Representations and Analysis of Mechanisms by Means of Motor Algebra and Graph Theory (1st Report) —Definition of Degrees of Freedom and Velocity Analysis—

Abstract

A new definition of degrees of freedom of mechanisms is presented in terms of pair-loop matrices derived from pair-axis-motors and circuit matrices. A motor or a set of screw coordinates is an extended form of a vector by which instantaneous motion of a rigid body can be represented completely and uniquely. Superpositions of velocities correspond to summations of motors. The definition is valid for mechanisms with multiple closed loops and with critical forms such as pantograph. Pair-loop matrices have enough information of constraints of mechanisms to set up loop equations which determine magnitude ratios of relative velocities on all pairs. An algorithm based on pair loop equations is presented in order to simulate motion of mechanisms. Output examples of simulation program coded in APL show the effectiveness and conciseness of this algorithm. © 1988, The Japan Society for Precision Engineering. All rights reserved.