Abstract
In this chapter we consider spatial displacements that are pure rotations in threedimensional space. These are transformations that have the property that one point of the moving body M has the same coordinates in F before and after the displacement. Because the distance between this fixed point and points in M are constant, each point in the moving body moves on a sphere about this point. If the origins for both the fixed and moving frames are located at this fixed point, then the spatial displacement is defined by a 3x3 rotation matrix. The study of spherical kinematics benefits from both the properties of linear transformations and the geometry of a sphere.
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© 2011 Springer New York
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McCarthy, J.M., Soh, G.S. (2011). Spherical 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_8
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DOI: https://doi.org/10.1007/978-1-4419-7892-9_8
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Online ISBN: 978-1-4419-7892-9
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