Kempe's Universality Theorem for Rational Space Curves

Abstract

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

The final publication is available at Springer via http://dx.doi.org/10.1007/s10208-017-9348-x

References in corpus (2)

• Planar Linkages Following a Prescribed Motion
• The Rational Motion of Minimal Dual Quaternion Degree With Prescribed Trajectory

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