A Linear Complementarity Approach to the Frictionless Gripper Problem

Abstract

This article deals with static unilateral phenomena arising in grasping mechanisms and caused by the possible loss of contact between elastic grippers and rigid objects. The problem is formulated as a linear complementarity problem (LCP) that is derived from the equilibrium equations of forces and the compatibility equations for the displacements, as well as from the complementarity inequality restriction describing the contact. A variant of the infeasibility-reducing, complementary pivot al gorithm of Lemke is used for the numerical solution of the arising LCP. Form and force closure conditions are fulfilled in an auto matic way from the solution of the aforementioned LCP. The used algorithm guarantees rapid convergence to the solution of the problem. The theory is illustrated by numerical examples.