Traditional Euler-Lagrange methods for the dynamic analysis of kinematic chains require repetitive calculation of the kinematic constraints. This becomes very inefficient as the number of joints (or kinematic constraints) increases. This paper presents a new approach for the dynamic analysis of constrained dynamic systems. The salient feature of this approach is the separation of the kinematic analysis from the dynamic analysis. Following this separation, the resulting dynamic system becomes instantaneously unconstrained. While the discussion is mainly oriented towards the analysis of planar mechanisms, the model can be readily extended to the analysis of spatial mechanisms. A methodology for computer-aided symbolic derivation of the dynamic equations based on this approach is presented, and a numerical example which demonstrates a significant reduction in computing time for the dynamic analysis of a planar mechanism, as compared with conventional solution approaches, is provided.