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Designing mechanical devices, called linkages, that draw a given plane curvehas been a topic that interested engineers and mathematicians for hundreds ofyears, and recently also computer scientists. Already in 1876, Kempe proposed aprocedure for solving the problem in full generality, but his constructionstend to be extremely complicated. We provide a novel algorithm that producesmuch simpler linkages, but works only for parametric curves. Our approach is totransform the problem into a factorization task over some noncommutativealgebra. We show how to compute such a factorization, and how to use it toconstruct a linkage tracing a given curve.

Planar Linkages Following a Prescribed Motion