低副机构的一种平面五级组运动分析

Closed Form Displacement Analysis of a Planar Fifth Class Group with Lower Pairs

采用复数与矢量结合的方法，对低副机构中一种８杆１２副的平面五级组运动分析问题进行了求解．首先根据不同的环路列出矢量方程，然后将方程转化成复数形式，经过代数消元后得到了输入输出方程．对次数的判定后证明方程的解为４２个，即该平面五级组可以有４２种构型．最后对一个实例进行了计算，给出了４组实根值．推导过程中的符号运算采用计算机代数系统“Ｍａｔｈｅｍａｔｉｃａ”．

The closed form displacement analysis of one kind of planar fifth class groups with 8 links and 12 lower pairs is solved by the method of combining vector with complex number. First, the vector equations are established according to different loops. Then the equations are changed into the form of complex number. The problem is reduced to a single unknown equation after algebraic elimination. The input output equation, which is proved to be a 42th degree polynomial equation, is obtained. It shows that this construction of fifth class group has 42 structures. Last, a numerical example is studied. Four real roots are listed. The symbolic computation is carried out by computer algebra system Mathematica.