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The objective is develop the mathematical modeling of the nonlinear characteristics of mechanical transmission in an industrial robot type Gantry and present the design of a prototype. The robot consists of prismatic joints and ball screw driven by electric AC motors. The torque generated at the output of the gearbox results in the angular displacement of the spindle shaft, whose movement is transformed into linear movement of a link on the previous in orthogonal directions, causing him to relocate. The mathematical formulation of the equations of the prismatic joints position becomes an easier task due to kinematic decoupling between the orthogonal joints of the robot. The torque and position data can be obtained from experiments where the sensor signals are captured through an acquisition and control board (dSPACE). However, the mechanical transmissions have nonlinearities that hinder the precision control and impair performance, causing delays and loss of motion. Such as modeling will be in the transmission system geared motor coupling screw-nut, has been the formulation of mathematical models using the Newton-Euler method in dynamic equilibrium from the free-body diagrams of the screw-shaft and nut displaced-mass. Is thus obtained two ordinary differential equations of second order (one for rotation and one for translation). Due to the existence of non-linearity of backlash, these two equations are combined and coupled through a mathematical relationship in discrete time. This dynamic model of prismatic joint is generalized to the two degrees of freedom. As future job prospects, it is planned to experimentally validate the prototype of the robot already in road building. It is hoped that this work will contribute to schemes of compensation for non-linearity and precise control of industrial robots low cost in unhealthy, dangerous and high mechanical stress tasks.

MODELAGEM MATEMÁTICA DA TRANSMISSÃO MECÂNICA EM UMA JUNTA ROBÓTICA COM FUSO DE ESFERAS