Sleepy Slothers Design Documentation

DESIGNDOCUMENTATIONTEAM SLEEPY SLOTHERS

JASON CHUA | TRENT HAZY | CARLOS PLASENCIA | MAYRA VEGA

DESIGN DOCUMENTATION | 1

EXECUTIVE SUMMARY Our goal for this stage of the Self-Mobile, Arboreal, Rainforest Telemetry System (SMART) Project was to design a half-scale sloth robot that could traverse an approximately 20-foot long nylon rope in a biomimetic fashion. We applied an iterative, testing-heavy approach to the design of our final slothbot, supplementing this real world observational analysis with modeling software and applets. Our team considered many variables during the design process, including transmission ratio, material selection, linkage path analysis, and structural integrity, and a thorough exploration of these variables allowed us to converge upon a final robot that met all of the design requirements.

FIGURE 1. OUR SLOTHBOT, SLEEPY THE SLOTH

Our final robot design couples a high-torque drivetrain with a system of four bar linkages designed to give our robot a smooth, biomimetic gait. The drivetrain employs a Tamiya planetary gearbox with a 400:1 reduction ratio, and a system of chains and sprockets that act as a 1:1.43 multiplier, giving the slothbot an overall drivetrain reduction ratio of 1:280. The four bar linkages that form the robot’s legs trace out a semicircular path, giving the slothbot a smooth gait.

The robot met all of the functional design criteria presented to us. It easily crawled the entire length of the rope without human assistance, and did so at an appropriate speed. The arrangement of our linkages also gave the slothbot a distinctly biomimetic gait including the diagonal stride pattern typical of sloth locomotion.

Although we were pleased with the performance of our robot, there are a few things we would improve for the next version of the slothbot. Firstly, we would do more work to determine how we might reduce slippage on the rope. This exploration might include adjusting the relative timing of each arm and tweaking each arm path. Additionally, we would endeavor to reduce the overall width and weight of the robot to reduce the strain on the robot’s arms and implement lower-friction bearings to increase overall efficiency.

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THE TEAM

FIGURE 2. THE TEAM - JASON, MAYRA, TRENT, AND CARLOS

FIGURE 3. SLEEPY THE SLOTH HANGING OUT


TABLE OF CONTENTS

EXECUTIVE SUMMARY ......................................................................................................... 1

THE TEAM ............................................................................................................................... 2

TABLE OF CONTENTS .......................................................................................................... 3

DESIGN DEVELOPMENT ....................................................................................................... 5

COUPLER CURVE DEVELOPMENT ................................................................................................................................................ 5 JOINT DEVELOPMENT .......................................................................................................................................................................... 6 ARM DEVELOPMENT ............................................................................................................................................................................. 6 POWERTRAIN DEVELOPMENT ......................................................................................................................................................... 7 CHASSIS DEVELOPMENT .................................................................................................................................................................... 8 TWITTER DOCUMENTATION .............................................................................................................................................................. 8

DESIGN ANALYSIS ................................................................................................................ 9

FREE BODY DIAGRAM ANALYSIS ................................................................................................................................................. 9 MOTOR CHARACTERIZATION ........................................................................................................................................................ 10

RESULTS OF MODELING .................................................................................................... 10

WORKING MODEL ................................................................................................................................................................................ 10 MATLAB ........................................................................................................................................................................................................ 11

RESULTS OF FINAL TESTING ............................................................................................. 11

DESIGN VALIDATION ............................................................................................................................................................................. 11 UNEXPECTED CHALLENGES ........................................................................................................................................................... 12

CONCLUSIONS ..................................................................................................................... 12

APPENDIX A. SCREENSHOTS OF SLOTH LOCOMOTION ............................................. 14

APPENDIX B. JOINERY METHODS .................................................................................... 15

APPENDIX C. CHASSIS DEVELOPMENT PICTURES ....................................................... 16

APPENDIX D. MOTOR PLOTS ............................................................................................ 17

APPENDIX E. WORKING MODEL FIGURES ..................................................................... 18

APPENDIX F. MATLAB PLOTS .......................................................................................... 20

APPENDIX G. MOTOR AND POWER TRANSMISSION EQUATIONS ............................ 22

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STRIDE LENGTH .................................................................................................................................................................................... 22 ESTIMATED CRANK SPEED ............................................................................................................................................................ 22 ESTIMATED GEAR RATIO ................................................................................................................................................................ 22 POWER AND TORQUE REQUIRED .............................................................................................................................................. 22

APPENDIX H. FINAL TESTING DATA ............................................................................... 23

VOLTAGE .................................................................................................................................................................................................. 23 CURRENT ................................................................................................................................................................................................... 23 POWER CONSUMPTION UNDER LOAD .................................................................................................................................... 23 KINEMATICS ............................................................................................................................................................................................. 23

APPENDIX I. TWITTER DOCUMENTATION .................................................................... 24


DESIGN DEVELOPMENT Our development process began with a search for videos of sloths crawling. After a bit of hunting, we found an excellent breakdown of the sloth’s gait on YouTube courtesy of the Phyletisches Museum. Representative screenshots from the video are shown in Appendix A. From this video, we noticed that the sloth has a fairly long, diagonal stride pattern with its limbs pushed out to the very ends of its body. We also noted that the sloth hangs down using long hook-shaped claws. These observations gave us a good starting point from which to begin construction of our robot.

COUPLER CURVE DEVELOPMENT Early on, we decided on using four-bar linkages for our robot’s arms. We made this decision for a number of reasons. Firstly, the coupler curve traced out by a four-bar linkage can be made roughly semi-circular, mimicking the path traced by a sloth’s arm. Secondly, the ubiquity of the four-bar linkage made it easy for us to quickly test and iterate on link lengths using online java modeling applets and other modeling software. Figure 4 below shows an early version of our linkages and coupler curve next to our final linkage and coupler curve. Our efforts to stretch out our coupler curve while maintaining the same base linkage length are evident in the nearly twofold increase in the flat portion of the curve.

FIGURE 4. LINKAGE DIMENSIONS AND COUPLER CURVE AT DESIGN REVIEW 1 (LEFT) AND OUR FINAL LINKAGE DIMENSIONS AND COUPLER CURVE (RIGHT)

The final linkage lengths we decided on were 12.14 cm for the ground link, 4 cm for the input link, 11 cm for the coupler, and 8 cm for the follower. These dimensions gave us a semicircular coupler curve with a flat portion that was approximately 11.5 cm long.

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FIGURE 5. SIDE VIEW RENDERING OF CHASSIS AND LINKAGES

JOINT DEVELOPMENT We used plastic screwposts to join the links with one another and to the body. These screwposts were heavily tightened to reduce lateral motion, but this resulted in a non-negligible amount of friction from the joints rubbing against one another. This friction was partially mitigated by inserting small nylon washers between some of the links, reducing the amount of surface area rubbing against each other.

We made sure that the connection between the axles and the linkages were extra secure. We filed our axles into a D-profile in order to reduce the chance of rotational slippage. These D-profile axles were mated with D-profile joints and secured with air hardening clay and Gorilla glue. A picture of the various joins used in the robot can be seen in APPENDIX B. Joinery Methods

ARM DEVELOPMENT The design of our arm was based on the hook-like claws sloths use to hang from trees. The first iteration of arms we designed was composed of two parts – a vertical piece that connected to the top link in our four-bar, and a horizontal piece that cantilevered out from this link. When we ran some initial tests, we encountered some difficulties with this design. The design did not take into account the bending which would occur as a result of the body’s weight. Because the vertical piece was only ⅛” aircraft plywood, and was supporting about 450g of mass, it would

experience a bending moment and cause the sloth to veer off course over time. As a result of


this, we decided to insert joint reinforcements and extend the length of the horizontal pieces. Both these alterations dramatically improved the sloth’s movement on the rope. Figure 6 illustrates this improvement in arm rigidity.

FIGURE 6. ARMS BEFORE (TOP) AND AFTER (BOTTOM) REINFORCEMENT

POWERTRAIN DEVELOPMENT After analyzing the diagonal gait of sloths, we began visualizing the transfer of power from the motor to the arms and how we would best mimic this gait. Most importantly we recognized that each set of arms needed to run at the same speed, but at opposite locations in the coupler curve. Our team set out to create a system in which power would be transferred from the motor to the near axle, and then from that axle to the further one. In our first week of the project our team was so preoccupied with the details of our parts, such as size, pitch, and fit with other components that we made the mistake of ordering all steel parts: ¼” diameter axles and four sprockets with ¼” bore. When these parts arrived several days later we realized their immense weight made them unsuitable for our purposes, and quickly replaced them with ¼” aluminum rod

for our axles and plastic sprockets with clamping mounting hubs. Our planning also helped us see that we would need a smaller sprocket to mount on the output shaft of the motor. We mounted the three larger sprockets with clamping hubs and the pinion sprocket with a set screw to guarantee minimal slip.

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We used a steel chain to transfer power from the motor to the drive axels. This setup virtually eliminated slip in the drivetrain and gave us a massive margin of safety. We used a system of two chains to drive our linkages. One chain ran from the motor to the rear axle, and another ran from the rear axle to the front axle. In this manner, we were able to provide synchronous power to both axles. A diagram of power transmission can be seen below in Figure 7. Power Transmission in the robot

FIGURE 7. POWER TRANSMISSION IN THE ROBOT

CHASSIS DEVELOPMENT Once the four-bar linkages had been designed we began work on the sloth’s body. During this stage, our team had two major design considerations: size and rigidity. The size of the body was determined by size of the linkage system and the spacing between them. By tracing the paths of each component of the four-bar linkage, we found the minimum body length that ensured that the linkages in the same plane did not make contact. This length ended up being 40 cm, the maximum to-scale length of an average sloth. Some development pictures can be seen in Appendix C.

The 5.25 cm width of our robot was determined by proportionally scaling the chassis length to the dimensions of a real sloth. In an attempt to ensure overall rigidity, our team inserted two cross beams between the two sides of the body. These braces were positioned at 45-degree angles to ensure flexural rigidity in both the x and y-axis. In addition to giving our robot a stiff body, the braces gave us surfaces to mount other components such as the motor and on/off switch.

TWITTER DOCUMENTATION Our team decided to use the popular microblogging platform Twitter to keep an electronic record of our design process. This allowed us to easily keep a record of the steps and milestones of our project even while mobile. It also ensured that we kept on the schedule we’d laid out at


the beginning of the project. We linked our account to our blog, and the ~20 documentation tweets (and links to pictures and videos) from @sleepythesloth can be seen in Appendix I.

DESIGN ANALYSIS In conjunction with our design development and testing process, we performed analysis on a select number of our robot’s subsystems. Specifically, we constructed a free body diagram to perform a force analysis of our body design and characterized our motor. These analyses allowed us to better understand how our robot was performing, and acted as a check on our design decisions.

FREE BODY DIAGRAM ANALYSIS Our team diagrammed the various forces on our sloth and isolated those acting on the four-bar linkage. This helped us understand how power was being transmitted from the axles, through the four-bar linkage, to the sloth’s arm. It also furthered our understanding of the interaction between the rope and the arms. The diagram revealed how the tension in the rope and the weight of the sloth divide the normal force into both horizontal and vertical components.

The diagram, seen in Figure 8. Free Body Diagram with selected forces labeled and linkage paths traced out also provided a foundation for our team to calculate the position and velocity of the arm, as well as the forces acting on it. These calculations were founded upon several key variables including the axle’s angular velocity as well as the distances and angles between the linkages.

FIGURE 8. FREE BODY DIAGRAM WITH SELECTED FORCES LABELED AND LINKAGE PATHS TRACED OUT

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MOTOR CHARACTERIZATION For our design we decided to utilize a Tamiya motor with planetary gear box set to generate the high torque low rpm required of the design. This gear set allowed for a large speed reduction in a very compact space and with little added weight. We ran tests to characterize our motor and decided on 3 V as an appropriate operating point, achieving this through the use of two 1.5 V batteries. The design requirements ask that our sloth run at a speed between 3 and 8 cm/s. We chose to aim for a speed of 5cm/s and calculated that if our motor were running at maximum efficiency of 54% we would need a speed reduction of about 400:1. With a stride length of 11.5cm this speed reduction allowed us to run at a desired drive shaft angular velocity of 26.087 rpm. Our final operating range for out motor, however, was slightly below maximum efficiency and hence our motor was also running at a slower rpm. Plots of motor power and efficiency can be seen in Appendix D. Motor Plots Our system of chains and sprockets eventually led to an overall drive train reduction ratio of 1:280 which was appropriate in achieving our final successful velocity of 5.26 cm/s.

RESULTS OF MODELING The slothbot required advanced planning to ensure that we had time to order the correct parts and cut the body and links on the laser cutter. Since the laser cutter had limited availability, it would have been difficult to make late changes to elements of the design. This meant we needed accurate models from which to base our decisions. We needed estimates for motor torque requirements, drive-train power requirements and four-bar linkage motion requirements. To do this, we used computer modeling programs to estimate force, power and torque requirements for our sloth bot. We prototyped and used virtual models to design our four-bar linkages to specifications.

WORKING MODEL We used Working Model to simulate the motion of our first linkage prototypes. An assortment of figures and graphs we generated using Working Model can be seen in Appendix E. For our prototypes we worked on adjusting the lengths of a four-bar linkage to create an appropriate coupler curve for our application. We wanted the coupler point to have a semi-circular motion and modeled the associated four-bar linkage in Working Model (Figure 15. Modeled Coupler Curve). The velocity of the coupler point was plotted in both the x- and y- directions (Figure 16. x and y velocity of coupler point). Due to lack of control of variables in the virtual environment we could not use the values from Working Model, however, we were able to use the plot to see where peak velocities occurred in our range of motion. We also used Working Model to plot the torque of our motor to again see where peak values occurred in our range of motion. The torque motor simulation was modeled to recreate the hand’s collision with the rope (Figure 17. Dynamic model of arm on rope). A plot of motor torque shows that the peak values occur when the hand is in contact with the rope (Figure 18. plot of motor torque from dynamic model), which is necessary if the sloth bot is to pull itself along the rope.


MATLAB After finalizing our four-bar linkage with the initial modeling we moved on to a Matlab analysis of our sloth. Using the positions and lengths of our links we were able to do a position analysis of our coupler point. A plot of the x- and y- positions of the coupler point shows a semicircular path for our sloth hand. We were then able to get plots of velocity in the both the x- and y- directions versus the angle of the crank arm. These plots can be seen in Appendix F. Matlab Plots

These x and y velocity points also helped us get a sense of Power required. Assuming that that 2 hands are on the rope at all times we found our Force (see Appendix G. Motor and Power Transmission Equations for force calculations), which we multiplied by various velocities as the arm moved along the rope. This resulted in a maximum required power of .122W and maximum required Torque of .045 Nm assuming an 80% linkage efficiency. The torque range of the Tamiya motor that we selected encompassed this value.

RESULTS OF FINAL TESTING The final presentation of our slothbot took place on Friday, March 11. During this presentation our sloth was able to successfully traverse upside down along a nylon rope while meeting general design and performance requirements. It had to move in a biomimetic fashion, meaning that like a real sloth it not only had to move at a measured pace (within the range of 3-8 cm/s) but to achieve a biomimetic gait diagonal pairs of limbs had to move together. Our slothbot moved at a pace of 5.25 cm/s while keeping a steady and smooth sloth-like stride. The performance of our slothbot can be attributed to our team’s successful design of our four-bar linkages, powertrain and also to our skillful assembly.

DESIGN VALIDATION The four-bar linkage we designed from prototyping and virtual modeling gave us an appropriate stride for the arms of our slothbot. Just as our position analysis in Matlab showed the hands on our slothbot moved in a semicircular path, flat when in contact with the rope to maximize the propelling force and with enough arc when rising to clear the opposite hand. By taking measurements of current while the slothbot moved along the rope we could calculate the input power of the motor. We saw that when the hand moved onto the rope the required input power was 0.79 watts, when the hand moved along the rope the power was 1.01 watts, and when the hand lifted off the rope the power was 1.31 watts. These measurements and calculations can be seen in Appendix H. Final Testing Data

Comparing our power measurement for when the hand moved along the rope of 1.01 watts to our calculated estimate of input power of 0.1225 watts reveals significant losses. This is due to a number of factors. Firstly, the calculated input power assumed a generous 80% linkage efficiency. We had significant losses due to friction in our joints because of our need to very tightly fasten links together to reduce wobble, and we had high stresses caused by our large weight making it likely that our actual linkage efficiency was far short of 80%. Furthermore, we used a 4 stage planetary gearbox, which introduced additional losses with each transmission


stage. At the interface between our arms and the rope, we noticed a moderate amount of slippage, which resulted in the motor having to work harder to achieve our desired speed. Finally, our calculated input power was based on the assumption that the motor was running at peak efficiency, which it was not as can be seen in our motor characterization plots in Appendix D. Motor Plots When taken together, these sources of power loss contributed to our rather large discrepancy between calculated and measured power.

We based our estimates for required input power and gear reduction on a sloth moving at 5 cm/s. Running at 3 volts with an overall speed reduction of 1:280 was an accurate estimate since our sloth travelled at 5.25 cm/s. The difference in actual speed and desired speed occurred because our motor was not running at maximum efficiency and we were limited in how exact our gear reduction could be. We also had to overestimate power requirements when choosing output torque from our motor to overcome high friction when the slothbot is under load. We made reinforcements to our linkages during our design development to reduce friction and overcome high stress and it was successful in helping our slothbot move more steadily and without much slippage. When off the rope our crank arm moved .28 rev/s compared to .25 rev/s while on the rope. Our careful assembly produced a slothbot that had minimal speed losses on the rope.

UNEXPECTED CHALLENGES Few improvements to our slothbot came from trial and error. Our body and linkage design and purchased parts were sufficient in creating an ideal motion so we didn’t have to make major changes after it was assembled. We were instead able to focus our time on reducing the effects of fatigue on the links under test conditions.

One challenge we faced was that after several trial runs, our links would become loose due to stress on the screw posts keeping them together. Therefore we had to be sure and tighten the screw posts before testing. Once we noted this problem and addressed it, we were able to successfully run our slothbot without incident.

Another unexpected issue we encountered was that the location of the powertrain created an uneven weight distribution. This sometimes caused the slothbot to lean to one side, get off-course, and miss the rope. With further testing we realized this only occurred when there was too much slack in the rope. With a good amount of tension on the rope the weight distribution was not an issue; our sloth could balance itself better and travel more steadily.

CONCLUSIONS Overall, we were pleased by the performance of our slothbot. It completed the trial course with only minor difficulties, and performed within the ideal ranges for speed and maintained a biomimetic appearance. Our calculations show that our crawler allowed the motor to run very near its peak efficiency and peak power.

We learned that in a complex project like this, it is important to plan ahead and create a project plan to ensure that everything comes together by the deadline. Also, we learned the importance


of building in large margins of safety in our calculations because real-world conditions often differ considerably from modeled environments.

The biggest strength of our design was its ability to maintain arm speed even under heavy loads while maintaining a slothlike stride. Connecting both axles to the drivetrain with metal chains ensured that we would have few losses between the motor and the axles. The biggest weakness of our design was our large power loss due to friction, slippage and a multiple stage transmission. In future revisions of the design, we would ideally construct the bot out of lighter materials, add more grip to the bot’s arms to reduce slippage on the rope, and design our joints to minimize lateral slop without increasing friction.


APPENDIX A. SCREENSHOTS OF SLOTH LOCOMOTION

FIGURE 10. HIGH SPEED VIDEOGRAPHY OF SLOTH LOCOMOTION

Source: http://www.youtube.com/watch?v=TjiiQ_ZDCy4&feature=player_embedded

FIGURE 9. MOTION CAPTURES OF SLOTH LOCOMOTION.


APPENDIX B. JOINERY METHODS


APPENDIX C. CHASSIS DEVELOPMENT PICTURES

FIGURE 11. PROTOTYPING CHASSIS SIZE USING FOAMCORE AND TRACED OUT COUPLER CURVE

FIGURE 12. LINKAGES AND CHASSIS READY FOR ASSEMBLY


APPENDIX D. MOTOR PLOTS

FIGURE 13. MOTOR POWER VS. RPM. OPERATING RANGE IS BETWEEN THE DASHED LINES.

FIGURE 14. MOTOR EFFICIENCY VS. RPM. OPERATING RANGE IS BETWEEN THE DASHED LINES.

0 0.2 0.4 0.6 0.8 1

1.2 1.4 1.6 1.8

0 2000 4000 6000 8000 10000 12000 14000

Watts

RPM

Power v RPM

Power (Watts)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2000 4000 6000 8000 10000 12000 14000

Ef0iciency

RPM

Ef0iciency

Ef8iciency


APPENDIX E. WORKING MODEL FIGURES

FIGURE 15. MODELED COUPLER CURVE

FIGURE 16. X AND Y VELOCITY OF COUPLER POINT


FIGURE 17. DYNAMIC MODEL OF ARM ON ROPE

FIGURE 18. PLOT OF MOTOR TORQUE FROM DYNAMIC MODEL


APPENDIX F. MATLAB PLOTS

FIGURE 19. COUPLER POSITION PLOT

FIGURE 20. X-VELOCITY OF COUPLER POINT. VELOCITY (CM/S) VS. CRANK ANGLE (RADIANS)


FIGURE 21. Y-VELOCITY OF COUPLER POINT. VELOCITY (CM/S) VS. CRANK ANGLE (RADIANS).


APPENDIX G. MOTOR AND POWER TRANSMISSION EQUATIONS

STRIDE LENGTH 11.5cm (from coupler curve)

ESTIMATED CRANK SPEED

! !"#!!.! !"

∙ !!"!"#

∙ !" !"#! !"#

= 26.087 !"#

!".!"# !"#! !"#

∙ !! !"#! !"#

∙ !!"#!"!"#

= 2.73 !"#/!"!

ESTIMATED GEAR RATIO !" =

!!"#!!"

=26.087 !"#10,378 !"#

= 397.8: 1

POWER AND TORQUE REQUIRED let η = .8 (estimated linkage efficiency)

m= .798 kg

g = 9.8 !!!

!! = .5

!"!" = !!"#

!"# =!!!!

∙!!!!

. 8 !(2.73 !"#!"# ) =

!!!!!"!

∙ 0. 05!/!0

!!"# = !!"#!

=. 098 !. 8

= .1225!

! 2.73 !"#!"# = .1225 !

! = .045 !"


APPENDIX H. FINAL TESTING DATA

VOLTAGE V = 3 volts (2 AA Batteries)

CURRENT Current when hand contacts rope, ICONTACT = .46 amps

Current when hand moves along rope, IMOVING = .67 amps

Current when hand lifts off rope, ILIFT = .87 amps

POWER CONSUMPTION UNDER LOAD Input Power, PIN = I x V

PCONTACT = 1.38 Watts/ 4 arms = .37

PMOVING = 2.01 Watts/ 4 arms = .50

PLIFT = 2.61 Watts/ 4 arms = .65

KINEMATICS Angular velocity of crank arm, !CRANK_NOLOAD = 5 revolutions/ 18 s = .28 rev/s

Angular velocity of crank arm, !CRANK_LOAD = 5 revolutions/20s = .25 rev/s


APPENDIX I. TWITTER DOCUMENTATION


FIGURE 22. @SLEEPYTHESLOTH TWITTER FEED

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Sleepy Slothers Design Documentation