Geometrical kinematic solution of serial spatial manipulators using screw theory

Kinematics of a robot manipulator is an essential component of robotic analysis that includes control, motion planning, and design. Previous studies have proposed several different methods to provide an exact solution for kinematics. However, most of the methods are mathematically complicated and not sufficiently intuitive to express the geometrical meaning of kinematics. In this study, the exact solution to kinematics is derived based on the screw theory. The most important contribution of this study is providing a geometrical intuition of kinematics. Two arbitrary screws in space are equivalent to the sum of the mutual moment relation. In the study, general case solutions and special cases of parallel and perpendicular configuration were examined, and their geometrical meaning was discussed. The proposed method was used to analyze two industrial manipulators, and practical effectiveness was verified. The method could be applied to various manipulator configurations and the solution provides the geometrical intuition effectively. Additionally, the geometrical meaning of the solution can be used in design and motion planning.