The article provides a description of the coordinated motion of a multi-parametric mechanical system with multiple degrees of freedom by defining its trajectory by an interpolation curve in a configurational space that intersects interpolation nodes defined by the work conditions of the respective machine. The complete working cycle of machine movement is divided into separate motion phases - time intervals between subsequent passes of node points on the movement trajectory. The article puts a complete work cycle of a metallurgical furnace crane charging machine as an example. A simulated motion of the crane charging machine in its work cycle is simulated. The mathematical model of coordinated motion is obtained by forming a matrix i×n of generalized coordinates, which determines the position of a multiparameter mechanical system, where i is the number of generalized coordinates, n is the number of interpolation nodes on the time axis. Description of the full cycle of movement is carried out by using the Heaviside step function. As an example, the full cycle of operation of a crane loading machine for metallurgical furnaces with smooth start-up and braking modes in separate phases of its operation is considered. To describe smooth movements, a special dimensionless function in polynomial form is introduced that satisfies the required boundary conditions at the ends of time intervals in which its value itself, as well as the first and the second time derivatives, vanish. The simulation of the movement of the crane loading machine in its full working cycle is performed using the Mathcad computer algebra package and the cyclograms of the kinematic characteristics of its main components-the bridge, the main truck and the cab with the trunk-are constructed.