Dynamic modelling of a multi-cable driven parallel platform with guiding devices

In this paper, a mathematical model is presented to numerically simulate the dynamical responses in a multi-cable suspension platform taking into account the slack cables and guiding devices. The state change of the cable (slack versus tensioned) is considered and is described mathematically by a complementary condition equation, and the interactions between the guiding wheels and the shaft wall are described by the Heaviside step function. The Lagrange’s equation with constraints is used to derive the dynamic equations of the system, and a non-smooth generalized-α algorithm for non-smooth phenomena of multibody dynamics is applied to numerically solve the equations. The simulation results have shown the dynamic responses of the platform and the cable tension characters when different cables are excited by different longitudinal excitations. Moreover, the results have illustrated how the cable tension differences may affect the pressure on the shaft wall applied by the guiding devices.