Modelling of kinematic higher pairs by lower pairs

Kinematic joints are classified in lower pairs and higher pairs. Most multibody modelling techniques focus on lower pairs, because a complete classification in six types is available. Higher pairs are more diverse. In this article, higher pairs that can be exactly modelled by lower pairs are investigated. A complete classification of higher pairs that can be modelled by a chain of five single-degree-of-freedom lower pairs with a central revolute joint at the contact point is proposed. Two-dimensional cases and surfaces with discontinuities are also considered. The equivalent chains can be used for exact and approximate modelling of higher pairs and as design alternatives. Illustrative examples and applications to a bicycle on toroidal wheels and a railway wheelset on a roller rig are shown.