Planar linkages following a prescribed motion
- 13 April 2016
- journal article
- Published by American Mathematical Society (AMS) in Mathematics of Computation
- Vol. 86 (303) , 473-506
Abstract
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, Kempe 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.Keywords
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Funding Information
- Austrian Science Fund (P26607)
- Austrian Science Fund (P26607)
- Austrian Science Fund (W1214)
- Austrian Science Fund (P27229)
- Austrian Science Fund (P26607)
- Austrian Science Fund (P26607)
- Austrian Science Fund (W1214)
- Austrian Science Fund (P27229)
- Austrian Science Fund (P26607)
- Austrian Science Fund (P26607)
- Austrian Science Fund (W1214)
- Austrian Science Fund (P27229)
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