Dynamic Analysis of a Spherical Four Bar Mechanism

Abstract

Abstract Spherical mechanisms are designed so that the points in each link are constrained to move on concentric spheres This paper develops the equations of motion for spherical four bar mechanisms. While the kinematics of these linkages have been extensively studied, the dynamics equations do not seem to have been previously derived. As design techniques for these mechanisms become more efficient, the equations of motion are required to evaluate their performance. The complete dynamics equations of a four-bar spherical mechanism are derived using the input and output joint angles and the Euler parameters of the coupler as generalized coordinates. These coordinates provide a convenient representation of the constraint equations associated with the closed chain. An example analysis is provided.