Abstract

TORREALBA, R; CLAVIJO, A  and  DELGADO, M. Mathematical modelling and simulation of a microprocessor manipulator robot: Two approaches. Rev. Fac. Ing. UCV [online]. 2006, vol.21, n.3, pp.121-139. ISSN 0798-4065.

This work has educational purposes and constitutes a didactic tool for the teaching of robotics. In particular, the mathematical modelling and simulation of a microprocessors (chips) manipulator robot in electronic board assembling line is presented. The modelling problem is treated using two different approaches: the classical approach using Newton’s equations and the energetic approach using Lagrange’s equations. The final expressions obtained from these two approaches are compared as well as the development of the models. Regarding the final expressions, some differences were found in the models. Regarding the development of the model, it was found that the Lagrangian approach is simpler than the Newtonian approach. This is due to the fact that the Lagrangian approach does not require deep knowledge of kinematics and kinetics of rigid bodies, and also because it manipulates scalar equations which are easier to work with than the vectorial equations obtained from Newtonian mechanics. With the simulation, the response of the position of the manipulator in presence of different inputs (forces and torques) is studied, being the results of both models practically the same. As real system data was not available, the validation of the models was done as follows: a matrix from minimum-time-positioning curves for each manipulator body (link) was obtained, generating acceleration, velocity and position values for each time instant of the path. Then, introducing these values into the respective differential equations, the necessary forces and torques values to make the manipulator tip describe the required path were calculated. Finally, these values were introduced as inputs in the simulation, generating the same values of the kinematics variables stated initially as outputs.

Keywords : Robotics; Modelling; Simulation; Lagrange’s Approach; Newton’s Approach.

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