A method to get the forward kinematics of parallel kinematics mechanisms based on the fixed point iteration

The fixed point iteration method was proposed to solve the forward kinematics of parallel kinematics mechanisms as a new method. In every iteration through the reverse kinematics the previous iteration intermediate position and posture determined stick orientation vectors. And the stick ports, which were obtained by multiplying stick orientation vectors and given stick lengths, determined the next iteration intermediate position and posture. The final position and posture satisfying the convergence conditions would be obtained. 6-SPS was taken as an example to verify that this method was available and correct. Compared with the Newton iteration, this method possesses more advantages, such as simpler formula, higher speed of the convergence, smaller program workload, and less influence of initial values on the convergence.