Summary: The present work is a generalization of the work of Ribberfors and Reitz (2000 Eur. J. Phys. 21 151-7). These authors study a system consisting of a collar that is restricted to move in a path defined by a rod of some prescribed form which passes through the collar. We generalize the analysis of this system by means of canonical treatment. We show in this way that this excellent example can also be used in advanced courses on mechanics to show the power of the methods of analytical mechanics. We have that the present treatment of this example will be useful for advanced undergraduate and graduate students as well as for the teachers of these courses on classical mechanics.