Forward displacement analysis for lps + 3tps , lpt + 2tps , lpps + 4tps type pmts are performed based on result elimation method . closed form solutions for forward displacement of these hybrid type pmts are derived , numerical examples are given for illustration 基于结式消元法分别对1ps + 3tps型、 1pt + 2tps型和1pps + 4tps型并联机床进行了位置正解分析，获得了封闭形式的解析解。
The paper proposes the elimination by eliminant with aid of basic sets ( eeabs ) , in order to solve the problems in the theories and methods of polynomial system of equations ? limination at present , and to find the multi - solutions of mechanism science ~ research 针对目前多项式方程组的消元理论和方法中存在的问题和不足，本文提出了基组结式消元法，并用以求解机构学研究中的多解问题。
The main idea of this method is to choose a set according to the order of polynomials , to eliminate by making use of bezout eliminant , get zero set from the improved formula about set of zero points , so that a polynomial system of equation ~ set of zero points can be got only by one time arrangement 该方法的主要思想是：根据多项式秩的大小选取基组，采用贝左结式消元，用改进型零点集结构式确定零点集，从而只需一次整序就可求得一个多项式方程组的零点集。
Absolute coordinates of spherical joints on movable platform are chosen as unknwn , a direct displacemeat analysis which is based on resultan eliminatiom method for 2nys + 2tps type pmts is presented , the 7th degree input - outpul closed form equation with one wtwn is obtained , and all of the roots for all unknowns are gained 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2rps + 2tps型并联机床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。
The paper applies algebraic geometry , computational geometry , approximation theory to study the following problems : the nother type theory and the riemann - roch type theory of the piecewise algebraic curve ; the number of real intersection points of piecewise algebraic curves ; the real piecewise algebraic variety and the b - net resultant of polynomials 本文应用代数几何，计算几何，函数逼近论等学科的基本理论，分别就分片代数曲线的n ( ? ) ther型与riemann - roch型定理；分片代数曲线的实交点数；实分片代数簇以及多项式的b -网结式进行研究。
A great number of calculating results show that eeabs is effective and practicable . in addition , the method has been successfully applied into optimum design of two types of range - changing mechanism of gantry crane and the software systems of optimization design and analytical calculation of straight - arm gantry crane and ? ptimization design and analytical calculation of balance pulley compensation gantry crane ? has been compiled 另外，作者还对基组结式消元法在两种门座式起重机变幅机构优化设计中的应用做了成功的尝试，并编制了“变幅补偿直臂架门机的优化设计和分析计算”和“平衡滑轮式补偿门机的优化设计和分析计算”软件系统。
A set of nonlinear equations of precise synthesis are established for special case according to co - planarity and equal distance conditions . by resultant elimination , 3 polynomial equations containing 3 variables are obtained . all of the groups of real solution within a certain value range are generated with computer graphic method 针对实现两个函数，每个函数四个精确点的rssr机构，通过结式消元法消元，得到三元高次多项式方程组，并采用计算机图解法，在一定值范围内解出了方程组的全部实数解。
