一种新型四自由度并联机器人运动学正问题的求解

对一种新型四自由度并联机器人运动学正问题进行了研究，利用３个变量构造 出求解正问题的３个约束方程，然后运用符号计算和析配消元法推导出了只含有一 个变元的３２次多项式方程，并且应用计算机软件系统Ｍａｔｈｅｍａｔｉｃａ进行了求正问 题实解的数值验证。

This paper presents the closed-form solution of the direct kinematics problem of a new 4-DOF parallel robot. Since the derivation of closed-form direct  kinematics is very complicated, it is desirable to find a set of possible simplest constraint equations as the basic equations. This will not only help to simplify the derivation procedure but also help to avoid the  extraneous solutions. According to geometric conditions, we constructed a set of three equations in three  variables. Then making use of symbolic computation method and Dialytic method, the direct kinematics was reduced to a 32th order polynomial equation in one variable. Two numerical examples for the real  solutions of the direct kinematics are given by the  software Mathematica.