Study on the differential properties of a robot end-effector motion using the curvature theory

Abstract

In this paper, tool trihedron for timelike ruled surface with spacelike ruling and spacelike directrix is constructed. Transition relations among surface trihedron, tool trihedron, generator trihedron, natural trihedron and also Darboux vectors for each trihedron are obtained. Then, the curvature theory of the constructed frame is applied to determine the differential properties of the motion. Finally the dynamical motion of the tool frame along the trajectory planning is determined.