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中文摘要：
使用分次字典序Groebner基与Sylvester结式相结合的代数方法，研究了给定固定铰链位置的平面四杆机构五精确点轨迹综合问题．首先建立单个轨迹点的封闭方程；然后计算5个轨迹点方程组分次字典序Groebner基，从89个基中选取23个基构造Sylvester结式，不需要提取任何公因式，可直接获得一元36次方程及其全部封闭形式的解析解．为了对结果进行验证，使用同伦连续法对同一个数字算例进行计算，2种方法所得结果一致，说明该机构轨迹综合在复数域内最多有36组解．
英文摘要：
The problem of synthesizing a planar 4-bar linkage with given two fixed pivots such that the coupler curve passes through five given points is considered with the Groebner-Sylevester hybrid approach. Firstly, the closed-form equations of the single point are constructed. Next, the reduced Groebner basis under degree lexicographic ordering for the closed-form equations is obtained using computer algebra. Selecting 23 Groebner bases from 89 ones, a 23 × 23 Sylvester＇s matrix can be constructed. A 36th degree univariate equation is obtained directly from the determinate of the matrix. The same result can be obtained with continuation method. A numerical example is given and it verifies that the problem has at most 36 solutions in the complex field
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