On Higher-Pair Modelling in Planar Mechanisms

The use of complex numbers for systematically writing the constraint equations of planar mechanisms is often limited to linkages (i.e., mechanisms containing only lower pairs). The possible presence of higher pairs in these mechanisms is usually managed through either equivalent linkages or apparent velocity/acceleration equations. Both these methods are simple to implement for a single mechanism configuration, but become cumbersome when continuous motion has to be analyzed. Other approaches use ad hoc auxiliary equations. Here, a general notation that brings to select particular auxiliary equations is proposed. The proposed notation, over being numerically efficient, is easy to present in graduate and/or undergraduate courses for extending the complex number method to higher pairs.