, Volume 46, Issue 1, pp 183–194 | Cite as

Mapping similarity between parallel and serial architecture kinematics

  • Paul Zsombor-MurrayEmail author
  • Anton Gfrerrer
Parallel Manipulators


First the principles of mapping spatial points to surfaces is introduced in the context of the inverse kinematics of a general six revolute serial wrist partitioned robot. Then the advantage of choosing ideal frames is illustrated by showing that in the case of some architectures an image space formulation, though possible, may be an impediment to clear geometric insight and a satisfactory and much simpler solution. After showing how the general point mapping transformation is reduced to classical Blaschke-Grünwald planar mapping a novel three legged planar robot’s direct kinematics is solved in image space and then using conventional “distance” constraints. The purpose is to show why the latter approach yields spurious solutions and how the displacement pole rotation performed with kinematic mapping reliably avoids this problem. In conclusion certain other new and/or interesting reduced mobility parallel robots are discussed briefly to point out some advantages and insights gained with an image space approach. Particular effort is made to expose in detail how mapping simplifies and extends the solution of direct kinematics pertaining to Calvel’s “Delta” 3D translational robot.


Kinematic mapping Parallel Serial Manipulator Inverse Direct Kinematics Distance Constraints 


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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMcGill UniversityMontréalCanada
  2. 2.Institut für GeometrieTU-GrazGrazAustria

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