Kempe’s Universality Theorem for Rational Space Curves.

We prove that every bounded rational space curve of degree <italic>d</italic> and circularity <italic>c</italic> can be drawn by a linkage with 92d-6c+1<inline-graphic></inline-graphic> 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 explicit construction of the linkage. [ABSTRACT FROM AUTHOR]