Planar linkages following a prescribed motion. (English) Zbl 1404.70007

Summary: Designing mechanical devices, called linkages, that draw a given plane curve has been a topic that interested engineers and mathematicians for hundreds of years, and recently also computer scientists. Already in 1876, A. B. Kempe [ Proc. Lond. Math. Soc. 7, 213–216 (1876; JFM 08.0544.04)] proposed a procedure for solving the problem in full generality, but his constructions tend to be extremely complicated. We provide a novel algorithm that produces much simpler linkages, but works only for parametric curves. Our approach is to transform the problem into a factorization task over some noncommutative algebra. We show how to compute such a factorization, and how to use it to construct a linkage tracing a given curve.


70B15 Kinematics of mechanisms and robots
68W30 Symbolic computation and algebraic computation
70G55 Algebraic geometry methods for problems in mechanics
16Z05 Computational aspects of associative rings (general theory)
14P05 Real algebraic sets
12Y05 Computational aspects of field theory and polynomials (MSC2010)


JFM 08.0544.04


Full Text: DOI arXiv


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