Geometric characterization of the workspace of non-orthogonal rotation axes. (English) Zbl 1304.70003
Summary: In this article, a novel characterization of the workspace of 3R chains with non-orthogonal, intersecting axes is derived by describing the set of singular orientations as two tori that separate two-solvable from non-solvable orientations within \(SO(3)\). Therefore, the tori provide the boundary of the workspace of the axes’ constellation.{
}The derived characterization generalizes a recent result obtained by Piovan and Bullo. It is based on a specific, novel representation of rotations, called unit ball representation, which allows to interpret the workspace characterization with ease.{
}In an appendix, tools for dealing with angles and rotations are introduced and the equivalence of unit quaternion representation and unit ball representation is described.
MSC:
| 70B10 | Kinematics of a rigid body |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
| 15A16 | Matrix exponential and similar functions of matrices |
Keywords:
non-orthogonal Euler angles; rotation decomposition; rotation representation; kinematic analysis; singularity analysisReferences:
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