关键词: 并联机构, 拟Newton法, 位置正解, 虚工作空间

Abstract: The iterative search algorithm, based on Newton’s method, is an important numerical algorithm for solving the direct position analysis of parallel mechanism. But, the Jacobian matrix of the mechanism is needed at each step of the iterative process. On the basis of Newton’s method, the quasi-Newton method is applied to solve the direct position analysis of parallel mechanism, in which the Jacobian matrix is instead of the current value of the function. So, the amount of the computation of each iteration can be reduced. A virtual workspace organization is defined, and the reason why the virtual workspace of 6-RUS is constrained is analyzed. Also the limitations of the iterative search algorithm when is applied to solve the direct position analysis of this kind mechanisms are analyzed, and an equivalent method is proposed. Further, the restriction of the virtual workspace of coupled fewer degrees of freedom mechanism is analyzed. The use of dummy mechanisms and improved Jacobian matrix makes the iterative search algorithm can be applied to this type of mechanisms. Numerical examples show that: compared to Newton’s method, the total number of iterations of quasi-Newton’s method has not increased significantly, but due to the small amount of computation for each iteration, the computational efficiency significantly improved, providing some theoretical guidance to the direct position analysis of parallel mechanism in the application of real-time occasions. The use of the equivalent method expands the virtual workspace of the mechanism, increasing the scope of application of the iterative search algorithm.

Key words: direct position analysis, parallel mechanism, quasi-Newton method, virtual workspace