Design of Compliant Climbing Feet

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Design of Compliant Climbing Feet

• Alan Asbeck
• 9/14/04

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Overview

• Definitions
• Claw attachment model
• Geometrical considerations
• Other design considerations
• Examples

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Definitions
Claw
Axial direction
Toe
Foot
Wall
Normal direction
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Claw Attachment Model

• Find appropriate compliances in the Normal and
  Axial directions

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Sangbae's sticky system model
An element also has sticky system
Substrate Sticky element Sticky structure
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Sticky system model (2)

1,3 compression internal force 2 Detached
element ( if Fi lt k(Yi h0) , where Fi
is sticky force of sticky element) 4 Zero
internal force 5 Tensile force ( Fi gt k(Yi
h0)) F external force k stiffness of
structure (modulus)
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Claw Attachment ModelNormal Direction

• First, slide foot down wall until some claws
  have caught asperities
• Then, examine the forces in the normal direction.

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Claw Attachment ModelNormal 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 asperitiessome claws don't attach!

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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

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Maximum sticky force vs structure
stiffness(Sangbae's results)
? Make foot very compliant in axial direction
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Claw attachment model Axial direction
Asperity
Attached claw acts like a spring
Unattached claw has no axial forces acting on it
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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

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Geometrical Considerations

• Center of Rotation for Normal, Axial compliances
• Claw angle change

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Centers 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
Away from the wall
At the wall
Inside the wall (virtual)
Center of Rotation
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Normal CoR Force Analysis

• Assumed loading strategy
• Push foot into wall until all toes touch wall
• Pull foot down with our load

Away from the wall
Inside the wall (virtual)
F
F
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!
Motion away from the wall in response to force
causes claw to disengage. Also, claw skips over
wall before finding another asperity. ? BAD!
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Normal CoR Force Analysis (2)
At the wall
F
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!
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Claw Angle Change
Theta

• 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.

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Normal CoR cont'd
Some more options
Far from claw
Close to claw

• 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)

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Application of Normal CoR principles

• If the toes are flexible near the claw, this
  will put the CoR very close to the claw.

F
F
Toe deforms from force. This causes the CoR to
be quite close to claw.
Flexible
F
F
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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

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Other Design Considerations

• Damping and Springiness
• Detaching from wall

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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.

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Detaching from Wall
Typical ways claws get stuck in wall
Fdetachment
Fdetachment
Entire claw gets stuck in a large deep hole
prevent by changing the claw design
Tip of claw binds in a deep hole prevent by
pulling the claw out along its axis
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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
• Have a rigid toe and push the base of the toe
• Pull the claw out from the back of the claw

Fdetachment parallel to claw tip
rigid
Fdetachment parallel to claw tip
not rigid
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Examples!
First, examples of stuff that didn't work and why

• Normal Center of rotation way off wall
• Both have good disengagement mechanisms

This one is actually inside the wall

• Too compliant close to claw tipnormal center of
  rotation really close to claw, causing claw angle
  changes

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• Normal center of rotation slightly off wall
• Probably too springy/not enough damping
• No mechanism for disengagement

• Normal Center of Rotation very close to
  wallgood
• Very compliant in both normal and axial
  directionsgood
• No mechanism for disengagement.. Bad!

• 4-bar linkage-based designs would be good except
  they need to be really big, and tend to distort
  in undesired ways.

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Spider's foot
(Close-up)

• BUT, Normal center of rotation far off wall
  not good for hooking on asperities

• Mechanism providing much compliance in the
  normal direction, like Sangbae's sticky
  modelgood for sticking to surface

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Good examples

• Normal Center of Rotation very close to wall,
  and pretty far backgood.
• 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)

• Normal Center of Rotation very close to
  wallgood. ..maybe a little too close to claw
• Very compliant in both normal and axial
  directionsgood
• Mechanism for disengagement (pull at back of
  claw)

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The End(finally)
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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
  tipsmaybe 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