This paper presents an investigation of the advantages of a new formulation in the study of mechanical systems with holonomic and nonholonomic constraints. The formulation, originally proposed for systems of constrained particles, provides an efficient and robust means of simulating general multibody systems in the presence of redundant, degenerate and intermittent constraints. The structure of the formulation also allows the use of a dynamics code for pure kinematics analysis with a simple substitution. In addition, the formulation separates applied and constraint forces explicitly allowing recovery of constraint forces by straightforward means. Several examples are given to demonstrate the effectiveness of the formulation in special circumstances.