We consider the problem of efficiently simulating large interconnected mechanical systems. For applications such as haptic rendering of large, complex virtual environments, dynamic simulation software and hardware is still too slow to afford accurate performance in real-time. In particular, mechanisms with closed kinematic chains require solutions for a set of differential equations with algebraic constraints (DAEs) that are often too complex to be computed in real-time by present-day single-processor machines. On the other hand, the structure of most state-of-the-art algorithms does not easily lend itself to parallelization. In this paper, we propose and experimentally verify a technique for DAE simulation that profitably uses a degree of randomization to achieve efficient parallelization.