可调球面三自由度并联机构的位置分析与动态仿真

Positional Analysis and Dynamic Simulation of Adjustable Spherical Three-DOF Parallel Mechanism

基于Groebner基法和计算机符号处理技术对可调球面三自由度并联机构的位置进行了符号求解。该法通过对变量排序、建立多项式对的集合、求SP多项式和约简等运算,将非线性方程组化简为等价的三角化方程组,得到了封闭形式的解析解。在此基础上,研究了调节构件几何参数对欧拉角的变化规律,并应用Pro/E软件建立了机构动态仿真模型,进行了运动学和动力学仿真分析。

Symbolic solutions were acquired concerning the positional analysis issues of adjustable spherical three-DOF parallel mechanism based on Groebner base method and computer symbolic manipulating technique. A set of nonlinear polynomial equations were transformed into a set of equivalent triangularization equations in order to obtain the close formed analytical solution through the following a series of processes： ordering of variables, making up of all pairs of polynomial, seeking SP polynomial, reduction and so on. Then the variety regularity of the Euler＇ s angle was researched when adjusting geometric parameters. Dynamic simulation model of the adjustable spherical three-DOF parallel mechanism was established, and simulation analysis of kinematics and dynamics were made by Pro/E software.