A Statistical Approach to the Forward Kinematics Nonlinearity Analysis of Gough-Stewart Mechanism

摘要

Both the forward and backward kinematics of the Gough-Stewart mechanism exhibit nonlinearbehavior. It is critically important to take account of this nonlinearity in some applications suchas path control in parallel kinematics machine tools. The nonlinearity of inverse kinematics isstraightforward and has been first studied in this paper. However the nonlinearity of forwardkinematics is more challenging to be considered as there is no analytic solution to the forwardkinematic solution of the mechanism. A statistical approach including the Bates and Wattsmeasures of nonlinearity has been employed to investigate the nonlinearity of the forwardkinematics. The concept of standard sphere has been used to check the significance of thenonlinearity of the mechanism. It is demonstrated that the length of the region, defined as thelinear approximation of the lifted line, has a significant impact on the nonlinearity of themechanism.