Dynamic Force and Torque Analysis of Mechanisms Using Dual Vectors and 3 × 3 Screw Matrix

Abstract

The method of determining dynamic force and torque distributions in mechanisms by using dual vectors and 3 × 3 screw matrix is presented. The dual equilibrium equations for each moving link of a mechanism are written as a null resultant dual force vector in a reference system located on the link. The resulting 6 × (n – 1) equilibrium equations for an n-link mechanism are solved for the unknown force and torque components at the pair locations, and for the input force or torque required to drive the mechanism to produce the specified dual output force. The dynamics of the mechanism is governed by introducing the dual inertia force acting on a link, which is determined as the negative of the time rate of change in the dual momentum of the link due to its own mass and mass moments of inertia, in the dual equilibrium equation for that link. Dynamic analyses of the 4R plane and the RCCC space mechanisms are performed. Dynamic transmissivities are defined. The RCCC mechanism is analyzed in a numerical example and the results of the dynamic distributions are compared with those of static distributions.