The purpose of this work is to develop a singular perturbation-based approach to modeling closed kinematic chains. First, a kinematical analysis is developed to show that closed kinematic chains cannot be modeled in general using only independent generalized coordinates. Second, the Lagrangian formulation is used to develop the DAE system for closed kinematic chains. Next, differential algebraic equations (DAEs) are described, followed by discussion of standard techniques for their solution and the limitations of the standard techniques with respect to model-based control design. Then, a singular perturbation approach to solving the DAE that arise from closed kinematic chains is developed. Using this model makes it possible to solve an ODE which is an approximation of the DAE. Finally, the technique is illustrated using the Rice Planar Delta Robot.