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J. Selig (2004)
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Quadratic constraints on rigid-body displacementsASME J. Mech. Robot., 2
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J. Selig (2010)
Quadratic constraints on rigid-body displacementsJournal of Mechanisms and Robotics, 2
C. Wampler (2006)
On a Rigid Body Subject to Point-Plane ConstraintsJournal of Mechanical Design, 128
(1886)
) . { see also the review of this book by F . Morley in Bull
(2010)
A unified approac h to direct kinematics of some reduced motion parallel manipulators. ASME Journal of Mechanisms and Robo
(1990)
Theoretical Kinematics, Dover P ublications
J. Selig (2004)
Geometric Fundamentals of Robotics
P.J. Zsombor-Murray, A. Gfrerrer (2010)
A unified approach to direct kinematics of some reduced motion parallel manipulatorsASME J. Mech. Robot., 2
In this paper the rigid-body displacements that transform a point in such a way that it remains on a particular plane are studied. These sets of rigid displacements are referred to as point-plane constraints and are given by the intersection of the Study quadric of all rigid displacements with another quadric in 7-dimensional projective space. The set of all possible point-plane constraints comprise a Segre variety. Two different classes of problems are investigated. First instantaneous kinematics, for a given rigid motion there are points in space which, at some instant, have no torsion or have no curvature to some order. The dimension and degrees of these varieties are found by very simple computations. The corresponding problems for point-sphere constraints are also found. The second class of problems concern the intersections of several given constraints. Again the characteristics of these varieties for different numbers of constraints are found using very simple techniques.
Acta Applicandae Mathematicae – Springer Journals
Published: Jul 23, 2011
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