Forward kinematics analysis of parallel manipulator using modified global Newton-Raphson method

In order to obtain direct solutions of parallel manipulator without divergence in real time, a modified global Newton-Raphson (MGNR) algorithm was proposed for forward kinematics analysis of six-degree-of-freedom (DOF) parallel manipulator. Based on geometrical frame of parallel manipulator, the highly nonlinear equations of kinematics were derived using analytical approach. The MGNR algorithm was developed for the nonlinear equations based on Tailor expansion and Newton-Raphson iteration. The procedure of MGNR algorithm was programmed in Matlab/Simulink and compiled to a real-time computer with Microsoft visual studio.NET for implementation. The performance of the MGNR algorithms for 6-DOF parallel manipulator was analyzed and confirmed. Applying the MGNR algorithm, the real generalized pose of moving platform is solved by using the set of given positions of actuators. The theoretical analysis and numerical results indicate that the presented method can achieve the numerical convergent solution in less than 1 ms with high accuracy (1×10⁻⁹ m in linear motion and 1×10⁻⁹ rad in angular motion), even the initial guess value is far from the root.