A numerical method for forward kinematics of general Stewart manipulator using natural coordinates

In this paper, a numerical method for forward kinematics of general Stewart manipulator using natural coordinates is presented. The kinematic equations are in quadratic forms and the corresponding Jacobian matrix is a linear function of coordinates because of using natural coordinates. According to the characteristics of the kinematic equations, the Newton-Raphson algorithm is simplified to decrease the renewal time of iterations between equations and Jacobian matrix, and used to solve the kinematic equations. The singularity and convergence problems of the algorithm are discussed. Furthermore, the method using natural coordinates is compared with the traditional method using rotation matrix through numerical examples. Comparison results show that the method using natural coordinates is very accurate, more efficient, and has a greater convergence domain.