Transmission mechanism interconnecting bodies coaxially rotating with variable velocity, being called "Distributive Oscillating Transmission", and piston variable volume machine cooperating with this mechanism, being called "Toroidal Hermetic Engine". Distributive Oscillating Transmission consists of frame (10), bodies (1 ,2 ,3 ,4), carrier (6) and planet (5). Bodies are supported on central shaft via cages, each with two discs interconnected via bars appropriately shaped and spaced along discs periphery, so that to support bodies and to allow their required relative motion. Carrier rotates around same axis, bearing a planet, being called "poly-planet", because it cooperates with gear fixed on frame and bodies via toothing of variable gear ratio, being called "odonto-knodax" (cam gear) and deployed spirally both on planet and bodies' bars, so that planet cooperates with all bodies simultaneously and continuously, distributing to them required power. Toroidal Hermetic Engine consists of hollow toroidal shell (10), toroidal pistons (1 ,2 ,3, 4) and Distributive Oscillating Transmission. Shell has units equally spaced along its periphery with ports to transfer mass and/or energy, each unit being called "stathmos" (station), pistons moving within shell form between them consecutively the volumes required by any thermodynamic, hydrodynamic or refrigeration cycle, a kinematic process, being called "meta-stathmeusis" (re-stationing), is added to this cycle, via which a cycle completed at a "stathmos" is forwarded to next "stathmos", while, because each piston has both faces active and number of pistons is equal to number of strokes of complete cycle, the stroke performed at a piston's rear face is performed afterwards at its front face, so that each stroke is always performed between two pistons and all strokes are performed consecutively between any two pistons, an operation being called "diadocho-kinesis". Pistons are supported about machine shaft via cages, "odonto-knodaces" are arranged on their bars, while introducing only carrier and "poly-planet" all pistons and machine shaft are interconnected. Applications of this machine are pneumatic or hydraulic, motor or pump, refrigeration machines, Stirling engine being of exceptional interest, and internal combustion engine with a clearly smoother and more efficient operation, while case in which carrier is fixed to stationary frame and shell forms drive shaft is of particular interest since residual energy of exhaust gases is used via reaction.