The Dynamics of Tractor-Semitrailer Vehicles: The Jackknifing Problem

The equations of motion for a tractor-semitrailer vehicle, in which both the tractor and semitrailer can pitch, roll, yaw and translate, are derived and solved numerically in their nonlinear form for steering and braking inputs. The linearized equations are also determined and solved for comparison with the nonlinear model. The results demonstrate the occurrence of jackknifing of the nonlinear model, even without the application of braking forces, for certain steering inputs while the linearized model is stable. Violent jackknifing caused by braking is found to take place in the nonlinear model whenever braking forces at the rear tractor wheels are of sufficient magnitude to limit or reduce the side forces occurring there; locking of the wheels is not required. Jackknifing can not always be prevented by damping (short of locking) at the hitch, but the action can be slowed down considerably.