The development of a computationally-effective recursive lagrangian formulation, applied to robot manipulators with revolute and prismatic joints, is presented. These equations result in an efficient and explicit set of closed second-order non-linear differential equations with vector cross-product terms in symbolic form. The method is simple and straightforward to follow, and readily identifies the interaction and coupling reaction forces/torques between neighbouring joints of a manipulator. The model is accurate, without having to resort to simplifying assumptions. The computational load is such that it can easily be implemented on microcomputers and still give real-time performance.