An algorithm for real-time forward kinematics of 6-degree-of-freedom parallel mechanisms

This article proposes a forward kinematics algorithm based on closed-loop feedback solution for real-time pose estimation of 6-degree-of-freedom parallel mechanisms. First, a feedback forward kinematics algorithm with second-order error dynamics built in joint space is presented and its convergence is analyzed. Taking a Stewart platform as an example, fast convergence and high solving accuracy of the algorithm are shown in simulation. However, while applying the algorithm to forward kinematics of a 6-degree-of-freedom redundantly actuated parallel mechanisms, solving errors will be growing slowly and non-convergent, which is caused by redundancy character of the parallel mechanisms. Then a modified algorithm, of which second-order error dynamics is built in Cartesian space, is developed. Considering velocity information is usually difficult to measure or estimate accurately in reality, the performance of feedback forward kinematics algorithm without joint velocity feedforward is also evaluated. Finally, the algorithm is implemented into real-time degree of freedom control of the redundant parallel mechanisms which is calibrated by a coordinate measuring machine. Experiment results show that the proposed algorithm can solve the pose with relatively high accuracy under static conditions and is effective and feasible for real-time pose estimation of parallel mechanisms.