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Kempe’s universality theorem for rational space curves. (English) Zbl 1430.70006
Summary: We prove that every bounded rational space curve of degree \(d\) and circularity \(c\) can be drawn by a linkage with \(\frac{9}{2} d-6c+1\) revolute joints. Our proof is based on two ingredients. The first one is the factorization theory of motion polynomials. The second one is the construction of a motion polynomial of minimum degree with given orbit. Our proof also gives the explicit construction of the linkage.

MSC:
70B05 Kinematics of a particle
14H50 Plane and space curves
65D17 Computer-aided design (modeling of curves and surfaces)
68U07 Computer science aspects of computer-aided design
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