An elementary proof is given to show that a parametrised algebraic curve in the plane may be traced out, in the sense of A. B. Kempe, by a finite pinned linkage.Additionally it is shown that any parametrised continuous curve γ : [0, 1] → R 2 may be traced out by an infinite linkage where the valencies of the joints is uniformly bounded.We also discuss related Kempe universality theorems and give a novel correction of Kempe's original argument.
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S. C. Power (2017) studied this question.
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