Simulación del Modelo Matemático de la Cinemática Diferencial de Robots Seriales Planos Configuración RRR y RPR

Abstract

This article presents the model and simulation of the serial robot configurations of the types RRR and RPR, applying the theories of differential kinematics, to obtain the representation of its mathematical model (Jacobian matrix) and its simulation. The differential kinematics in robotics is the relationship between vector spaces, so it is possible to make the velocity map in the joint space in the end effector workspace. We present the differential kinematic model that is obtained from the position kinematics by differentiation techniques and with the help of the asymmetric matrix we obtain the information that is part of the Jacobian matrix, which allows us to know the velocities of the joint variables as a function of linear and angular velocity in the end effector and vice versa. The simulation of the manipulators is carried out validating the mathematical differential model; through the validation of the differential kinematics of serial chains it is possible to apply the procedure to complicated manipulator robots. The method presented here is the basis of a useful tool for solving complex robots, as in the case of redundant, parallel and hybrid serial manipulator robots.