Abstract
In this chapter we develop the geometry of spatial displacements defined by coordinate transformations consisting of spatial rotations and translations. We consider the invariants of these transformations and find that there are no invariant points. Instead there is an invariant line, called the screw axis. Thus, the geometry of lines becomes important to our study of spatial kinematics.We find that a configuration of three lines, called a spatial triangle, generalizes our results for planar and spherical triangles to three-dimensional space.
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© 2011 Springer New York
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McCarthy, J.M., Soh, G.S. (2011). Spatial Kinematics. In: Geometric Design of Linkages. Interdisciplinary Applied Mathematics, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7892-9_12
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DOI: https://doi.org/10.1007/978-1-4419-7892-9_12
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Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-7891-2
Online ISBN: 978-1-4419-7892-9
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