1. Design of Compliant Climbing Feet Alan Asbeck 9/14/04

2. Overview: Definitions Claw attachment model Geometrical considerations Other design considerations Examples

3. Definitions Wall Normal direction Axial direction Toe Foot Claw

4. Claw Attachment Model Find appropriate compliances in the Normal and Axial directions

5. Sangbae's sticky system model Substrate Sticky element Sticky structure An element also has sticky system

6. Sticky system model (2) 1,3 : compression internal force 2 : Detached element ( if F i < k(Y i – h 0 ), where F i is sticky force of sticky element) 4: Zero internal force 5: Tensile force ( F i > k(Y i – h 0 )) F : external force k : stiffness of structure (modulus) 1 2 3 4 5 F h0h0 YiYi k

7. Claw Attachment Model: Normal Direction = Asperity First, slide foot down wall until some claws have caught asperities Then, examine the forces in the normal direction.

8. Claw Attachment Model: Normal Direction Attached claw Unattached claw Sticky system model: sticky elements "attach" to surface if they touch surface Claw attachment model: claws must hook on surface asperities–some claws don't attach!

9. Claw attachment model vs. sticky system model Analysis is the same as in the sticky system model, EXCEPT that the unattached claws cannot attract the surface So, fewer elements stick to the wall, even while all elements push away from the wall  Attached elements must stick really well! (Have a large detachment force)  Design foot so as many elements attach as possible

10.  Make foot very compliant in axial direction Maximum sticky force vs structure stiffness (Sangbae's results)

11. Claw attachment model: Axial direction = Asperity Attached claw acts like a spring Unattached claw has no axial forces acting on it

12. Conclusions from Axial direction  Allow toes to stretch far enough that most toes catch asperities (recall normal direction conclusions) Distance necessary to stretch depends on asperity size Best if the load is equally shared between toes.  make the compliance softer in the axial direction

13. Geometrical Considerations Center of Rotation for Normal, Axial compliances Claw angle change

14. Centers of Rotation Away from the wall At the wallInside the wall (virtual) = Center of Rotation There is a Center of Rotation (CoR) for the claws' normal compliance, and a second one for the axial compliance. Some options for the Normal compliance CoR:

15. Normal CoR Force Analysis Away from the wall F Motion away from the wall in response to force causes claw to disengage. Also, claw skips over wall before finding another asperity.  BAD! Inside the wall (virtual) Since claw cannot go further into the wall, the center of rotation is forced down and out to increase the length. This pushes the NEIGHBORING toes away from the wall, since they are coupled through the rest of the foot.  BAD! F Assumed loading strategy: Push foot into wall until all toes touch wall Pull foot down with our load

16. Normal CoR Force Analysis (2) At the wall Putting the center of rotation as close to the wall as possible minimizes antagonistic forces, since all forces are axial. No motion of toe occurs.  Good! F

17. Claw Angle Change Claw only attaches to wall for certain claw angles: if it is too shallow or too steep, it will not attach. So, prevent claw from rotating out of desired angle range Empirically: around Theta = 45-75 degrees from wall normal works well (but this should be further investigated). This is different than Will's results (45-60 degrees) because we are hooking asperities, not penetrating a surface. Theta

18. Normal CoR cont'd Close to claw Far from claw Some more options: When the CoR is close to the claw, a large angle change occurs for a given normal displacement of the claw tip.  Thus, having a CoR far from the claw is best (i.e. in the limit, the toe translates in the normal direction)

19. Application of Normal CoR principles If the toes are flexible near the claw, this will put the CoR very close to the claw. F Flexible F F F Toe deforms from force. This causes the CoR to be quite close to claw.

20. Axial CoR Should be as far away from wall as possible (in the limit, just have translation) Practically should be at least 4-5+ cm away from wall for small vertical motions Matters when designing 4-bar linkages and flexures for the toes

21. Other Design Considerations Damping and Springiness Detaching from wall

22. Damping and Springiness We care about the spring constant and damping between the claw tip and the base of the toe Matters in both axial and normal directions: often, a claw will weakly grab a (bad) asperity, then break free after stretching a little. We want the claw to scrape against the wall as much as possible while looking for a new asperity. Skipping over stretches of wall is bad. Should be investigated more. I think that a low Q- factor is better, probably something critically damped. It seems like underdamped toes bounce more.

23. Detaching from Wall Typical ways claws get stuck in wall: F detachment Entire claw gets stuck in a large deep hole – prevent by changing the claw design F detachment Tip of claw binds in a deep hole – prevent by pulling the claw out along its axis

24. Detaching from Wall (2) Need to have some way of ensuring that the claws are pulled out the same direction they were put in to the wall. Options: 1.Have a rigid toe and push the base of the toe 2.Pull the claw out from the back of the claw F detachment parallel to claw tip rigid F detachment parallel to claw tip not rigid

25. Examples! First, examples of stuff that didn't work and why: Normal Center of rotation way off wall Both have good disengagement mechanisms Too compliant close to claw tip— normal center of rotation really close to claw, causing claw angle changes This one is actually inside the wall

26. Normal center of rotation slightly off wall Probably too springy/not enough damping No mechanism for disengagement 4-bar linkage-based designs would be good except they need to be really big, and tend to distort in undesired ways. Normal Center of Rotation very close to wall—good Very compliant in both normal and axial directions— good No mechanism for disengagement.. Bad!

27. Spider's foot (Close-up) Mechanism providing much compliance in the normal direction, like Sangbae's sticky model—good for sticking to surface BUT, Normal center of rotation far off wall – not good for hooking on asperities

28. Good examples Normal Center of Rotation very close to wall—good...maybe a little too close to claw Very compliant in both normal and axial directions—good Mechanism for disengagement (pull at back of claw) Normal Center of Rotation very close to wall, and pretty far back—good. Axial Center of Rotation is infinitely far back because of tube mechanism Not so compliant in both normal and axial directions (currently being improved) Mechanism for disengagement (rigid toes)

29. The End (finally)

30. Detaching from Wall (3) Original Spinybot's claws disengaged abruptly from all wall surfaces, even when attempts were made to pull parallel to the claw tips. Why? Possibilities: –On a very small scale, the tip of the claw was binding in a small (deep) hole –Actually weren't pulling parallel to claw tips—maybe some changed angles or the legs didn't pull in the correct direction –??? Abrupt disengagement causes the robot to shake and jostle the other attached feet