The Mathematical Modeling of a Double-Pendulum System as a Physical Model of Flexible Arm Robot

In this paper, a double-mass and spring system is considered as a benchmark for future studies on flexible arm robots. By using an appropriate control method and applying suitable external torques, the system can be completely stabilized and controlled. This requires the exact mathematical model of system. To achieve mathematical description, the system behavior is described by Lagrange's equations. Then these dynamical equations are written in the form of state-space equations. Finally, simulation results are presented to show the effectiveness of derived mathematical model for further analysis and synthesis.