COBEM99

S22 Mecatrônica

Title:

MODELING OF A CLOSED-LOOP CHAIN MANIPULATOR BY THE RECURSIVE NEWTON-EULER METHOD

Summary :

ABSTRACT: IN THIS ARTICLE, A METHOD IS PROPOSED TO OBTAIN THE EQUATIONS OF MOTION OF A PANTOGRAPHIC CLOSED-LOOP CHAIN MANIPULATOR, WITH THREE DEGREES OF FREEDOM, USING THE NEWTON-EULER FORMULATION. THE MATHEMATICAL MODEL IS DEVELOPED DIVIDING THE MECHANISM IN OPEN-LOOP CHAINS WHILE PRESERVING THE CONSTRAINT RELATIONS DUE TO THE PANTOGRAPHIC MOUNTING. IN EACH OF THE OPEN-LOOP CHAINS, AN EXTERNAL FORCE APPLIED IN ITS EXTREMITY MAY BE DETERMINED BY MEANS OF A VECTORIAL EQUATION SYSTEM SO THAT THE TORQUES IN THE PASSIVE JOINTS AXIS ARE NULL. THESE JOINTS ARE THE ONES WHERE THERE IS NO ACTUATOR PROVIDING EXTERNAL TORQUE. AFTER THESE FORCES ARE DETERMINED, THEY ENTER AS REACTION FORCES IN ANOTHER OPEN-LOOP CHAIN, DETERMINING THE SOLUTION OF THE INVERSE DYNAMICS PROBLEM. THROUGH THE ADEQUATE MANIPULATION OF SOME INPUT VECTORS OF THE INVERSE DYNAMICS PROCEDURE, IT IS POSSIBLE TO OBTAIN THE MASS MATRIX OF THE SYSTEM AND THE VECTORS RELATED WITH THE ACTION OF THE GRAVITY, CORIOLIS AND CENTRIFUGE INERTIA FORCES, SETTING UP THE DIRECT DYNAMIC SYSTEM. RESULTS OF SIMULATIONS ARE PRESENTED FOR SOME TRAJECTORIES. THE METHOD, WITH SMALL MODIFICATIONS, CAN BE ADAPTED TO OTHER CLOSED-LOOP CHAIN MECHANISMS AS LONG AS THE CONSTRAINTS RELATING THE PASSIVE TO THE ACTIVE JOINTS ARE ESTABLISHED. KEYWORDS: ROBOTICS, CLOSED-LOOP CHAIN, INVERSE DYNAMICS MODELING

Author :

Martins, José Luiz Ferreira
Noronha, Roberto F. de
Silva, Marcelo Tomaz Zambon da
Soares, Leonardo A. G.

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