Direct kinematics analysis of the Tip-Tilt-Piston parallel manipulator by Ostrowski Homotopy continuation method

The analysis of the direct kinematics is the foundation for studying other performances of the parallel robot. For most parallel manipulators the direct kinematics is challenging. Newton-Raphson method is popular method for solving system of nonlinear equations that is based on initial guess. The Homotopy continuation method has advantage over conventional numerical iteration method, which is not rely on the initial values. In this paper, we apply two methods, Newton-Raphson Homotopy continuation method and Ostrowski Homotopy continuation method, to solve nonlinear equations of direct kinematic of Tip-Tilt-Piston parallel manipulator and all of 8 solutions of direct kinematic solution of this manipulator was found by these methods. The results showed that Ostrowski Homotopy continuation method reduces Computation time for solving direct kinematic problem of the proposed manipulator up to 70-80 % than Newton-HCM.