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The rational motion of minimal dual quaternion degree with prescribed trajectory. (English) Zbl 1417.53012
Summary: 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.

MSC:
53A17 Differential geometric aspects in kinematics
70B10 Kinematics of a rigid body
70B15 Kinematics of mechanisms and robots
65D17 Computer-aided design (modeling of curves and surfaces)
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