On Forward Kinematics of a 3SPR Parallel Manipulator

This letter presents a new numerical method to solve the forward kinematics (FK) of a parallel manipulator with a three-limb spherical-prismatic-revolute (3SPR) structure. Unlike the existing numerical approaches that require the manipulator’s Jacobian matrix and its inverse at each iteration, the proposed algorithm requires much less complex computations to estimate the FK parameters. A cost function is introduced that measures the difference between actual FK values and its estimates. At each iteration, the problem is handled in two steps. First, the estimates of the platform orientation from the heave estimates are obtained. Then, the heave estimates are updated along the gradient direction of the proposed cost function. To evaluate the performance of the proposed algorithm, we compare results with those of a Jacobian-based (JB) approach for a 3SPR parallel manipulator.