Submitted to Mechanism and Machine Theory
by Elon Rimon, Joel W. Burdick
http://robby.caltech.edu/papers/mmt2.ps.Z
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Abstract:
Using a configuration space approach, this paper develops a 2 nd order mobility theory for a body, B, in frictionless quasi-static contact with rigid stationary bodies A 1; \Delta \Delta \Delta; A d. This analysis ultimately leads to a coordinate invariant 2 nd order mobility index, an integer that captures the inherent mobility of B in an equilibrium grasp. The 2 nd order index differentiates between grasps which are deemed equivalent by 1 st order, or instantaneous, theories, but are physically different. We further show that 2 nd order effects can be used to lower the effective mobility of an equilibrium grasp, and hence can be used to prove new lower bounds on the number of contacting bodies needed to immobilize an object. 1
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