A Biologically Inspired Robot for Assistance in Urban Search and Rescue

Home , Autonomous robot, Rescue robot, Rhex, Uncrewed vehicle

ALEXANDER HUNT

Submitted in partial fulfillment of the requirements

For the degree of Master of Science in Mechanical Engineering

Advisor: Dr. Roger Quinn

Department of Mechanical and Aerospace Engineering

CASE WESTERN RESERVE UNIVERSITY

May 2010

Table of Contents A Biologically Inspired Robot for Assistance in Urban Search and Rescue ...... 0 Table of Contents ...... 1 List of Tables ...... 3 List of Figures ...... 4 Acknowledgements...... 6 Abstract ...... 7 Chapter 1: Introduction ...... 8 1.1 Search and Rescue ...... 8 1.2 Robots in Search and Rescue ...... 9 1.3 Identified Specifications ...... 10 1.4 Robotic Locomotion ...... 13 Chapter 2: Background ...... 15 2.1 Reduced Actuation Robots ...... 15 2.2 Search and Rescue Robots ...... 20 2.3 Situational Awareness Mast ...... 23 Chapter 3: Design and Manufacturing of USAR WhegsTM ...... 25 3.1 Working Model Simulations ...... 26 3.2 Chassis ...... 30 3.3 Locomotion ...... 34 3.4 Gearing ...... 40 3.5 Torsion Device ...... 40 Internal Linear Spring Design 1 ...... 42 Internal Linear Spring Design 2 ...... 43 External Linear Spring Design ...... 44 Torsion Spring Design ...... 45 Comparison ...... 46 Pursued Designs ...... 47 3.6 Wheel-Legs ...... 50 3.7 Electronics ...... 61 Chapter 4: Tests ...... 66

4.1 Wheel-Leg Test ...... 66 4.2 Lab Runs ...... 68 Chapter 5: Results ...... 70 5.1 Specifications ...... 70 5.2 Wheel-Leg Test Results ...... 73 5.3 Lab Runs Results ...... 75 Tracks ...... 75 Wheel-legs ...... 76 Chapter 6: Conclusions and Future Work ...... 79 6.1 Conclusions ...... 79 6.2 Future Work ...... 79 Appendix A. Motor calculations ...... 81 Torque Calculations ...... 81 Speed Calculations ...... 82 Motor Chosen ...... 82 Appendix B. Shaft Calculations ...... 83 Weight Calculations ...... 83 Torque Calculations ...... 84 Works Cited ...... 87

List of Tables

Table 2.1 Power to mass ratio, and speed comparison of several legged robots (Allen, 2004), (Saranli, Buehler, & Koditschek, 2001)...... 18 Table 5.1 - Comparison of WhegsTM I, WhegsTM II, Lunar WhegsTM, and USAR WhegsTM across several areas of interest ...... 72 Table 5.2 - Weight of various sections of USAR WhegsTM ...... 72 Table 5.3 - Vertical displacement of center for all 3 specimens in position 1 ...... 73 Table 5.4 - Horizontal displacement of center for all 3 specimens in position 1 ...... 73 Table 5.5 - Vertical displacement of all 3 specimens in position 2 ...... 74 Table A.1 - Data of Maxon RE 40, 150W motor and 26:1 planetary gear set ...... 82

List of Figures

Figure 1.1 - Comparison of ground compaction between a wheel and a leg (Martin-Alvarez, De Peuter, Hillebrand, Putz, Matthyssen, & de Weerd, 1996)...... 14 Figure 2.1 - Prolero ...... 16 Figure 2.2 – Rhex (Saranli, Buehler, & Koditschek, 2001) ...... 17 Figure 2.3 - WhegsTM II ...... 19 Figure 2.4 - Dagsi WhegsTM ...... 20 Figure 2.5- Inuken VGTV shown in three positions ...... 21 Figure 2.6 - iRobot Packbot with arm and camera extensions ...... 22 Figure 2.7 - OmniTread OT-8 climbing stairs ...... 23 Figure 2.8 - SAM8 on Packbot ...... 24 Figure 3.1 - Robot in final configuration next to graduate student ...... 25 Figure 3.2 - Comparison of a wheel and a wheel-leg climbing an obstacle (Allen, 2004)...... 26 Figure 3.3 - Fastest climbing configurations for (a) 1.0r, (b) 1.1r, (c) 1.2r and (d) 1.3r obstacles ...... 27 Figure 3.4 - Whegs Vehicle climbing obstacle demonstrating importance of foot length, contact angle, and open space ...... 29 Figure 3.5 - Chassis with bearings installed ...... 32 Figure 3.6 - Front chamfer adds clearance to climb larger obstacles ...... 33 Figure 3.7 - The interlocking system between the back plate (left) and left plate (right) flipped away from eachother ...... 34 Figure 3.8 - Chassis with motors and tracks attached...... 37 Figure 3.9 - Current Mini WhegsTM iteration featuring differential steering ...... 38 Figure 3.10 - Coupling between the drive motor and drive shaft ...... 39 Figure 3.11 - Exploded view of the first Internal Linear Spring Torsion Device shown from back to front – back plate, center plate with wheel-legs, bearing, and front plate...... 43 Figure 3.12 - Exploded view of the second linear spring torsion device ...... 44 Figure 3.13 - External Linear Spring Torsion Device showing back plate and legs(red), front plate and arm (blue), guiding rod (black), mounting bracket (orange) pre-tension rod (light blue) and thrust bearing (green) ...... 45

Figure 3.14 - Exploded View of torsion device showing wheel mount (green), sealed bearings (blue), outer hub (red), center mandrel (black), and torsion spring (gray) ...... 46 Figure 3.15 - Photo of linear spring torsion device near completion...... 48 Figure 3.16 - Torsion device fully assembled ...... 49 Figure 3.17 - Torsion device disassembled into main components ...... 49 Figure 3.18 - SolidWorks capture of bracket mounted to wheels ...... 50 Figure 3.19 - Diagram depicting the different layers in the carbon fiber curing process (Diagram modified from SE 85GT - Epoxy Prepreg System (v2))...... 51 Figure 3.20 – First carbon fiber foot design ...... 52 Figure 3.21 – Second carbon fiber foot design ...... 53 Figure 3.22 –Leg Design 3 ...... 54 Figure 3.23 - Leg design 3 under stress ...... 54 Figure 3.24 - SolidWorks capture of the final wheel-leg design ...... 56 Figure 3.25 – A concept drawing of all 20 layers of carbon fiber placed on the mold. Layers 1, 2, 3, 6, 8, 9, 10, 13-20 are made with woven fibers while layers 4,6,11 and 12 are made with unidirectional fibers...... 58 Figure 3.26 - Second wheel-leg design attached to torsion device and packed with foam...... 60 Figure 3.27 - Close up of third wheel-leg design ...... 61 Figure 3.28 – Final robot in track configuration ...... 63 Figure 3.29 - Robot in final configuration with wheel-legs attached ...... 64 Figure 3.30 - Robot in final configuration with mast fully deployed ...... 65 Figure 4.1 - Wheel-leg in vertical position...... 66 Figure 4.2 - Wheel-leg in horizontal testing position...... 66 Figure 4.3 - Horizontal position under load...... 67 Figure 4.4 - Measurement process of vertical position under load ...... 68 Figure 5.1 - Photograph showing the broken wheel-leg...... 77 Figure 5.2 - Separation between carbon fiber layers ...... 78

Acknowledgements

First, I would like to thank the Biologically Inspired Robotics Lab and the faculty in the Mechanical and Aerospace Engineering Department for all their support and help.

I received so much advice, from so many people, that without it, the robot would never have made it out of computer modeling. I would specifically like to thank my advisor

Roger Quinn and Richard Bachmann, both of whom have served as fantastic mentors for me in the lab, inspiring me to be creative and produce elegant solutions to the problems I encountered. I would also like to thank Arkady Polinkovsky, Matt Blanchard, and

Takahiro Hoshino who had a direct hand in developing and building some of the parts for

USAR WhegsTM.

I would also like to thank my friends and family, who constantly support me in everything I do, from school work to sports. They are a constant crutch for when I get down on myself, and continue to push me to be a better person in all aspects of life.

Finally, I would like to thank the Office of Naval Research for partially funding this project through the Naval Postgraduate School.

A Biologically Inspired Robot for Assistance in Urban Search and Rescue

Abstract

ALEXANDER J HUNT

This research developed a robot capable of operating in urban search and rescue conditions. USAR WhegsTM implements several new features in to WhegsTM robot design, some more successful than others. It is the first quadruped WhegsTM robot of this scale. It uses differential steering for control, and is able to switch between tracks and a wheel-leg system quickly and efficiently. This is also the first implementation of carbon fiber wheel-legs on a WhegsTM vehicle. The quick change-system is very effective, though the differential steering does seem to provide some control problems for the wheel-legs. The carbon fiber wheel-legs significantly decrease the inertia of the robot.

The robot is 18.75 inches long, can travel 6.25 feet per second, and can climb 6 inch obstacles.

Chapter 1: Introduction

1.1 Search and Rescue Search and rescue can be divided into many different scenarios, ranging from urban search and rescue (USAR) to wilderness search and rescue (WiSAR). USAR situations often include searching for many people in a relatively small location, such as a building collapse due to an earthquake. WiSAR situations however, involve looking for one person in a large geographic location, such as someone lost on a mountain. Another common search and rescue situation includes the collapse of a mine, which despite many advances in structural technology, still occurs frequently. Several tragedies in the past decade have highlighted the need and importance for efficient USAR deployment. These include the destruction of the World Trade Center buildings in 2001, Hurricane Katrina in

2005, and the mudslides of La Conchita, California in 2005 (Voyles & Choset, 2008).

In these and other search and rescue situations current methods for finding missing persons involve the use of specially trained teams. These teams consist of trained firefighters, specialists, and search dogs. Engineers determine if buildings are structurally sound enough to enter, while firefighters do most of the searching. Search dogs are often able to sniff out humans when visibility is very poor. Cameras are placed on poles and pushed through voids in the collapsed structures to look inside, determine if there are any survivors, and evaluate whether or not the place can be entered safely.

These teams often work on little to no sleep because teams have only 72 hours to find a trapped survivor before the likelihood of finding the victim alive drops to nearly zero

(Voyles & Choset, 2008).

1.2 Robots in Search and Rescue Recent trends show robots being implemented in USAR scenarios more and more, and the Center for Robot-Assisted Search and Rescue (CRASAR) is leading this initiative. Started at the University of South Florida under the National Institute for

Urban Search and Rescue, and now affiliated with Texas A&M “CRASAR’s mission is to improve disaster preparedness, prevention, response, and recovery through the development and adoption of robots and related technologies” (Murphy, CRASAR:

Center for Robotic Search and Rescue). So far CRASAR has been involved in training specialists in controlling new robots for search and rescue, and deploying the robots when needed. It has deployed robots in several catastrophes to date, including the destroyed

World Trade Centers, the mudslides at La Conchita, and Hurricane Katrina disaster relief.

“It serves as a crisis response and research organization which strives to direct and exploit new technology development in robotics and unmanned systems for humanitarian purposes worldwide” (Murphy, CRASAR: Center for Robotic Search and Rescue).

There are many advantages to using robots in USAR environments. Robots can reduce personal risk to humans and dogs by entering unsafe areas for them, allowing buildings that have been declared structurally unsound to be explored for possible survivors without the risk of death (Blackburn, Everett, & Laird). In the case of the mudslides, areas could continue to be searched remotely even if the area was under threat of another mudslide (Murphy, Trial by Fire, 2004). Robots can also be used by structural engineers to look at buildings from the inside in order to ascertain the structural integrity and determine if it is safe for rescuers to enter and search more thoroughly for victims.

Robots are also capable of getting into smaller voids than humans or dogs, allowing

9 exploration in otherwise impossible to reach places. Several voids in the collapsed World

Trade Center buildings were too small for a person or dog to enter, but the robots entered from 5-20 meters, much further than the camera on a pole method (Murphy, Trial by Fire,

2004).

Mobility obstacles for robots in USAR environments can range greatly, and not every robot will be able to overcome every obstacle. Smaller robots allow for the ability to get into smaller crevices and voids, but larger robots can overcome larger obstacles. In the instance of the collapsed World Trade Center, there was a lot of steel, and voids were less than a meter wide and very hot (Murphy, Trial by Fire, 2004). In buildings that have collapsed due to mudslides or hurricanes, obstacles consist of large pieces of furniture including couches and desks which are nearly impossible to surmount by robots small enough to get inside. In the case of the Hurricane Katrina relief, the robot used had to climb onto and over a mattress, 2x4s, and other pieces of wood strewn across the hallway

(Micire, 2008). Robots also encounter many different surfaces with varying traction ranging from carpet to muddy linoleum. This in itself can cause many problems as having too much traction can lead to an inability to turn on carpet, but not enough traction renders the robot incapable of traveling anywhere on the muddy linoleum.

1.3 Identified Specifications Several needs of search and rescue robots have been identified from experiences of working with several different robots in the field. These needs are listed in the following pages.

 A rescue robot should be man packable (Murphy, Trial by Fire, 2004). For most

rescue sites, a car will not be able to drive up to the place of interest, so one person

should be able to carry the robot to the point of use. The robot will need to be

quickly assembled on site as every minute in a search and rescue situation is critical.

 Robots must be equipped with a minimum of one pan, zoom, autofocus, and tilt

camera (Murphy, Trial by Fire, 2004), (Micire, 2008). It is very important that the

operator be able to look around with the camera to assess the situation. The

operator should also not be wasting precious minutes focusing the camera.

However, the focus should be able to be overridden if there is dust or particles in the

air that would cause the camera to focus elsewhere. Color cameras offer better

determination if there are any victims around, black and white cameras can offer

higher resolution for the same bandwidth.

 The camera must be raised from the floor. At the World Trade Center deployment,

the floor was littered with lots of paper, causing the cameras of the robots to be

obstructed about 18% of the time (Murphy, Trial by Fire, 2004). Raising the

camera away from the floor would ensure that they are in full use a much greater

percentage of time. Cameras near the ground also have a tendency to get covered in

mud and muck. Raising the camera would make them less likely to get semi-

permanently obstructed by the mud. Also, if the ceiling were high enough after the

void was cleared, it would allow the operator to get a more natural view of the area

(Murphy, Trial by Fire, 2004). It is often disorienting for the operator to have a

belly view of the surroundings, when humans are used to a view that is several feet

in the air.

 Safety lines are almost certainly a must, and any robot should be designed with that

in mind (Micire, 2008). The tether must be strong enough to assist in vertical

movement of the robot as well as provide a communication line to reduce the risk of

communication dropout. Steel beams and concrete in a building collapse can often

make it impossible to communicate wirelessly with a robot.

 The robot must be waterproofed or at least be water resistant (Micire, 2008). In

many instances the robot will be placed in muddy or moist conditions. Broken

pipes often lead to pools of water in a building, and the robot must not fail under

such conditions. Also, the robot often goes through contaminated areas, and must

be decontaminated following each run. This simplest and most efficient solution to

this involves washing off the robot with a partial bleach or alcohol mixture

(Murphy, Trial by Fire, 2004).

 The robot should be invertible or self-righting in some way (Murphy, Trial by Fire,

2004). If the robot were to flip over, the mission should be able to continue, and the

robot should be able to get out of the problematic situation.

 Having the robot be able to “limp” home under partial failure is also beneficial

(Murphy & Stover, Rescue Robots for Mudslides: A Descriptive Study of the 2005

La Conchita Mudslide Response, 2008). If a robot were to lose part of its mobility

for some reason, it should be able to get back to base so it can be repaired.

 Two way audio is desirable so that the workers can communicate with any found

victims, and so that the operator can listen for any cries for help during the search

(Murphy, Trial by Fire, 2004).

 The robot must be able to carry additional payload. Different USAR environments

call for different equipment for properly carrying out the search and rescue task.

Sometimes an infrared camera able to detect heat is useful, or the addition of

another camera can provide benefits. The robot should also be able to carry medical

supplies, because if someone is found, it is often hours before the rescuers can

create a safe entry to the area (Murphy & Stover, Rescue Robots for Mudslides: A

Descriptive Study of the 2005 La Conchita Mudslide Response, 2008).

 Search and rescue robots need a vigorous testing procedure. Many robots were only

laboratory tested before being put in the field, and they had some clear issues that

could have been identified and fixed if more realistic field testing had been

performed (Murphy & Stover, Rescue Robots for Mudslides: A Descriptive Study

of the 2005 La Conchita Mudslide Response, 2008).

1.4 Robotic Locomotion Robots have used many forms of locomotion over the years. Wheels have many advantages. Over smooth terrain, wheels offer a very efficient mode of transportation.

Wheel speed is easily controlled, and the knife edge constraint on wheels creates easy steering of the robot. However, when an obstacle is encountered, the wheel must be made large enough to roll on top of it.

Tracks have been added to wheeled vehicles and offer significant improvements in several areas. Tracks distribute the weight of the vehicle over a larger area, reducing ground forces on any specific wheel, and increasing traction. Steering must be done with differential drives, and a motor is needed for each side of the vehicle. For climbing, tracked vehicles offer a significant advantage over wheels because the front wheel for a

13 tracked system can be raised, or a second track system can be used, as in the case of the

Packbot, to help the robot climb over larger obstacles (Packbot).

Legs are a much more complicated form of locomotion, but offer many advantages for irregular and rough terrain. Often they take many motors, and use more power, but they have the advantage of being lifted and placed on top or over the obstacle.

This ability to be placed where needed allows the leg to get greater force from the terrain for travel compared to wheels and tracks. The legs obtain this greater force because they have discontinuous ground contact, while wheels and tracks have continuous ground contact. This continuous contact causes the buildup of ground material in front of the wheel, whereas in the case of the leg, discontinuous contact causes buildup to fall behind the leg as demonstrated in Figure 1.1 (Martin-Alvarez, De Peuter, Hillebrand, Putz,

Matthyssen, & de Weerd, 1996)Error! Reference source not found.. The buildup of material aids in travel for the leg while it impedes travel for a wheel.

Figure 1.1 - Comparison of ground compaction between a wheel and a leg (Martin-Alvarez, De Peuter, Hillebrand, Putz, Matthyssen, & de Weerd, 1996).

Chapter 2: Background

2.1 Reduced Actuation Robots Legs offer many advantages for travel over the rough terrain of search and rescue situations, but their typically larger power requirements, complicated software for control, expense and slow movement demand the need for a more elegant solution.

Reduced actuation legged robots have been researched for more than a decade with several promising results.

Two of the reduced actuation legged robots described below make use of some bio-inspiration in determining their gaits. Cockroaches and other insects use different gaits for different situations, and these robots do as well. The fastest gait for a cockroach is the tripod gait, in which the front and back legs of one side of the cockroach move in sync with the middle leg on the other side and 180 degrees out of phase with the other 3 legs (Wilson, 1966). This gait ensures that there are at least three legs on the ground at all times, a relatively stable stance, as it forms a triangle on the ground. Additionally, the front legs of the cockroach reach above its head, allowing for it to travel irregular terrain with relative ease (Watson, Ritzmann, Zill, & Pollack, 2002). When the cockroach wishes to move slower, it often uses a wave gait, in which only one leg is moving at a time, with the other five legs on the ground, and extremely stable stance. Some robots are able to do this as well.

Prolero was built as a Mars rover prototype developed under the European Space

Agency with no claims of bio-inspiration used in its design (Martin-Alvarez, De Peuter,

Hillebrand, Putz, Matthyssen, & de Weerd, 1996). A photo of Prolero can be found in

Figure 2.1. It contains six legs with just one degree of freedom each. Each leg is L

15 shaped, and rotates around itself in the sagittal plane. Prolero walks in a wave gait to reduce interaction forces between legs. This also reduces problems with lifting a leg over an object, as it is automatically out of the way as it is placed on top of each obstacle during each swing phase. Although Prolero is only centimeters high, it can overcome obstacles up to 10 centimeters (Martin-Alvarez, De Peuter, Hillebrand, Putz, Matthyssen,

& de Weerd, 1996).

Figure 2.1 - Prolero

Another reduced actuation robot is RHex, shown in Figure 2.2, developed at

McGill University (Saranli, Buehler, & Koditschek, 2001). Much like Prolero, Rhex has six sagittal rotating legs each driven by its own motor to swing its foot in a circle. Driven by its six motors, it can travel over obstacles much higher than its own body clearance.

Unlike Prolero its legs are compliant. RHex travels over broken ground very quickly and efficiently and without any terrain sensing. Also, unlike Prolero, each leg is accelerated and decelerated through its rotation, moving slowly during stance, but quickly during the rest of rotation so it can return to stance again. These rates can also be controlled,

16 allowing for more complex behaviors such as turning and gait changes. The original

Rhex can run up to one body length per second and is .53 meters long (Saranli, Buehler,

& Koditschek, 2001). More recent RHex versions can run much faster (Weingarten,

Lopes, & Koditschek, 2004).

Figure 2.2 – Rhex (Saranli, Buehler, & Koditschek, 2001)

The WhegsTM series developed at Case Western University takes the idea of reduced actuation that Prolero and RHex have taken advantage of, and reduces the number of actuators even more. Instead of putting one leg at each joint, it places three or four legs around a central hub called a wheel-leg. A set of four or six of these wheel-legs can then be run with just one propulsion motor, as the swing phase for each leg contains the stance phase of two other legs, and variable speeds controlling stance and swing phases are no longer needed. Using chains and sprockets to drive all of the wheel-legs with one motor, front and back legs of one side are placed in phase with the middle leg on the opposite side of the robot, and directly out of phase with the other three (Quinn,

Kingsly, Offi, & Ritzmann, 2002). This allows the robot to travel with a simple tripod gait. Each hub is connected by a mechanical spring system which allows for passive gait adaptation. WhegsTM I could move at 5.5km/h or three body lengths per second, and could climb obstacles 1.5 times its leg length (Allen, 2004).

Table 2.1 Power to mass ratio, and speed comparison of several legged robots described above. Table 2.1 shows the advantages of using one motor over multiple in both weight and speed.

CWRU R-II Rhex WhegsTM II Number of Motors 18 6 1+ Power Per Motor 6 20 90 Total Power 108 120 90 Gear-Motor Mass 2.7kg 1.8kg .87kg Power/Mass 40W/kg 67W/kg 103W/kg Velocity/Length .16 1.04 3+ Table 2.1 Power to mass ratio, and speed comparison of several legged robots (Allen, 2004), (Saranli, Buehler, & Koditschek, 2001).

WhegsTM II, shown in Figure 2.3, contains many of the implementations of

WhegsTM I, but has the addition of a body joint, much like a cockroach. The body joint allows for the robot to climb even higher objects as it is able to rear its front end up over larger obstacles, just as a cockroach does. The body joint is also pitched downwards when the front of the robot clears the beginning of the obstacle. This prevents high centering which would cause the robot to fall over backwards. Additionally the body joint can be flexed if the robot were to catch on a rock in order to get a foothold in an otherwise unreachable position. The addition of the body joint adds another 59% in

18 climbing ability, letting WhegsTM II surmount an obstacle nearly 2.4 times its leg length.

(Allen, 2004)

Figure 2.3 - WhegsTM II

Several other WhegsTM robots have been made that demonstrate the versatility of the WhegsTM platform. Robb’s WhegsTM demonstrates the ability of the WhegsTM platform to move through an orchard without getting caught up in the uneven ground, dead branches or steel pipes (Schroer, Boggess, Bachmann, Quinn, & Ritzmann, 2004).

DAGSI WhegsTM, shown in Figure 2.4, is 81 cm long and is the largest WhegsTM robot

(Boxerbaum, Oro, Peterson, & Quinn, 2008). This is proof of how the WhegsTM vehicles can be scaled and how robust they can be. It also implements a body joint with compliance which allows for the robot to more readily adapt to its environment while maintaining the versatility that a drivable body joint allows. There is the Mini-WhegsTM version only 8 cm long that shows how WhegsTM can be scaled down just as well as it is scaled up (Morrey, Lambrcht, Horchler, Ritzmann, & Quinn, 2003). The new Mini-

WhegsTM is driven with two motors and it steers with a differential drive and there are there are 4 legs on each of its 4 wheel-legs as well. Lunar WhegsTM is a proof of concept

19 moon rover (Dunker, Lewinger, Hunt, & Quinn, 2009). It is able to travel on loose sand has additional space for mission task attachments, and has a scoop for collecting lunar regolith. The latest robot in design is Beach-Whegs, and will be an amphibeous Whegs robot capable of exploring along the coast, in and out of the water (Boxerbaum, et al.,

2009).

Figure 2.4 - Dagsi WhegsTM

2.2 Search and Rescue Robots Inuktan VGTV built by American Standard Robotics is a tracked robot that has been used in the three above situations, but was originally developed for industrial and air conditioner inspection. It has a polymorphic chassis capable of changing its body shape, as shown in Figure 2.5 (Micire). The VGTV has shown itself to be successful in multiple situations. The VGTV has gone through a few iterations, with its original making it about 18 meters into the World Trade Center rubble before detracking (Murphy 2004).

The newer VGTV Extreme was unsuccessful at the mudslides of La Conshita, lasting

20 only 2 min and 4 min on each of its two runs, respectively (Murphy 2006). Both failures were due to de-tracking on the wet carpet of the buildings. However, these de-tracking problems were not realized in a search in the aftermath of Katrina, where it successfully completed two runs in a thirty minute period.

Figure 2.5- Inuken VGTV shown in three positions

Packbot is a commercial robot built by iRobot Corporation and is a very accomplished robot in the field. It drives on two tracks with differential steering, just like the VGTV, however it has two more “flipper” tracks that are on the front of the robot and are used to climb over larger obstacles, and up stairs. The robot can travel about 5.8 mph and can be carried by just one person. Packbot is also deployable in less than 2 minutes.

With over 2500 Packbots built, the model has continued to evolve in the field and can be outfitted with dozens of different sensors and accessories making it a very effective robot.

Packbot is shown in Figure 2.6.

Figure 2.6 - iRobot Packbot with arm and camera extensions

Two other classes of search and rescue robots are snake and serpentine robots.

These robots are multi-segmented mechanisms that gain propulsion either through relative joint motion from wheels, legs or tracks placed on the segments. They have the advantage of fitting through very small openings while still being able to climb vertical steps. The OmniTread OT-8, shown in Figure 2.7, built by researchers at the University of Michigan is one such robot that shows a lot of promise (Granosik, Hansen, &

Borenstein, 2005). With five segments, the OmniTread moves along the ground using a track system on every face of every segment, and is able to move each joint with a pneumatic bellows system. It can travel at 10 cm/s, over curbs 45.7 cm high, and across gaps 66cm wide even though it is only 127 cm long (Granosik, Hansen, & Borenstein,

2005).

Figure 2.7 - OmniTread OT-8 climbing stairs

2.3 Situational Awareness Mast The situational awareness mast or SAM is made by a company called Geosystems

(Zippermast). Based on a design that Hollywood uses for its lights, it is nicknamed the

ZipperMast because it works much like a 3D zipper. There are three thin steel segments that roll up much like a tape measure. When they are unrolled, they interlock together to form a sturdy triangle. The SAM comes in many different sizes, ranging from the 10 lb

SAM-8 model which can raise up to 8 feet to the 150 lb SAM-20 model which can raise

200 lb, 20 feet. The SAM can also be made waterproof.

There are many uses for the SAM, though it was originally designed to allow operators to steer robots under vehicles and raise up a camera to look around from a small base. Other uses include camera surveillance, emergency response, and numerous military operations in all terrains. So far different SAMs have already been included on

23 many different types of robots. It has been put on smaller robots, like the iRobot Packbot

(Figure 2.8) or Harris Corporation “ADAM”, to larger military vehicles like the Foster

Miller TAGS-CX (Zippermast).

Figure 2.8 - SAM8 on Packbot

Chapter 3: Design and Manufacturing of USAR WhegsTM

Figure 3.1 - Robot in final configuration next to graduate student

3.1 Working Model Simulations WhegsTM robots have shown an incredible ability to traverse irregular terrain and overcome obstacles. Traditionally, three spoke wheel-legs have been used on these robots as they offer the maximum theoretical obstacle clearance of 1.7r, as shown in comparison to a wheel in Figure 3.2.

Figure 3.2 - Comparison of a wheel and a wheel-leg climbing an obstacle (Allen, 2004).

However, the exact number of spokes, the size, and shape of efficient wheel-legs has not been determined experimentally. Prototyping and buildings robots and different wheel-leg sets is expensive, so computer modeling and simulation can provide valuable insights into this area.

Philip Dunker and Alexander Boxerbaum, students from the Mechanical and

Aerospace Engineering Department of Case Western Reserve University, created a simulation in Working Model 2D involving modeling a WhegsTM robot, having it climb over a block obstacle, and recording the time it takes to reach the end of the obstacle

(Dunker & Boxerbaum, Evolving WhegsTM: Optimization of Wheel-Legged Climbing using a Genetic Algorithm, 2008). It is a genetic algorithm that involves creating fifty

26 different robots in each generation, and having the fastest robots “reproduce” to create the following generation with similar phenotypes. Each robot has five variable parameters: number of legs, hub radius, degrees of leg contact, degrees of base exposed, and distance between the axles.

This was done on 5 different obstacle heights: 1.0, 1.1, 1.2, 1.3, and 1.4 times the radius of the wheel-leg. Each trial lasted for 50 generations, and the results are analyzed next.

The simulation found convergence of a specific wheel-leg design on all the obstacles up to 1.3r (1.4r was not achieved in simulation); however each simulation converged on a different design based on the obstacle height. The fastest designs for each simulation are depicted in Figure 3.3. A five spoke wheel-leg was found as the fastest for 1.0r, seven spokes for 1.1r, and three spokes for the higher 1.2r and 1.3r obstacles.

Figure 3.3 - Fastest climbing configurations for (a) 1.0r, (b) 1.1r, (c) 1.2r and (d) 1.3r obstacles

The first noticeable result is the use of three wheel leg systems for climbing larger obstacles (Dunker & Boxerbaum, Evolving WhegsTM: Optimization of Wheel-Legged

Climbing using a Genetic Algorithm, 2008). This supports the decision to use the three

27 wheel-leg system on previous Whegs™ robots. Another result evident from looking at the data is that the wheelbase of the robot for the fastest climbers was found to occur so that a back wheel leg would contact in the exact position that the front wheel leg did

(Dunker & Boxerbaum, Evolving WhegsTM: Optimization of Wheel-Legged Climbing using a Genetic Algorithm, 2008). This minimizes the time the rear leg spends searching for a foothold on top of the obstacle.

Closer inspection of the fastest one hundred models from any generation gives further detail into designing better wheel-legs. Five spokes remains very dominant for

1.0r, and there are nothing but three spokes in the 1.4r group. In the 1.1r group, there are wheel legs of three, five, seven, and eight spokes all showing signs of performing well.

The 1.2r simulation contained a few three spoke designs, but was mostly dominated by four spoke wheel-legs. These results show that although the three leg design is a factor in quick climbing, and necessary in very high climbing, the number of legs may not play as big a part for all other obstacles.

Further examination of the data showed that the contact angle of the foot played a very important factor. For each number of spokes subset in the fastest one hundred, there was a distinct one or two angle pair for the degrees of foot contact and degrees of exposed inner hub. These radii showed several things. First it ensured that the contact angle of the foot on obstacle was flat, giving the most friction for climbing on top as shown in figure. If the angle was not great enough, then the spoke would contact the corner of the obstacle before the foot could touch the top and bounce away. If the angle was too great, the leg could not get a proper foothold on the object to climb it, causing the

28 leg to slip off. The second thing the angles showed is that the amount of time the foot is contacting the ground on its radius should be maximized. This allows the robot to travel the furthest distance when there is less space between the feet. Finally, the amount of empty space should be maximized, making the hub as small as possible while still maintaining the necessary contact angle to climb the object. These things can be seen in

Figure 3.4.

Figure 3.4 - Whegs Vehicle climbing obstacle demonstrating importance of foot length, contact angle, and open space

Several experiments were performed in an attempt to get the robots to climb a staircase but with little success; the interaction with the environment was not behaving with much accuracy in the simulation. However, one conclusion drawn from the experiments is that placing the center of mass more forward on the robot allows it to climb better than a center of mass positioned towards the rear of the robot. If the center of mass is in the back, the robot has a tendency to flip over backwards, while a forward center of gravity alleviates this problem.

There are several limitations to the simulation, many of which can only be overcome by physical modeling. The way Working Model calculates ground contact forces is often inconsistent and inaccurate. Often the robot will bounce off the ground or an object even if the elasticity of the contact objects are both set to very low. The program also had bugs associated with adding fixed objects to the robot body, and the

29 objects were often flung around the screen. Secondly, each simulation optimized a robot for climbing one obstacle of a certain height. WhegsTM robots are made to travel over uneven terrain with both small and large obstacles, and routinely encountering a specific sized obstacle does not occur. In future simulations, a varying terrain can be used to test wheel-leg performance for more realistic situations. Nevertheless, the simulations provide some interesting data and several important conclusions can be made.

These limitations and conclusions were incorporated into the design of the current wheel-legs. The ratio of the distance between the wheel-legs and size of the wheel-legs is engineered so that the back feet step a little forward of where the previous front foot was placed. This ensures that efficient climbing over obstacles takes place even when there is some slipping between the foot and the surface. Secondly, the wheel-legs are designed to be compliant on the end in order to reduce impact forces and minimize the chance of the leg bouncing off of obstacles. This compliance also ensures that a good grip is found when climbing on top of the obstacle, and minimal slipping occurs during walking.

Finally, the center of mass is shifted forward on USAR WhegsTM in an attempt to keep the robot from high centering and flipping over when climbing stairs.

3.2 Chassis The main concern in the design of the chassis was to keep things simple. Since this is a prototype, aesthetics, size, weight, and efficiency are less important than strength and functionality. The main chassis is built as a simple block, where each side is rectangular. All material in the chassis is 3/8 inch 6061 aluminum and is able to withstand nearly every stress situation USAR WhegsTM will encounter. The front and back panels are solid aluminum, while the sides have some extraneous material removed

30 in order to reduce weight. Material was left on the top and bottom and a vertical bar in the middle, where additional holes can be added to the robot as the design progresses and refines. Bearing holes also have significant material around them for strength. Inside the main chassis, there is an inner bearing rail running on each side, which is used to align a second row of bearings and hold the motor. Although it adds some weight, the addition of the second rail adds significant strength to the drive system. When forces on the track pull the wheels together, the bearings in the rail are pulled apart and the rail is in tension, resisting this movement. The final part of the chassis is a support on the bottom which holds the SAM 8 the batteries, and other parts of the electronic system. The support is a bare-bones system. There is a ring underneath the SAM 8 which has supports that branch to the sides and corners. There is also a thin block of material for mounting the batteries.

All other material is removed from the support. It is mostly supported by pins and not screws. The pins are located underneath the SAM 8, and connect the bottom support in to the side rails. The bottom support is also screwed into the back for additional stress distribution and alignment.

Figure 3.5 - Chassis with bearings installed

Ground and obstacle clearance are of some concern for USAR WhegsTM. Two design features help alleviate this. The shafts are moved below center to increase the overall ground clearance. Also, the front of the robot has an angle on the bottom which significantly adds to obstacle clearance. Without the slant, there is only .4” from the corner of the robot to the track edge. With the addition of the slant, USAR WhegsTM has a clearance of .85”, allowing the robot to climb much higher obstacles at least 1.5 inches while in its track form. The beveled front chassis also makes the robot less likely to catch on obstacles and stairs when climbing with the wheel-legs.

Figure 3.6 - Front chamfer adds clearance to climb larger obstacles

Connecting the sides of the chassis with the front and back involves a complicated interlocking system. This interlocking system, shown in Figure 3.7, allows for only two degrees of freedom, ensuring that the screws are mostly used in tension and not in shear where they most often fail.

Figure 3.7 - The interlocking system between the back plate (left) and left plate (right) flipped away from eachother

The simpler design makes for quicker and easier assembly and disassembly. As

USAR WhegsTM is a prototype, parts often need to be changed or adjusted, and the quicker the robot can be assembled and disassembled allows for a quicker turnaround in finding out how the changes affect the robot. When there are fewer parts and connections, there are fewer places for failure as well.

The design of USAR WhegsTM places the center of gravity slightly forward from middle as determined from the Working Model simulations. This is done by placing the

SAM 8, the most massive component of the robot, more forward. This also allows for more area in the rear of the robot to house the electronics, keeping the wiring more compact.

3.3 Locomotion USAR WhegsTM is designed to have two interchangeable forms of locomotion, a track system as well as a wheel-leg system. The tracks are useful for relatively flat

34 ground, when the mission tasks may involve working on a road or in a relatively unobstructed building. Tracks more evenly spread out the weight of the robot. If the ground is soft mud or sand, the robot is less likely to sink into the ground when using a track system as compared to a leg system. If the mission tasks involve more uneven terrain, such as debris from a collapsed building or a rocky rubble pile, then the wheel- legs provide a much better choice for overcoming the obstacles. In order to achieve this interchangeability, the track system is permanently attached to USAR WhegsTM, while the wheel-legs are quick pin attachable and detachable from the track system. This allows for quick on-site changes in and out of each system based on operator discretion.

The reason for the quick change ability is that it is not often known what the specifics of a search and rescue mission are going to require. Having a system that is quickly adaptable to the situation after arriving on site is very advantageous.

The addition of tracks also can help the robot from getting stuck on rocks and other such objects. WhegsTM robots have been known to get hung up when a rock gets underneath the body and the robot can no longer get a foothold with either the front or back wheel-legs. The addition of a body joint in the past has helped in this aspect, though it has not completely alleviated the problem. Having treads that run the entire length of the robot plays into the same fundamental design consideration used in the making of Omnitred where there is “maximal coverage of all sides…with propulsion elements” (Granosik, Hansen, & Borenstein, 2005). Whenever any tracks are touching the terrain, they will help propel the robot forward as compared to when chassis parts are touching the ground they will create friction and prevent the robot from moving forward.

Each system necessitates different speed and torque requirements. When traveling over even ground, USAR WhegsTM requires more speed and less torque.

Ideally the robot can go at a fast walking speed, or about 2 m/s. For a wheel size of 4.28” this comes out to be 350 revolutions per minute. When the robot is going through uneven terrain, it needs to run slower for stability and control. It also needs greater torque for lifting itself over obstacles. The estimated torque needed for lifting the robot over an obstacle is about 34 N-m. The calculations for this can be found in Appendix A.

The motors being used are 150W Maxon motors with a 26:1 gear reduction. This motor gives USAR WhegsTM a speed of 1.53 m/s on tracks and a torque of 35 N-m. The decision for having the lower speed and higher torque takes several things in to consideration. First, since WhegsTM vehicles are made for climbing, having the required torque is more important than achieving high speeds. Also, Maxon motors are very durable. Using pulse width modulation (pwm) control allows for the motors to be safely overvoltage while only minimally affecting long term performance. The motors are rated for 12V, and are over voltaged by 50% increasing torque and speed by the same margin.

This would give the robot a speed of 2.3 m/s on tracks under no load, and adding an additional safety factor in climbing over obstacles.

Differential steering is used on USAR WhegsTM, as the use of tracks necessitates it. This is the same type of steering that tanks and bulldozers use. In differential steering, each side of the robot or vehicle is controlled by separate motors. One motor controls the track on the right side of the robot, while the other motor controls the track on the other side. By adjusting the speed and direction of each track, the speed and direction of the

36 entire robot can be controlled. To turn right, the left side of the robot must travel faster than the right. For even more acute turns, the left motor turns forward while the right motor turns backwards. This phenomenon of differential steering allows the robot to turn in place, giving it a turning radius of zero body lengths. Figure 3.8 shows the chassis with the two motors and tracks attached.

Figure 3.8 - Chassis with motors and tracks attached.

Using two motors and differential steering has both advantages and disadvantages. An alternating gait is no longer controllable as it is with previous

WhegsTM robots. However, by using four spokes on each wheel-leg instead of two, the need for a quadruped gait is less critical. The additional drive motor also adds significant weight to the robot. The current Mini WhegsTM is proof that this type of robot is still able to perform exceptionally well over rough terrain. The two motors actually make it more

37 maneuverable than previous Mini WhegsTM versions, due to the zero turning radius. The lack of gait control does not seem to hamper its ability to maneuver over even or uneven ground.

Figure 3.9 - Current Mini WhegsTM iteration featuring differential steering

The design of the drive shafts proved to be non-trivial. This is because USAR

WhegsTM is not wide enough to allow for a coupling of the drive shaft of the motor directly to the shaft of the wheel. The motors were placed next to the drive shaft, and gears were found that can transmit the required torque of the motor. A gearing of 1:1 was chosen as an adjustment of the speed and the torque was initially deemed not necessary.

Figure 3.10 - Coupling between the drive motor and drive shaft

Half inch steel shafts are used for the drive shafts, giving a safety factor of 3 for the stall torque of the motor. Aluminum shafts of the same diameter were chosen for the rest of the wheels for weight savings. The calculations for shaft forces can be found in

Appendix B.

A track tensioning system was left out of USAR WhegsTM for several reasons.

There is little wear-in period for a belt as compared to a chain whose joints wear out over time. Therefore, the distance between the axles only needs to be found properly once, and it holds true for most of the robot’s life. The addition of a tensioning system would add unnecessary complications to the design.

3.4 Gearing After observing the robot run with the tracks, and the speed it was able to achieve, it became apparent that when the wheel-legs are placed on the robot, it could achieve speeds that are likely to be dangerous to the robot’s components. The current diameter for the tracks is about 4.28” and the wheel-legs for the robot are at approximately 15”.

This increase of 3.5 times in diameter increases speed by approximately the same amount. This means USAR WhegsTM could get up to nearly 7 m/s or 15 mph, an extremely fast and unnecessary speed for such a small system. A careless operator could easily destroy the robot by running it too fast with the wheel-legs mounted on it. The implementation of a quick and easy system that could gear the robot speed down will help prevent this circumstance.

This project is being worked on by Rose Glinka, a senior in the Mechanical and

Aerospace Engineering department. The system will be easily integrated into the current robot design and features a 3:1 gear reduction in the robot’s speed.

3.5 Torsion Device The torsion device is a necessary part of the WhegsTM robot design as it allows for passive gait adaptation over irregular terrain. Several torsion device designs were pursued in the creation of this WhegsTM robot, three linear spring designs and one torsion spring design. Both a linear spring design and a torsion spring design were manufactured and the final design was a modification of the original torsion spring design.

The design of torsion devices for the WhegsTM series of robots is constantly evolving. There has not been a design that is easy to construct, durable, and fully reliable. The first design in WhegsTM II used dental rubber bands as the spring

40 mechanism; however they would break. O-rings were then used, which worked well until they wore and failed over time, as o-rings are not intended for repeated stretching and deformation. Newer designs have utilized torsion springs inside a chamber. These designs last longer than the o-ring design, but there are still many problems with them.

The best springs for the torsion device use many coils, and are therefore long and take up a lot of horizontal space on the robot. WhegsTM robots are better suited when the legs are placed closer under the robot body, as it makes the robot less likely to get caught on rocks and other objects. Also, the torsion springs are only meant to be safely preloaded a maximum of 360 degrees before binding, twisting, and permanent deformation occur.

Current systems require more travel than this, giving more opportunity for the design to fail. Pre-tensioning the torsion spring systems is also a difficult procedure. The system must be wound by hand, and then the securing cap must be placed on top. If the operator is not careful, the system will often slip, causing the system to unwind. Newer torsion devices hope to alleviate some of these problems.

The newest torsion device concept is one containing a linear spring. The idea is to wrap a linear spring around in a circle, fully contain it, and then compress it with a radial traveling component attached to the other part of the torsion device. This creates many improvements over previous designs. It cuts down on the horizontal distance the torsion device takes up, by only needing to be slightly wider than the diameter of the spring. It makes it easier to combine the torsion device with the wheel-legs, even further cutting down on the horizontal distance the wheel-legs are splayed from the center of the robot. This makes the robot slimmer and more maneuverable in complex environments.

The linear spring design also cuts down on the weight of the robot, as the wheel-legs and

41 the torsion device are combined, reducing material needed to attach the wheel-legs to the robot. All linear spring designs should be more readily adjustable than previous torsion spring designs. Different size springs can easily be swapped in and out of the device, and stoppers can be placed into the slot, allowing for different pre-tension forces to be applied. With an easier adjustment system, field tests determining the best pre-tension and stiffness (based on robot size and weight) can be run more quickly than in the past.

There are a few drawbacks to this design, as linear springs are not made to be bent in circles, but rather for linear compression. This means that the radius of curvature must be small enough that on a differential scale, the spring can still be treated as traveling linearly. It is estimated that for springs of the needed size, the curvature should be a minimum of about five inches in diameter. This means that although the torsion device will be narrower, it will expand in the radial direction by a significant amount. This is an acceptable tradeoff though because the wheel-legs will be placed over top of the device and will need to take up space radially. So far, three designs have been introduced: two with a fully enclosed spring, and the other with an exposed spring.

Internal Linear Spring Design 1 The internal device shown in Figure 3.11 is made up of the following components. There is a front and back plate to contain the system, a middle plate that attaches to the wheel-legs, a middle bearing, the linear spring, two stopping bars, and the travel mechanism. The front and back plates are fixed in orientation with each other, and are fixed to the drive sprocket, allowing the middle section to travel freely between them.

The middle section has a large C shaped groove around the outside that houses the spring, and two smaller groves which the stopping bars travel through. The stopping bars are

42 held between the front and back plates in the notches shown and travel through these smaller grooves to hold the pre-tension and limit the range of motion. There is a middle bearing to allow smooth motion of the wheel-legs when the spring winds up. The travel mechanism is a pin that is attached to the front plate and travels through the grooves in the middle plate, where it causes the spring to compress when the wheel-legs are winding up.

Figure 3.11 - Exploded view of the first Internal Linear Spring Torsion Device shown from back to front – back plate, center plate with wheel-legs, bearing, and front plate.

Internal Linear Spring Design 2 The second internal device is designed by Matthew Klein and is shown in Figure

3.12. This design reduces the number of large plates needed in the system to two, significantly reducing the weight. The top plate shown has holes for the attachment of wheel-legs. The shoulder screws keep the two sections together as well as limiting the

43 range of motion for the torsion device. This design also features interchangeability between a three leg system and a four leg system. Testing will be done with these devices to determine the effect of a different number of wheel-legs on a WhegsTM robot in field situations.

Figure 3.12 - Exploded view of the second linear spring torsion device

External Linear Spring Design The external linear spring torsion device may be based on the same principles as the internal systems, but its design is fundamentally different. The components of the external system shown in Figure 3.13 are: a back mounting plate, front mounting plate/arm, bent guiding rod, mounting bracket, removable pre-tension rod, and thrust bearing. In the external device, only the front plate and arm is fixed to the drive shaft.

The legs are attached to the back plate, which is around a bearing so that it can rotate and

44 compress the spring. These pieces are separated by a thrust bearing to keep them moving smoothly in relation to each other. The spring fits around the bent rod. It is captured by a hole in the front arm on one side, and fixed to the mounting bracket on the other. This mounting bracket is attached to both the wheel-legs and the bent guiding rod. During operation, the guiding rod slides through the arm, compressing the spring and “winding” the mechanism. The pre-tension rod is only used to put the system together, and can be unscrewed after assembly and pre-tensioning to let the robot operate normally.

Figure 3.13 - External Linear Spring Torsion Device showing back plate and legs(red), front plate and arm (blue), guiding rod (black), mounting bracket (orange) pre-tension rod (light blue) and thrust bearing (green)

Torsion Spring Design A torsion spring device was also pursued. It was originally designed and constructed by Arkady Polinkovsky, a graduate student in the Mechanical and Aerospace

Engineering Department. The torsion spring device includes a steel mandrel that runs

45 through the middle of an outer aluminum hub. This hub is relatively thin, and contains an outer ring to which wheel-legs can be attached. The mandrel is supported on each side by a bearing, and can be divided into two sections. The bottom contains a lip to catch the torsion spring, along with tapped holes along the circumference facing radially for shoulder screws. These screws exit out of the aluminum hub through slots and are used for the pre-tensioning system and range of motion limiters. The rest of the mandrel is a shaft which the spring wraps around, and prevents the spring from twisting under high loads. The spring exits the device through a slot in the hub, which also contains it.

Figure 3.14 - Exploded View of torsion device showing wheel mount (green), sealed bearings (blue), outer hub (red), center mandrel (black), and torsion spring (gray)

Comparison Each solution has its own positive and negative factors. The internal mechanisms are more robust than the external and can resist impacts of a much higher scale. They also have the capability of being fully sealed from the outside, preventing dirt and grime from interfering with the mechanism. The external device however is easier to disassemble and reassemble: the necessary components are all visible and easily

46 accessed. The external device is also significantly lighter than any of the internal devices, as the spring is contained by a guiding rod inside, rather than an entire container around it. The torsion spring design offers a lower moment of inertia, since most of the mass is close to the center of the device. After all these considerations, two designs were pursued in the creation of USAR WhegsTM, one internal linear spring design, and the torsion spring design. The second internal linear spring design was chosen for its robustness and interchangeability. The torsion spring design was chosen for its durability and dependability.

Pursued Designs The internal linear spring design is being pursued by Matthew Klein. It does not offer the quick connection system that the torsion spring design contains, however USAR

WhegsTM does offer screws on the connection devices which allow for the connection of the torsion devices and further testing of this design. The current build follows the initial design described earlier and is shown in Figure 3.15.

Figure 3.15 - Photo of linear spring torsion device near completion.

Several adjustments were made to the torsion spring device to properly integrate it with USAR WhegsTM. First the shaft was adjusted so that the quick-release pin can slide through it and attach to the robot. The new design of the mandrel shaft was made of aluminum to reduce weight, and features a tapered design that contours to the outside of the pin. This allows the pin to slide completely into the inside of the mandrel, keeping it from sticking out where it could get depressed by accident when passing by an object.

Sealed bearings were chosen to replace the open bearings of the system to prevent dirt

USAR WhegsTM from getting inside and binding up the system. Finally the initial design did not include a way to transmit torque from the drive system to the torsion device and wheel-leg. After pursuing several different options, the choice was made to have a six

48 spoke castellation design stick out from a piece connected to the wheel, and the corresponding indentation be machined in to the mandrel. This decision was made for two reasons. First the increased surface contact between the two parts over other designs transmits less force for the same torque and allowed for the part to be fabricated from aluminum rather than steel. This design also allows for plenty of space for the quick- release pin shaft to slip through the middle, and catch on washers inserted into the other side of the castellation piece described later.

Figure 3.16 - Torsion device fully assembled Figure 3.17 - Torsion device disassembled into main components

The connection between the track wheels and the torsion devices involves an aluminum piece permanently attached to the front and back wheels of each side. The aluminum piece is a double sided part that has a six pronged castellation system that interlocks with the attaching wheel-legs, and contains a hole in the center for the quick- release pin to slide through to lock. The other side fits snugly into the existing holes of the wheels. The balls on the quick release pin hold against a small steel washer in order to prevent wear and fatigue failure. Any system with the corresponding castellation design and a quarter inch quick pin can be clipped in to the wheel.

Figure 3.18 - SolidWorks capture of bracket mounted to wheels

3.6 Wheel-Legs The wheel legs are made from carbon fiber using the carbon fiber facility available in the Aerostructures Lab of the Biorobotics Complex and a process that has been used in the making of Micro Air and Land Vehicles. This process involves making a mold out of Ren Shape 5008 and baking carbon fiber onto that mold. The exact shape of the mold desired is first designed in SolidWorks and then cut out in the Biologically

Inspired Robotics Lab with the HURCO CNC machine. The mold is then sanded into the desired shape. Then the mold is covered in Teflon to keep the carbon fiber and epoxy from bonding to the mold. The carbon fiber layers are placed over top in the desired shape and with the desired thickness. Two different types of carbon fiber are used.

There are cross hatched carbon fiber pieces, where the fibers are weaved together to form strength in all directions. There are also unidirectional carbon fiber pieces which have all the fibers facing one direction, making it extremely strong in one direction, but

50 containing almost no strength laterally. After the carbon fiber is laid on the molds, the entire thing is covered in a layer of perforated Teflon followed by breather. This is then vacuum sealed and baked at a little over 100 oC until the epoxy in the carbon fiber pieces flow into the desired shape and harden, locking the carbon fiber into the shape of the mold.

Figure 3.19 - Diagram depicting the different layers in the carbon fiber curing process (Diagram modified from SE 85GT - Epoxy Prepreg System (v2)).

Three carbon fiber wheel-leg designs have been pursued. A large limitation in current USAR robots is that smaller robots cannot climb up stairs to a second story, where possible survivors of a disaster may be found. In the creation of all three designs, the main consideration was for the ability of USAR WhegsTM to climb stairs. This means that the leg should be compliant to absorb the impact of stepping on top of the stairs, and then maintain strength for lifting the robot. A leg that could adjust its contact angle with the step (as described by the Working Model simulations) would be ideal, and this would also likely be achieved through compliance. Each design was made about 3 inches long,

51 and could be placed on Lunar WhegsTM for testing, though no design has made it that far in the process.

The first design, created by Matthew Blanchard and shown in Figure 3.20, features a strong center with two flexible side contact points. It is mirrored across center so that both forwards and backwards stepping is possible and equally achievable. One mold was made, and several different legs were made, each with a different number of layers. These different amounts were then tested for durability, and their relative strengths were assessed.

Figure 3.20 – First carbon fiber foot design

The other two designs were created by Takahiro Hoshino for a senior project class in the Fall of 2009. His first design was based loosely on insect feet, where the foot

52 comes out from the base and splays out to reduce shock (Figure 3.21). The design takes a simple flat shape parallel to the direction of travel, twists 90 degrees as it goes away from the hub, and then circles forward and back on itself. This design is easy to construct, as it is one strand that wraps through the entire shape.

Figure 3.21 – Second carbon fiber foot design

The last design features a similar strong base structure to the leg that Matthew

Blanchard made, but it is not mirrored and only has shock absorption in one direction.

The shock absorption is more complicated; as the forces are absorbed by a flexible part that is capable of sliding off the end of the leg for even greater compliance as shown in

Figure 3.22 and Figure 3.23.

Figure 3.22 –Leg Design 3

Figure 3.23 - Leg design 3 under stress

The design used for this robot is a modified version of Takahiro’s first design.

The design was flipped around, and the hook end was extended and wrapped back towards the base. The design was also made to be 15 inches in diameter, and thicker to accommodate the larger robot. Previous wheel-leg designs that had hooks on the front often got caught on objects as they were just releasing from the ground and entering the swing phase, preventing the leg from rotating and keeping the robot from moving forward. By rounding out the front part and bringing it all the way back to the hub, it is much less likely to get caught on obstacles. Finally, the mold was made so that all four wheel-legs are connected together and can be slid onto and attached to the torsion device as once piece. This speeds up the process for creating the wheel-legs and adds to the strength of the design around the hub.

The foot also extends for approximately 35 degrees of the entire wheel-leg. This combined with its flexibility create a smoother ride than rigid stick legs. Also since it is flexible and adaptable, it should be more efficient for traveling over rough terrain, passively adapting to the ground. The initial contact point is curved, and when combined with the flexing should allow for a significant contact area upon impact when climbing over obstacles and up stairs. This was done according to the desired design features discovered during the Working Model simulations.

Figure 3.24 - SolidWorks capture of the final wheel-leg design

This bend in the design also works to give the impact-compliance non-linear spring properties. When the leg heel impacts, and bends backwards, it contacts the stiff part of the leg, creating more resistance and making it harder for the leg to deform.

When the leg impacts the ground, the initial shock is absorbed by the highly compliant section, but during continuous ground contact, the leg is stronger and more stable.

The layering of the carbon fiber was done meticulously with a total of 20 different layers on the mold. The first design used 10 layers, and this was determined to be too flexible during the testing procedure. An additional 5 layers were added, mainly to the bottom sections which were determined to be the problem area. This wheel-leg experienced failure, so another 5 layers were added. Each layer concentrated on adding strength and rigidity to certain sections, so that each area is able to withstand the forces

56 that it receives. A diagram of each layer is shown in Figure 3.25, with the first test wheel-leg ending at 10 layers, the second wheel-leg with 15, and the most recent wheel- legs, including all wheel-legs on USAR WhegsTM, containing all the layers.

Figure 3.25 – A concept drawing of all 20 layers of carbon fiber placed on the mold. Layers 1, 2, 3, 6, 8, 9, 10, 13-20 are made with woven fibers while layers 4,6,11 and 12 are made with unidirectional fibers.

A neoprene rubber rated at Shore A 60 cushions the impact of the wheel-leg on the ground. This is the strength normally used in tires, and provides a balance of durability and flexibility for the robot. The rubber is textured and also acts as a gripping surface since the hard carbon fiber is very smooth and unable to get traction on other smooth surfaces like tile or wood. The chosen rubber is also impact and weather resistant, increasing durability. It is attached to the wheel-legs with a two-part epoxy wherever ground contact is likely to occur.

The wheel-leg is attached to an aluminum ring by eight 8-32 screws. These screws are assembled as follows: a spring washer, regular washer, the carbon fiber wheel- leg, aluminum ring, and a nut holding it in place on the far side. Since the carbon fiber is relatively thin and may flex during the large force impacts of climbing over obstacles, the spring washer is used to maintain a strong hold during vibrations. Clamping forces are desired of shear forces on the screws, especially on such thin material. This necessitates the use of the large washer and nut for creating large friction forces rather than shearing forces on the sides of the carbon fiber holes. The aluminum piece is then screwed in to the torsion devices, creating a secure hold for the wheel-leg.

After the second design of the wheel-leg was attached to the torsion device, it became apparent that the legs were too compliant to support walking. The solution to this was to pack parts of the wheel-legs with foam and wrap the ends in electrical tape.

The foam serves as a dampener, lessening the noise and movement of the ends of the wheel-legs. The electrical tape keeps the foam in place, and allows the wheel-leg to deform, however it prevents the wheel-leg from springing completely open, limiting the

59 spring back forces of the robot on the ground. A picture of the second configuration is shown in Figure 3.26.

Figure 3.26 - Second wheel-leg design attached to torsion device and packed with foam.

The second configuration experienced failure, and further layers were added to the wheel leg. More detail on the failure can be found on page 76. A new leg was made to replace the broken leg, and all legs had 3 additional layers placed over the failure area, and an additional 2 more layers for rigidity. The addition of the three layers increases thickness by 2.5x and therefore makes the area over 15x stronger as strength increases by thickness cubed. Also, the additional layers connect the ends of each wheel-leg with the next wheel-leg, significantly reducing the flexibility of the leg. The legs now experience

60 no noticeable flex under robot weight, though some compliance still exists under high load. The reduced flex also spreads the stresses out over more parts of the wheel-leg, reducing peak stresses on each leg. The most recent wheel-leg configuration can be found in Figure 3.27

Figure 3.27 - Close up of third wheel-leg design

3.7 Electronics USAR WhegsTM is remote controlled and all components are available commercially and are located on board the robot. Currently there is no logic control for the robot, and the remote operator makes all decisions. The radio controller is a 6 channel 1.2 gHz Futaba. Two channels are used to control the robot steering and speed.

Two more control the SAM 8, and the final two channels are open to future components of the robot.

Two 7 cell batteries connected in series supply 18V and power to all the electronics on board USAR WhegsTM. This is simpler than previous WhegsTM designs which include a 5V logic and servo power batteries on board. This is possible because of the 5V output on the motor controller, which is used to give power to the radio control.

The SAM 8 module can operate on 12 and 24 volts supply, within the range of the two batteries used for the motors. A 25 A fuse was initially put in series with the batteries to prevent the robot from drawing too much current and damaging any of its components.

This was removed however, as the Sabertooth can handle 50 A and has built in overcurrent protection.

The speed controller is the Sabertooth 2X25 made by Dimension Engineering. It is able to do differential control of two motors automatically with two PWM input signals. The controller often has a small spike in current whenever the input is returned to neutral, which has a tendency to make Maxon motors overheat over time. This necessitates the addition of an inductor in series with each motor. These are 220 µH inductors available through DigiKey®. The speed controller and the inductors are screwed in to the back side of the chassis. The heat dissipation fins of the speed controller were removed for space considerations and the metal on the back part of the controller directly contacts the aluminum wall. Since the entire chassis is aluminum, it can easily dissipate the heat created.

Figure 3.28 – Final robot in track configuration

Figure 3.29 - Robot in final configuration with wheel-legs attached

Figure 3.30 - Robot in final configuration with mast fully deployed

Chapter 4: Tests

4.1 Wheel-Leg Test A stiffness test was performed on the wheel legs to determine their strength and preliminarily assess their ability to support USAR WhegsTM. This test involved placing the wheel-leg in two different positions, a vertical static position (Figure 4.1), and a horizontal climbing position (Figure 4.2)

Figure 4.1 - Wheel-leg in vertical position. Figure 4.2 - Wheel-leg in horizontal testing position.

For the first position, the leg was fixed to a 2x4 with a C-clamp and the wheel-leg was loaded by hanging weights through the central hub (Figure 4.3). A steel piece of music wire was fixed horizontally to the top of the hub and used as a reference guide for vertical displacements from the 2x4 (Figure 4.4). A string with a weight attached to the

66 music wire hung down vertically and was used to measure horizontal displacements. The second position contained very little to no horizontal displacement, so only vertical displacement from the ground was measured.

Figure 4.3 - Horizontal position under load.

Figure 4.4 - Measurement process of vertical position under load

This test was performed on 3 different carbon fiber layerings. The first layering ending with ten layers, the second was this first layering, but re-baked with five more layers, and the third was all fifteen layers baked at once. Results can be found in section

5.2 Wheel-Leg Test Results.

4.2 Lab Runs After construction the USAR WhegsTM was driven in the hallway and rooms of the lab to determine speed and maneuverability. A distance of 30 feet was marked off in the hallway, and the robot was timed as it raced from one end to the other. The robot was also visually assessed for its turning radius. This was done for both tracks and wheel

68 legs, and the results can be found in 5.3 Lab Runs Results. Accurate data was obtained for the tracks, however one of the wheel-legs experienced failure after a short time, and testing of the robot’s speed, maneuverability, and climbing ability with wheel legs has not been fully assessed.

Chapter 5: Results

5.1 Specifications USAR WhegsTM has several new innovative features when compared to previous

WhegsTM robots. Table 5.1 contains a comparison of USAR WhegsTM and several other

WhegsTM robots.

USAR USAR TM TM Lunar Whegs Whegs WhegsTM I1 WhegsTM II2 WhegsTM3 (w/o WL) (w/ WL) Dimensions (inches)

Length 19.5 18.5 23.6 18.75

Width 19.5 14 15.4 14.2 17.5 Height 2.5 2.25 2.4 3 (chassis) Ground Clearance 2.75 2.875 .983 5 Weight (lbs) 7 8.5 11 32.46 39.3 Speed

Feet/s 4.9 4.5+ 3.8 6.25 TBD Body 3 3+ 1.91 4 TBD Lengths/s Motors

Torque (N-m) 22.7 64.6 2 X 53

Power (W) 90 90 2 X 150 26:1 74:1 Custom spur Transmission Integrated Integrated 26:1 Integrated Planetary gear Planetary Planetary 2.14 Wheel-leg radius 4.5 inches 4 inches 3.75 inches 7.5 inches inches4 Pushrod Steering Pushrod Type, Rack and Type, ± 20 Differential Configuration ± 30 degrees Pinion degrees Turning Radius 1.5 1.25 0.85 0 Variable (body lengths) 2 Channel RC 3 Channel RC 6 channel RC User Interface 6 Channel RC transmitter transmitter transmitter transmitter 16 V NiMh 7.2 volt Power Supply 9.6 Volt NiMh and 8.4 V 16 V NiMh NiCad NiMh

1 Data taken from (Quinn, Kingsly, Offi, & Ritzmann, 2002) 2 Data taken from (Allen, 2004) 3 Data taken from (Dunker, A Biologically Inspired Robot for Lunar Exploration and Regolith Excavation, 2009) 4 Radius of the wheels and tracks

Table 5.1 - Comparison of WhegsTM I, WhegsTM II, Lunar WhegsTM, and USAR WhegsTM across several areas of interest

Since USAR WhegsTM has a significant weight increase over previous WhegsTM robots, individual components of the robot were separated and weighed. The results for this can be found in Table 5.2 - Weight of various sections of USAR Whegs.

Part(s) Weight Chassis 7.73 Motors and gears 6.00 Electronics 3.19 Wheel sprockets, shafts, and treads 5.54 Wheel-legs and torsion devices 6.84 SAM 8 10.00 TOTAL 39.3 Table 5.2 - Weight of various sections of USAR WhegsTM

Analyzing these results shows there are several areas of improvement in weight for further designs of USAR WhegsTM. First, the chassis is over designed to prevent failure during testing. An in depth analysis of the forces on the chassis could be performed, and some significant weight could be reduced from this section. The use of two motors adds significant weight to the robot when compared to previous one motor designs. Preliminary tests suggest that the motors are overpowered for the system, and smaller motors could be substituted to reduce weight. The last place for improvement could be in the wheel sprockets and treads. More efficient designs could be made for these parts. This weight reduction would also lower the inertia in the drive system, which would make the robot more responsive to operator commands.

5.2 Wheel-Leg Test Results The displacement results for the vertical placement stress test are found in Table

5.3 and Table 5.4.

Mold 0 lbs 1 lb 2 lbs 4 lbs 6 lbs 1 0.00 -0.19 -0.81 -2.19 -3.38 1 0.00 -0.19 -0.81 -2.13 -4.13 2 0.00 0.00 0.00 -0.06 -0.13 2 0.00 0.00 -0.06 -0.06 -0.13 3 0.00 0.00 0.00 -0.06 -0.13 Table 5.3 - Vertical displacement of center for all 3 specimens in position 1

Mold 0 lbs 1 lb 2 lbs 4 lbs 6 lbs 1 0.00 1.31 2.19 3.56 4.06 1 0.00 0.81 2.19 3.38 4.50 2 0.00 0.00 0.00 0.00 0.06 2 0.00 0.00 0.00 0.06 0.19 3 0.00 0.06 0.13 0.38 0.63 Table 5.4 - Horizontal displacement of center for all 3 specimens in position 1

Notes: In the first test of Mold 1, the next leg contacted the 2x4 with 6lbs of weight. This skewed the results for the displacement of this mold in the final column.

Tests of the first mold indicated that the current layering system would not be strong enough to hold the robot, and would break quickly. The robot should be at its stiffest in this position, and four inches of displacement over 7.5 inches of leg length is not considered acceptable. Observations showed that most of the deflection was occurring at the first bend in the leg, and so more layers were added to this area. The results are non-linear since once the leg starts to experience horizontal displacement, the

73 force of the weight becomes eccentric from the fixed ground contact point of the leg.

This creates more stress on the curve, the weakest area of the leg.

Tests show a significant increase in the strength of the leg under the vertical load between the first layering and the second. The addition of four more layers, or 80% increase across the first bend nearly eliminated deflection. This makes sense since stiffness increases with thickness cubed, and a thickness of 1.8 times more should yield a stiffness 5.8 times greater.

The results also show consistency between adding layers as test molds 2 and 3 have very similar results. Slight differences in the results between tests of the same mold can be attributed to the accuracy of the placement of the clamp, which is ±.125 inches.

The tests with the wheel-legs in the horizontal position proved to be inconclusive.

These results are shown

Mold 0 lbs 1 lb 2 lbs 4 lbs 6 lbs 1 0.00 -1.25 -1.75 -2.63 2 0.00 -1.13 -2.13 -2.88 -3.63 2 0.00 -0.13 -2.19 -3.38 3 0.00 -0.69 -1.25 -2.75 -3.25 Table 5.5 - Vertical displacement of all 3 specimens in position 2

Notes: Molds 1 and 2 both collapsed under 6 lbs of force. Though nothing broke, the twisting that occurred made getting a vertical displacement reading impossible.

The results vary greatly, and do show any consistent results. This is due to the accuracy of the placement of the clamp. Since the clamp is placed on a curve, very slight changes (<.0625 inches) cause large changes in the orientation of the wheel leg. These large changes cause significant differences in the deflection of the wheel leg.

5.3 Lab Runs Results

Tracks

USAR WhegsTM performed admirably in the hallway with its tracks. On the tile floor, it was able to achieve speeds of approximately 6.25 feet per second or 4 body lengths per second. This makes it the fastest robot to date in the lab. Having such a fast speed will help in the transportation of the robot, as it will not need to be carried medium length distances, cutting down on the time of moving between deployments.

The robot also has a turning radius of zero body lengths with the tracks. This makes for very tight cornering, and good control in tight spaces.

The robot did experience a couple of de-tracking experiences when climbing obstacles and going over rough terrain. This experience was likely due to the slack in the tracks when the robot was finally assembled. Different tracks were placed on the robot, which provided a tighter fit and de-tracking has not been seen again. A tensioning system may be necessary to keep the tracks tight and on the wheel sprockets.

Wheel-legs

Initial runs of USAR WhegsTM on the second configuration of the wheel-legs proved to be less remarkable. The robot was walked up and down the hallway several times before failure of one of the wheel-legs discontinued further testing. The first problem noted was that the wheel legs made for a rougher ride than originally anticipated. The robot bounced around significantly, and went out of control at moderate to high speeds. Secondly, the rubber traction on the wheel-legs provided too much friction for turning. The first time the robot attempted to turn in place, it blew a fuse of

20 A, as the motors were not able to overcome the frictional forces. After the fuse was replaced, the robot was once again steered up and down the hallway with gradual turns to keep it on path. The motors were able to provide enough torque without pulling too much current; however, one of the wheel-legs was not able to take these forces and snapped across the middle as shown in Figure 5.1.

Figure 5.1 - Photograph showing the broken wheel-leg

This was an unanticipated result; however, further examination of the system provides insight into the situation. Large side forces on the wheel legs were not anticipated because of the discontinuous nature of stepping. However, there is significant ground contact still occurring, and the differential steering causes the wheel-legs to get pushed sideways as the robot attempts to turn. This problem has not been realized before because previous steering methods for large WhegsTM robots pivot the wheel-legs, steering them like a car. Treating the wheel-legs as having the knife-edge constraint prevents these side forces from occurring. Mini WhegsTM, although it does have differential steering, have plastic wheel-legs with a low coefficient of friction on most surfaces. In addition, Mini WhegsTM is very light, further reducing frictional forces

After the wheel-legs were strengthened additional runs were made, and some climbing was performed. The robot was able to climb over a 6 inch obstacle, though the wheel-legs experience failure coming down the back end of the obstacle. Several carbon fiber layers separated as shown in Figure 5.2. The splitting occurred between layers that baked at different times. The carbon fiber layers were epoxied back together, for a temporary fix, and the robot operates as it did before. This problem can be eliminated by baking all the carbon fiber layers together in one mold, allowing for the layers to properly bond together.

Figure 5.2 - Separation between carbon fiber layers

Chapter 6: Conclusions and Future Work

6.1 Conclusions USAR WhegsTM implements many new features on a WhegsTM robot, some successful, others not as successful. Differential steering provides great maneuverability while using tracks; however it has been unsuccessful inside with the use of wheel-legs.

The forces created by the sideways movement of differential steering cause failure in the current wheel-leg design. The new carbon fiber wheel-legs are strong enough to support the robot, but it causes significant vertical movement during forward locomotion. The quick change torsion devices allowing for the robot to quickly change between track and wheel-legs is very successful. There is a tight fit between the connections, and once placed on the robot, they cannot be removed without depressing the pin. More extensive tests over irregular terrain has not been achieved, and only time will tell if the torsion devices will continue to hold their tight tolerances.

6.2 Future Work There are many areas that must be improved and worked on before USAR

WhegsTM is ready for field testing and use in USAR situations. New wheel-legs need to be made with only one bake, and which will hold together under high forces. The chassis also needs a covering which is waterproof. This will keep particles from getting in the electronics and drive system as well as allow for the decontamination of the robot after assisting in a USAR situation.. Finally the quick change gear set for the drive train must be fabricated and implemented in to the robot. Tests can be performed to characterize the robots maneuverability, speed, and climbing ability. When these things are accomplished, the robot will be ready for more challenging environments.

Changes can also be made to the robot design to increase its maneuverability.

Areas can be made lighter as described earlier. Also, a new track system which is more stable, able to eject particles, and less likely to experience de-tracking can be developed.

After it has been determined that the locomotion capabilities of the robot is satisfactory, sensors and a proper user interface need to be developed and implemented with USAR WhegsTM. These additions include a pan/tilt/zoom camera, two-way audio, and a lightweight tether. Areas of the robot can be further designed to carry medical supplies and water to victims of an urban disaster.

Appendix A. Motor calculations

Torque Calculations Assumptions Robot Weight – 40 lbs Leg length – 7.5 inches Worst case scenario: Motor must be able to lift entire robot with one leg.

Figure A.1 - Free body diagram of forces on wheel leg

in-lbs =33.9 N-m

Multiply by a safety factor of 2.

Trequired = 67.8 N-m

Speed Calculations Assumptions No load speed of motor will be reached Track radius – 2.14” Speed – Walking speed - 4.5 mph = 4752 in/min

Motor Chosen The Maxon RE 40, 150 W, with a 26:1 planetary gear set was chosen to run the robot. Values given from documentation are shown below.

Stall Torque 1.68 N-m No Load Speed 7000 RPM Nominal Voltage 12 V Transmission Efficiency 81% Table A.1 - Data of Maxon RE 40, 150W motor and 26:1 planetary gear set

These values combined with an overvoltageing of the system to 18V give a total output torque of 53 N-m and no load speed of 327 RPM. This lower output torque is considered acceptable since there will be two motors driving the robot, giving a theoretical total of 106 N-m of output torque at maximum efficiency.

Appendix B. Shaft Calculations Stress on the shaft occurs from two sources, the weight of the robot and the torque from the drive motor.

Weight Calculations Assumptions Simple beam in bending Wheel sprocket placed 1.25” from bearings, and two bearings .5 inches apart Circular cross section Use of 4140 Steel with yield strength of 60,000 psi Worst case scenario: All robot weight on one shaft.

Figure B.1 - Free Body Diagram of forces on shafts

The reaction forces at B1 and B2 can be found through summing the forces and moments about the far right to zero. This gives B1=140 lbs and B2= 100 lbs. Given these values, the minimum radius needed for the shafts can be calculated as follows.

where M is the moment on the beam.

Where σ is the stress, M is the moment, c is the distance from center of the shaft, and I is the moment of inertia, which for a cylindrical beam is

Combining equations 3, 4, and 5 yields

Rearranging 6, and solving for r yields

.00106

Torque Calculations Assumptions Circular cross section Use of 4140 Steel with yield strength of 60,000 psi Must hold under stall torque

Beginning with the stress equation for circular beam under torque

It can be rearranged and solved for r

.170

Based on these values, the total stress in .5 inch and .375 inch shaft sizes were calculated to determine the smallest size shaft needed.

Using equations 6, 8 and 10, for .5 inch and .375 inch diameter shafts sizes, the total stress in each shaft is calculated.

A shaft of .375 inches only gives a safety factor of 1.3 while the larger .5 inch shaft gives a safety factor of 3.1. It was determined that the safety factor of 1.3 is not enough, and the .5 inch shafts are used.

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