Generally speaking, the flexible manufacturing systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, a recursive formulation is developed for the dynamic analysis of open-loop flexible manufacturing systems. The nonlinear generalized Newton-Euler equations are developed for rigid and deformable bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The method to solve equations of motion for open-loop systems consisting of interconnected rigid and deformable bodies is presented in this paper. This method applies recursive method with the Newton-Euler method for deformable bodies to obtain a large, loosely coupled system equations of motion. The solution techniques used to solve for the system equations of motion can be more efficiently implemented in the modern computer systems. The algorithms presented in this paper are demonstrated by using cylindrical joints that can be easily extended to revolute, slider and rigid joints. The recursive formulation developed in this investigation is illustrated by a practical numerical example.