Universal Grey Method Based on Hyper-chaos for Solving Forward Displacement of Generalized Parallel Mechanism

The forward displacement of the generalized parallel mechanism can be converted to nonlinear equations for solving, but it is very difficult to find all solutions because of the strong coupling of the nonlinear equations. Universal grey mathematics was applied to the mechanism synthesis, and based on interval arithmetic toolbox INTLAB the universal grey computing toolbox UG_V1 was compiled. Combining universal grey iterative method with hyper-chaotic sequences and taking hyper-chaotic sequences generated by hyper-chaotic neural network system as the initial values of universal grey Newton iterative method, all solutions were found and the calculation steps were given. Example of the generalized parallel mechanism 4SPS-2CCS shows the method is correct and effective. The universal grey method based on hyper-chaos can run within the real range, and it provides a new approach for solving forward displacement in the generalized parallel mechanism and other strongly nonlinear equations.