Unified Kinematics of Parallel Schönflies Robots

  • Paul Zsombar-MurrayEmail author
  • Martin Pfurner
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


A suffcient set of constraint equations to carry out kinematic analysis is detailed in the context of 4 degree of freedom (dof) fully parallel 4-legged Schönflies manipulators. The set inevitably contains data pertaining to joint variables, end effector (EE) and fixed frame (FF) space design parameters. Therefore the equations are sometimes readily adaptable to direct kinematics (DK), inverse kinematics (IK), design problems or some combination by choosing any set of equation parameters to be unknowns, as many as there are equations. Numerical examples are presented. These serve to caution the reader regarding the pitfalls in one-size-fits-all methodology. It is observed that limited angular displacement workspace plagues many designs.


computational algebraic geometry Kinematics parallel robot Schönflies motion 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mechanical EngineeringMCGill UniversityMontrealCanada
  2. 2.Unit Geometry & CADUniversity of InnsbruckInnsbruckAustria

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