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Factorization of Rational Curves in the Study Quadric and Revolute Linkages
Published 1 Feb 2012 in math.RA, cs.RO, and math.AG | (1202.0139v4)
Abstract: 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.
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