Spherical Kinematics

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.