A COMPUTATIONAL METHOD FOR THE DYNAMIC ANALYSIS OF PLANAR LINKAGES WITH APPLICATIONS

摘要

This paper presents a computational method for generating the equations of motion of planar linkages consisting of interconnected rigid bodies. The formulation uses initially the rectangular Cartesian coordinates of an equivalent constrained system of particles to define the configuration of the mechanism. This results in a simple and straightforward procedure for generating the equations of motion. The equations of motion are then derived in terms of relative joint variables through the use of a velocity transformation matrix. The velocity transformation matrix relates the relative joint velocities to the Cartesian velocities. For the open loop case, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For the closed loop case, suitable joints should be cut and few cut-joints constraint equations should be included for each closed loop. Examples are used to demonstrate the generality and efficiency of the proposed method.