An adequate mathematical model including all components of an automatic system is a prerequisite for the most cost-effective implementation of the device’s potential capabilities. Such a strict nonlinear mathematical model must make it possibility to minimize the actuator drives number, reduce the measurement information amount (the number of measuring sensors) and analyze transient processes in actuator drives. The traditional application of Lagrange equations with constraint multipliers in dynamics models of non-free systems leads to an increase in their dimensionality. The variables of such models are all coordinates, all (including dependent) velocities and also constraint multipliers. The article develops the application of the theoretical mechanics rigorous methods non-free systems to minimize the dimensionality of nonlinear mathematical models of parallel manipulators as the systems with geometric constraints, taking into account the dynamics of actuator electric drives. The transition to equations in redundant coordinates, free from constraint multipliers, excludes from consideration not only multipliers, but also dependent velocities. The application of the proposed approach to modeling the stand Ball and Beam dynamics is considered.