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Four bar linkage coupler curve Chris Peterson and Hirotachi Abo
 

Summary: Four bar linkage coupler curve
Chris Peterson and Hirotachi Abo
Let k = R. Consider the following problem:
Problem. Compute the equation of the four bar linkage curve obtained by
taking the points A = (0, 0), B = (0, 2), C = (x1, y1) and D = (x2, y2) in A2
k
(see Problem Set 7 for the definition).
To solve this problem, we use the elimination theory. Consider the fol-
lowing ideal in k[x1, x2, y1, y2, X, Y ]:
I = (x2
1 + y2
1 - 1, x2
2 + (y2 - 2)2
- 1, (x1 - x2)2
+ (y1 - y2)2
- 1,
(X - x1)2
+ (Y - y1)2
- 4, (X - x2)2
+ (Y - y2)2

  

Source: Abo, Hirotachi - Department of Mathematics, University of Idaho

 

Collections: Mathematics