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We prove that every bounded rational space curve of degree d and circularityc can be drawn by a linkage with 9/2 d - 6c + 1 revolute joints. Our proof isbased on two ingredients. The first one is the factorization theory of motionpolynomials. The second one is the construction of a motion polynomial ofminimum degree with given orbit. Our proof also gives the explicityconstruction of the linkage.

Kempe's Universality Theorem for Rational Space Curves