If r<a, the path described by P will be a contracted cycloid; if r>a, the path is an extended cycloid. (I think there’s a case for using this nomenclature the other way round, but most a...If r<a, the path described by P will be a contracted cycloid; if r>a, the path is an extended cycloid. (I think there’s a case for using this nomenclature the other way round, but most authors seem to use “contracted” for r<a and “extended” for r>a.) It should not take long to be convinced, by arguments similar to those in Section 19.1, that the parametric equations to a contracted or extended cycloid are
