Rotary machine of the deformable rhombus type comprising a. a rotor (3) which is a deformable rhombus (4) in contact with the inner surface of an enclosure (1) forming a stator (2), said deformable rhombus (4) comprising four pistons (6) connected, in mutual succession, by a pivoting articulation (7) and thus forming a closed chain; and b. a transmission mechanism (14) for transmitting the movement between the pistons (6) and a rotary shaft (15) coaxial to the central axis of the machine, characterized in that said transmission mechanism (14) comprises: a first bearing body (16) mounted fixedly on at least one piston (6), preferably on each piston (6), the axis of said first bearing body (16) passing at the centre of the piston (6) and connected to a second bearing body (19) of which the centre passes through the central axis of the machine and is secured to said rotary shaft (15), the first bearing body (16) being connected to the second bearing body (19) directly or via an intermediate transmission member (18) - and in that the reduction ratio of the first (16) to the second bearing body (19) is equal to 2 and is positive.