the dynamics of a ma­ nipulator very accurately. Unfortunately, for practical arm designs, the resulting models are complex and a considerable amount of research ef­ fort has gone into improving their numerical efficiency with a view to real time solution [32,41,51,61,77,87,91]. In recent years, improvements in electric motor technology coupled with new designs, such as direct-drive arms, have led to a rapid increase in the speed and load-carrying capabilities of manipulators. However, this has meant that the flexibility of the nominally rigid links has become increasingly significant. Present generation manipulators are limited to a load-carrying capacity of typically 5-10% of their own weight by the requirement of rigidity. For example, the Cincinatti-Milicron T3R3 robot weighs more than 1800 kg but has a maximum payload capacity of 23 kg.