A Unified Algorithm for Analysis and Simulation of Planar Four Bar Motions Defined With R and P Joints

Abstract

This paper presents a single, unified, and efficient algorithm for animating the coupler motions of all fourbar mechanisms formed with revolute (R) and prismatic (P) joints. This is achieved without having to formulate and solve the loop closure equation for each type of fourbar linkages separately. Recently, we developed a unified algorithm for synthesizing various fourbar linkages by mapping planar displacements from Cartesian space to the image space using planar quaternions. Given a set of image points that represent planar displacements, the problem of synthesizing a planar fourbar linkage is reduced to finding a pencil of generalized manifolds (or Gmanifolds) that best fit the image points in the least squares sense. In this paper, we show that the same unified formulation for linkage synthesis leads to a unified algorithm for linkage analysis and simulation as well. Both the unified synthesis and analysis algorithms have been implemented on Apple's iOS platform.