Abstract
Via Study’s kinematic mapping G the 6-parametric Lie group SE(3) of direct Euclidean displacements can be identified with a certain hyperquadric.M 6 in 7-dimensional real projective space. The mapping has nice geometric properties; for instance one parametric rotation groups are represented by straight lines on M 6, coordinate transformations in Euclidean 3-space are represented by special automorphisms of M 6. With the help of G Euclidean kinematics can be considered as a point-geometry in the sense of Felix Klein’s Erlangen program.
We give an application in the field of motion design: The problem of constructing a motion interpolating a sequence of given positions can be solved by constructing an appropriate curve interpolating the corresponding points on Study’s quadric.
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© 2000 Springer Science+Business Media Dordrecht
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Gfrerrer, A. (2000). Study’s Kinematic Mapping — A Tool for Motion Design. In: Lenarčič, J., Stanišić, M.M. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4120-8_1
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DOI: https://doi.org/10.1007/978-94-011-4120-8_1
Publisher Name: Springer, Dordrecht
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