Abstract: A closed system rotary machine has an inner shaped element (1) and an outer shaped element (2) which define therebetween cavities or capsules having a variable volume (V1, V9). The contact points which define the capsules (C1, C9) are disposed along lines of action (CA1, CA2, CA3) which are concurrent at junction points BN and BM, where the cavities begin and end respectively. The contacts (C2) at points located on the tangent (T) common to both pitch circles (6, 7) are osculating elements with a shared centre of curvature which is situated at the rolling point (R) of the pitch circles (6, 7). The invention can be used to ensure that the capsules form and disappear very gradually and to facilitate the distribution of the capsules when they are forming and disappearing in order to increase the leak paths.