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, Volume 62, Issue 1, pp 115–126 | Cite as

Geometry of the motion of robot manipulators

  • Adolf Karger


A p-parametric robot is a mapping g of Rp into the homogeneous space P=C6×C6/Diag(C6×C6) given by the formula g(u1,...,up=exp u1X1..... exp upXp, where C6, is the Lie group of all congruences of E3 and X1,..., Xp are fixed vectors from the Lie algebra of C6. We characterize the set g(Rp) locally by a system of PDE and give some geometrical properties of g as a p-dimensional motion for p<6. We also characterize the Frenet frame of g and show how to construct it for the robot manipulator given by its axes X1,...,Xp.


Number Theory Geometrical Property Algebraic Geometry Homogeneous Space Topological Group 
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  1. [1]
    Blaschke W.: Kinematik und Quaternionen. Berlin,Deutscher Verlag der Wiss.,1960Google Scholar
  2. [2]
    Karger A.: Two-parametric motions in E3. Apl.mat.32, 96–119, (1987)Google Scholar
  3. [3]
    Karger A.: Classification of 3-dimensional Euclidean space motions with transitive group of automorphisms and 3-parametric robots with constant invariants. To appearGoogle Scholar
  4. [4]
    Karger A., Novák J.: Space kinematics and Lie groups. 1st. edn,New York-London:Gordon and Breach 1985Google Scholar
  5. [5]
    Müller H.R.: Sphärische Kinematik. 1st edn.Berlin:Deutscher Verlag der Wiss.1962Google Scholar
  6. [6]
    Ránky P.G.,Ho C.Y.: Robot modelling. Berlin: Springer Verlag 1985Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • Adolf Karger
    • 1
  1. 1.Matematicko-fyzikální fakultaUniversita KarlovaPraha 8Czechoslovakia

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