基于代数法的平面四杆机构五精确点轨迹综合  

Five Precision Points Path Synthesis of Planar Four-Bar Linkage Using Algebraic Method

作　　者：黄昔光[1] 廖启征[1] 魏世民[1] 徐强[1] 

机构地区：[1]北京邮电大学自动化学院,北京100876

出　　处：《北京邮电大学学报》2008年第2期1-4,25,共5页Journal of Beijing University of Posts and Telecommunications

基　　金：国家"973计划"项目(2004CB31800);国家自然科学基金项目(50475161);教育部高等学校博士学科点专项基金项目(20050013006);国家"863计划"项目(2007AA04Z211)

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.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

关 键 词：轨迹综合 机构综合 GROEBNER基 Sylvester结式 

分 类 号：TH112[机械工程—机械设计及理论]