In such engines different types of mechanisms translate reciprocating motion of the pistons into rotary output shaft motion by way of a combination of mechanical components such as cams, locks, gear-cams, planetary gear trains, non-circular gears, shaft-gears, elliptical eccentric gear arrangements. The pistons are generally vane type, arcuate type or a variation of these types. In the Wankel, the rotor replaces the piston.

In the toroidal chamber design, the mechanisms generating the desired movement of the pistons are housed on one side or both sides of the toroid or the annular ring. The output shaft is connected to the mechanism.

In Rotary Internal Combustion Engines a major disadvantage arises from the complexity of the mechanisms that contain reciprocating elements with reversal of direction, complex and odd shapes and have not been fabricated on commercial scale.

Experimentation on the Wankel engine too since 1957 has not resulted currently in production for automobiles and the automotive industry as a whole. In the Wankel engine rotor design the disadvantage is the low torque, high speed, high fuel consumption, special tooling, special sealing, gears exposed to the heat of combustion, large power wastage that all are inherent to the triangular rotor design.

Reference to US patent 3,822, 971, the means used to perform the cycles in the four-

stroke intemal combustion engine do not provide repetitive cycles with the first order elliptic gears rotating around their foci due to the great precision required in fabrication in addition to the complications created by the requirement for dynamic balancing of the planetary system. Also the tolerances for normal wear and tear incorporated into the design is not achievable in practice with the gear arrangement disclosed resulting in piston reversal and irregular cycles. Thus it is found that the engine disclosed in US3, 822, 971 is not practical.

The object of this invention is to alleviate the complexities in the design of the mechanisms.

The term combustion in the present context is used to describe the burning of the fuel-air mixture.

A further object of this invention is to provide a solution to the fundamental problem of tolerance margin both for fabrication and for normal wear and tear in operation without appreciably affecting engine performance.

A still further object of this invention is to make use of higher order of at least twin non- circular gears rotating about their geometric centers and the uniform polygonal contour of which defines the order of the gear. Thus a three-sided polygon will define a third order non-circular gear. A square will be termed as a fourth order non-circular gear, and so on.

The contour of each of these polygons is a repetitive curve that produces a long dwell followed by a short dwell. One set is in mesh with another set with a phase difference.

According to a first aspect of the present invention there is provided a rotary piston four-stroke internal combustion engine of the revolving block type operated with the sequence of suction, compression, power and exhaust strokes of a four-stroke internal combustion engine, in which the moving parts rotate generally unidirectionally,

and comprising a toroidal chamber split along a plane perpendicular to the toroidal axis in which two piston sets, each including at least two pistons, capable of orbiting within the toroidal chamber, each piston set having arms extending radially through the circumferential slot formed around the chamber and coupled to a power transmission and a manifold adapted to control the induction and discharge of compressible fluid to spaces between the pistons, whereby the combustion of the fluid or decompression of the fluid in one of the spaces causes the piston of one set to advance along its orbit relative to the piston of another set so rotating an output shaft, said output shaft being coupled to the transmission, said transmission comprising an epicyclic gear system having: a central circular gear coaxially coupled to a disc plate carrying the piston sets, a circular planetary gear meshed with the central circular gear, a non-circular planetary gear coaxially coupled with the circular planetary gear, and said non-circular planetary gear meshing with a non-circular reaction gear, with a total number of firing cycles in one revolution of the shaft output rotation is equal to n*m* (p+1)/4 where n is the number of pairs of pistons, m is the order of the non-circular gears and the circular gear ratio = the ratio of the number of teeth of the circular planetary gear to the number of teeth of the central circular gear and p+1= p/ (the circular gear ratio) characterised in that the non-circular planetary gear is coupled to rotate around its geometric axis.

According to a second aspect of the present invention there is provided a rotary piston two-stroke internal combustion engine of the revolving block type operated with the sequence of power/exhaust/scavenging, compression strokes of a two-stroke internal combustion engine, in which the moving parts rotate generally unidirectionally,

and comprising a toroidal chamber split along a plane perpendicular to the toroidal axis in which two piston sets, each including at least two pistons, capable of orbiting within the toroidal chamber, each piston set having arms extending radially through the circumferential slot formed around the chamber and coupled to a power transmission and a manifold adapted to control the induction and discharge of compressible fluid to spaces between the pistons, whereby the combustion of the fluid or decompression of the fluid in one of the spaces causes the piston of one set to advance along its orbit relative to the piston of another set so rotating an output shaft, said output shaft being coupled to the transmission, said transmission comprising an epicyclic gear system having: a central circular gear coaxially coupled to a disc plate carrying the piston sets, a circular planetary gear meshed with the central circular gear, a non-circular planetary gear coaxially coupled with the circular planetary gear, and said non-circular planetary gear meshing with a non-circular reaction gear, with a total number of firing cycles in one revolution of the shaft output rotation is equal to n*m* (p+1)/2 where n is the number of pairs of pistons, m is the order of the non-circular gears and the circular gear ratio = the ratio of the number of teeth of the circular planetary gear to the number of teeth of the central circular gear p+ 1 = p/ (the circular gear ratio) characterised in that the non-circular planetary gear is coupled to rotate around its geometric axis.

According to a third aspect of the present invention there is provided a rotary piston motor of the revolving block type in which the moving parts rotate generally unidirectionally, and comprising a toroidal chamber split along a plane perpendicular to the toroidal axis in which two piston sets, each including at least two pistons, capable of

orbiting within the toroidal chamber, each piston set having arms extending radially through the circumferential slot formed around the chamber and coupled to a power transmission and a manifold adapted to control the induction and discharge of fluid pulses to spaces between the pistons, whereby the decompression of the fluid in one of the spaces causes the piston of one set to advance along its orbit relative to the piston of another set so rotating an output shaft, said output shaft being coupled to the transmission, said transmission comprising an epicyclic gear system having: a central circular gear coaxially coupled to a disc plate carrying the piston sets, a circular planetary gear meshed with the central circular gear, a non-circular planetary gear coaxially coupled with the circular planetary gear, and said non-circular planetary gear meshing with a non-circular reaction gear, with a total number fluid pulses in one revolution of the shaft output rotation is equal to n*m* (p+1)/2 where n is the number of pairs of pistons, m is the order of the non-circular gears and the circular gear ratio = the ratio of the number of teeth of the circular planetary gear to the number of teeth of the central circular gear p+1= p/ (the circular gear ratio) characterised in that the non-circular planetary gear is coupled to rotate around its geometric axis.

According to a third aspect of the present invention there is provided a rotary piston pump of the revolving block type in which the moving parts rotate generally unidirectionally, and comprising a toroidal chamber split along a plane perpendicular to the toroidal axis in which two piston sets, each including at least two pistons are capable of orbiting within the toroidal chamber, each piston set having arms extending radially

through the circumferential slot formed around the chamber and coupled to a power transmission and a manifold adapted to control the induction and discharge of fluid pulses to spaces between the pistons, whereby the rotation of an input shaft causes the piston of one set to advance along its orbit relative to the piston of another set so compressing a fluid pulse in the space between the pistons said input shaft being coupled to the transmission, said transmission comprising an epicyclic gear system having: a central circular gear coaxially coupled to a disc plate carrying the piston sets, a circular planetary gear meshed with the central circular gear, a non-circular planetary gear coaxially coupled with the circular planetary gear, and said non-circular planetary gear meshing with a non-circular reaction gear, with a total number fluid pulses in one revolution of the input shaft is equal to n*m* (p+1)/2 where n is the number of pairs of pistons, m is the order of the non-circular gears and the circular gear ratio = the ratio of the number of teeth of the circular planetary gear to the number of teeth of the central circular gear p+1= p/ (the circular gear ratio) characterised in that the non-circular planetary gear is coupled to rotate around its geometric axis.

According to a fourth aspect of the present invention there is provided a rotary piston compressor of the revolving block type in which the moving parts rotate generally unidirectionally, and comprising a toroidal chamber split along a plane perpendicular to the toroidal axis in which two piston sets, each including at least two pistons are capable of orbiting within the toroidal chamber, each piston set having arms extending radially

through the circumferential slot formed around the chamber and coupled to a power transmission and a manifold adapted to control the induction and discharge of fluid pulses to spaces between the pistons, whereby the rotation of an input shaft causes the piston of one set to advance along its orbit relative to the piston of another set so compressing a fluid pulse in the space between the pistons said input shaft being coupled to the transmission, said transmission comprising an epicyclic gear system having: a central circular gear coaxially coupled to a disc plate carrying the piston sets, a circular planetary gear meshed with the central circular gear, a non-circular planetary gear coaxially coupled with the circular planetary gear, and said non-circular planetary gear meshing with a non-circular reaction gear, with a total number fluid pulses in one revolution of the input shaft is equal to n*m* (p+1)/2 where n is the number of pairs of pistons, m is the order of the non-circular gears and the circular gear ratio = the ratio of the number of teeth of the circular planetary gear to the number of teeth of the central circular gear p+1= p/ (the circular gear ratio) characterised in that the non-circular planetary gear is coupled to rotate around its geometric axis.

According to a fifth aspect of the present invention there is provided a rotary piston compressor of the revolving block type in which the moving parts rotate generally unidirectionally, and comprising a toroidal chamber split along a plane perpendicular to the toroidal axis in which two piston sets, each including at least two pistons are capable of orbiting within the toroidal chamber, each piston set having arms extending radially

through the circumferential slot formed around the chamber and coupled to a power transmission and a manifold adapted to control the induction and discharge of fluid pulses to spaces between the pistons, whereby the rotation of an input shaft causes the piston of one set to advance along its orbit relative to the piston of another set so compressing a fluid pulse in the space between the pistons said input shaft being coupled to the transmission, said transmission comprising an epicyclic gear system having: a central circular gear coaxially coupled to a disc plate carrying the piston sets, a circular planetary gear meshed with the central circular gear, a non-circular planetary gear coaxially coupled with the circular planetary gear, and said non-circular planetary gear meshing with a non-circular reaction gear, with a total number fluid pulses in one revolution of the input shaft is equal to n*m* (p+1)/2 where n is the number of pairs of pistons, m is the order of the non-circular gears and the circular gear ratio = the ratio of the number of teeth of the circular planetary gear to the number of teeth of the central circular gear p+1= p/ (the circular gear ratio) characterised in that the non-circular planetary gear is coupled to rotate around its geometric axis.

According to the present invention there is provided an annular cylindrical toroidal chamber split along a plane perpendicular to the toroidal axis wherein one set of two arcuate pistons or more rotate unidirectionally by accelerating and decelerating out of phase with another equivalent set of two arcuate pistons or more. Each set contains an equal number of arcuate pistons. The arcuate pistons of one set are mechanically

coupled to the arms of a disc at equal spacing over the circumference of the disc plate.

The disc plate is located in a housing and the arms protrude from the housing into the annular chamber through a circumferential slot along its inner periphery and unto which the arcuate pistons are mounted. The sealing of the annular cylinder between consecutive arcuate pistons is effected by the spring effect of two arcuate piston rings of the one set acting as the piston crown and the spring effect of two arcuate pistons rings of the other set acting as the cylinder head. Sealing of the annular cylinder containing the arcuate pistons between the chamber and the rotating disc is effected by a circumferential mechanical seal which is spring loaded and provided with adjusting screw. Sealing between the two disc plates onto which are mounted the two sets of arcuate pistons is effected by annular circular seals. Sealing of the annular cylinder between the arcuate piston rings and the circumferential mechanical seal is effected by an obturator. To the disc plate, at its geometric center, a circular gear is mechanically fixed. The arcuate pistons of the set, the corresponding circular disc plate and the gear revolve as one assembly block around the central output shaft and independent from it by way of bearings. To the output shaft is keyed an arm that holds a small shaft mounted on bearings. On the one side of the arm is a circular gearthat meshes with the circular gear of the disc plate. On the other side of the arm is a noncircular gear. The noncircular gear meshes with an identical noncircular gear that is held to the housing in a fixed position. The assembly thus formed is an epicyclic gear train. During the passage of the piston, portholes that are positioned at predetermined locations are alternately covered and uncovered and act as the inlet and exhaust ports. The number of'cycles per revolution'listed in the matrix requires different methods of covering and uncovering the portholes. In the one category, as in the preferred embodiment, the movement of the pistons covers and uncovers the portholes. In a different category known but not made part of the preferred embodiment, two sets of portholes are required wherein external means are provided for one set to be uncovered during one revolution of the output shaft and the second set of portholes to be uncovered during the next revolution thus

altemating between one set for one rotation and the other set for the next rotation of the output shaft. This is repeated in a reciprocating manner over the continuous output rotation. This category obviously is more complicated and more expensive for fabrication and is not pursued in the present invention. According to this invention, several identical units can be coupled in tandem to generally produce power output or input in multiples of one unit.

A specific embodiment of the invention will now be described by way of example, wherein four pairs of pistons in a Spark Ignition engine are used, four on each set, with fourth degree non-circular gears, compression ratio of 6 and ratio of circular gears of 2: 3, and twelve firing cycles for each revolution of the output shaft, as highlighted in the attached matrix of cycles per revolution, and with reference to the accompanying drawings in which:- Figure 1 shows an axial cutaway view of a water-cooled engine.

Figure 2 shows an axial cutaway view of an air-cooled engine.

Figure 3 shows the main components of the engine, motor, pump, compressor mechanism in plan view.

Figure 4 shows schematically the main components of the engine, motor, pump, compressor mechanism across the output shaft.

Figure 5 shows the instantaneous position of the two sets of piston pairs wherein firing occurs between the two consecutive pistons 2 & 6 at position zero and 4 & 8 at position Tr.

Figure 6 shows the firing positions between pistons 6 & 3 at position n/3 and 5& 8 at position 4Tr/3.

Figure 7 shows the firing positions between pistons 3 & 7 at position 2#/3 and 5 & 9 at position 5Tr/3.

Figure 8 shows the firing positions between pistons 7 & 4 at position n and 9 & 2 at position 2#.

Figure 9 shows the firing positions between pistons 2 & 6 at position #/3 and 4 & 8 at position 4#/3 Figure 10 shows the firing positions between pistons 6 & 3 at position 2#/3 and 5 & 8 at position 5#/3 Figure 11 shows the firing positions between pistons 3 & 7 at position Tr and 5 & 9 at position 2# Figure 12 shows the firing positions between pistons 7 & 4 at position #/3 and 9 & 2 at position 4#/3 Figure 13 shows the firing positions between pistons 2 & 6 at position 2#/3 and 4 & 8 at position 5#/3 Figure 14 shows the firing positions between pistons 5 & 8 at position Tr and 6 & 3 at position 2Tr Figure 15 shows the firing positions between pistons 5 & 9 at position n/3 and 3 & 7 at

position 4Tr/3 Figure 16 shows the firing positions between pistons 9 & 2 at position 2Tr/3 and 7 & 4 at position 5n/3 Figure 17 shows schematically the annular cylinder with the spark plugs in position and the distribution of exhaust and intake portholes.

Figure 18 portrays the graph of the unidirectional motion of the four pistons with output shaft rotation and the firing positions. The pistons rotate through 120 degrees for one complete revolution of the output shaft.

Figure 19 shows a close-up view of the substantially constant spacing during the ignition and combustion phase.

Figure 20 represents the third order non-circular gear.

Figure 21 represents the fourth order non-circular gear.

Figure 22 represents the eighth order non-circular gear.

Figure 23 represents the engine assembly.

Figure 24 represents three engines coupled in tandem along a given axis.

Engine Firing Cycles For one Revolution of the Output Shaft<BR> No of Order ½ 2/3 3/4 4/5 5/6 6/7 7/8 8/9 9/10 10/11 11/12 p/(p+1)<BR> Pistons<BR> 2 pairs 1st 1 3/2 2 5/2 3 7/2 4 9/2 5 11/2 6 (p+1)/2<BR> 3 pairs 1st 3/2 9/4 3 15/4 9/2 21/4 6 27/4 15/2 33/4 9 3(p+1)/4<BR> 4 pairs 1st 2 3 4 5 6 7 8 9 10 11 12 (p+1)<BR> 5 pairs 1st 5/2 15/4 5 25/4 15/2 35/4 10 45/4 25/2 55/4 15 5(p+1)/4<BR> n pairs 1st n/2 3n/4 n 5n/4 3n/2 7n/4 2n 9n/4 10n/4 11n/4 3n n(p+1)/4<BR> 2 pairs 2nd 2 3 4 5 6 7 8 9 10 11 12 (p+1)<BR> 3 pairs 2nd 3 9/2 6 15/2 9 21/2 12 27/2 15 33/2 18 3(p+1)/2<BR> 4 pairs 2nd 4 6 8 10 12 14 16 18 20 22 24 2(p+1)<BR> 5 pairs 2nd 5 15/2 10 25/2 15 35/2 20 45/2 25 55/2 30 5(p+1)/2<BR> n pairs 2nd n 3n/2 2n 5n/2 3n 7n/2 4n 9n/2 5n 11n/2 6n n(p+1)/2<BR> 2 pairs 3rd 3 9/2 6 15/2 9 21/2 12 27/215 33/2 38 3(p+1)/2<BR> 3 pairs 3rd 9/4 27/4 9 45/4 27/2 63/4 18 81/4 45/2 99/4 27 9(p+1)/4<BR> 4 pairs 3rd 6 9 12 15 18 21 24 27 30 33 36 3(p+1)<BR> 5 pairs 3rd 15/2 45/4 15 75/4 45/2 105/4 30 135/4 75/2 165/4 45 15(p+1)/4<BR> n pairs 3rd 3n/2 9n/4 3n 15n/4 9n/2 21n/4 6n 27n/4 15n/2 33n/4 9n 3n(p+1)/4<BR> 2 pairs 4th 4 6 8 10 12 14 16 18 20 22 24 2(p+1)<BR> 3 pairs 4th 6 9 12 15 18 21 24 27 30 33 36 3(p+1)<BR> 4 pairs 4th 8 12 16 20 24 28 32 36 40 44 48 4(p+1)<BR> 5 pairs 4th 10 15 20 25 30 35 40 45 50 55 60 5(p+1)<BR> n pairs 4th 2n 3n 4n 5n 6n 7n 8n 9n 10n 11n 12n n(p+1)<BR> 2 pairs m m 3m/2 2m 5m/2 3m 7m/2 4m 9m/2 5m 11m/2 6m m(p+1)/2<BR> 3 pairs m 3m/2 9m/4 3m 15m/4 9m/2 21m/4 6m 27m/4 15m/2 33m/4 9m 3m(p+1)/4<BR> 4 pairs m 2m 3m 4m 5m 6m 7m 8m 9m 10m 11m 12m m(p+1)<BR> 5 pairs m 5m/2 15m/4 5m 25m/4 15m/2 35m/4 10m 45m/4 25m/2 55m/4 15m 5m(p+1)/4<BR> n pairs m nm/2 3nm/4 nm 5nm/4 3nm/2 7nm/4 2nm 9nm/4 5nm/2 11nm/2 3nm nm(p+1)/4 Motor, Pump & Compressor Pressure Pulses For One Revolution of the Input/Output Shaft<BR> No of Order ½ 2/3 3/4 4/5 5/6 6/7 7/8 8/9 9/10 10/11 11/12 p/(p+1)<BR> Pistons<BR> 2 pairs 1st 2 3 4 5 6 7 8 9 10 11 12 (p+1)<BR> 3 pairs 1st 3 9/2 6 15/2 9 21/2 12 27/2 15 33/2 18 3(p+1)/2<BR> 4 pairs 1st 4 6 8 10 12 14 16 18 20 22 24 2(p+1)<BR> 5 pairs 1st 5 15/2 10 25/2 15 35/2 20 45/2 25 55/2 30 5(p+1)/2<BR> n pairs 1st n 3n/2 2n 5n/2 3n 7n/2 4n 9n/2 5n 11n/2 6n n(p+1)/2<BR> 2 pairs 2nd 4 6 8 10 12 14 16 18 20 22 24 2(p+1)<BR> 3 pairs 2nd 6 9 12 15 18 21 24 27 30 33 36 3(p+1)<BR> 4 pairs 2nd 8 12 16 20 24 28 32 36 40 44 48 4(p+1)<BR> 5 pairs 2nd 10 15 20 25 30 35 40 45 50 55 60 5(p+1)<BR> n pairs 2nd 2n 3n 4n 5n 6n 7n 8n 9n 10n 11n 12n n(p+1)<BR> 2 pairs 3rd 6 9 12 15 18 21 24 27 30 33 36 3(p+1)<BR> 3 pairs 3rd 9/2 27/2 18 45/2 27 63/2 36 81/2 45 99/2 54 9(p+1)/2<BR> 4 pairs 3rd 12 18 24 30 36 42 48 54 60 66 72 6(p+1)<BR> 5 pairs 3rd 15 45/2 30 75/2 45 105/2 60 135/2 75 165/2 90 15(p+1)/2<BR> n pairs 3rd 3n 9n/2 6n 15n/2 9n 21n/2 12n 27n/2 15n 33n/2 18n 3n(p+1)/2<BR> 2 pairs 4th 8 12 16 20 24 28 32 36 40 44 48 4(p+1)<BR> 3 pairs 4th 12 18 24 30 36 42 48 54 60 66 72 6(p+1)<BR> 4 pairs 4th 16 24 32 40 48 56 64 72 80 88 96 8(p+1)<BR> 5 pairs 4th 20 30 40 50 60 70 80 90 100 110 120 10(p+1)<BR> n pairs 4th 4n 6n 8n 10n 12n 14n 16n 18n 20n 22n 24n 2n(p+1)<BR> 2 pairs m 2m 3m 4m 5m 6m 7m 8m 9m 10m 11m 12m m(p+1)<BR> 3 pairs m 3m 9m/2 6m 15m/2 9m 21m/2 12m 27m/2 15m 33m/2 18m 3m(p+1)/2<BR> 4 pairs m 4m 6m 8m 10m 12m 14m 16m 18m 20m 22m 24m 2m(p+1)<BR> 5 pairs m 5m 15m/2 10m 25m/2 15m 35m/2 20m 45m/2 25m 55m/2 30m 5m(p+1)/2<BR> n pairs m nm 3nm/2 2nm 5nm/2 3nm 7nm/2 4nm 9nm/2 5nm/2 11nm 6nm nm(p+1)/2

Referring to the drawings, the engine construction comprises eight pistons 2,3, 4 & 5 rotating within an annular cylindrical toroidal chamber formed by two halves 10 and 12. A piston set is provided by a plurality of pistons 2,3, 4 & 5 coupled to a transmission via a plurality of arms extending radially from a circular plate 14 to which the pistons are mechanically held through gudgeon pins 16,17, 18 &19 respectively. A circular gear 26 is held onto the circular disc plate 14 by bolts. Circular gears 28 & 29 mesh with gear 26.

Gear 28 is keyed to shaft 32. Gear 29 is keyed to shaft 33. Both shafts 32 and 33 are supported by and rotate freely on the arm 34. Arm 34 is keyed to the output shaft 36. To shaft 32 is keyed a non-circular gear 38. To shaft 33 is keyed a noncircular gear 39 identical to gear 38. Both noncircular gears 38 and 39 mesh with an identical gear 40.

Gear 40 is mechanically held in fixed position to the cover. The mechanism described is housed in a housing 42 and covered by plate 44. The fuel-air mixture is introduced into the cylindrical chamber through the manifold 46 and ignited by two spark plugs at each of the firing positions. The burned gases are then exhausted by way of annular manifold 52. Also pistons 6,7, 8 and 9 are mechanically coupled to disc 20 by way of gudgeon pins 22,23, 24 and 25 respectively. Circular gears 56 & 57 mesh with gear 54. Both gears 56 and 62 are keyed to shafts 58. Also gears 57 and 61 are keyed to shaft 59. Both shaft 58 and 59 are supported by and rotate freely on the arm 60. Arm 60 is keyed to the output shaft 36.

Gears 61 and 62 mesh with identical gear 63. Gear 63 is ih turn mechanically fixed onto the cover 64 & 59 held on arm 60. Gears 61 and 62 mesh with identical gear 63. This in turn is held onto the cover 64. The Y-axis represents the rotation of the pistons and the X- axis represents the rotation of the output shaft. The W-axis represents the relative position of the portholes and spark plugs on the annular chamber of figure 4 in clockwise direction, wherein 4 pairs of pistons 2, 3, 4 & 5 on the one set and 6,7, 8 & 9 on the other set are shown. The parallel curved lines indicate the arcuate piston lengths and in between two adjacent sets of two arcuate pistons is the space confined between them. Pistons 2,3, 4 &5 of the one set rotate as one block. Pistons 6,7, 8 & 9 of the second set rotate as another block independently from the first set but with a phase shift with respect to the first

set. Space 70 is the minimum space during exhaust stroke. Space 72 is the maximum space at the intake stroke. Space 74 is the maximum volume during the power stroke and space 76 is the minimum clearance volume during combustion. 78 is the bum duration at constant volume. Points 80 through 91 inclusive are the ignition points and the start of combustion and power cycles. The number of power strokes for one complete revolution of the output shaft is given by the formula : n*m* (p+1)/4. Power stroke occurs generally at (360) (4)/n*m* (p+1) degrees rotation of the output shaft wherein n is the number of pairs of pistons starting with n=2, m is the order of non-circular gears starting with m=1, and (p+1) is the denominator of the circular gear ratio p/(p+1). In the example with 12 power strokes there are two simultaneous firings for every 60 degrees rotation of the output shaft.

In the operation of the engine, starting with piston 6, piston 2 has completed the power stroke and advanced toward piston 6 and uncovered exhaust porthole 107 ready to exhaust the burnt gases. The compressed charge within the volume 76 at the ignition point 80 is ready to be ignited by the two spark plugs 48 and 50. The other pistons 3,4 & 5, which are mounted on the same disc plate 14 as piston 2, accelerate and advance toward the pistons 7,8 & 9 respectively of the disc plate 20 onto which the piston 6 is mounted. At this point all pistons rotate slowly, in the same direction and substantially in parallel to each other. Thus piston 3 advances toward piston 7 and exhausts the burnt gases through porthole 103. At the same time piston 3 draws a new charge of fuel-air mixture through porthole 92, while piston 6 has advanced slightly to cover the exhaust port 102. Piston 4 has completed the power stroke and advanced toward piston 8 and uncovered exhaust porthole 104 ready to expel the burnt gases. The compressed charge within the volume 76 at the ignition position 82 is ready to be ignited by the two spark plugs 49 and 51. Piston 5 advances toward piston 9 and exhausts the burnt gases through porthole 106. At the same time pistons 5 draws in a new charge through porthole 95, while piston 8 moves slightly to cover exhaust port 105. Piston 6 completes the power stroke and uncovers porthole 102 ready to expel the burnt gases. At the same time piston 6 advances and compresses the

charge against piston 3. The compressed charge within the space 76 at ignition position 81 is ready to be ignited by the two spark plugs 53 and 55. Piston 7 has advanced toward piston 4 and expelled burnt gases through porthole 104. At the same time the intake charge is drawn in through porthole 93, while piston 3 advances slightly to cover the exhaust port 103. Piston 8 has completed the power stroke, uncovered exhaust porthole 105 and ready to exhaust the burnt gases. At the same time piston 8 compresses the charge by moving toward piston 5. The compressed charge within space 76 at ignition position 83 is ready to be ignited by the spark plugs 45 and 47. Piston 9 draws in a new charge of fuel-air mixture through intake porthole 96 while piston 5 as advanced slightly to cover the exhaust porthole 106. At the same time piston 9 exhausts the burnt gases through porthole 107. Piston 2 advances toward piston 6 and draws in a new charge of fuel-air mixture through porthole 97 while piston 9 advances slightly to cover exhaust porthole 107. At the same time piston 2 exhausts the burnt charge through porthole 102.

Piston 3 completes the power stroke and uncovers porthole103 ready to expel the burnt gases. At the same time piston 3 moves to compress the charge against piston 7. The compressed charge within space 76 at ignition position 84 is ready to be ignited by the two spark plugs 57 and 59. Piston 4 advances toward piston 8 and exhausts the burnt gases through porthole 105. At the same time piston 4 draws in the charge through porthole 94 while piston 7 moves slightly to cover the exhaust porthole 104. Piston 5 completes the power stroke and uncovers the exhaust porthole 106 ready to exhaust the burnt gases. At the same time piston 5 advances to compress the charge against piston 9. The compressed charge within space 76 at ignition position 86 is ready to be ignited by the two spark plugs 41 and 43. Piston 6 advances towards piston 3 and draws in a new charge through porthole 102, while piston 2 advances slowlyto coverthe exhaust porthole 102. At the same time piston 6 exhausts the burnt gases through porthole 103. Piston 7 completes the power stroke and uncovers porthole 104 ready to exhaust the burnt gases. At the same time piston 7 advances and compresses the charge against piston 4. The compressed charge within space 76 at ignition position 85 is ready to be ignited by the two

spark plugs 49 and 51. Piston 8 advances toward piston 5 and exhausts the burnt gases through porthole 106. At the same time piston 8 draws in a new charge of fuel-air mixture through porthole 95 while piston 4 advances slightly to cover the exhaust porthole 105.

Piston 9 completes the power stroke and uncovers porthole 107 ready to exhaust the burnt gases. At the same time piston 9 advances to compress the charge against piston 2. The compressed charge within space 76 at ignition position 87 is ready to be ignited by the two spark plugs 48 and 50. Piston 2 completes the power stroke and uncovers exhaust porthole 102 ready to exhaust the burnt gases. At the same time piston 2 advances to compress the charge against piston 6. The compressed charge within space 76 at ignition position 88 is ready to be ignited by the two spark plugs 53 and 55. Piston 3 advances to draw in a new charge of fuel-air mixture through porthole 93, while piston 6 moves slightly to cover exhaust porthole 103. At the same time piston 3 drives the burnt gases through exhaust porthole 104. Piston 4 completes the power stroke and uncovers porthole 105 ready to exhausts the burnt gases. At the same time it moves to compress the charge against piston 8. The compressed charge within space 76 at ignition position 90 is ready to be ignited by the two spark plugs 45 and 47. Piston 5 advances toward piston 9 and draws in a new charge of fuel-air mixture through porthole 96, while piston 8 moves slightly to cover the exhaust porthole 106. At the same time piston exhausts the burnt gases through porthole 107. Piston 6 now completes the power stroke and uncovers porthole 103 ready to exhaust the burnt gases. At the same time it compresses the charge against piston 3 within space 76 at ignition position 89 and is ready to be ignited by the two spark plugs 57 and 59. Piston 7 draws in a new charge of fuel-air mixture through porthole 94, while piston 3 advances slightly to cover the exhaust port 104. At the same time piston 7 exhausts the charge through porthole 105. Piston 8 completes the power stroke and uncovers the exhaust porthole 106 ready to exhaust the burnt gases. At the same time piston advances and compresses the charge against piston 5. The compressed charge within space 76 at ignition position 91 is ready to be ignited by the two spark plugs 41 and 43. Piston 9 draws in a fresh charge of fuel-air mixture through porthole 97, while piston 5

advances slightly to cover exhaust porthole 107. At the same time piston 9 exhausts the burnt gases through porthole 102. The movement of the pistons through 120 degrees rotation and one complete revolution of the output shaft have been completed. The piston input/shaft output angular rotational relationship using the second order non-circular gears is given by the following relationship : ei2 = (po- (N3/N4) [tan-'(a/b) tanquo] For the third order non-circular gears shown in figure 19, the piston input/shaft output angular rotational relationship is given by the following relationship : ei3 = (po-2/3 (N3/N4) [tan-' (a/b) tan (3/2) (po] For the fourth order non-circular gears shown in figure 20, the piston input/shaft output angular rotational relationship is given by the following relationship : 0i4 = (po-1/2 (N3/N4) [tan-'(a/b) tan2ço] wherein oui2, Ai3, Oi4 are the piston input rotation in degrees using second, third and fourth order non-circular gears respectively, (po is the shaft output rotation associated with the corresponding order of gears, N3/N4 is the ratio or circular gears, a is half the major axis of the non-circular gear contour, b is half the minor axis of the non-circular gear contour. For the fifth and higher order non-circular gears, the following relationship between piston input/shaft output angular rotation applies to the repetitive sections of the associated non- circular contours: IF2VI + IF3VI = k wherein the arc between the two apexes of the non-circular gear is a sector of an ellipse.

This sector along the perimeter of the non-circular gear repeats itself between each apex or pointed tip and k is a constant number defined bythe geometry of the non-circular gear and provides an infinite number of options from which selections will need to be made for any preferred embodiment and given by the following generic relationship.

6im = (po- (2/m) (N3/N4) [tan-" (a/b) tanipo] wherein m is the order of the non-circular gear and 0im is the generic piston input rotation

in degrees using mth order non-circular gear. Other terms are as described above.

Figure 23 shows three identical and equally sized engines, motors, pumps or compressors 110,112 and 114 wherein mechanical shaft coupling 116, between 110 and 112, and mechanical shaft coupling 118, between 112 and 114, are used to obtain three times the output power at the power takeoff shaft 120 of one, or requires three times the power input of one at the input shaft 120.