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Published in:
2011 | OriginalPaper | Chapter
Spatial Kinematics
Authors : J. Michael McCarthy, Gim Song Soh
Published in: Geometric Design of Linkages
Publisher: Springer New York
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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.