The 2DOF Trebuchet

The 2 Degree-of-Freedom (DOF) trebuchet is similar to the 1DOF trebuchet but for the presence of the sling. The relevant dimensions are shown in the figure above. L₁ is the length between the main pivot and the counterweight, L₂ is the length between the main pivot and the launch hook, L₃ is the length of the sling, w and t are the height and thickness of the arm, respectively. The angle beta is the offset between the throwing arm and the launch hook. In general, a higher value for beta will launch the projectile forwards, while a low value for beta will launch the projectile upwards, or even backwards!