Driven by advances in miniaturized electronics, many robotic systems today consist of modular hardware components. This leads to numerous computing units that are distributed within such systems. In order to make better use of such hardware structures from a computational point of view, the implementation of classical control approaches should be reconsidered. Following this idea, a method for distributed computation of motion dynamics of robotic systems using Field Programmable Gate Arrays is discussed. In this approach, local low-level actuator controllers are regarded as interconnected nodes, which are aware of their actuated degree of freedom and the resulting motion of the attached rigid body link element. A modified recursive Newton-Euler algorithm is computed by these nodes, where each node only exchanges data with the neighboring nodes. In the computations, a linear dependency on the dynamic parameters is kept in order to simplify the direct use of dynamic parameters estimated from experimental data. Implementation details and experimental results using a robotic manipulator arm are presented. The experiments show that the method allows compliant motion control. Payloads and external forces acting on a link are considered in the distributed computation of the model by informing the node controlling the respective link of the additional forces.