Kempe's Universality Theorem for Rational Space Curves
arXiv:1509.08690 · doi:10.1007/s10208-017-9348-x
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