Kinematic interpretation of the Study quadric's ambient space

07/31/2017

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by   Georg Nawratil, et al.

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It is well known that real points of the Study quadric (sliced along a 3-dimensional generator space) correspond to displacements of the Euclidean 3-space. But we still lack of a kinematic meaning for the points of the ambient 7-dimensional projective space P^7. This paper gives one possible interpretation in terms of displacements of the Euclidean 4-space. From this point of view we also discuss the extended inverse kinematic map, motions corresponding to straight lines in P^7 and linear complexes of SE(3)-displacements. Moreover we present an application of this interpretation in the context of interactive motion design.