Static Force and Torque Analysis Using 3 × 3 Screw Matrix, and Transmission Criteria for Space Mechanisms

Abstract

The method of determining the static force and torque distributions in space mechanisms by use of the 3 × 3 screw matrix is presented. Transmissivities in favor of rotation and translation, and angles of transmission in space mechanisms are defined. Transmissivities are used to show why some space mechanisms have no dead center positions. In the process, the dual equilibrium equations, one for each link, are written in dual vector form, then they are solved simultaneously for the dual force components. Explicit expressions for forces and torques in the RCCC and RSSR space mechanisms are obtained. Torque distribution in the spherical four-bar mechanism is reduced from the results for the RCCC space mechanism. The numerical example considers a symmetrical crank-rocker RSSR space mechanism, where the output torque is due to the load inertia. Variations in the input torque, output torque, mechanical advantage, and transmission angle for one cycle are given for both geometric inversions.