On the mechanics of natural compliance in frictional contacts and its effect on grasp stiffness and stability

This paper considers the effect of natural material compliance on the stiffness and stability of frictional multi-contact grasps and fixtures. The contact preload profile is a key parameter in the nonlinear compliance laws governing such contacts. The paper introduces the Hertz-Walton contact compliance model which is valid for linear contact loading profiles. The model is specified in a lumped parameter form suitable for on-line grasping applications, and is entirely determined by the contact friction and by the material and geometric properties of the contacting bodies. The model predicts an asymmetric stiffening of the tangential reaction force as the normal load at the contact increases. As a result, the composite stiffness matrix of multi-contact grasps governed by natural compliance effects is asymmetric, indicating that these contact arrangements are not governed by any potential energy function. Based on the compliant grasp dynamics, the paper derives rules indicating which contact point locations and what preload profiles guarantee grasp and fixture stability. The paper also describes preliminary experiments supporting the contact model predictions.