Mechanism design and dynamics analyses for an under-actuated three-joint acrobot

The acrobot is an under-actuated three-joint planar robot that mimics the human acrobat who hangs from a bar and tries to swing up to a perfectly balanced upside-down position with his/her hands still on the bar. In this paper we first design the under-actuated three-joint acrobot which like human being both in actuate and appearance. And then, dynamic model is derived by Lagrange equations, and controllable of the acrobot is analyzed. Finally, simulation shows that the acrobot is satisfied with respond quickly and allowable static error.