Factorization of rational curves in the study quadric

• We introduce an algorithm for synthesis of linkages generating a prescribed motion.
• Any generic rational curve can be obtained as coupler curve of a closed linkage.
• The algorithm produces rotational joints and, in special cases, prismatic joints.
• The algorithm uses factorization of polynomials over the dual quaternions.
• New families of closed 6R linkages are given as special cases of the method.

For every generic rational curve C in the group of Euclidean displacements we construct a linkage such that the constrained motion of one of the links is exactly C. Our construction is based on the factorization of polynomials over dual quaternions.