Simulation of multibody systems is associated with deriving equations of motion and finding numerical solution of the equation. The combination of the differential equations and constraints yields index-3 differential-algebraic equations (DAE's) that are not, in general, easily solvable by standard integration schemes. Moreover at singular configurations, some methods can fail. This paper focuses on the discussion of two problems: determining the singular configurations and their neighborhood and overcoming the singularity smoothly. Overcoming the singularity is discussed with using the Principle of Compatibility, so far not well-known. In this principle the equations of motion are rewritten in the form which can be solved by numerical techniques smoothly, even over singular configurations without detector. The idea of this approach is introducing so-called generalized reaction forces which appear in the equations of motion system for the dynamical in comparison with the system without constraints. The formulation is proven to be more stable and accurate under repetitive meeting singular configurations. These generalized reaction forces can be determined by using the ideality condition of constraints which employs the null space of constraints imposed to the system. Some numerical experiments are carried out to verify the efficiency and speed of the approach.