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The kinematic image of RR, PR, and RP dyads.
- Source :
-
Robotica . Oct2018, Vol. 36 Issue 10, p1477-1492. 16p. - Publication Year :
- 2018
-
Abstract
- SUMMARY: We provide necessary and sufficient conditions for all projective transformations of the projectivized dual quaternion model of rigid body displacements that are induced by coordinate changes in moving and/or fixed frame. These transformations fix the quadrics of a pencil and preserve the two families of rulings of an exceptional three-dimensional quadric. Moreover, we fully characterize the constraint varieties of dyads with revolute and prismatic joints in the dual quaternion model. The constraint variety of a dyad with two revolute joints is a regular ruled quadric in a three-space that contains a “null quadrilateral.” If a revolute joint is replaced by a prismatic joint, this quadrilateral collapses into a pair of conjugate complex null lines and a real line but these properties are not sufficient to characterize such dyads. We provide a complete characterization by introducing a new invariant, the “Study fibre projectivity,” and we present examples that demonstrate its potential to explain hitherto not sufficiently well-understood phenomena. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02635747
- Volume :
- 36
- Issue :
- 10
- Database :
- Academic Search Index
- Journal :
- Robotica
- Publication Type :
- Academic Journal
- Accession number :
- 131389402
- Full Text :
- https://doi.org/10.1017/S0263574718000504