Geometric and algebraic approach to the inverse kinematics of four-link manipulators

Abstract

This paper presents an example of the application of geometric and algebraic approaches to the inverse kinematics problem of four-link robot manipulators. A special arm configuration of the robot manipulator is employed for solving the inverse kinematics problem by using the geometric approach. The obtained joint variables as angular positions are defined in the form of cubic polynomials. The other kinematic parameters of the joints, such as angular velocities and angular accelerations, are the time derivatives of these polynomials. It is evident that there is no definite difference between the results of the two approaches. Consequently, if an appropriate arm configuration for the geometric approach can be established, the inverse kinematics can be solved in a simpler and shorter way.