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Rational motions with generic trajectories of low degree. (English) Zbl 1448.70006
Summary: The trajectories of a rational motion given by a polynomial of degree \(n\) in the dual quaternion model of rigid body displacements are generically of degree \(2n\). In this article we study those exceptional motions whose trajectory degree is lower. An algebraic criterion for this drop of degree is existence of certain right factors, a geometric criterion involves one of two families of rulings on an invariant quadric. Our characterizations allow the systematic construction of rational motions with exceptional degree reduction and explain why the trajectory degrees of a rational motion and its inverse motion can be different.

70B10 Kinematics of a rigid body
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