Mathematical modelling of translational motion of rail-guided cart with suspended payload

In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart, driven by a travel mechanism, is modelled as a discrete six degrees of freedom (DOF) dynamic system. The hoisting mechanism for lowering and lifting the payload is considered and is included in the dynamic model as one DOF system. Differential equations of motion of the cart elements are derived using Lagrangian dynamics and are solved for a set of real-life constant parameters of the cart. A two-sided interaction was observed between the swinging payload and the travel mechanism. Results for kinematical and force parameters of the system are obtained. A verification of the proposed model was conducted.