A comparative study of recursive methods

Summary Recursive methods represent a well-established and wide-spread technique for generation of dynamical equations of mechanical systems. Their main objective is to obtain computational schemes involving as few operations as possible. In this paper, we show that, besides the consideration of simplification resulting from a careful representation of geometric relationships between contiguous links, only two factors determine the overall efficiency of these methods. These factors are: the choice of an appropriate reference point for the kinematic and kinetic equations, and the frame of decomposition used to represent the involved vectors and tensors. Further, we derive a computational scheme which compares advantageously with existing methods. As only elementary laws of mechanics are applied, the exposition is also suitable for practising engineers seeking to understand the main differences between existing methods. A comparison with one of the reportedly most effective non-recursive method elucidates the advantages and bounds of the present approach.