Mathematical Model of Speeds Change Device on the Basis of Switched Differential Mechanisms

The geometry and kinematics of a dynamic system with several degrees of freedom and controllable friction clutches are considered. The necessary kinematic transmission ratio between the input and output links is obtained using the friction clutches. The model uses a smooth approximation of the discontinuous function of the moment of friction. This allows continuous numerical integration of the equations of motion without changing their structure, i.e., preserving their number. The switching from one speed of rotation of the output link to another is controlled by specifying time functions that implement the pressure of the clutch discs. An example of a numerical study of such a mechanism consisting of three differentials and four clutches is considered. Dynamic processes for this system are analyzed.