Using the Single Reciprocal Screw to Confirm Mobility of a Six-Revolute Linkage

Abstract

Overconstrained kinematic chains have been discovered mostly by analytical or geometrical means or through a synthesizing procedure. In a few instances they have succumbed to computer-aided methods, and those solutions can, in effect, be reduced to a single one. This loop, of six revolutes, is described by parametric conditions that provide little information about its physical make-up. The existence of a lone screw reciprocal to the system defined by the loop's joint screws is the basis here for demonstrating analytically the linkage's mobility and determining its mode of assembly. In addition, it is shown that seven new linkages can be developed from this solution as isomeric variants.