This paper presents an explicit to integrate differential algebraic equations (DAEs) method for simulations of constrained mechanical systems modeled with holonomic and nonholonomic constraints. The proposed DAE integrator is based on the equation of constrained motion developed in Part I of this work, which is discretized here using explicit ordinary differential equation schemes and applied to solve two nontrivial examples. The obtained results show that this integrator allows one to precisely solve constrained mechanical systems through long time periods. Unlike many other implicit DAE solvers which utilize iterative constraint correction, the presented DAE integrator is explicit, and it does not use any iteration. As a direct consequence, the present formulation is simple to implement, and is also well suited for real-time applications.