Solutions to Systems of Non-Linear Equations That Arise in the Kinematic Synthesis of Spatial Mechanisms

Abstract

Determining the key dimensions of a mechanism for a prescribed performance is called the “synthesis” of the mechanism. The prescribed performance is given by a specifying position or motion specifications at “precision points”. These specifications lead to a system of equations whose solutions give the desired key dimensions of the mechanism. Synthesis for two or three positions leads to a nonlinear system. Different types of mechanisms give different forms of synthesis equations. In this paper, two spatial mechanisms - a three-link mechanism with an intermediate higher pair for function generation and a five-link motion generator mechanism- are considered.