Design Parameter Space of Planar Four-bar Linkages

  • M. John D. Hayes
  • Mirja Rotzoll
  • Manfred L. Husty
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


A new algebraic input-output relation for planar four-bar mechanisms is a quartic curve in the input-output joint angle parameter plane. This equation contains four terms with quadratic coefficients of link lengths which all factor into the product of two linear terms. The structure of these eight linear factors suggests that they are the eight faces of an octahedron in a design parameter space of the link lengths. In this paper we show that the design parameter octahedron space implies a complete classification scheme for all 27 possible planar 4R mechanisms, in addition to linkages containing one, or two prismatic joints.


Algebraic input-output relation planar four-bar linkage design parameter octahedron 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • M. John D. Hayes
    • 1
  • Mirja Rotzoll
    • 1
  • Manfred L. Husty
    • 2
  1. 1.Department of Mechanical and Aerospace EngineeringCarleton UniversityOttawaCanada
  2. 2.Unit Geometry and CADUniversity of InnsbruckInnsbruckAustria

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