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Forward Displacement Analysis of 5SPS-1CCS Parallel Manipulator Based on Hyper-Chaotic Newton Method

Forward displacement analysis of parallel manipulators lead finally to solve the complex nonlinear equations, and its process is extremely difficult. The Newton iterative method is an important iterative technique for high-dimension nonlinear equations, but it is comparatively sensitive to initial value. To take chaos sequences as initial points of Newton iterative method, it can rapidly find all solutions of nonlinear equations. The novel approach of Newton iterative method based on parameter coupled hyper-chaotic mapping for solving nonlinear equations is presented. The mathematic model of the generalized 5SPS-1CCS parallel manipulator is created based on quaternion. A numerical example is given out, and its result is compared with the result of homotopy continuation method. The analysis results show that the new algorithm is simple, high efficiency, universal and can be used to forward displacement analysis of other coupled parallel manipulators.