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Sharp Linkages


In this chapter, we consider a special kind of overconstrained \(6\)R closed linkages which we call sharp linkages. These are linkages with the property that their bond diagram looks like a \(\sharp \) sign. We give a construction of this linkage using the bond theory and motion polynomial factorization methods. These two methods are introduced recently in [6, 7]. Another type of 6R linkages is also introduced. To my knowledge, both types of linkages are new.


  • Dual quaternions
  • Motion polynomials
  • Factorization
  • Bond theory
  • Overconstrained \(6\)R linkages

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Fig. 1


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  3. 3.

    One can check that \(L_c\) does not fulfill the necessary conditions of Waldrons double Bennett hybrid, Dietmaier 6R linkages or Bricard plane symmetric 6R linkages as an exercise.


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We would like to thank Gábor Hegedüs, Hans-Peter Schröcker and Josef Schicho for discussion and helpful remarks. The research was supported by the Austrian Science Fund (FWF): W1214-N15, project DK9.

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Correspondence to Zijia Li .

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Li, Z. (2014). Sharp Linkages. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham.

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