Mathematical Modelling of an extended Swinging Atwood Machine

Abstract

An extended model for a variable-length pendulum’s mechanical application is being derived from the Swinging Atwood Machine (SAM). An electrical component consisting of an electromagnet and armature coil is attached on the link connected to the counterweight mass on the left-hand side of the modified SAM to provide an excitation force for the system when an electric current is induced. The extended SAM presents a novel SAM concept being derived from a variable-length double pendulum with a suspension between the two pendulums. The equations of motion are simulated to see the trajectory of the two pendulums. The results of original numerical simulations show some compact regions of attraction at some regimes. Therefore, the extended SAM’s nonlinear dynamics presented in the current work can be thoroughly studied, and more modifications can be achieved. The new technique can reduce residual vibrations through damping when the desired level of the crane is reached. It can also be used in simple mechatronic and robotic systems.