A Comparative Study of Natural and Exact Elastic Balancing Methods for the RR-4R-R Manipulator

If elastic elements are introduced into the mechanical architecture of a robotic manipulator, a free vibration response (Natural Motion) arises that can be exploited to reduce energy consumption in cyclic motions, such as pick-and-place tasks. In this work, this approach is applied to the RR-4R-R manipulator, which is derived from the SCARA robot by replacing the prismatic joint that drives the vertical motion of the end-effector with a four-bar mechanism. This mechanical modification lowers friction and facilitates the introduction of a balancing elastic element. If the elastic element is designed to provide indifferent equilibrium at any position (exact elastic balancing), the actuators need only to overcome the inertial forces; this approach is convenient for slow motions. Conversely, if the elastic element balances gravity exactly only in the median vertical position of the end-effector, Natural Motion around this position arises, and it can be exploited to reduce energy consumption in fast cyclic motions, where inertial forces become prevalent. The threshold of convenience between exact balancing and natural balancing has been evaluated for the RR-4R-R robot by means of a multibody model, assessing different performance indices: the maximum torque of the four-bar actuator, the integral control effort, and the mechanical energy. The simulation campaign was carried out considering different trajectory shapes and the influence of finite stop phases, highlighting the potential benefits of exploiting Natural Motion in robotized manufacturing lines.