Application of graph theoretic modelling to industrial belt-driven gantry robots

In this paper we investigate the modelling of an industrial belt-driven gantry robot(1) using graph theoretic modelling (GTM). The design of the robot is such that the kinematic driver is fixed to the base frame while the end-effector is free to move in a straight line relative to the base. The power is transmitted to the end-effector using a pulley/belt arrangement. This arrangement has the benefit of radically reducing the system inertia, which permits the robot to operate at higher speed, Further increase in the operational speed of the robot is now limited by the induced vibration due to the belt flexibility. Using graph theoretic modelling we study the robot dynamics considering the base and belt flexibilities. To incorporate the pulley into the formulation, a multi-terminal model is introduced that can be used in the GTM for any simple or compound pulley with fixed or moving shaft.