No slip. vs Sliding with infinite friction

Size: px

Start display at page:

Download "No slip. vs Sliding with infinite friction"

Ella O’Neal’
5 years ago
Views:

1 No slip NSF vs Sliding with infinite friction Comments on Special for Banff 2014 Pulling by Pushing, Slip With Infinite Friction, and Perfectly Rough Surfaces Kevin Lynch, Matt Mason Int J of Robotics Research, 1995 and Wobbling, toppling, and forces of contact Tad McGeer Am. J. of Physics, 1989 Matt Kelly, Mechanical Eng, Cornell U Andy Ruina, Gregg Stiesberg, Physics,

2 Motivation/inspiration: 1) Mechanics (apparent) paradoxes are interesting a) friction and b) dynamics 2) Make a good robot good simulation c) deal with these things, or d) do something worse Conclusions: 3) Slip with is possible e) In natural situations f ) Is a useful model 4) No-slip BCs violates (or something, sometimes) g) In natural problems h) So slip is better

3 Value system (in this talk): 1) Don t violate, symmetries of space, etc. 2) Approximate constitutive laws are OK (like etc). 3) The model should have a high-precision meaning. 4) No concern for computation speed. 5) 2D for simpler pictures etc.

4 Coulomb/DaVinci/Amonton friction equation: A A F N N F B B The friction force B BN Relative slip velocity. on A from B on A from B The magnitude of the friction force BM B A B A B An upper bound on the friction force during slip during stationary contact

5 If you don t like divide by zero etc: A A F N N F B B µn N Filename:tfigure2-friction-angle φ tan sin sin if if

6 sin Constitutive 0. relation for friction Coulomb friction A surface in the space of force angle sliding velocity sin force magnitude hapter 0. sin if if if if sin Single constitutive tan parameter: sin the friction angle (PD control) (Side force) (Nothing special about if (horizontal acceleration of base) ) if 1

7 Recall Conclusions: 3) Slip with is possible e) In natural situations: 3 examples & demo f ) Is a useful model 4) No-slip BCs violates (sometimes) g) In natural problems h) So slip is better

8 Dragging stick (similar to Lynch/Mason 1995)

9 Constitutive relation for friction Coulomb friction A surface in the space of sliding velocity v sliding force normal force F N Single constitutive parameter: the friction angle Nothing special about. Surface becomes two quarter planes ( ) and one half plane ( ).

10 Dragging stick (cont d) Force per weight θ = 15 deg θ = 45 deg Drag Force Force per weight Coefficient of Friction Normal Force θ = 15 deg θ = 45 deg Coefficient of Friction F= 0.5 W N = 0 Nothing special happens when.

11 Dragging stick (cont d) Chapter 0. Athoughtexperiment ASimpleProblem-TheFallingPencil Contact Models - Two Old, One New Summary Athoughtexperiment Infinite non-slip friction ASimpleProblem-TheFallingPencil model Coulomb friction model Contact Models - Two Old, One New Infinite sliding friction model Summary A micro-mechanism that implements. Athoughtexperiment Infinite non-slip friction model Coulomb friction model Infinite sliding friction model pencil pencil pencil pencil The tip slides up the groove wall sin then slides over the top of the groovethen wall free-falls and collides with the next groov Frictionless G. Stiesberg Simulating Intermittent Contact G. Stiesberg Simulating Intermittent Contact Chapter 0. No vertical force, G. Stiesberg Simulating Intermittent Conta vertical some horizontal force, gear teeth if (Demo) if

12 Infinite friction example 2: A wheel e shows too-large a bearing hole. ĵ î F N θ C r R Filename:tfigure-primitivewheel To figure out the forces involved we draw points. F x F y gure-primitivewheelfbd G µ =0 µ = A wheel d φ r θ r is not α R α R just a lever. Filename:tfigure-primitivewheelFBD2 α α

13 Infinite friction example 3: A pulley For all force at D is vertical D R r C fixed axle For Pulley g ĵ M î F A small axle makes an efficient pulley Filename:pfigure-s01-p2-3 for arbitrarily large

14 For a dragging stick and for journal bearings (wheel and pulley), infinite friction slip seems a reasonable worst case (biggest friction) model.

15 Recall Conclusions: 3) Slip with is possible e) In natural situations: 3 examples & demo f ) Is a useful model 4) No-slip BCs violates (sometimes) g) In natural problems h) So slip is better

16 Simulation of a falling pencil (McGeer 1989) Start nearly vertical at rest Tip is in non-slip infinite frictional contact with surface, equivalent to a pin joint constraint θ l y x (Usherwood video)

17 Simulation of a falling pencil (cont d) Integrate the constrained EOM until the normal force vanishes f n f t θ Release constraint when normal force gets to zero.

18 Simulation of a falling pencil (cont d) Released constraint when normal force went to zero. Surprise! Tip of pencil immediately accelerates through the floor. Why?

19 Simulation of a falling pencil (cont d) Agraphicalproofthatthetipmustacceleratethroughthe floor: JUST BEFORE LIFTOFF JUST AFTER LIFTOFF mg Why did simulation fail? mg f t f t f t Relaxing the constraint is equivalent to adding atangential force at the tip that causes it to accelerate through the surface Conclusion: infinite non-slip friction is not a physically consistent contact model

20 Simulation of a falling pencil (cont d) Three choices: 1) Allow slip (with infinite friction or whatever). 2) Allow the ground to suck. f f n 3) Allow interpenetration. f t 0 t

21 The root of all evil: Contact mass matrix relates force and acceleration at contact point ACC FORCE ACC FORCE (mass matrix video)

22 Constitutive relation for friction Coulomb friction A surface in the space of sliding velocity v (a) sliding force normal force F N Single constitutive parameter: the friction angle Nothing special about. Surface becomes two quarter planes ( ) and one half plane ( ).

23 Motivation/inspiration: 1) Mechanics (apparent) paradoxes are interesting a) friction and b) dynamics 2) Make a good robot good simulation c) deal with these things, or d) do something worse Conclusions: 3) Slip with is possible e) In natural situations (e.g., our robot sims) f ) Is a useful model 4) No-slip BCs violates (or something else) g) In natural problems h) So slip is better

Steinkamp s toy can hop 100 times but can t stand up

Steinkamp s toy can hop 100 times but can t stand up Steinkamp s toy can hop 1 times but can t stand up (appendices only) Gregg Stiesberg 1, Tim van Oijen 2, Andy Ruina 3 1 grs26@cornell.edu, Physics, Cornell University, Ithaca, NY 2 T.P.vanOijen@tudelft.nl,