On Higher-Pair Modelling in Planar Mechanisms

  • Raffaele Di GregorioEmail author
Conference paper
Part of the Mechanisms and Machine Science book series (Mechan. Machine Science, volume 73)


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.


Planar Mechanisms Rolling Contact Sliding Contact Noncircular gears Higher Education 


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This work has been developed at the Laboratory of Advanced Mechanics (MECH-LAV) of Ferrara Technopole, supported by FAR2018 UNIFE funds and by Regione Emilia Romagna (District Councillorship for Productive Assets, Economic Development, Telematic Plan) POR-FESR 2007-2013, Attività I.1.1


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of FerraraFerraraItaly

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