基于数字—符号法的空间4自由度并联机构位置正解

采用动平台四个铰心的绝对坐标作为输出变量，用结式消元法对空间4自由度并联机构进行了位置正解分析，得到了其7次的一元输入输出方程，由此得到了全部位置正解。消元过程中引入了数字—符号方法，将结构参数处理为数值量，将关节变量处理为符号量，将数字、符号推导过程转化为矩阵运算过程，由于结构参数以数值量的形式出现在方程推导中，降低了符号推导的难度，符号推导不需要复杂的符号处理软件的支持。给出了一个数字实例，经验算其解满足原始方程且无增根。

NUMERIC-SYMBOLIC APPROACH FOR DIRECT DISPLACEMENT SOLUTION OF A 4-DOF SPATIAL PARALLEL MECHANISM

Absolute coordinates of spherical joints on movable platform are chosen as unknowns ,a direct displacement analysis which is based on resultant eliminatiom method for a 4-DOF spatial parallel mechanism is presented, 7 degrees input-output closed form equation with one unknown is obtained,and all of the roots for all unknowns are gained. Numeric-symbolic technique is introduced in the procedure of resultant elimination, procedure of number-symbol manipulation is transformed into that of matrix manipulation.Because joint variables are treated as symbols and all structure parameters are treated as real num-bers,the complexity of derivation for input-output equation is reduced.The solution is verified with a numerical example,its rsults without extraneous roots agree with the original equations.