On the Bases of Wrench Spaces for the Kinematic and Dynamic Analyses of Mechanisms

The aim of this paper is to find out a computational procedure for the kinematic and dynamic analysis of mechanisms with closed loops of sub-Lie-algebras, utilizing the theory that a basis of the wrench space having an influence on motion is automatically decided. It is shown that the analysis of a closed loop mechanism can be performed by selecting loop-cut-joints and colnputing wrenches of these joints from the condition that virtual works of passive joints are zero. The required number of parameters for wrenches of loop-cut-joints are automatically determined in this procedure. The wrenches acting on active joints can be expressed by the linear combinations of wrenches of loop-cut-joints and those expressing gravity forces and dynamic forces. The torques required for driving active joints can be computed from the condition of virtual works.