Parts entropy and the principal kinematic formula

Abstract

Assembly systems that are able to function in the presence of uncertainties in the positions and orientations of feed parts are, by definition, more robust than those that are not able to do so. Sanderson quantified this with the concept of ldquoparts entropy,rdquo which is a statistical measure of the ensemble of all possible positions and orientations of a single part confined to move in a finite domain. In this paper the concept of parts entropy is extended to the case of multiple interacting parts. Various issues associated with computing the entropy of ensembles of configurations of parts with excluded-volume constraints are explored. The rapid computation of excluded-volume effects using the ldquoPrincipal Kinematic Formulardquo from the field of Integral Geometry is illustrated as a way to potentially avoid the massive computations associated with brute-force calculation of parts entropy when many interacting parts are present.