Dynamic Modelling of the Spring Attached Two-Link Planar Manipulator

Robot dynamics is required for simulation, control, analysis of robot motion planners and controllers. There are a number of dynamic modelling investigations of robots with the different approaches and these investigations mostly focus on the link flexibility, joint friction or actuator dynamics. In addition to that these studies present dynamic model without any attached linear or torsion springs. In this study, the dynamic modelling of a two-link rigid manipulator with attached torsion springs is presented using the Lagrangian approach. The Lagrangian approach is a variational method that relies on the potential and kinetic energy of the mechanism, making it well-suited for the analysis of the two-link planar manipulator considered in this study. Initially, the two-link mechanism equations of motion are derived without any attached torsion springs. Subsequently, two torsion springs are attached to the joints of the mechanism, and the existing equations of motion are modified accordingly. The study also presents the kinetic, potential and total energies of the two link-manipulator, angular positions of the links and their velocities. By considering the dynamic modelling of the torsion spring attached two-link rigid manipulator, this study contributes to understanding and analysis of the two-link manipulators and the dynamic effects of the attached springs.