Forward Displacement Analysis of the 5SPS-1CCS Generalized Stewart Parallel Robot Mechanism Based on Hyper-Chaotic Methods

The forward displacement analysis of parallel mechanism is attributed to find the solution of complex nonlinear equations which is a very difficult process. The more CCS kinematic chains are the more complicated the forward displacement is. Newton iterative method is an important one-dimension and multi-dimension technique which is sensitive to the initial point. Take chaotic sequences as the initial value of Newton iterative method, we can find all the solutions of equations quickly. The paper investigated the initial point generated by hyper-chaotic circuit system and provided a new method and calculation step of finding the all real number solutions of nonlinear equations which was based on hyper-chaotic circuit system and Newton iterative method. Using quaternion, the mathematical model of forward displacement for the generalized 5SPS-1CCS Stewart parallel robot mechanism was established and an example was given. Compared to the topological continuations method the result shows the calculation is brief and general. It can be used in forward displacement of other parallel mechanism. The research builds the theory basis for dimensional design, trajectory planning and controlling of this type of manipulator.