Alternative formulation of the theory of gearing Francesca Di Puccio, Marco Gabiccini, Massimo Guiggiani * Dipartimento di Ingegneria Meccanica, Nucleare e della Produzione, Universita ` di Pisa, via Diotisalvi 2, 56126 Pisa, Italy Received 11 March 2004; received in revised form 14 September 2004; accepted 4 October 2004 Abstract In this paper the theory of gearing is presented by means of a new approach that does not need reference systems. All equations are written in terms of vectors and therefore are valid regardless of the reference sys- tem actually employed. The overall formulation becomes more compact and clearer. As an example, the proposed approach is applied to the generation of spiral bevel gears. To actually perform all calculations, only one reference system is required, thus avoiding the chain of reference systems typical of the traditional approach. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Gear generation; Theory of gearing; Gear geometry; Conjugate surfaces; Envelope of surfaces; Equation of meshing; Spiral bevel gears 1. Introduction Theory of gearing looks like a pretty difficult subject. It is based on the envelope of surfaces and it involves a lot of geometry and complex relative motions. Some books like Theory of Gearing by Litvin [1] are now classical, not to mention more recent contributions, still in the form of books, like [2] and [3] by the same author. This theory has been widely employed and it would be 0094-114X/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mechmachtheory.2004.10.003 * Corresponding author. Tel.: +39 050 836618; fax: +39 050 836665. E-mail address: guiggiani@ing.unipi.it (M. Guiggiani). www.elsevier.com/locate/mechmt Mechanism and Machine Theory xxx (2004) xxx–xxx Mechanism and Machine Theory ARTICLE IN PRESS