Dynamic model and performance assessment of the natural motion of a SCARA-like manipulator in pick-and-place tasks

The energy efficiency of manipulators performing cyclic motions can be enhanced by utilizing the so-called natural motion, namely, the natural oscillations that occur when elastic elements are placed in series or parallel with the actuators. In this paper, the natural motion of the RR-4R-R robot is discussed. This manipulator exhibits a 4-DOF mobility similar to that of the widespread SCARA robot, but the vertical prismatic joint is replaced by a four-bar mechanism. This modification, along with the adoption of a direct-drive actuator for the four-bar mechanism, makes it easier to achieve the elastic balancing of the robot, allowing the exploitation of its natural motion. The robot dynamics is analysed using the Lagrangian approach. Two types of elastic balancing are considered: one using a torsional spring and one using a linear coil spring. A simplified model of the vertical motion is then proposed, decoupled from the inertial effects of the horizontal motion, and used to estimate the vertical natural period. The behaviour of the manipulator with natural elastic balancing is compared with that obtained with exact elastic balancing, which provides an indifferent equilibrium in any robot position. This comparison is first carried out in the time domain, and then the space of the robot operating conditions is sampled through multibody simulations, performed to investigate the threshold of convenience between exact and natural balancing. Simulation results indicate that exploiting the natural motion of the RR-4R-R manipulator can significantly reduce energy consumption in a wide range of industrial applications involving pick-and-place tasks.