An explicit cosimulation scheme is developed to study the coupling of smooth and nonsmooth systems using kinematic constraints. Using the force-displacement decomposition, the coupling constraints are formulated at the velocity level, to preserve consistency with the impulse-momentum equations for frictional contacts in the nonsmooth solver, which however potentially leads to instability of the explicit cosimulation. To improve the stability of the cosimulation without affecting the format of the coupling constraints, guidelines for the modification of the prescribed motion are developed following the spirit of Baumgarte’s stabilization technique and the characteristics of the proposed integration scheme, which prescribes a combination of position, velocity, and acceleration to the constrained bodies. Using modified inputs, the stability of the cosimulation is tested using a rigidly connected two-mass oscillator model, which shows clear improvement compared to that with unaltered inputs. The performances of the cosimulation with modified inputs are further illustrated using a double-pendulum system and a complex flexible multibody system coupled with a particle damper. It follows that cosimulation results well agree with those obtained using monolithic simulation or simplified models, verifying the explicit smooth/nonsmooth cosimulation. The results also show a higher efficiency of the explicit cosimulation scheme, which requires much less computational time to obtain similar results, compared to the implicit smooth/nonsmooth cosimulation.