11-6台体型Stewart并联机构位置正解的半解析算法

Semi-analytical Algorithms for Forward Position Analysis of A General 11-6 Stewart Parallel Mechanism

针对6自由度并联机构的正运动学无全解析解或全解析解推导困难的现状,提出1种11-6台体型Stewart冗余并联机构,并构建了1种区别于传统全解析法和数值法的半解析算法。首先,通过构建虚拟支链,将11支链构型转换成具有低耦合度的12支链的并联机构,并基于特征点的尺度关系,推导出转换机构的全解析解;然后,运用Newton-Raphson法,数值求解了6个杆长协调方程,并分析了72种情况下迭代次数与初值偏差的关系,据此得到求解不同支链时的最优方程。

Aiming at the present situation that forward kinematics of most 6-DOF (degrees of freedom)parallel mechanisms can't be described with whole analytical solutions,and a very few of them can be described with.whole analytical solutionsbut also with these difficulties in calculation,a general 11-6 Stewart redundant parallel mechanism is proposed and a semi-analytic method is established which is different from traditional whole analytical method and numerical method.First,a configuration with 11 kinematic chains is transformed into a parallel mechanism with 12 kinematic chains with a low coupling by constructing virtual kinematic chains and whole analytical solutions of mechanisms is constructed based on scales relations between feature points.Then,by using Newton-Raphson,six coordination equations is calculated and optimal equations to calculate different kinematic chains is obtained according to analyzing 72 kinds of relations between iterations and initial value deviation.