General Theorems Concerning Full Force Balancing of Planar Linkages by Internal Mass Redistribution

Abstract

Two basic questions concerning the full force balancing of n-linked planar mechanisms with pinned and sliding joints are resolved. A contour theorem is shown to differentiate between mechanisms which can be fully force-balanced and those which cannot. (Mechanisms with axisymmetric link groupings are excluded.) In addition, a generalization of the Method of Linearly Independent Vectors for single degree of freedom mechanisms is given, and it is proven that the “apparent” minimum number of counterweights producing full force balancing by internal mass redistribution alone equals n/2.