Abstract:
A gearset including an internal ring gear; a first pinion gear disposed within the internal ring gear and having teeth meshing with teeth of the internal ring gear; a disc having a central axis collinear with a central axis of the internal ring gear and a slot along a portion of a diameter of a first side thereof; a first pinion shaft having a first end, a second end, and an offset driving lug extending from the second end, the first pinion shaft extending through a hole of the first pinion gear, the offset driving lug of the first pinion shaft engaging with a first end of the slot; a second pinion gear disposed with the internal ring gear and having teeth meshing with teeth of the internal ring gear, the teeth of the second pinion gear not meshing with the teeth of the first pinion gear; a second pinion shaft having a first end, a second end, and an offset driving lug extending from the second end, the second pinion shaft extending through a hole of the second pinion gear, the offset driving lug of the second pinion shaft engaging with a second end of the slot.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a Section 111(a) application relating to and claiming the benefit of commonly owned, co-pending U.S. Provisional Patent Application Ser. No. 61/945,877 entitled “PLANETARY CRANK GEAR DESIGN FOR INTERNAL COMBUSTION ENGINES,” filed Feb. 28, 2014, the entirety of which is incorporated herein by reference. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The exemplary embodiments relate to an internal combustion engine with improved torque characteristics, and, more particularly, to an internal combustion engine having a planetary crank gear mechanism having a piston and a connecting rod that are caused to travel along a straight line in axial alignment with the engine&#39;s cylinder. 
       BACKGROUND OF THE INVENTION 
       [0003]    Internal combustion engines, such as those used in automobile engines, are typically of the reciprocating type in which a piston moves up and down in a cylinder, transmitting its motion through a connecting rod to a crankshaft to convert heat energy into the mechanical work that drives the vehicle. Over the years, research has continued to improve the internal combustion engine, but such engines have yet to reach their full potential. Even the most modern internal combustion engines convert only one third of the energy of the consumed fuel into useful work. The rest of the energy is lost to waste heat, to the friction of moving engine parts, or to pumping air into and out of the engine. One of the major reasons for the low efficiency of internal combustion engines is the variation of the gas pressure in the cylinder, which drops dramatically as the piston travels downward. The most significant reason for this is the increase in gas volume within the cylinder as the piston descends. 
         [0004]    In any conventional engine, the gas pressure within the cylinder is at its maximum immediately after combustion of the fuel-air mixture, when the piston is at the top of its stroke. At this point, the piston, connecting rod and crankshaft are aligned with the center line of the cylinder bore. This position is commonly known as Top Dead Center (“TDC”). Also at this time, the angle formed between the connecting rod and the crankshaft is effectively 0 degrees. Because of this alignment, no torque can be imparted to the crankshaft. As the crankshaft rotates out of the 0 degree mark, the angle between the connecting rod and the crankshaft increases, allowing the gas pressure within the cylinder to drive the piston downward with great gas force. This gas force, which is conveyed to the crankshaft via the connecting rod, in turn, drives the crank pin of the crankshaft, forcing it to rotate and produce torque. This occurs between 0 degrees and 180 degrees or one half of a complete revolution of the crankshaft. This is commonly known as the power stroke of the engine (in reality, the effective power stroke is less than 180 degrees of rotation). It is the rotational torque of the crankshaft that provides useful mechanical energy. 
         [0005]    With most engines, this torque reaches its highest value when the crankshaft has rotated 30 to 35 degrees past TDC. At this point, the piston has traveled approximately 25% of its total stroke. Because the piston has traveled down by this amount, the gas volume within the cylinder has increased substantially. This increase in gas volume reduces the gas pressure within the cylinder by 50% or more. As the crankshaft continues to rotate, a point is reached where the angle formed between the connecting rod and the crankshaft is 90 degrees. This point is commonly considered to be the point of maximum leverage. For most engines, the point of maximum leverage, where the angle between the connecting rod and the crankshaft is 90 degrees, occurs when the crankshaft has rotated 70 to 75 degrees past TDC. At this point, the gas pressure within the cylinder has dropped to about 30% of its initial value. When the crankshaft has rotated to 90 degrees past TDC, the piston has traveled almost 60% of its entire stroke and the remaining gas pressure within the cylinder has dropped to less than 20% of its initial value. The remaining 90 degrees of the power stroke effectively produces very little torque. 
         [0006]    It is therefore obvious that engines of this type are inherently inefficient. The average automobile engine to date is only about 20 percent efficient. The most sophisticated prototypes to date achieve an efficiency of just over 40 percent. These prototype engines are diesel engines, which, because of their much higher compression ratios, are inherently more efficient than gasoline engines. This is in itself a remarkable achievement, but these engines operate under ideal laboratory conditions. If these engines were to be put to use in everyday automobiles, their efficiency would be reduced. This still leaves a lot of room for further improvements. 
         [0007]    Past attempts to enhance the reciprocating piston engine motion have utilized the principles of hypocycloid motion to provide a means of converting a straight line motion of a piston rod to a rotational motion. These previous attempts utilize hypocycloid gearing mechanisms to obtain strict rectilinear motion of the connecting rod to eliminate the piston side thrust. However, these prior attempts have multiple gears and counterweights, and would be difficult to assemble/disassemble. A radical design change of at least some of the components in the conventional engine would be needed in order to achieve a substantial increase in engine efficiency. 
       SUMMARY OF THE INVENTION 
       [0008]    A first exemplary embodiment introduces a design change to the conventional internal combustion engine by replacing the crankshaft with a planetary crank gear mechanism. One effect of the exemplary embodiments is to increase engine efficiency by minimizing the dramatic gas volume change within the cylinder as the piston moves through the engine stroke. A second exemplary embodiment requires additional components, but allows conversion of more of the available heat energy to mechanical energy. This additional improvement is mechanical and is incorporated within the planetary crank gear mechanism. This second exemplary embodiment allows for the greatest increase in efficiency. The exemplary embodiments are applicable to any type of multiple-cylinder engines, generators, compressors, pump fields, and similar devices employing crank shafts and pistons. 
         [0009]    In the first exemplary embodiment, a crankshaft with a planetary crank gear mechanism includes a piston and a connecting rod that are caused to travel along a straight line axially of a cylinder. As a result, this linear motion eliminates the side load on the piston because the connecting rod never pushes sideways on the cylinder wall. Friction between the piston and the cylinder wall is substantially reduced, which translates to greater mechanical energy output. Moreover, the planetary crank gear mechanism of the exemplary embodiments provides a period of much slower piston downward motion during the period of combustion to expend energy on the top of the piston for a longer time per degree of power stroke rotation. It also allows for an increase in the output torque of the planetary crank gear system, as compared to a conventional engine with similar stroke length, by about fifteen to twenty five percent. 
         [0010]    For a further improvement in the engine efficiency, in a second exemplary embodiment, additional components are added which are driven by the pinion shafts of the planetary crank gear system. It is the combination of the original planetary crank gear mechanism with these additional components that increases the overall efficiency of the exemplary embodiments. The additional components keep all of the rotating components of the exemplary embodiments in alignment with each other, share the loads, increase the effective crank length, and provide a means to balance the motion of the reciprocating components In the second exemplary embodiment, it nearly perfectly-balanced one-cylinder engine can be achieved. With a properly developed system of this type it may be possible to achieve twice the output torque of any conventional engine of equal displacement while using the same amount of fuel. 
     
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         [0011]    For a more complete understanding of the present invention, reference is made to the following detailed description of exemplary embodiments considered in conjunction with the accompanying drawings, in which: 
           [0012]      FIG. 1  is a schematic isometric view of a planetary crank gear system for a one cylinder engine of an embodiment of the present invention; 
           [0013]      FIG. 2  is an exploded schematic view of the planetary crank gear system components of an embodiment of the present invention shown in  FIG. 1 ; 
           [0014]      FIG. 3  is a schematic full-sectional front view of the single piston and associated planetary crank gear system assembly of an embodiment of the present invention shown in  FIG. 1 , and also showing the piston is at the top dead center of travel; 
           [0015]      FIG. 4  is a schematic cross-sectional plan view of the mechanical movement of an embodiment of the present invention; 
           [0016]      FIG. 5  is a plot of the linear displacement of the piston vs. degrees of driven disc or carrier rotation over one complete engine cycle for an embodiment of the present invention and for a conventional internal combustion engine, where both engines have equal stroke lengths; 
           [0017]      FIG. 6  is a plot of the percentage of the chamber volume above the piston face vs. degrees of driven disc or carrier rotation over one complete engine cycle for an embodiment of the present invention and for a conventional internal combustion engine, where both engines have equal stroke lengths; 
           [0018]      FIG. 7  is a plot of the linear velocity of the piston vs. degrees of driven disc or carrier rotation over one complete engine cycle for an embodiment of the present invention and for a conventional internal combustion engine, where both engines have equal stroke lengths; 
           [0019]      FIG. 8  is a plot of the linear acceleration of the piston vs. degrees of driven disc or carrier rotation over one complete engine cycle for an embodiment of the present invention and for a conventional internal combustion engine, where both engines have equal stroke lengths; 
           [0020]      FIG. 9  is a plot of the torque comparison of an embodiment of the present invention vs. a conventional internal combustion engine over one complete engine cycle for an initial force that decreases with the piston displacement, where both engines have equal stroke lengths; 
           [0021]      FIG. 10  is a schematic exploded isometric view of the additional components of the exemplary planetary crank gear system shown in  FIG. 1  which are driven by the pinion shafts of the planetary crank gear mechanism in an embodiment of the present invention; 
           [0022]      FIG. 11  is a schematic illustration of the driving lug path of an embodiment of the present invention over one complete planetary carrier revolution; 
           [0023]      FIG. 12  is a plot showing the effect of different driving lug offsets on the piston displacement in an embodiment of the present invention; 
           [0024]      FIG. 13  is a plot of the magnitude of the driving lug velocity around an elliptical path of an embodiment of the present invention over one complete engine cycle; 
           [0025]      FIG. 14  is a theoretical gas pressure diagram of an embodiment of the present invention vs. a conventional internal combustion engine over one complete engine cycle, where both engines have equal stroke lengths; 
           [0026]      FIG. 15  is a plot of the output torque of an embodiment of the present invention vs. a conventional internal combustion engine over one complete engine cycle, where both engines have equal stroke lengths; and 
           [0027]      FIGS. 16(A) through 16(G)  are schematic illustrations of engine layouts for embodiments of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0028]    Referring to  FIGS. 1 through 3 , a planetary crank gear system  1  for a one cylinder engine according to a first exemplary embodiment includes two identical gearsets  2  (on the left side of  FIG. 1) and 3  (on the right side of  FIG. 1 ) mounted back-to-back with enough space between them to allow room for a crank pin  4 . The space between the two gearsets  2 ,  3  is for the crank pin  4 , which is journalled within one end of a connecting rod  5 . The other end of the connecting rod  5  is attached to the bottom of a piston  6  by a joint  60 . The piston  6  slides up and down through a cylinder head  7 . Internal ring gears  8 ,  9  are fixed in place, such that they are attached to a crankcase  10  portion of the engine block, and do not rotate with respect to the crankcase  10 . The rotating members of the planetary crank gear system  1 , which are described in detail hereinafter, rotate with respect to the fixed internal ring gears  8 ,  9 . In each gearset  2 ,  3 , there are two planet pinion gears  11 ,  12  for gearset  2 , and two planet pinion gears  13 ,  14  for gearset  3 . Each planet pinion gear  11 ,  12 ,  13 ,  14  has equal pitch diameter and has exactly one-half of the number of teeth as the internal ring gears  8 ,  9  to utilize the principles of hypocycloid motion. The planet pinion gears  11 ,  12 ,  13 ,  14  comprising the same one of the gearsets  2 ,  3  are mounted 180 degrees apart from each other (e.g., planet pinion gears  11  and  12  are mounted 180 degrees apart from each other and planet pinion gears  13  and  14  are mounted 180 degrees apart from each other). The planet pinion gears  11 ,  12 ,  13 ,  14  are also offset axially (see  FIG. 3 ) to prevent the gear teeth of pinion gears  11 ,  12 ,  13 ,  14  from interfering with each other. The planet pinion gears  11 ,  12 ,  13 ,  14  are mounted within conventional pinion carrier assemblies  16 ,  17 . 
         [0029]    The pinion carrier assemblies  16 ,  17  are supported by shafts  18 ,  19  extending from the centerline of the carrier assemblies  16 ,  17  on one side of each gearset  2 ,  3 , respectively. The inside of each carrier assembly  16 ,  17  does not have a support shaft. The interspace between the inner faces of the carrier assembles  16 ,  17  allows room for the crank pin  4  to pass as it reciprocates up and down. Pinion shafts  20 ,  21 ,  22 ,  23  on which the planet pinion gears  11 ,  12 ,  13 ,  14  are mounted are fixed to these planet pinion gears  11 ,  12 ,  13 ,  14 , respectively, and, therefore, rotate together. The pinion shafts  20 ,  21 ,  22 ,  23  also pass through bearings  52 ,  54 ,  53  and  55 , respectively, before extending beyond the carrier assemblies  16 ,  17  on the outside of each unit. On the inside of the system  1 , one pinion shaft  20  from the left gearset  2  and one pinion shaft  21  from the right gearset  3  are directly connected through a web of material  56  and  57  to a journal (i.e., the crank pin  4 ). The center line  58  of the crank pin  4  is directly in line with the pitch circle  59  of the planet pinion gear  11 . This effectively forms the appearance of a conventional crankshaft comprising the pinion shaft  20 , the crank pin  4 , and the pinion shaft  21  (hereinafter referred to collectively as the “crankshaft”). The offset of the crank pin  4  in relation to the center line of the pinion shafts  20 ,  21  is only half that of a conventional engine of equal stroke; and the pinion shafts  20 ,  21  are used to drive the pinion gears  11 ,  13  and are not directly connected to the output shaft of the engine. The other two pinion gears  12 ,  14  in the respective gearsets  2 ,  3  are driven to rotate about the internal ring gears  8 ,  9  by the motion of the carriers  16 ,  17 , and act as idlers which also share the load and help to balance the entire rotating assembly. The inner sides of the pinion shafts  20 ,  21 ,  22 ,  23  (i.e., toward the crank pin  4 ) are supported by covers  24 ,  25 , which may be attached to the respective carriers  16 ,  17  with screws. According to the exemplary embodiment described with respect to  FIGS. 1 ,  2  and  3 , the piston  6  travels uniformly from top to bottom of the stroke and the connecting rod  5  travels in a purely linear motion. In some embodiments, the connecting rod  5  and the piston  6  can be formed as a single piece and the total weight of the piston  6  and the connecting rod  5  can be reduced. The exemplary embodiment eliminates the piston side thrust because the connecting rod  5  does not push sideways on the cylinder wall  7 , thus allowing for the use of new materials in engine design (e.g., ceramics). Therefore, burning various fuels at high temperatures, increasing engine efficiency, and eliminating exhaust pollution, may result. Moreover, the linear motion of the exemplary embodiments allows for a significant tightening of the tolerances between the piston  6  and the cylinder wall  7 , further increasing engine performance and reducing wear between the piston  6  and the cylinder wall  7 . 
         [0030]      FIG. 4  is a schematic cross-sectional plan view of the mechanical movement of an embodiment of the present invention. Referring to  FIG. 4 , one planet pinion gear  11  having half the pitch diameter of the internal ring gear  8  (e.g., the diameter of pitch circle  59  of planet pinion gear  11  is equal to half the diameter of pitch circle  63  of the internal ring gear  8 ) is keyed to the left pinion shaft  20  at the end of the crankshaft  20 - 4 - 21  and meshes with the internal ring gear  8 . The distance  26  between the center of the crank pin  4  and the center of the planet pinion gear  11  is equal to one-fourth of the stroke length  27  or the pitch radius of the planet pinion gear  11 . When the piston  6  moves from the TDC to the bottom dead center (“BDC”) position, indicated in  FIG. 4  with the outline of the piston  6  shown in dashed lines, the planet pinion gear  11  is turned around the axis of the left pinion shaft  20 . This rotation is forced by the gas force acting on the crank pin  4  through the connecting rod  5 . As described above, planet pinion gear  12 , which has a pitch circle  61  with equal diameter to that of pitch circle  59 , acts as an idler and rotates about internal ring gear  8  in opposition to the planet pinion gear  11 . Since the planet pinion gear  11  makes one revolution for each revolution of the crankshaft  20 - 4 - 21 , the center of the crank pin  4  will travel up and down in a perfect straight line with a stroke length  27  equal to the pitch diameter of the internal ring gear  8 . This allows for engine designs having any desired stroke length. With this arrangement, the linear distance traveled by the crank pin  4  is equal to the pitch diameter of the internal ring gear  8  or  9 , which determines the engine&#39;s stroke length  27 . In the exemplary embodiments, the length of the connecting rod  5  is greater than or equal to the stroke length  27 . 
         [0031]      FIG. 5  shows displacement curves of the piston  6  of the exemplary embodiments in comparison to a displacement curve for a conventional engine. Displacement curve  510  corresponds to the first exemplary embodiment described above with reference to  FIGS. 1 ,  2  and  3 . Displacement curve  520  corresponds to a second exemplary embodiment including a driving lug offset, which will be described in further detail below. Displacement curve  530  corresponds to a conventional engine. As can be seen, the piston displacement curves  510  and  520  of the exemplary embodiments show that the piston  6  travels uniformly from the top to the bottom of the stroke over a longer time than for a conventional engine of similar displacement, as shown by displacement curve  530 . When the output shafts  18 ,  19  of the exemplary embodiment of  FIGS. 1 ,  2  and  3  are at 90 degrees, the piston  6  has traveled exactly 50% of the stroke length  27 . In a conventional engine, this is not the case because of the angle of the connecting rod: the piston travels approximately 60% of its stroke in the first 90 degrees, and the 50% stroke positions occur at approximately 81 degrees before and after TDC. This 10% difference provides a period of much slower downward motion of piston  6  during the period of combustion, thereby expending energy at the top of piston  6  for a longer time per degree of power stroke rotation of the exemplary embodiments. This effectively reduces the rate of change in gas volume during the combustion period after TDC, as also shown in  FIG. 6 . 
         [0032]      FIG. 6  shows gas volume of the combustion chamber for various cylinders. Volume curve  610  corresponds to the first exemplary embodiment described above with reference to  FIGS. 1 ,  2  and  3 . Volume curve  620  corresponds to the second exemplary embodiment including a driving lug offset. Volume curve  530  corresponds to a conventional engine. The curves shown in  FIG. 6  demonstrate a much slower rate of the change in gas volume of the combustion chamber for the exemplary embodiments than for the conventional engine. For example,  FIG. 6  compares the change in gas volume of the combustion chamber at 60 degrees after TDC for an engine according to the exemplary embodiments (15% with driving lug offset, as shown in displacement curve  520 , and 25% without driving lug offset, as shown in displacement curve  510 ) with the change in gas volume for the conventional engine at the same position (32%). This difference in the gas volume change between the two types of engines has a significant effect on the gas pressure and engine performance. Because the piston has traveled a smaller linear distance within the cylinder as the crankshaft approaches its point of maximum leverage at 90 degrees, and, therefore, continues to be subject to a greater force from gas pressure within the cylinder, the torque output of an engine according to the exemplary embodiments is generally higher than that of a conventional engine of similar displacement. 
         [0033]      FIG. 7  shows curves of piston velocity for various cylinders. Velocity curve  710  corresponds to the first exemplary embodiment described above with reference to  FIGS. 1 ,  2  and  3 . Velocity curve  720  corresponds to the second exemplary embodiment including a driving lug offset. Velocity curve  730  corresponds to a conventional engine. It can be seen that, at TDC and BDC, the piston velocity is zero for both the exemplary engines and a conventional engine. This is because the piston  6  reverses direction at TDC and BDC in order for the velocity to go from a “plus” to a “minus”. The maximum velocity of piston  6  in the conventional engine occurs at about 74 degrees before and after TDC, not at 90 degrees before and after TDC as in the exemplary embodiments. The asymmetric velocity profile of the conventional engine is a result of the geometry characteristics which cause the dissymmetry in piston motion. Such dissymmetry does not occur in the exemplary embodiments, in which, when the carrier assembly  16  and  17  is rotated, the velocity of the reciprocating motion of the crank pin  4  follows a sinusoidal pattern. At the 0 degree of rotation (i.e., in the TDC position), the crank pin  4  is stationary. As the carrier assemblies  16 ,  17  are rotated, the crank pin  4  begins to accelerate, reaching a maximum linear velocity at 90 degrees past TDC. With the continued rotation of the carrier  16  and  17  from the 90 degrees position to the BDC at 180 degrees, the crank pin  4  decelerates until it is again stationary. There are no abrupt starts and stops involved with the linear motion of the crank pin  4  in the exemplary embodiments, allowing for smooth operation at high RPMs. The effective RPM range of an engine using the exemplary embodiments is similar to that of conventional engines. 
         [0034]      FIG. 8  shows curves of piston acceleration for various cylinders. Acceleration curve  810  corresponds to the first exemplary embodiment described above with reference to  FIGS. 1 ,  2  and  3 . Acceleration curve  820  corresponds to the second exemplary embodiment including a driving lug offset. Acceleration curve  830  corresponds to a conventional engine. It can be seen that the piston acceleration and deceleration of the conventional engine are greater in the top half of the crankshaft rotation than in the bottom half, because the connecting rods are not infinitely long, resulting in a non-sinusoidal motion. At TDC and BDC, the piston is reversing its direction of motion, so piston velocity is zero, but that velocity is changing very rapidly, producing large values of acceleration. This explains why failure of the connecting rod of a conventional engine often occurs at the point. As shown by acceleration curves  810  and  820 , in the exemplary embodiments, the maximum acceleration found at TDC and BDC are more symmetric. Further, acceleration curve  820  shows that the driving lug offset of the second exemplary embodiment, which will be described in further detail below, can be used to optimize the peak acceleration at TDC and BDC, moving those two peaks closer to the same value. 
         [0035]      FIG. 9  is a plot comparing the torque generated by the exemplary embodiments to that generated by a conventional engine, over one complete engine cycle, for an initial force of 100 pounds that decreases with the piston displacement, where both engines have equal stroke. Torque curve  930  indicates the torque generated by a conventional engine. The planetary crank gear system  1  of the first exemplary embodiment increases the output torque of the supported shafts  18  and  19  of the planetary assemblies  16  and  17  by about sixteen percent over the conventional engine of similar stroke length by themselves, as shown by torque curve  910 . A greater increase in engine efficiency can be obtained through the use of the additional components (driving lugs  28 ,  29 ,  30  and  31 ) in the planetary crank gear system  1  of the second exemplary embodiment. These additional components, which are described more fully herein below, are driven by the pinion shafts  20 ,  21 ,  22 ,  23  from the planetary crank gear system  1 . Torque curve  920  of  FIG. 9  illustrates the torque generated by the second exemplary embodiment, which incorporates a driving lug offset  32 . As can be seen, the generated torque is increased by about 115% over the conventional engine of similar stroke length. 
         [0036]      FIGS. 3 ,  10  and  11  illustrate the additional components introduced in the enhanced planetary crank gear system  1  of the second exemplary embodiment. An additional mechanism, discussed hereinafter, is added to the planetary crank gear system  1  described above with reference to  FIGS. 1-3  to increase further the overall efficiency of the exemplary embodiments. For simplicity, only the left side, including pinion shafts  20 ,  22 , encircled in  FIG. 10 , will be described herein, since the right side, including pinion shafts  21 ,  23  is essentially a mirror image of the left side. Extending from the end of the pinion shafts  20  and  22  are two smaller diameter stub shafts, which will be referred to herein as driving lugs  28  and  29 . The position of the center line of the driving lug  28  is offset by driving lug offset  32  from the center line of the pinion shaft  20 , as shown in  FIG. 3 . The direction of the driving lug offset  32  is approximately opposite the crank pin journal  4 . When the pinion shaft  20  rotates, the driving lug  28  orbits around the center of rotation of the pinion shaft  20 . As the entire planetary crank gear system  1  is rotated 360 degrees, the path of the driving lugs  28  and  29  is an ellipse  33 , as shown in  FIG. 4  and  FIG. 11 . The X-axis (top to bottom length) of this ellipse is the small axis, while the Y-axis (left to right) is the large axis. The dimensions of the ellipse  33  are determined by the stroke of the crank pin  4  (i.e., engine stroke  27 ) and the size of the driving lug offset  32 . Sliding bearings  34   35 ,  36  and  37  are fitted over the driving lugs  28 ,  29 ,  30  and  31 . 
         [0037]    Still referring to  FIGS. 3 ,  10  and  11 , the driving lugs  28  and  29 , with corresponding sliding bearings  34  and  35 , are then indexed into slots  42  and  43  in a disc  38 , which correspond to slots  44  and  45  on the opposite side of the planetary crank gear system  1 . The disc  38  is then driven by the driving lugs  28 ,  29 . The disc  38  is centered over the planetary carrier support shaft  18  and has an output shaft  40  extending from the side opposite the slots  42 ,  43 . The side of the disc  38  having slots  42 ,  43  across its face also has a hole  46  in its center. The central hole  46 , which corresponds to central hole  47  in disc  39 , extends into the shaft portion of the disc  38  to allow room for bearing  49 , which supports the planet carrier assembly  16 , and which correspond to bearing  50  supporting the planet carrier assembly  17 . The outside of the shafts  40  and  41  are supported by bearings  48  and  51 , respectively, which are mounted in the lower crankcase  10  portion of the engine block. The power output torque of the engine is taken from the shaft  40 . Since there are two complete planetary gearsets  2 ,  3  mounted back-to-back, as shown in  FIG. 1 , there are also the two driven discs  38 ,  39  and the two output shafts  40 ,  41 . 
         [0038]    The exemplary embodiments include a shaft (not shown) extending from both ends of the engine block. In the case of the exemplary embodiments, both output shafts (not shown) are independent parts. For several reasons, both of these shafts need to be synchronized with each other. The first and most important reason is to keep all of the rotating components in alignment with each other. The second reason is to allow both assemblies (i.e., gearsets  2  and  3 ) to share the work load. The third reason, in the case of a single cylinder engine, is to provide a means to balance the motion of the reciprocating components. Balancing of the rotating components can be achieved within the gearsets  2  and  3  alone. 
         [0039]    A gear-driven shaft (not shown), commonly known as a jackshaft, is mounted between the front and back output shafts adjacent to the gearsets  2  and  3 . In the case of a single cylinder design, two shafts are needed. For balancing purposes, these shafts should rotate in opposite directions with respect to each other. Also, both of these shafts should rotate at the same speed as the output shafts  40 ,  41 . Each of these shafts has a counterweight attached to them. The counterweights are used to counterbalance the action of the reciprocating components within the engine. With this design, it should be possible to achieve a nearly perfectly-balanced one-cylinder engine. In the case of a properly-designed engine with an even number of cylinders, no counter balancing should be required. In this case, a single shaft may be used. 
         [0040]    Referring to  FIGS. 4 ,  5 ,  6  and  11 , the design of the exemplary embodiments allows for a variable leverage point between the planetary carrier assembly  16  and the output shaft  40 . In the exemplary embodiments, this is accomplished through the combination of offset driving lugs  28 ,  29 ,  30 ,  31  on the pinion shafts  20 ,  21 ,  22 ,  23  and the slotted driven discs  38 ,  39 . As the planetary crank gear system  1  is rotated from the 0 degree position to the 90 degree position, the effective leverage angle formed between the driving lugs  28 ,  29 ,  30 ,  31  and the center of rotation of the slotted discs  38 ,  39  increases from a minimum amount to a maximum amount. During this phase of operation, the driving lugs  28 ,  29 ,  30 ,  31  travel toward the outer edge of the driven discs  38 ,  39 . This, in turn, increases the amount of leverage between the driving lugs  28 ,  29 ,  30 ,  31  and the center line of rotation of the driven discs  38 ,  39 . The purpose of this is to increase the effective moment arm provided by the crankshaft to provide a far greater output torque up to and also beyond the 90 degree position of rotation as compared to a conventional engine of similar stroke length, as shown in  FIG. 9 . 
         [0041]    Torque generated at any given time by the second exemplary embodiment, including offset driving lugs  28 ,  29 ,  30 ,  31 , may be expressed in terms of the gas force F g ; the angle β between the vertical center line of the piston and the line connecting the center of the crank pin  4  to the center of the driven pinion shafts  20  and  22 ; the angle θ between the vertical center line of the piston  6  and the line connecting the center of the internal ring gears  8 ,  9  to the center of the driving lugs  28 ,  30 ; the crank length L c  (e.g., the radius of the pitch circles  59  and  61 ); the linear offset distance δ (e.g., the driving lug offset  32 ); and the current ellipse radius distance R(θ).  FIG. 11  illustrates these parameters in relation to the elements of the second exemplary embodiment. The torque, as plotted in  FIGS. 9 and 15 , may be calculated according to the expression: Torque=F g *{2*R(θ)*sin(θ)+[L C +δ]*sin (β)}. 
         [0042]    As described above, in one exemplary embodiment, a driving lug offset  32  is present between the center lines of pinion shafts  20 ,  21 ,  22  and  23  and the respective center lines of driving lugs  28 ,  29 ,  30  and  31 . With no offset, as in the first exemplary embodiment described above, the center lines of the pinion shafts  20 ,  21 ,  22  and  23  will be coincident with the respective center lines of driving lugs  28 ,  29 ,  30  and  31 . In such an embodiment, the path of the driving lugs  28 ,  29 ,  30  and  31  is a circle  62  with diameter equal to half of the stroke length  27 . In this embodiment, the maximum moment arm is equal to one-fourth of the stroke length when the output shafts are at 90 degrees past TDC. As described above with reference to the second exemplary embodiment, to increase the effective moment arm offered by the crankshaft  20 - 4 - 21 , the center lines of the driving lugs  28 ,  29 ,  30  and  31  are moved away from the respective center lines of the pinion shafts  20 ,  21 ,  22  and  23  by the desired driving lug offset  32 .  FIG. 12  shows the effect of different values of the driving lug offset  32  on displacement curves for piston  6  while traveling from TDC to BDC. As the entire planetary crank gear assembly  1  rotates, the path of the driving lugs  28 ,  29 ,  30  and  31  is an ellipse  33 , as shown in  FIG. 11 . The length of the semi-major axis of this ellipse  33  is equal to the sum of the crank length  26  and the driving lug offset  32 , represents the effective moment arm provided by the crankshaft  20 - 4 - 21 . 
         [0043]    The curves shown in  FIG. 12  correspond to varying values of λ, which represents the size of the driving lug offset  32  as a ratio to the crank length  26 , and which is determined by dividing the driving lug offset  32  by the pitch radius of the planet pinion gears  11 ,  12 ,  13  and  14 . Curve  1210  shows linear displacement of the piston  6  plotted against rotation of the carrier assemblies  16  and  17  for a value λ=0 (i.e., for the first exemplary embodiment in which no driving lug offset  32  is used). Curves  1220 ,  1230 ,  1240 ,  1250  and  1260  show linear displacement of the piston  6  plotted against rotation of the carrier assemblies  16  and  17  for varying values of λ in the second exemplary embodiment, in which a driving lug offset  32  is used. Curve  1220  corresponds to a value λ=0.1, curve  1230  corresponds to a value λ=0.2, curve  1240  corresponds to a value λ=0.3, curve  1250  corresponds to a value λ=0.4, and curve  1260  corresponds to a value λ=0.5. As can be seen in  FIG. 12 , the rate of change of gas volume within the cylinder  7  varies according to the position of the piston  6 , and is a function of the driving lug offset  32 . Thus, the size of the driving lug offset  32  may be used to control the rate of change of the volume of the compressed gas in a combustion volume above the face of the piston  6  to produce more rotary power during the combustion period after TDC. 
         [0044]    Referring to  FIG. 13 , another factor also helps to improve the power output with the second exemplary embodiment described above. This is the fact that the rotational relationship between the planetary carrier assembly  16  and the driven disc-output shaft  38  is not uniform. If the driven disc  38  is rotated at a constant angular velocity, the angular velocity of the planetary carrier assembly  16  will fluctuate up and down. This fluctuation in angular velocity occurs two times per revolution. The amount of this fluctuation is directly related to the amount of offset  32  of the driving lugs  28 ,  29 . When the driven disc  38  is rotating at a constant speed, the speed of the planetary carrier assembly  16  is at its slowest at the 0 degree (i.e., TDC) position and the 180 degrees (i.e., BDC) position. The speed of the planetary carrier assembly  16  is at its highest value at the 90 degrees and 270 degrees positions. The average speed of the planetary carrier assembly  16 , which occurs four times per revolution, is equal to the speed of the driven disc  38 . 
         [0045]      FIG. 14  shows the compression and combustion pressure in the second exemplary embodiment as compared to those of a conventional engine. Curve  1410  shows compression pressure for the second exemplary embodiment. Curve  1420  shows combustion pressure for the second embodiment. Curves  1430  and  1440  show compression pressure and combustion pressure, respectively, for a conventional engine. It may be seen that the compression and the combustion pressures in the second exemplary embodiment are greater before and after the TDC than those of a conventional engine of similar stroke length. The same may be true of the first exemplary embodiment. The greater gas pressure helps to generate greater gas force exerted on the top of the piston in the exemplary embodiments. 
         [0046]      FIG. 15  shows torque output in the second exemplary embodiment as compared to that of a conventional engine. Curve  1510  shows torque output of the second exemplary embodiment, while curve  1520  shows torque output of a conventional engine. It may be seen that, as a result of the greater compression and combustion pressures shown in  FIG. 14 , the mean torque output from the output shafts  40 ,  41  over one cycle is 83% greater for the second exemplary embodiment for the conventional engine. Achieving twice the power output torque of any conventional engine of equal displacement while using the same amount of fuel is obtainable. 
         [0047]    Conventional engines may be constructed according to an array of different designs, including single, in-line, opposed, and V-Type designs. FIGS.  16 (A)-(G) show exemplary embodiments that are equivalent counterparts to known conventional engines.  FIG. 16(A)  shows an exemplary embodiment including a single cylinder, as described above.  FIG. 16(B)  shows an exemplary in-line engine having four cylinders arranged, one after the other, in a straight line. Due to the perfect linear motion of the piston  6  and the connecting rod  5  in the exemplary embodiments, a second cylinder can be easily added to the same crank pin journal  4 , with two pistons connected with one connecting rod and firing consecutively, as shown in  FIG. 16(C) . Other exemplary embodiments are comparable to Boxer/Flat engines with multiple pistons that all move in the horizontal plane, as shown in  FIG. 16(D)  with four cylinders and  FIG. 16(E)  with six cylinders.  FIG. 16(F)  shows an exemplary X-engine configuration having two reciprocating assemblies for a total of four pistons coupled to each crank pin bearing a crankshaft, in a manner similar to a conventional X-engine. An exemplary V-type engine may have two rows of cylinders set normally at a 90-degree angle to each other, as shown in  FIG. 16(G) . 
         [0048]    It should be understood that the embodiments of the invention described herein are merely exemplary and that a person skilled in the art may make many variations and modifications without departing from the spirit and scope of the invention. All such variations and modifications are intended to be included within the scope of the invention as defined in the appended claims.