used to hold the frontlegs f or the two frontscrews. Also, a short length of PVC was fitted to the end of the cross fitting so that a cap could be placed on it The cap was used to add and remove D cell batteries.


54 Figure 3 6 : A PVC end cap with the spring for battery contact. The legs of the testbed each consisted of a horizontal and vertical section. The horizontal sections of the legs were cut to a length that spaced the centers of the left and right screws 14 inches apart. The centers of each screw formed a square with 14 inch sides; whi ch permitted the crossscrew and diamond screw The horizontal and vertical sections were connected using 90o PVC fittings. Since the fork assemblies on the screw assem blies were already tall, the vertical sections of the legs were kept short. None of t he literature reviewed mentioned the importance of the vertical C.G. in screw vehicle performance. Finally, end caps were attached to the end of the vertical sections of PVC to provide a mounting surface for the screw assem blies.


55 Figure 37 : Front plane, testbed model. This figure illustrates the 14 inch distance between the centers of the left and right legs. Figure 38 : Trimetric, test bed model.


56 Figure 3 9 : A photograph of the testbed. 6. 2 ScrewA ssem blies The screw assem blies consisted of a fork assem bly, a motor and the screw. More detail is provided, regarding the components of the screw assem blies in section 5.1. The two screwassemblies were permanently removed from the body of the Tyco Terrain Twister to mount to the frame of the tes t bed. Since the testbed used four screws, two Terrain Twisters were utilized. Bolts were fed through the center of the forks to attach to the PVC end caps. The end cap was able to twist about the PVC legs to allow the screws to be positioned for the i nline screw crossscrew or diamondscrew configurations


57 6 .3 Wiring and C ontrols Several considerations had to be made concerning the wiring in order to build a successful test bed. The wiring of the testbed had to be able to withstand frequent transportation, rough off road terrain and watery conditions. Furthermore, it had to be easy to access the wires to make modifications or repairs. Finally, the wiring had to result in logical controls that would be easy to remember. The wires within the Terrain Twister motors were utilized in the test bed circuitry. T he motor wires were soldered to longer wires and insulated with shrink tubing With four motors containing two wires per motor, a total of eight wires were connected to an electri cal barrier strip The barrier strip, located on the underside of the T fitting, consisted of eight pairs of terminals and two holes for mounting it. Each wire that led from the motor to the barrier strip had a corresponding 6 foot wire that led from the barrier strip to the switch box. Sections of shrink tubing were placed around all of the 6 foot wires to neatly hold them together like a cable tether. The wires leading to the barrier strip we re all color coded to prevent confusion. Specifically, the r ight handed screws had purple and blue wires while the lefthanded screws had orange and white wires. The purple wires we re the same polarity as the orange wires, while the blue and white wires share d the same polarity as well. Wires from the frontscrew s led to the outer barrier strip terminals and wires from the rearscrews led to the inner barrier strip terminals Furthermore, the screws on the left side of the vehicle led to the left terminals on the barrier strip and vice versa.


58 Figure 40 : The b arrier strip wiring To supply power to the circuit, a brown wire was attached to the bolt at the end cap and a gray wire was attached to the bolt at the rear T fitting. The bolts that the brown and gray wires we re connected to we re used to hold springs that contacted the D cell batteries. The brown and gray wires we re connected to the barrier strip with a ring terminal secured to the bolts that mount ed the barrier strip to the frame. In total, there we re ten wires leading into the barrier strip Each w ire leading to the barrier strip consisted of a corresponding wire that was soldered to a switchbox. The switchbox contained four 3 position switches. On each switch the center position did not supply power and the forwardand back ward positions d id The switches we re positioned in the same order as the barrier strip. In other words, the outside switches we re for the frontscrews and the left switches we re for the left screws.


59 The individual switches consisted of six terminals; two in the front, two in the middle and two in the back. For a given motor, a wire of one polarity was soldered to the back left terminal and the wire of opposite polarity was soldered to the back rightterminal. A wire from each terminal wa s directed to the terminal diagonal from it to reverse the polarity when the switch was flipped to the front. The wires that provide d the power we re soldered to the middle terminals such that one polarity was soldered to the middle left terminal and the opposite polarity was soldered to the middle right terminal The first switch, for the frontleft screw was directly connected to the power. The remaining switches we re provided power by wiring them in parallel with the first switch. The described wiring wa s done by chaining the middle terminals to the middle terminals of the adjacent switch until all we re electrically in contact. Figure 41 : The s witchbox wiring. In order to have the correct amount of batteries, a spacer assembly was built. The spacer assembly consist ed of a 0.75 inch diameter PVC pipe with two caps placed on either end. The overall length of the spacer was 3 inches. Each cap ha d a hole dri lled in the center so a screw could pass


60 through them. The spacer was then bolted to the inside of the T fitting so one end was firmly in contact with the inside surface of the T fitting. Finally, a spring and washer we re secured to the opposite end of the spacer. The purpose of the spring and washer was to provide an electrical connection between the batteries. The entire system was wired so that pushing the switches forward causes the screws to rotate outward from the frame Pushing the switches back cause s each screw to rotate in the opposite direction of the forward position. Finally, the center position was th e off position, and the motors would not spin. Figure 42 : Switch patterns for forward, right and clockwise locomotion 6. 4 Modifications After initial testing to see if the testbed functioned various ch anges were made Some of the changes were made to facilitate ease of use, other changes were necessitated by unforeseen issues, and some were required for specific studies. The six D cell batteries used did not provide enough power to the motors to move the vehicle, so a motorcy cle battery was use d. The negative


61 battery terminal was wire d directly to one of the barrier strip mounting bolts The positive terminal was wire d to a kill switch that was wired to the other barrier strip mounting bolt Since the battery was bulky, it was kept in a backpack and worn on the tester while the vehicle was driven. Likewise since the long cable used for the switchbox was clumsy and all of the testing occurred with one locomotion at a time the switchbox tether was removed and the switchbox was mounted to the rear of the testbed with Velcro. Figure 4 3 : The author shown alongside the testbed. A motorcycle battery in a backpack is utilized to power the testbed. Over time, PVC began to expand at the joints Initially, the joints were held together with tight press fits However, the expansion of the PVC caused each joint to bec o me loose, and the vehicle flexed during testing. In order to remedy the situation, PVC cement was used for permanent joints. Since the screws had to be able to hinge for t he crossscrew and diamond screw the end caps that the screw assembly mounted to were not glued.


62 Instead, masking tape was used to allow easy adjustment of the screws hinge angle Though an advantage of a screwvehicle is the potential for floating scre w s, the testbed did not have adequate screw buoyancy to keep it afloat. Instead, the Terrain Twister utilized a plastic hull, filled with Styrofoam, to maintain buoyancy. Therefore, in order to investigate various quadscrew configurations in water, a floating hull was constructed. Hollow cylindrical foam was used to provide buoyancy on water for the testbed vehicle. Twelve gauge wire provided a sturdy framework to hold the foam in position when the vehicle was in water. Finally, to provide stability, small sections of foam were placed between the frontand rearscrews. When the vehicle was in the cross screw or diamondscrew configuration, the screw s held the long foam cylinder in the center so that the additional small sections of foam were not needed. Figure 44 : The f loating testbed setup.


63 A final modification was required for underwater tests. Four 4 pound dive weights were tied to the horizontal portion of each leg to submerge the testbed. To provide the appropriate buoyancy, the testbe d was tied to canvas wrapped around a floating tube. The motorcycle battery was placed in a 3 gallon bucket, and the bucket was kept in the middle of the tube. As a result, the testbed was fully submerged and suspended underwater. Figure 45 : The inflatable tube used to suspend the testbed.


64 CHAPTER 7: EXPERIMENTS 7.1 Experimental G oals The g oal of the experiments herein was to provide insight into the locomotion of the inline screw crossscrew and diamond screw in different terrains when attempting longitudinal, lateral and rotational locomotion. Initial tests were performed to observe the direction of locomotion for each configuration on each terrain. Further tests were performed to determine the maximum velocity of each configuration on each terrain. In the literature reviewed, drawbarpull capacity and power and torque requirements were of interest for designing a full scale tank. However, in this study, power and torque requirements and drawbar pull capacity were not a concern. Again, the primary goal of this study was to investigate alternatives to the double screw to find the best configuration from the standpoint of omnidirectional locomotion. Therefore, vector analys e s, observations on ve hicle trafficability and calculations of maximum velocity were adequate to determine which configuration had the best omnidirectional capability. As discussed in chapter 2, the double screw was thoroughly researched on a wide gamut of terrains. Therefore, since the behavior of a double screw was already known, it was also tested for the purpose of


65 comparison. In particular, the Terrain Twister was used for the double screw tests From the previous research available screw vehicle performance due to screw design parameters and screw to terrain interaction was given. Therefore, further testing on screw design optimization was unnecessary for the research in this thesis In addition, as discussed in chapter 5, the screws utilized by the Terrain Twister and the t est bed closely matched the screw geometry of an all terrain vehicle. Therefore, testing could be performed on nearly any surface. The force vector analys e s in c hapters 3 and 4 and compiled in appendi ces A through C provided a model for predicting the direction of locomotion for each configuration. Since no benefit was predicted from the splitscrew the S crossscrew or the S diamond screw over their counterparts the inline screw crossscrew and diamond screw minimal testing was performed on them. Nonetheless, testing was performed on the splitscrew in grass, pavement and water to validate the force vector diagrams used 7.2 Methodology 7.2.1 Test L ocations. Specific test locations were selected to test omnidirectional locomotion on a variety of terrains The locations were chosen such that each terrain consisted o f a single medium over a large, level surface. Each terrain was located as follows:


66 Grass : S ince grass was easy to find, s everal locations were used. The requirements were that the ground was level with minimal bumps and the grass was maintained at a height of 1 to 2 inches. Dirt : A large area of loose dirt was found in Palm Harbor, FL. A large section of flattened dirt was utilized for testing. Marsh: A marshy surface was exposed during low tides in the Gulf of Mexico in the Palm Harbor, FL area. The marshy surface was flat and consisted of seaweed vegetation on top of a mixture of watersaturated dirt and sand Sand : Dry sand was l ocated in a volleyball court at the USF Riverfront Park in Tampa, FL. The sand was raked to provide a smooth testing surface. Clay : Dry clay was located at a baseball field at the USF Riverfront Park in Tampa, FL. The clay was characterized by a thin layer of loose clay particles at the surface and hard, compact clay underneath. Pavement : The pool deck around the swimming pool used for water testing w as utilized for tests concerning pavement. Gravel : A gravel parking lot near a boat launch in Palm Harbor, FL provided the gravel testing surface. The size of the gravel averaged approximately 1 inch in diameter. Water: A swimming pool 30 feet long, 12.5 feet wide, and 4 to 8 feet deep was used for testing on the surface and underwater.


67 Snow : T he Tampa Bay Skating Academy in Oldsmar, FL provided snow for testing A large deposit of snow was provided from the skatingrinks ice resurfacing vehicle. The powdery snow was leveled and spread using a rake to provide a large, flat testing surface. 7.2.2 Testing Directions. Several directions of loco motion were tested on each test site. The directions tested varied between the double screw and quad screw configurations because the double screw could not perform the same combinations of screw rotations. The directions tested in each terrain were as follows: Double screw : L ongitudinal locomotion lateral locomotion skid turning Quadscrew configurations : L ongitudinal locomotion lateral locomotion rotational locomotion In this thesis lateral loco motion for the double screw include d straight lateral movement, arc turning and pivot turning While arc and pivotturning were expected from the doublescrew, only straight lateral locomotion was acceptable for the quadscrew configurations A nother distinction between the double and quadscrew configurations was they each rotated in a different manner. The quad screw configurations could rotate the frontand rearsets of screws in the opposite direction to rotate, so they had specific tests for rotational locomotion. Since the double screw could not rotate in the same manner as the quadscrew, the effectiveness of skid turning was observed for the double screw instead.


68 7.2.3 Test S etup. At each test location, two pairs of cones were set up. The first pair of cones marked the starting line and the second pair of cones marked the finish line. Measuring tape was used to maintain 10 feet between the inside of each pair of cones. The 10 foot course was used to observe the behavior of the quadscrew configurations during longitudinal locomotion on each terrain. As will be discussed, the diamond screw was an exception due to the limited capability of its lon gitudinal locomotion. The cones were not used for the doublescrew because it was not being compared for speed or slip tests Figure 46 : An example of the test setup. For the inline screw the slip percentage was desired to be known to understand its e fficiency. In order to calculate the slip percentage, the number of screw revolutions and the distance the vehicle moved in a given time had to be known. White tape was placed on the screw s of the testbed to count the number of revolutions, while the time it took to cross 10 feet provided the speed. Since the screws moved at relatively high speeds


69 Virtual Dub video editing software was used to observe the video frame by frame to count the number of ti mes the white tape showed up. Since the screws were measured to rotate no faster than 550 RPMs, the camera method was adequately accurate since it had 900 frames per minute. Finally, t he time to cover 10 feet was determined by the time elapsed on the video when the back of the vehicle crossed the inside of the start and finish cones. All tests were recorded with a digital camera so that a video library could be compiled. The library was useful for discussing the behavior of each configuration, troubleshooti ng issues that occurred in the field, determining the velocity of the quad screw, and finding the RPMs of the screws 7.3 Test O bservation s 7.3.1 Grass. On grass, longitudinal and lateral locomotion showed no issues for the doublescrew. Skid turn ing was generally effective, but occasionally the rotating screw would lose traction with the ground and no movement would occur. In cases where skidturn ing failed, the double screw was not immobilized because it could immediately move longitudinally. Lateral loco motion for the doublescrew resulted in arc turning. The inline screw worked well on grassy surfaces. When it was set to move longitudinally, it moved in a straight line with no issues When it was set to rotate, it rotated in a tight circle about its centerpoint. Finally, when it was set for lateral locomotion, it moved in a straight lateral direction as


70 anticipated by the force vector diagrams In summary, no issues or surprises arose for the inline screw in grass. Figure 47 : Test setup for grass terrain. The cross screw was able to move longitudinally with no issues on grass. Furthermore, it rotated much faster than the other configurations because the roll ing forces on each screw directly contributed to the rotation. Unfortunately, the crossscrew did not move in a predictable manner for lateral tests When set to move right, based on the switch combination to move the inline screw right, it attempted to move right but it quickly and frequently altered its path. Also, in some cases it did not go anywhere when set for lateral motion. Clearly, since the roll ing forces attempted to pull the crossscrew to the right while the tractive forces tried to pull it to the left, the system was unstable. Unlike the crossscrew the diamond screw mo ved laterally in the set direction with no issues However, it did not rotate as fast as the inline screw or cross screw The diamondscrew relied only on tractive forces for turning. Finally, the diamondscrew did not successfully move longitudinally. Similar to the crossscrew when attempting lateral locomotion, the diamond-


71 screw when set to move longitudinally encounter ed opposing tractive and rollingfor ces. In the diamondscrew tests, it stayed in plac e while the screws rotated. 7.3.2 Dirt. Most of the observations made from testing in grass applied to the testing in dirt. Nonetheless, each configuration performed slightly different in dirt compared to grass. In dirt, the double screw was able to move longitudinally, but it did not perform as well as it did in grass. When it encountered inconsistencies in the dirt, such as small hills or loose patches of dirt, it would slightly alter its path or become immobilized; immobilization was i nfrequent. Lateral locomotion rarely resulted in immobilization, but the double screw followed a wide arc. In addition, when attempting to skidturn, the double screw often became immobilized. In nearly all cases of immobilization, it could be extricate d by lateral or longitudinal locomotion The inline screw behaved similar to the double screw during longitudinal locomotion because it sometimes altered its path or became immobilized when it encountered terrain inconsistencies. During lateral and rotati onal locomotion, no issues were observed. Similarly, the crossscrew performed as it did in grass, except it also did not perform as well longitudinally. There were no cases of the crossscrew becoming immobilized.


72 Figure 4 8 : Tracks from the inline scr ew deviating in dirt. Regarding lateral motion, the diamond screw behaved as expected by moving in the proper direction and path with some path deviation due to terrain inconsistency. However, when set to move longitudinally, the diamondscrew behaved much different than in grass. Rather than going nowhere, when set to move forward it attempted to go in reverse and quickly buried itself or deviated its path erratically. In the case of the diamondscrew on dirt, the reverse rollingforces had slightly overcome the forward tractive forces. Finally, when attempting rotation, the diamond screw could make no more than two rotations before becoming immobilized. Since the screws rotated at a fast speed, the diamondscrew may have kicked up the dirt and buried itself when attempting to rotate. It is possible that slowing the RPMs of the screws may resolve the issue of the diamondscrew burying itself during rotation.


73 7.3.3 Marsh. The marshy terrain provided interesting information for each configur ation The wet soil provided low friction between the screws and soil, but was not slick to the point of causing the vehicle to slide uncontrollably on uneven surfaces. Furthermore, the cohesion in the terrain provided an adequately strong surface for the scre ws to push off of. Finally, since the marshy ground left behind easily visible tracks, pictures could be taken to illustrate the paths taken. Figure 4 9 : Tracks in marsh left by the inline screw. In the longitudinal tests, the double screw performed successfully and even navigated slightly bumpy terrain. During lateral locomotion, the double screw was able to pivotturn. However, sometimes, on seemingly identical terrain, it would arc turn with an increasingly narrow turning radius until it pivotturned. Interestingly, during skidturning the double screw had a turning radius approximately the same as f or pivotturning. There were cases of immobilization due to skidturn ing, but this was not frequent.


74 The inline screw performed perfectly in all modes of locomotion during marsh testing. The crossscrew had no dif ficulties with longitudinal or rotational locomotion. However, d uring lateral locomotion, sometimes the screws lacked enough torque to rotate, and other times the screws rotate d and kicked up mud. In either case, it did not go anywhere. Similarly, the diamondscrew could not move longitudinally because it either lacked torque or kicked up mud, but it had no issues during lateral and rotational locomotion tests 7.3.4 Sand. Fr om the literature reviewed, dry sand is a known challenge for screwvehicle s because it has minimal cohesion and high frictiona l properties. The tests performed in this thesis confirmed the literature because each configuration encountered difficulty in dry sand. The double screw was able to move longitudinally. However, when it encountered any uneven terrain, it often plowed into the sand and buried itself. During lateral lo comotion, the double screw followed a wide arc on flat sand but when it encountered uneven terrain the turning radius tightened temporarily. The tighter turning radius from uneven terrain was attributed to increased interaction between the blades and the sand. During the skid turning tests the double screw quickly buried itself in all cases The lack of cohesion between sand particles caused the moving screw to kick up sand, and the increased friction between the sand and stationary screw resisted the s kid turning locomotion. Furthermore, the low hull of the Terrain Twister quickly became grounded on the sand as the screw pushed sand away.


75 The inline screw also had difficulty on the loose, dry sand. In longitudinal tests, the inline screw quickly burie d itself when it encountered hills of sand. The tendency of the inline screw to bury itself was attributed to the rigid nature of the screw s mounting, wherein each screw was forced to plow through the sand. If the screws we re allowed to pitch, each scre w c ould individually conform to hills and pass over them. Figure 50 : Sand terrain test setup. The rake used to flatten the sand is shown. The sand was eventually raked flat enough to test the different modes of locomotion The forward locomotion was improved on flat sand, but even slight hills resulted in burial or large path deviations The inline screw performed better during lateral locomotion On flat terrain, and usually uneven terrain, the inline screw successfull y moved in a straight, lateral path. While attempting lateral locomotion i n uneven terrain the inline screw sometimes bur ied itself Finally, t he inline screw successfully rotated about its center in sand without any evidence of trouble. The cross screw was able to move longitudinally, but frequently deviated from a straight path. Since the screws pointed outward, a larger


76 contact area with the sand was made. Therefore, the cross screw was observed to contact hills of sand easier and alter its course. An advantage was the crossscrew seemed to bury itself less frequently during longitudinal tests. Lastly, similar to most terrains, the crossscrew could only move very briefly before burying itself during lateral locomotion, but it could rotate with ease. The diamondscrew attempted to move in reverse when set to move forward longitudinally and it quickly immobilized Furthermore, it could not make a single rotation when set to rotate. Nonetheless, it was able to cross the 10 foot test course without burying itself during lateral locomotion. However, in all lateral trials, the diamond screw moved in a large arc. The reason for the arc was likely the terrain was not perfectly level, or the screws were not rotating at the same RPMs 7.3. 5 Clay. For the double screw tests, longitudinal locomotion was possible and lateral locomotion resulted in a wide arc. S kid turn ing was unsuccessful because the rotating screw could not produce enough traction to turn it. Figure 51 : The test setup for clay terrain.


77 For the inline screw the longitudinal, lateral and rotational locomotion were all possible For the double screw and inline screw t he hard clay was difficult for the screws to penetrate, but not impossible Therefore, longitudinal loco motion for both cases was occasionally unsuccessful due to lack of traction. Furthermore, the rigid surface created unequal ground contact for the individual screws. Therefore, since the screws and terrain did not always hav e full contact, each screw did not always play an equal role in the direction of travel. Figure 52 : Inline screw tracks in clay. The tracks we re from longitudinal tests. The cross screw was not able to complete the 10 foot course for longitudinal locom otion; the wide angle of the screws may have exacerbated terrainto screw contact issues. Lateral locomotion was nearly successful for the crossscrew because the blades played a reduced role in the direction of travel. Finally, t here were no issues for the crossscrew while rotating.


78 The diamondscrew performed the similar to the crossscrew except its performance was better for lateral locomotion than the cross did for longitudinal. In addition, since the rolling forces which opposed the set direction for longitudinal locomotion, overcame the tractive forces, the diamondscrew moved in reverse when the switches were set to go forward Lastly, the diamond screw could not complete a single rotation. When attempting to rotate, it turned brief ly and removed the top layer of loose clay. Figure 5 3: Diamond screw rotation tracks in clay. 7.3. 6 Pavement. Clearly, pavement i s the least friendly surface for a vehicle employing screw locomotion Both the double screw and inline screw failed longitudinal locomotion because the threads had minimal traction. Also both configurations behaved the same for lateral loco mo tion because the blades played minimal role in the path The critical difference between the double screw and inline screw was that rotation was possible for the inline screw Specifically, the inline screw proved capable of rotating about


79 its center on pavement. If a screwvehicle operator comes across a surface such as pavement or solid rock, they can navigate it by using a combination of lateral and rotational locomotion. Figure 54 : The cross screw on pavement. The cross screw and diamondscrew displayed similar performance on pavement as they did on clay. However, since the pavement was more rigid than the clay, the blades played even less of a role and most of the motion produced was due to rolling forces. In addition, the rigid ground created inconsistencies in the screw to ground contact which exacerbate d the path deviation. In summary, the crossscrew performed equally poorly in longitudinal and lateral locomotion and excelled in rotating. Alternatively, the diamondscrew moved poorly a nd in reverse during longitudinal motion and performed poorly during lateral and rotational locomotion. It is possible that the crossscrew and diamond screw could have b e e n more effective in


80 lateral and longitudinal locomotion if the screws rotated slower, were made of a material with better grip, such as rubber, and there was a suspension system to allow equal ground contact between all of the screws. A) B) C) Figure 5 5 : Inline screw performance with minimal tractive force influence such as on pavement. A) Longitudinal (small force) B) Lateral C) Rotational


81 7.3.7 Gravel. In all cases, locomotion in gravel was bumpy, but this was expected in such a terrain. Regardless, the results were encouraging and the paths were surprisingly straight. The double screw was able to move longitudinally with no issues. D uring lateral locomotion the turning was not a tight circle like in marsh, but it did have a ti ghter radius than in dirt. It was presumed that the jutting rocks contacted the blades, causing them to play a large role in the direction of travel. Finally, skid turning was effective in gravel with the vehicle nearly pivoting about the endpoint of the stationary screw. Figure 56 : Test setup for gravel terrain. The inline screw also performed well on gravel. When moving longitudinally it would occasionally hit a jutting rock and be bumped off track. However, the path was nearly straight because the numerous jutting rocks self corrected the vehicle to its original path. The lateral locomotion was also effective, but it did have a tendency to go off track due to rocks


82 contacting the blades Rotation about the inline screws center worked effectively and with minimal deviation. The cross scre w and diamondscrew were not as successful on gravel. During longitudinal testing, the crossscrew frequently deviated from its path and stayed off track. It was possible that since the rollingforce contributed to the forward motion, the crossscrew was going fast enough to exacerbate the path deviation. Again, s imilar to all of the terrains discussed thus far, the crossscrew performed poorly during lateral locomotion, but rotated with ease. The diamondscrew produced no meaningful locomotion during longitudinal testing in gravel. The rolling and tractive forces must have been nearly equal because it exhibited paths in many directions. Lateral locomotion was successful for the diamond screw and less path de viation was observed in comparison to the longitudinal crossscrew locomotion Finally, rotation was also successful for the diamondscrew in gravel. Figure 57 : Path from the diamondscrew rotating in gravel.


83 7.3. 8 Surface of W ater. From the testing on wate r, it was clear that the tractive forces dominated while the rolling forces were negligible. In all cases where rolling forces were the only forces contributing to locomotion, no locomotion resulted. Furthermore, each configuration moved in the di rection that the net tractive forces dictated. On top of water, the double screw moved in a similar fashion to solid surface s As in every surface, except pavement, counterrotating the screws moved it forward and backward. However, for the double screw lateral locomotion on water resulted in turning about its center. The inline screw yielded interesting results on the surface of water. When set in the longitudinal setting, the vehicle moved with ease across the water. A unique aspect of the inline screw in wate r was its limited movement during lateral locomotion The locomotion of the vehicle during lateral testing appeared to be a straight, lateral path. However, the speed was minimal to the point that there was uncertainty if it was m oving due to the screws Clearly, forward and rotation are common means of travel in water, so the inline screw not being able to move laterally should not be a setback. Fortunately, when set up for rotation, the inline screw turned about its center.


84 Figure 58 : Test setup for the surface of water. The cross screw showed no issues with longitudinal motion on top of water, but when set to move right or left it went in the opposite direction. During longitudinal and lateral loco motion, the crossscrew was equally effective when ignoring the reverse nature of its lateral locomotion. The crossscrew exhibited no capability of turning in water. Contrary to the crossscrew t he diamondscrew performed the best in all tests from the standpoint of omnidire ctional locomotion It moved in the desired directions for longitudinal, lateral and rotational locomotion.


85 A) B) C) Figure 5 9 : Inline screw performance with minimal rolling force influence such as on water. A) Longitudinal B) Lateral (small force) C) Rotational 7.3. 9 Underwater. During underwater testing, video s w ere taken above the surface and below the surface of the water. The author, equipped with a snorkel and waterproof camera, operated the testbed and took underwater video while an assis tant took video from the surface. For every quadscrew configuration the underwater testing showed the same directions of locomotion as on the surface of water. As outlined in Dr.


86 Coles work, the only difference the depth of submersion makes is the driving torque and thrust. In particular, the driving torque and thrust reduce as air is introduced to the screw s [14]. Therefore, it was expected that each condition would result in s imilar paths as the surface of water. Figure 60 : Underwater view during testing. Figure 61 : Test setup for underwater testing.


87 7.3.10 Snow. The double screw easily navigated in snow In all modes of locomotion, the doublescrew performed successfully. Lateral locomotion resulted in pivot turning for the double screw. The double screw did occasionally bury itself. Burial occurred regardless of the mode of locomotion, but the frequ ency in which it buried itself was much less in snow than in sand In fact, it only buried itself when navigat ing tough obstacles. T he primary cause for the Terrain Twister burying itself was its low hull contacting mounds of snow. Figure 6 2 : The test course for snow The inline screw proved capable of moving in each of the desired directions. It was adept at moving longitudinally though flexibility to pitch would have be en beneficial for crossing piles of snow. Rotational locomotion was also effecti ve; however the low friction of the snow caused it to slide down slopes easily when rotating. Lateral locomotion a lso worked for the


88 inline screw but since it f ully relied on rollingforces the slick surface caused it to slide around on the snow. A ny portion of the snow that was not perfectly level played a large influence in changing the direction of the inline screw when it was tested for lateral locomotion. Lastly, the inline screw frequently buried itself during lateral locomotion As anticipated, the cross screw could not move laterally, while the diamondscrew could not move longitudinally. Furthermore, the cross screw performed well longitudinally as did the diamondscrew when moving laterally. An interesting observation was the cross screw quickly buried itself during rotation while the diamondscrew had no issues during rotation. It was presumed that the minimal friction in snow was detrimental to the rollingforces of the cross screw, while the cohesion in the snow was beneficial to the tractive forces that the diamond screw relied on for rotation. 7. 3.11 S plit S crew T ests The split screw was tested on a limited number of surfaces because it was similar to a d o uble screw with limited improvements. The splitscrew w as tested on grass, pavement, and water. Therefore, each extreme of terrain was tested for the splitscrew That is, the rigidscrew was tested on a rigid surface, a compliant surface and a fluid. Testing on the splitscrew demonstrated that it could not move in a straight, lateral direction on grass. Instead, it arced like a double screw because there were no counteracting tractive forces to straighten its path. On pavement and in water, the splitscrew was identical to the inline screw with respect to its possible directions of locomotion

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89 7.4 Turning Radius For this study, the circle that circumscribes a screwvehicle is defined as its plan. The plan for a double screw, inline screw, crossscrew, and diamondscrew are given in figure 63 For each configuration, a line is drawn connecting the vertices t o indicate the diameter of its plan. Measurements were made to determine the plandiameter of the double screw, inline screw, crossscrew, and diamondscrew Testing was performed in marsh because vi sible tracks were left behind. The tracks were used to determine the turning diameter for each configuration. Marsh was also useful because the double screw was able turn by pivotturning, skid turning and arc turning. A) B) C) D) Figure 63 : The plan and turning diameter. A) Double screw B) Inline screw C) Diamondscrew D) Cross screw

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90 Table 2 : Turning diameter and turningratio in marsh Inlinescrew Crossscrew Diamondscrew Steering Skid Pivot Arc Rotate Rotate Rotate turningdiameter (inches) 28 29 61 30 29 26 plandiameter (inches) 14.5 14.5 14.5 29 29 25 turningratio 1.931 2 4.207 1.034 1 1.04 Double-screw Table 2 clearly illustrates the quadscrew configurations had a 1:1 turning ratio while the double screw had a 2:1 ratio for pivotand skidturning. The data makes sense because the double screw turns about its end rather than its center. Figure s 64 and 65 show tracks from the turning tests

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91 A) B) C) Figure 64 : The double screws rotation tracks left in marsh. A) Pivot turning B) Arc turning C) Skid turning A) B) C) Figure 65 : Test bed rotation tracks left in marsh. A) Inline screw B) Cross screw C) Diamondscrew

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92 7. 5 Test Summary Table 3 is a performance matrix that summarizes the three types of locomotion Each quad screw configuration is rated on a scale from 0 5 The scale was based on each configurations ability to move in the set direction without deviating from the ir path or beco ming immobilized. 0: No movement or the path cannot be determined 1: Brief motion in the set direction followed by immediate and consistent immobilization or path deviation. 3: Clearly moves in the set direction with occasional immobilization or path devia tion. 5: Clearly and consistently moves in the set direction with no instances of immobilization and minimal path deviation. Table 3 : Quadscrew performance matrix Long. Lat. Rot. Long. Lat. Rot. Long. Lat. Rot. Average Surface Grass 5 5 5 5 1 5 0 5 5 4 Dirt 4 5 5 4 1 5 1* 4 2 3.75 Marsh 5 5 5 5 0 3 0 5 4 3.556 Sand 3 4 5 3 1 5 1* 3 1 3.125 Clay 2 5 5 2 1 5 1* 2 1 2.875 Gravel 5 4 5 2 1 5 0 4 5 3.444 Pavement 0 5 5 1 1 5 1* 1 1 2.375 Above Water 5 0 5 5 5* 0 5 5 5 3.75 Underwater 5 0 5 5 5* 0 5 5 5 3.75 Snow 5 3 4 3 0 1 0 4 5 2.778 Average 3.9 3.6 4.9 3.89 0.67 3.78 1.111 4.22 3.78 Inline Cross Diamond An asterisk indicates reversed locomotion Note: A ll values are generic units. There are several points of interest in table 3 Namely, the inline screw scored the same or higher than the other configurations in every

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93 category except lateral locomotion in water and longitudinal locomotion on pavement. Nonetheless, i t should be noted that the crossscrew and diamondscrew though they didnt score a 0, performed poorly for lateral and longitudinal locomotion on pavement. Another point of interest was the cross screw experienced reversed lateral locomotion on water, wh ile the diamond screw experienced reversed longitudinal locomotion on solid surfaces. For the crossscrew the tractive force of the blades pushed it laterally in reverse, explaining the low scores on solid surfaces and the reversed locomotion in water. Alternatively, for the diamondscrew the rolling forces were what pushed it longitudinally in reverse. The double screw could not be graded on the same performance matrix as the quadscrew configurations because it could not rotate in the same manner Also, the double screw usually did not move in a straight, lateral direction, which c ould be considered a useful function in cases whe re skid steering is not effective. Therefore, in the lateral direction, the double screw was scored based on how often it became immobilized or deviated from its general path.

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94 Table 4 : Doublescrew performance matrix Long. Lat. Skid Surface grass 5 A 5 4 dirt 4 A 5 3 marsh 5 P 5 4 sand 3 A 4 1 dry clay 3 A 5 2 gravel 5 A 5 5 pavement 0 S 5 0 above water 5 P 5 5 underwater snow 5 P 4 4 Average 3.5 4.3 2.8 Double-Screw S=straight, A=arc, P=pivot Note: All values are generic units Figure 66 shows the relationship between the longitudinal velocity of the inline screw and the percent the screws are slipping. The data confirms the studies reviewed by showing cohesive terrain of low friction being optimal for reducing slippage. From the literature sand was characterized by being loose and highly frictional. The dirt tested was located in Florida which can also be characterized by a high sand content. Therefore, the loose sand and dirt showed a relatively high slippage and low velocities. In comparison, grass, wet marsh, and snow were described as being cohesive and low friction surfaces. Again, grass, marsh, and snow moved the quickest and experienced the least slippage It should be noted that the underwater configuration experienced greater drag and was a much heavier setup than the above water configuration. Therefore, it was expected to experience far greater slippage.

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95 Figure 66 : A graph illustrating the correlation be tween forward speed and percent slip. Above water and underwater data P e r c e n t s l i p L N T L N 1 0 0 (4) Where: L= Screws lead N= number of blade revolutions T = Travel d istance Figures 67 69 and 70 are charts comparing speeds for the inline screw, crossscrew and diamondscrew 0.5 1 1.5 2 2.5 3 3.5 4 0 20 40 60 80 100Speed (Feet/Second)Percent Slip Sand Dirt Grass Deep grass Clay Snow Marsh Gravel Above water Underwater

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96 Figure 67 : Longitudinal speed s for the testbed configurations in different terrains From figure 67 on loose, frictional surfaces such as sand, dirt and gravel the crossscrew was faste st However, in cohesive lo w friction surfaces the inline wa s faste st The above observation makes sense when considering the rollingforces, which exist only for the crossscrew rely on friction, while friction works against the tractive forces. On water, the inline was fast er because the tractive forces we re exactly in the direction of motion. It was presumed that the crossscrew was slower than the diamondscrew for above water tests because of the testbeds setup. The float blocked the wake generated by the frontscrews of the cross screw configuration during forward locomotion 0 0.5 1 1.5 2 2.5 3 3.5 4 Speed (Feet/Second) Inline Cross Diamond

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97 A) B) Figure 68 : The test bed setup for the cross screw and diamondscrew in water. A) Cross B) Diamond Figure 69 : Lateral speed s for the testbed configurations in different terrains. 0 1 2 3 4 5 6 7 Speed (Feet/Second) Inline Cross Diamond

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98 For lateral locomotion the inline screw was always faster than the diamondscrew T he reason was likely because the rolling forces of the inline screw directly contribute d to its locomotion Appendix D shows the screws used for the testbed roll laterally further per revolution than they screw forward. Finally, in water the crossscrew and diamondscrew travelled at nearly the same lateral speed because the test beds float blocked screws in both configurations. Figure 70 : R otational speed s for the testbed configurations in different terrains T he cross screw was always faste st because the rollingforces directly contributed to rotat ion. Again, water was an exception because the importance of the rollingforces and tractive forces are fli pped. The diamondscrew was faste st in water for rotation because its tractive forces w ere exactly in the direction of rotation. 0 0.2 0.4 0.6 0.8 1 1.2 Speed (Rotations/Second) Inline Cross Diamond

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99 CHAPTER 8: CONCLUSIONS In this study, a thorough investigation of the double screw was performed. From the research, it was determined that improvements could be made from the standpoint of omnidirectional locomotion. In particular, the double screw could not follow a straight, lateral path, except on the most rigid of terrains, and could not turn about its center unless o n water. Furthermore, the double screw had only limited potential for turning on pavement. A number of solutions were given an initial investigation, and three were selected for a full study of omnidirectional locomotion. Specifically, the inline screw, the crossscrew and the diamondscrew were selected for this study. The study consisted of a force vector analysis, a mobility study, and maximum speed tests. The mobility studies showed the inline screw was the most versatile and predictable configurati on compared to the cross screw and diamond screw Basically, the inline screw was fully omnidirectional on all surfaces except pavement and water. Nonetheless the inline screw was able to navigate pavement and water by rotating about its center. On the contrary, the cross and diamondscrews exhibited limited lateral or longitudinal

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100 capabilities, respectively. Furthermore the direction of locomotion for the crossscrew and diamondscrew varied depending on the surface. The vector analys e s in this study verified all of the mobility test results Therefore, it can safely be confirmed that the inline screw was the most versatile of the three testbed configurations. In addition according to the vector analyses, the inline screw is the only configuration that experiences no inherent indeterminate or impure locomotion. Furthermore, the inline screw resolved issues of the doublescrew by allowing for straight, lateral loco motion and rotation about its center on all surfaces. A distinct advantage is the potential to maneuver over paved surfaces through a combination of lateral and rotational locomotion. E ach of the quadscrew configurations that were tested demonstrated a strong point In water, the diamond screw was clearly the optimal configuration fro m the standpoint of omnidirectional locomotion, because it was the only configuration capable of loco motion in all directions. Alternatively, the crossscrew proved to be the fastest in highly frictional soil such as sand or dirt and was the fastest on gravel. All in all, the inline quad screw, which is proposed for the first time in this thesis, represents the best overall versatility and performance in an omnidirectional screwdrive.

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101 LIST OF REFERENCES [1] Neumeyer, M. J., & Jones, B. D. (1965). Marsh screw amphibian. Journal of Terramechanics, 2 (4), 83 88. [2] Fales, W. K., Amick, D. W., & Schreiner, B. G. (1972). The riverine utility craft (RUC). Journal of Terramechanics, 8 (3), 23 38. [3] Dugoff, H., & Ehrlich, I. R. (1967). Model tests of bu oyant screw rotor configurations. Journal of Terramechanics, 4 (3), 9 22. [4] 1926 Fordson Snowmobile Retrieved October 1 3 2010, from http://commons.wikimedia.org/wiki/File:1926_Fordson_snowmobile.jp g [5] Messenger, B., & Mullins, P. (2003). The ultimate all terrain vehicle. Diesel Progress International Edition, 22 (1), 24 25. [6] Leonov, V., & Kenlip, O. (2005). In Mattel I. (Ed.), Screw drive vehicle California: 6,966,807 [7] Hara, M., Satomura, S., Fukushima, H., Kamegawa, T., Igarashi, H., & Matsuno, F. (2007). Control of a snake like robot using the screw drive mechanism. 2007 IEEE International Conference on Robotics and Automation, 6. [8] Knight, S. J., Rush, E. S., & Stinson, B. G. (1965). Trafficability tests with marsh screw amphibian. Journal of Terramechanics, 2 (4), 31 50. [9] Schreiner, B. G., Smith, R. P., & Green, C. E. (1970). Performance of riverine utility craft (RUC) in riverine environments (Technical No. M 70 5). Vicksburg, Mississippi: U.S. Army Enginee r Waterways Experiment Station. [10] Bauxite res idue management. (2009). Retrieved September, 17, 2010, from http://www.residuesolutions.com.au/Default.aspx [11] Kocak, D. M., Neely, J. W., Holt, J., & Miyake, M. (1999). A specialized ROV for cleaning groundwater recharge basins. Conference Proceedings, 2 567 79.

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102 [12] Johannessen, B. O., Jensen, H., Laurie, S., & Lorenzo, T. (1996). Mechanical oil recovery in ice infested waters (MORICE) phase 1 (Technical No. STF22 F96225). Trondheim, Norway: Sintef Civil and Environmental Engineering [13] Perez, M. L. (1997). A cost effective multi terrain autonomous vehicle for hostile environments. Proceedings of the American Nuclear Society Seventh Topical Meeting on Robotics and Remote Systems, 1 352 9. [14] Cole, B. N. (1961). Inquiry into amphibious screw traction. Institution of Mechanical Engineers -Proceedings, 175 (19), 919 940. [15] Gorton, J. V. (1966). New amphibious vehicle programs -2. Na val Engineers Journal, 77 (3), 407 412. [16] Kusmir, K. C. (1969). Land vehicle propulsion. Illinois: US Patent 3420326.

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103 BIBLIOGRAPHY Bakker, J. J. d. (1967). Amphibious vehicle Netherlands: Patent 3,333,563. Barriol, R., Goutierre, A., Longuemard, J. P., & Valls, A. (1985). Study of starting of an archimedes' screw which is pressing on the sea bottom and propelling a submarine vehicle. Revue De Physique Appliquee, 20 (12), 837 44. Becker, A. C. (1962). Snow traction unit. California: US Patent3059711. Bertrand, P. A. (1965). Tractor vehicle Canada: Patent 3224407. Breen, F. P. (1928). Spiral drive device Massachussets: US Patent 1685702. Chhabra, N. K. (1997). Hybrid Tracked/Swedish locomotion system for a land operated robot vehicl e. University of South Florida). Code, S. M. (1927). Amphibious vehicle Illinois: US Patent 1646611. Cutting, L. A., & Horne, J. C. (1955). Rotary hull vehicle California: US Patent 2706958. Foster, C. R., & Knight, S. J. (1957). Vehicle mobility on soft soils. Military Engineer, 49 (328), 92 94. Garate, J. J. C. (1966). Amphibious vehicles Spain: 3250239. Hart, D. S., Beller, L. D., & White, R. L. (1993). In Crude Tool Works (Ed.), Amphibious vehicle Alaska: US Patent 5203273. Hollis, O. A. (191 3). Tractor. Delaware: US Patent 1069875. Komoto, M., & Nakamura, M. (1984). Amphibian vehicle Japan: Patent 4476948. Mainguy, D. N. (1968). In Mainguy D. N., Andrews J. S.(Eds.), Amphibious vehicle Alabama: US Patent 3397668.

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104 Norton, R. L. (2006). Sc rews and fasteners. In M. J. Horton, O'Brien. V., D. A. George & S. Disanno (Eds.), Machine design an integrated approach (3rd ed., pp. 811). Upper Saddle River, NJ: Pearson Prentice Hall. Poole, N. M. (1970). Submersible pipe laying barges California: US Patent 3514962 Waquet, B. E. L. M. (1972). Amphibious vehicle with rotating floats France: Patent 3682127. Zhaung, J., Wang, Z., & Liu, J. (1990). Study on the dynamic characteristics of wheeled vehicles on sand. Winter Annual Meeting of the American Society of Mechanical Engineers, November 25, 1990 November 30, 108 211 217. Zimmerman, H. P., Jr. (1968). Steering device for amphibious vehicle Michigan: US Patent 3395671.

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106 Appendix A : S D iamond S crew F orce V ector s A) B) C) D) Figure A1 : Four symmetric screw rotations for the S diamondscrew A) Longitudinal (roll dominated) B) Rotational (impure skew motion) C) Lateral D) Longitudinal (traction dominated)

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107 Appendix B : S C ross S crew F orce V ector s A) B) C) D) Figure B1 : Four symmetric screw rotations for the S cross screw A) Longitudinal (roll dominated) B) Lateral C) Rotational (impure skew motion) D) Longitudinal (traction dominated)

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108 Appendix C : Mirrored T est B ed F orce V ector s A) B) C) D) Figure C1 : Four symmetric screw rotations for the mirrored inline screw. A) Longitudinal B) Lateral C) Rotational (indeterminate rotation direction) D) No locomotion

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109 Appendix C : (Continued) A) B) C) D) Figure C2 : Four symmetric screw rotations for the mirroreddiamond screw A) Longitudinal B) Lateral ( left or right is indeterminate) C) Rotational D) No locomotion

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110 Appendix C : (Continued) A) B) C) D) Figure C3 : Four symmetric screw rotations for the mirroredcrossscrew A) Longitudinal (forward or reverse is indeterminate) B) Lateral C) Rotational D) No locomotion

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111 Appendix D : Terrain Twister S crew C alculations The screw for the Terrain Twister was unique because the drum was shaped like a barrel with the middle of a larger diameter than the ends. The blade height varie d so most of the tips could contact level ground. The minimum and maximum values for each measurement are located in T able A1 Table A1 : Terrain Twister screw measurements Ends Center DrumDiameter 2.25 2.5 Length (inches) 9.125 9.125 Lead (inches) 5 5 BladeHeight (inches) 0.313 0.375 Calculations were made using the minimum and maximum values. The values that were furthest from being ideal, according to the reviewed research, were used to be conservative. The formula used to calculate the helix angle was : t a n 1L D h 1 8 0 ( 5 ) For one revolution, the distance travelled due to rolling is equal to the circumference of the outer diameter of the screw. Alternatively, the distance travelled in one revolution due to screwing is equal to the screws lead.

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112 Appendix D : (Continued) Figure D1 : The Terrain Twisters major diameter and lead. C i r c u m f e r e n c e D m ( 6 ) Where: Dm= major diameter S ince the travel distance, T, for rolling is the same as the circumference: T 2 8 7 5 i n c h e s 9 0 3 i n c h e s ( 7 ) T he screws that were used had a lead of 5 inches. Therefore, a vehicle using those screws will travel 1.8 times further per revolution for rolling compared to screwing.

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ABOUT THE AUTHOR Jon Timothy Freeberg was born in Arcadia, California in 1984, and in 2007 he earned a B achelor of S cience in Mechanical Engineering at the University of South Florida. For two years he worked as a manufacturing engineer intern at Conmed Linvatec in Largo, Florida where he wo rked in the shaver blade factory. His responsibilities among others, included validating packaging equipment, investigating pyrometers on induction bonder equipment, and introducing a new process of lubricating arthroscopic shaver blades. In 2009, he re turned to the University of South Florida to pursue his Master of Science degree in Mechanical Engineering.


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