Kempe's Universality Theorem for Rational Space Curves
arXiv:1509.08690v42 citations
Originality Highly original
AI Analysis
This solves a fundamental problem in geometric modeling and kinematics by establishing universality for rational space curves.
The authors proved that any bounded rational space curve of degree d and circularity c can be drawn by a linkage with 9/2 d - 6c + 1 revolute joints, providing an explicit construction method.
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.