On the representations of wrenches for the analysis of mechanisms

In order to find out an invariant formula for an analysis of a mechanism to its types and the motion spaces of its loops, the novel algorithm utilizing the duality relation between screw spaces and wrench spaces has been developed. Expressing wrenches on the dual basis of that for screws gives the concise expressions for determining the relation among wrenches acting on links and torques on the active joints. The analysis of the parallel mechanism with connecting chains, each of which has a loop with a motion space different from that of the mechanism is described as the example.