In this work, we present a formalism for the numerical time integration of nonsmooth dynamical systems composed of rigid and flexible bodies, kinematic joints and frictionless contact conditions. The proposed algorithm guarantees the exact satisfaction of the bilateral and unilateral constraints both at position and velocity levels, extending a previous work on the development of the generalized-α scheme for computational contact mechanics. Following the idea of Gear, Gupta and Leimkuhler, the equation of motion is reformulated so that the bilateral and unilateral constraints appear both at position and velocity levels which amounts to solving two complementarity conditions at both position and velocity levels at each iteration using a monolithic semi-smooth Newton procedure.