Factorization of Rational Curves in the Study Quadric and Revolute Linkages
This work addresses a specific problem in mechanical engineering and kinematics by enabling precise linkage design for rational curves, though it appears incremental as it builds on existing factorization methods.
The paper tackles the problem of constructing linkages whose constrained motion matches a given rational curve in Euclidean displacements, using factorization of polynomials over dual quaternions, and produces examples like Bennett mechanisms and new overconstrained 6R-chains.
Given a 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. Low degree examples include the Bennett mechanisms and contain new types of overconstrained 6R-chains as sub-mechanisms.