On equivalent motions in spatial linkages

Abstract

A common feature of spatial linkages is the restriction, perhaps multiply, of a form of motion to containment within portion of the chain while the gross configuration emulates a simpler linkage, such as the four-slider loop. We investigate this phenomenon by examining a group of related overconstrained linkages. In doing so we make use of displacement–closure equations, screw motors and the notion of the reciprocal screw.