The rational motion of minimal dual quaternion degree with prescribed trajectory

• There is a unique rational motion of minimal quaternion degree with given trajectory.
• It can be computed by simple polynomial algebra over the ring of dual quaternions.
• The minimal motion of Vivian's curve is a spherical circle rolling.

We give a constructive proof for the existence of a unique rational motion of minimal degree in the dual quaternion model of Euclidean displacements with a given rational parametric curve as trajectory. The minimal motion degree equals the trajectory's degree minus its circularity. Hence, it is lower than the degree of a trivial curvilinear translation for circular curves.

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