Kinematic Analysis of a Planar Eight-Bar Linkage: Application to a Platform-Type Robot

Abstract

The paper presents solutions to the forward position and velocity problems of a planar eight-bar, three degree-of-freedom, closed-loop linkage. The linkage is proposed as a programmable platform-type robot which can both position and orient the platform. A sixth-order polynomial equation in the angular displacement of the platform is derived which indicates that six configurations, for a given set of input angular displacements, are possible. The polynomial equation is important in the study of the limit positions of the linkage. The forward velocity problem is solved using first-order partial derivatives of the four output angular displacements with respect to the three independent input displacements. The partial derivatives provide geometric insight into the kinematic analysis of the linkage. A graphical method, which utilizes the instantaneous centers of zero velocity, is introduced as a check of the velocity analysis. The method is solely a function of the configuration of the linkage and is, therefore, a practical alternative to other methods which rely on velocity information. For illustrative purposes, the paper includes a numerical example of the linkage used as a planar platform-type robot.