关键词: 非线性方程, 牛顿迭代, 泰勒公式, 并联机器人, 多元函数

Abstract:

So far, the problem of Kinematics of the closedform solution remains a technical problem, and currently the most popular method in practice is the use of numerical solution method and the generalized geometric equations method. However, the derivations of these methods are very complicated, and there is no unique solution in the process of solving equations. To avoid these problems, we propose a triple nonlinear equation of parallel robot Newton iteration algorithm based on the Taylor formula multivariate function. Based on the mathematical principles, the antiparallel robot solutions can be obtained. The Taylor algorithm avoids multiple solutions tradeoffs skillfully, and the solution meets the demand of continuous exercise directly. In terms of rate of convergence, this algorithm is very promising. We apply the proposed algorithm in the CoDeSys environment, which proves that parallel kinematics can be applied flexibly in real time in CoDeSys environment via configuration.

Key words: nonlinear equation；Newtoniteration；Taylor formula；parallel robot；multiple functions