Forward kinematics of spherical parallel manipulators with revolute joints

The paper deals with the forward kinematics of spherical parallel manipulators (SPMs). A polynomial solution of forward kinematics is presented with a novel approach of utilizing the input-output (I/O) equations of spherical four-bar linkages. In this method, the closed-loop kinematic chain of an SPM is separated into two four-bar spherical chains, for which the input-output equations can be obtained. Based on the input-output equations of spherical four-bar linkage, an eighth-order polynomial equation of joint angles is obtained, which yields the orientation of the end-effector of an SPM in terms of the unit vectors for joint axes. Examples are included to demonstrate the application of the developed method.