Geometric Visualization of a Robot End-Effector Motion using the Curvature Theory

Abstract

This investigation is devoted to the construction of a robot trajectory using a ruled surface. Transition relations among surface trihedron, tool trihedron, generator trihedron, natural trihedron and also Darboux vectors for each trihedron are given. Then, the curvature theory of ruled surface under investigation is applied to determine the differential properties of a robot end effector motion. This information is then used to characterize the linear motion of the tool center point and the angular motion of the tool frame of the robot end effector for the trajectory planning. The differential motion properties of the tool frame and the TCP point, based on the curvature theory of a ruled surface, using the relationships between the four frames of reference are studied