Application of Secant-Bootstrap Method for Direct Kinematics of 3-DOF Translational Parallel Manipulator

The current paper investigates the closed solution of direct kinematics of a 3-DOF translational parallel manipulator with fixed actuators called a 3-PRC TPM. This solution approach is a combination of Secant theory and Bootstrap method called Secant-Bootstrap method. This method is used for solution of nonlinear kinematics of serial robots.The advantages of this method with respect to the conventional numerical methods such as Newton-Raphson are higher accuracy, better convergence and finding of all possible solutions simultaneously. In this study, for the first time, the Secant-Bootstrap method has been used for the solution of nonlinear kinematics of translational parallel manipulator. The results of current approach show an excellent correspondence with of those traditional numerical methods such as Newton-Raphson with better convergence and higher precision of all solutions.