Unifying screw geometry and matrix transformations

  • Samuel A
  • McAree P
  • Hunt K
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Abstract

Transformation matrices are widely used in robotics for kinematic
analysis and trajectory planning. Screw geometry offers better geometric
insight into such analyses. In this article we unify the two approaches
through the use of invariant properties of orthogonal matrices under
similarity transformations. We give a complete expression for the
finite screw motion in terms of the entires of a 3 x 3 dual-number
transformation matrix. Our analysis suggests that the finite screw
is suitable for trajectory planning, and we develop a concise expression
that gives the transformation matrix describing the displacement
at each point along the path of the finite screw motion.

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Authors

  • A. E. Samuel

  • P. R. McAree

  • K. H. Hunt

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