Heterocentric Distributive Oscillating Transmission mechanism, as a combination of interlaced planetary systems which interconnect a drive shaft and a plurality of elements, where each element, being a carrier, bears a planetary shaft on which two planets are fixed and cooperate simultaneously and continuously with a sun, fixed either on the mechanism frame or on a base rotatable with respect to this frame, and a sun, fixed on the drive shaft, some of the used toothings being of variable transmission ratio and called 'odonto-knodaces'(cam gears) and possibly also having stepwise deployment, achieving in any case unlimited progressiveness and precision. Toroidal Hermetic Rotary Engine, as a machine of volume variation, purely rotary and hermetically piston-bearing, consisting of toroidal pistons being interconnected via the aforementioned mechanism, and a hollow toroidal shell, which has units equally spaced along its periphery with ports to transfer mass and energy, each unit being called 'stathmos'(station), where the aforementioned pistons, moving within this shell, perform differentiated travels per each period and form between them consecutively the volumes required by any cycle, thermodynamic, hydrodynamic, refrigerating, or a combination of these, normal or optimized, a kinematic process, called 'meta-stathmeusis'(re-stationing) being added to this cycle, via which a cycle completed at a 'stathmos' is forwarded to the next 'stathmos', while, since each piston has both faces active and the number of pistons is equal to the number of periods of the thus extended cycle, the period performed at one face of a piston is afterwards performed at its other face, so that each period is always performed between two pistons and all periods are performed consecutively between any two pistons, this operation being called 'diadocho-kinesis'(successive motion). Applications are ICE, Electric Generators/Motors, Hydraulic Pumps/Motors, Refrigeration Machines, Stirling Engines.