  In this paper, a new numerical method to solve the forward kinematics (FK) of
a parallel manipulator with three-limb spherical-prismatic-revolute (3SPR)
structure is presented. Unlike the existing numerical approaches that rely on
computation of the manipulator's Jacobian matrix and its inverse at each
iteration, the proposed algorithm requires much less computations to estimate
the FK parameters. A cost function is introduced that measures the difference
of the estimates from the actual FK values. At each iteration, the problem is
decomposed into two steps. First, the estimates of the platform orientation
from the heave estimates are obtained. Then, heave estimates are updated by
moving in the gradient direction of the proposed cost function. To validate the
performance of the proposed algorithm, it is compared against a Jacobian-based
(JB) approach for a 3SPR parallel manipulator.
