Journal of Beijing University of Posts and Telecommunications

  • EI核心期刊

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2008, Vol. 31 ›› Issue (2): 1-4.doi: 10.13190/jbupt.200802.1.huangxg

• Papers •     Next Articles

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

HUANG Xi-guang,LIAO Qi-zheng,WEI Shi-min,XU Qiang   

  1. School of Automation, Beijing University of Posts and Telecommunications, Beijing 100876,China
  • Received:2007-07-19 Revised:1900-01-01 Online:2008-04-28 Published:2008-04-28
  • Contact: HUANG Xi-guang

Abstract:

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.

Key words: path synthesis, mechanisms synthesis, Groebner basis, Sylvester resultant

CLC Number: