A rotary machine with a deformable rhomb includes a rotor formed by a deformable rhomb in contact, with or without clearance, with an internal surface of a housing forming a stator and/or with an external surface of a central crown, the deformable rhomb including four pistons connected one following the other by a pivotal hinge with an axis parallel to a longitudinal axis of the housing and thus forming a closed chain; a transmission mechanism to transmit movement between the pistons and a rotation shaft coaxial to a central axis of the machine, the transmission mechanism including a first rolling body mounted fixedly on at least one piston, an axis of the first rolling body passing in the center of the piston and connected to a second rolling body, a center of which passing through the central axis of the machine and being integral with the rotation shaft, the first rolling body being connected to the second rolling body directly or by an intermediate transmission member, wherein a demultiplication ratio between the first and the second rolling body is equal to 2 and is positive.