Analysis and Synthesis of Schatz Six-Revolute Mechanisms.

Abstract

Based on geometrical intuition and computer graphics, we present the formation of two kinds of Schatz six-revolute mechanisms and two types of algebraic surfaces on which the corresponding reciprocal screw axes lie under any possible configurations. Then, we derive the general kinematic closed-form solutions and show the absence of stationary configuration of both mechanisms using four-by-four matrix and differential algebra. Moreover, the parametric formulations of coupler-point motion provide a complete higher-order analysis of the coupler curve. In practical application, this mechanism is further used for the dimensional synthesis, path and motion generation synthesis, by the nonlinear programming optimization method. At last, two numerical examples are taken to illustrate the design algorithm.