Kempe’s Universality Theorem for Rational Space Curves



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.


Dual quaternion Motion polynomial Factorization Bennett flip Linkage 

Mathematics Subject Classification

Primary 70B05 Secondary 13F20 65D17 68U07 


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Copyright information

© SFoCM 2017

Authors and Affiliations

  1. 1.Institute for Robotics and MechatronicsJoanneum ResearchKlagenfurtAustria
  2. 2.Research Institute for Symbolic ComputationJohannes Kepler University LinzHagenbergAustria
  3. 3.Unit Geometry and CADUniversity of InnsbruckInnsbruckAustria

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