Notice: Since RKM GbR sold all patents to an investor, this website serves as a historical record to document 16 years of development in mechanical engineering by Dr. Boris Schapiro and his team of supporters. The information presented here reflects the state of knowledge in 2009 and might not be accurate any more. Please contact Dr. Boris Schapiro for further details or information about his latest innovations.

This website is in no way affiliated with the new owner of the patents that where formerly held by RKM GbR. The new owner's Internet presence can be found at

Scientific and Technical Comments

  1. All drawings, stills and animations used in the presentation of the RKM technology are schematic illustrations and, thus, should not be viewed as finalized technical or production drawings. They illustrate only the basic geometry, the functional principle and the kinematics of the RKMs.

    In reality, for example, state-of-the-art valves of the appropriate type will not be located on curved surfaces or passed over by the sealing elements. A working medium will be supplied into and removed from the RKM motor's chamber through end faces not shown on the illustrations or, possibly, through the piston.

    Neither the valves, nor the injection pump, nozzle, the lubrication methods or the controls are the subject matter of this invention. The existing state-of-the-art components and technologies will be adapted to the RKMs' prototypes or developed a new by sub-contractors specializing in the respective fields during the R&D process.

  2. In all versions of the RKMs, the piston rotates about the axis «jumping» between two alternating locations. The piston's sequence of motion includes the following phases: (1) rotation of the piston, (2) jump of the axis, (1) rotation, (2) jump, etc.

    The inner contours of the working chamber are formed by smoothly conjugated circular arcs. During the working cycle, the corresponding portions of the piston progressively slide over the chamber's surfaces.

    The piston has a specially-shaped aperture fitted with an appropriate gear structure, which engages the driven power shaft, which continuously rolls over the gear structure of the aperture or vice versa. The power shaft (or two power shafts in the two-axis version of the RKMs, as described below) extends from the piston's aperture through the end faces of the housing and engages an exterior gear mechanism to transfer power.

    Schematic drawing showing the geometry of bioval piston in tri-oval working chamber of a single-shaft RKM motor. «A» marks the driven power transfer shaft.Image
  3. The piston, its aperture and the working chamber of the RKMs represent, in their cross sections, multi-oval figures which, mathematically, are related to the class of «figures of equal width». Those multi-ovals are non-analytical figures with a discontinuous second derivative of the contour line (the curvature). Hence, generally speaking, the trajectories of their centers of curvature are also non-analytical and, within the RKMs' geometry, have to have singular points.

    In relation to the piston, the trajectory of the power shaft axis has corner points, which correspond to extreme positions of the piston as related to the working chamber. Those corners, which represent singular points of the power shaft's trajectory, cannot be avoided or rounded to provide for the kinematically closed functioning of the gear.

    The reason why until now the geometry of «figures of equal width» could not be put to practical use in the gear design is that no conventional gear structure with the regular rolling on of the gears would permit the exact rolling-on of the singularities. The RKMs solve this problem by introducing the «inversely conjugated gear system», which makes it possible to have singular trajectories of the axes of rolling-on gears and, thus, allows the transfer of the angular momentum during the passage of the piston through its stop positions.

    Schematic drawing showing the functional principle of the RKM motor with bi-oval piston in tri-oval working chamber and one power transfer shaft.Image

    However the kinematics in the stop positions of the piston did not remain closed, as the position of its instantaneous axis of rotation, in the quasi-static case, remained ambiguous.

    The RKM machines address this problem by introducing short-term fixation of the piston's rotation axis. This fixation takes place when the piston leaves its stop position, which corresponds to the singularity of the power shaft's trajectory with respect to the piston. Along the regular portions of the trajectory, the inner and outer boundary conditions of the piston determine uniquely the trajectory. Thus, kinematics of the RKM machine becomes completely determined and assures reliable functioning of the entire dear mechanism.

    Schematic drawings showing movement of the axis of rolling-on gear on singular trajectory with help of inversely conjugated gearing.Image
  4. There are two classes of the RKM motors and pumps, namely with one or two driven power transfer shafts. In single shaft machines, the positions of the piston's «jumping» axes represent, relative to the housing, the corner points of a regular polygon of an odd order of symmetry (3, 5, 7, 9, etc.). Relative to the piston, the «jumping» axes are located at two separate fixed points.

    The dual principle is used in the two-shaft machines, where the axes of rotation of the piston «jump», relative to the chamber, between two separate points, which also serve as the axes of the driven power-transfer shafts. In this case, the piston's rotation axes are located at corner points of a regular polygon of odd order of symmetry (3, 5, 7, 9, etc.).

    Schematic drawing showing the functional principle of the RKM motor with tri-oval piston in bi-oval working chamber and two power transfer shafts.Image
  5. In effect, the conventional reciprocating (forth-and-back) piston machines can be viewed as a specific case of the RKMs' general principle. In such machines, all of the RKMs' curved elements become straight, and the magnitude of the piston axes' «jumps» reaches infinity, i.e. the movement of the piston simply changes direction. This similarity not only makes it possible to utilize the existing state-of-the-art machine building technologies in the RKM machines, but also offers a number of new technological possibilities and advantages.

    Schematic drawing showing the functional principle of the RKM motor with four-oval piston in five-oval working chamber and one power transfer shaft.Image
    ImageSchematic drawing showing the functional principle of the RKM motor with six-oval piston in seven-oval working chamber and one power transfer shaft.
    Schematic drawing showing the functional principle of the RKM motor with five-oval piston in four-oval working chamber and two power transfer shafts with forced afterburning system.Image
    ImageSchematic drawing showing the functional principle of the RKM motor with seven-oval piston in six-oval working chamber and two power transfer shafts.
  6. The RKM machines offer a very large compression factor, which is, unlike that in the Wankel motor, not limited by the geometry and kinematics of the engine. As the compressibility of the working medium to be used in the RKMs is finite, it necessitates the use of special accommodation chambers, or ignition recesses. These recesses hold the compressed working medium when the piston is in its stop positions and facilitate achieving high pressure and temperatures in the RKMs, thereby further increasing their efficiency.

    These recesses hold the compressed working medium when the piston is in its stop positions and facilitate achieving high pressure and temperatures in the RKMs, thereby further increasing their efficiency.Image
  7. Such accommodation chambers are not necessary for the pump applications of RKMs. The advantages of RKMs as compared to conventional pumps are summarized in the following table.

    Comparison of pump principles

    This rating matrix is a theoretical comparison of the different pump principles. Only the types, which carry a significant part of the market or have performance comparable with RKM-style pumps, have been included in this comparison. The total scare is calculated as a weighted su of specific scores multipled by a factor given in the rightmost column.

    Rating matrix
    Pump type
    The score is 1-5 compared to the ideal pump
    Ideal centrifugal
    (1 level)
    Screw spindle Tooth wheel Piston pump RKM
    with / without sealing
    1 to 4

    max. pressure p

    5 3 3 4 5 5 / 4 4
    max. flow Q 5 5 4 3 2 3 4
    max. delivery height H 5 3 4 3 5 5 / 4 4
    production costs 5 4 1 4 1 2 / 3 4
    overall efficiency 5 3 2 4 5 5 / 4 4
    volumetric efficiency rate 5 2 3 4 5 5 / 4 3
    hydr.-mech. efficiency rate 5 4 2 3 4 4 3
    wear & maintenance 5 5 2 4 3 4 2
    compactness / size 5 4 3 5 1 3 2
    pulsation 5 4 5 4 1 3 2
    min. viscosity 5 5 3 5 5 5 1
    max. viscosity 5 3 5 5 5 5 1
    Total 140 106 84 104 92 110 / 100  

    score: 1 to 5 (1 = worst score, 5 = best score)

    Grey marked fields are not included in the total

    Conclusion: RKM pumps are similar to the performance spectrum of tooth wheel and piston pumps. The centrifugal pump also has a similar score, but plays a special role on the pump market due to its high flow capacity and relatively low pressure.

    The comparison table was prepared on December 19th, 2005 by Danny Chenh Nhi Lai, graduate candidate, Polytechnische Hochschule, Ingolstadt, Germany

  8. Among other features, the RKM technology makes it possible the release of stored chemical energy (by combustion) within the ignition recesses and forced after-burning of working medium when it enters the working chamber, so that, essentially, the quasi-adiabatic expansion of the working medium takes place after the combustion. Consequently, the flame-quenching effect typical for the Wankel motor is to be suppressed in the RKM motor, resulting in a virtually complete combustion and cleaner exhaust gases.

    Schematic drawing showing spherical recess where ignition and combustion of the working medium takes place. Forced after-burning occurs when the working medium enters the working chamber.Image
  9. The advantages of the RKMs as compared to conventional piston internal combustion engines, the Wankel motor, fuel cells and electric batteries (all in their current state of development) are summarized in the following table below.

    ## Technical characteristics Piston engines Wankel Engine RKMs
    Fuel cells Electric batteries
    1 Power per volume ratio, in kW per liter. 0.5 - 0.8 1.2 1.5 - 4.0 0.07 0.07
    2 No. of active strokes per one cycle of the crankshaft or of the rotary piston 0.5 3 3 to 7 N/A N/A
    3 Efficiency up-to-date Up to 56% Approx. 35% Up to 61% Approx. 70% Approx. 70%
    4 Prospective efficiency Up to 65 % Up to 45 % Over 70% Approx. 80% Approx. 80%
    5 Estimated cost of 1 KW of power generated by the power shaft during engines useful life US$ 30.0 US$ 40.0 Less than US$ 30.0 US$ 250.0 US$ 100.0
    6 Ease of coupling/de-coupling of engine units to reduce fuel consumption and achieve functioning at or close to the engine's optimal efficiency No Yes Yes Yes Yes
    7 Normalized average ratio of length of torque arm to crankshaft eccentricity or an equivalent engine characteristic Determined by the crankshaft 0,5 Small 0,3 Large 1,0 N/A N/A
    8 Relative variation of torque arm during power stroke
    (max. = 1,0)
    0 to 1,0 0 to 1,0 Constant at 1.0 N/A N/A
    9 Self-ignition regime (diesel or hydrogen) Yes No Yes N/A N/A
    10 Emission vs. Emission limits Within limits can be reduced by better power and exhaust control can be reduced by better power and exhaust control & afterburning, excellent w/hydrogen Water stream only w/hydrogen as fuel Negligibly small
  10. Preliminary scientific analysis clearly demonstrates a number of advantages the RKM technology has over several existing and prospective power-generation technologies, including their theoretical potential. These advantages are not limited to several key technical characteristics but also include control of exhaust products and overall efficiency and economics.

  11. In spite of the apparent likeness, the RKM machines are quite different from turbines and the Wankel motor. Their seeming similarity with the Wankel is misleading and is limited only to the sickle-shaped working volumes. The essential differences of the two technologies are summarized in the following table:

    Element or technical characteristic compared The RKM technology The Wankel engine
    Working chamber Stationary Mobile
    Rotation of piston The rotatioin axis jumps between two fixed positions Axis positions move around a circle
    Ignition and combustioin Inside a compact ignition recess In a sickle-shaped working chamber
    Forced after-burning of gases entering working chamber Provided Not possible
    Contact of sealing element with the surfaces of working chamber or piston Surface contact, effective sealing, negligible underblowing of gases Line contact, poor sealing, significant underblowing of gases
    Wear of sealing materials Low High
    Compression factor Geometrically unlimited Limited by the geometry of the epitrochoid
    Design as Diesel engine Possible Not feasible
    Resources/useful life Large/long Small/short
    Efficiency High Low
    Fuel consumption Low High
    Exhaust controls Better than in conventional piston engines due to forced after-burning of gases Good only with expensive filters or catalytic converters

    There is, however, a feature that the Wankel motors and the RKMs have in common: both allow easy miniaturization because of their prismatic structure. The RKMs limits of miniaturization are substantially broader than those of the conventional piston machines and, theoretically, may reach the millimeter range.

  12. Not all technical issues and problems have been resolved at the present stage of the RKMs development. However, the RKM Partnership has identified several major venues to address those issues and achieve technical solutions which would allow to develop a compact, economical, environment-friendly and resources-saving RKM technology.

Basic kinematic of 1-axes model of the RKM machine
(with a single power shift):

Power shaft with gearing.






Basic parts assembled.






Tri-oval working chamber.






Parts: working chamber, lid with windows, shaft and piston.






Bi-oval piston.






Basic kinematic model completely assembled.