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Kempe’s Universality Theorem for Rational Space Curves

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Abstract

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.

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Acknowledgements

This work was supported by the Austrian Science Fund (FWF): P 26607 (Algebraic Methods in Kinematics: Motion Factorisation and Bond Theory). This is partially supported by the Austrian Ministry for Transport, Innovation and Technology (BMVIT) within the framework of the sponsorship agreement formed for 2015–2018 under the project RedRobCo.

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Correspondence to Zijia Li.

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Communicated by Teresa Krick.

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Li, Z., Schicho, J. & Schröcker, HP. Kempe’s Universality Theorem for Rational Space Curves. Found Comput Math 18, 509–536 (2018). https://doi.org/10.1007/s10208-017-9348-x

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  • DOI: https://doi.org/10.1007/s10208-017-9348-x

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