Contributions to the kinematics of pointing

Pointing consists in orienting a line OP of a rigid body, with its point O fixed, P mobile. The operation can thus be achieved in two steps, one to provide P with the desired longitude on the sphere centered at O, of radius OP¯, the other to provide P with the desired latitude. While this operation is simpler than a full rigid-body rotation, its kinematics is not yet fully recorded in the literature. In fact, the kinematics of pointing cannot be considered as being included in the kinematics of spherical motion, because the latter is known to form a Lie group, while pointing operations do not. This paper is an effort to shed light on the kinematics of pointing by means of the visualization of the workspace of the mechanism used for its realization. In doing this, a strategy is proposed for the planning of pointing trajectories using a three-revolute spherical wrist. The contributions proposed by the authors thus target the workspace visualization and the path-planning of three-axis wrists when used for pointing operations.