A dual quaternion solution to the forward kinematics of a class of six-DOF parallel robots with full or reductant actuation

The forward kinematics is the basis of the design and control of the parallel robots. This paper aims to provide an efficient solution to the forward kinematics of a class of six-degrees-of-freedom parallel robots for real-time applications. With a unit dual quaternion used as the generalized coordinates of the robot system, the forward kinematic equations are derived to be a set of quadratic ones. An efficient algorithm is proposed to get the actual solution to them. The convergence and singularity problems of the new algorithm have been discussed. We have provided a convergence strategy and revealed the internal relation of the singularity with that of the parallel robot, proving the feasibility of the algorithm and giving the working condition in the practical applications. The new algorithm have been compared to the Newton's method for an 8-UPS parallel robot, resulting in the time consumptions of 0.2187 milliseconds and 14.25 milliseconds respectively. And then we perform a simulation of the state-feedback control for an 8-PUS parallel robot. The two examples present the applications of the new algorithm and demonstrate its validity and efficiency.