Exact motion equations of mechanical systems are derivable using Newton-Euler, Lagrange and Hamilton equations. Resulting equations are generally complicated and highly non-linear, and hence have no closed form solutions. Numerical integration of such equations involves too much computation and therefore can generally not be done in real time. On the other hand, applications like real-time simulators and models to refer to in adaptive control need real time solutions for the response of the system. This paper presents a technique which yields approximate dynamic equations. These are simpler than exact motion equations, requiring a minimum amount of algebra, and hence enabling fast numerical integration. Equations are also suitable for analog implementation as they require the least amount of arithmetic making modules. The method is applied to open chain articulated systems, and sample digital and analog solutions are presented.