Abstract:
In a nutating engine (or more generally a rotary displacement device) the cycling of combustion occurs between inner and outer spherical surfaces. The combustion chambers are additionally defined only by the surfaces of teeth of specially designed gears. These gears are the Rotator ( 2 ), two consecutive of some number of free-planetary gears ( 3 A-E), and the lobed Nutating Member ( 1 ). The latter is enjoined to execute precessional rotation relative to the former and maybe both affixed with counterweights ( 11 A,B;  12 A,B) and subjected to reverse-English transforming the precessional rotation to a stress-free mode in both the Newtonian and Eulerian sense. The insertion of optional butterfly-shaped plugs ( 4 A-E,  5 A-E,  8 A-E) boosts the compression ratio. Truly, no past engine possesses the characteristics of the instant invention.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
   Not applicable 
   FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
   Not applicable 
   REFERENCE TO SEQUENCE LISTING 
   Not applicable 
   BACKGROUND OF THE INVENTION 
   This invention pertains to certain improvements in rotary internal combustion engines in general and nutating engines in particular. 
   PRIOR ART 
   For more than a century engineers have had a dream of replacing the reciprocating piston engine with a rotary piston device. It had been hoped that by so doing the inherently stressful conditions of reciprocation could be obviated providing for a far less massive construction and a smoother action. The effort has met with limited success: the only palpable effort has been the Wankel Drehkolbenmotor which became operational in a commercial sense only after the prodigious effort on the part of metallurgists on three continents. The problem, of course, was the seals. 
   Another thread of design has been the nutating engine in general and the spherical engine in particular. The hope was that by availing oneself of of the natural motion as analyzed by Leonard Euler in 1760 of a symmetric body, namely the uniform rotation of this body as its axis of rotation simultaneously precesses, i.e., sweeps out a cone shape in three dimensional space, that the aformentioned stressless condition might be realized. 
   To manifest this idea most efforts have sought to enclose the process within the confines of a spherical cavity. This could immediately nullify the “Newtonian” stress by fixing the center of mass of the main displacement element, i.e. that which is analogous to the piston, at the sphere&#39;s center. (The Wankel does not share this benefit.) This relief however comes with a heavy bill to pay: Given that both the spherical cavity and the main displacement member are of constant volume, certainly what remains can not be naively utilized as a combustion chamber for its volume must, throughout the cycling, likewise remain constant. 
   To allay this predicament, the spherical combustion chamber has, over the century, seen itself partitioned in one way or another, always to Pyrrhic effect: 
   Typically in Meyer U.S. Pat. No. 5,251,594; Oct. 12, 1993 the partition necessitates the slotting of the main displacement member to the effect of precluding its actual rotation. With this there is no possibility of recovering any kind of hitherto mentioned, natural motion. Additionally the sealing problem is far greater than for even the Wankel. 
   Millet U.S. Pat. No. 6,325,038 B1; Dec. 4, 2001 cleverly skews the drive shaft at some angle to the combustion chamber axis rendering the chamber amenable to partition. Though the sealing problem is far more tractable than Meyer there is again no rotation of the main displacement element and so no possibility of exploiting a natural motion. 
   Lim U.S. Pat. No. 5,336,067; Aug. 9, 1994 is a spherical engine of a different nature. By utilizing two sequences of cusps which slide over each other within the spherical cavity he at least holds out the hope for manifesting a simultaneous natural rotation and precession of the main displacement elements though he makes no mention of this. Then, to alleviate wear and tear upon these cusps he introduces vaguely certain cams and cam followers not aware, apparently, of the corresponding loss in seal integrity that that would necessarily occasion. 
   The instant invention is in some way similar to Lim and in some way its diametric opposite. 
   BRIEF SUMMARY OF THE INVENTION 
   I submit a nutating engine in which, between inner and outer concentric spherical surfaces, according to one aspect of the instant invention, a progression of free-planetary gears are engaged with and only with both a substantially circular toothed Rotator as well as a toothed Nutating Member possessing some number of lobes and an equal number of interjacent arches, this number being different by unity to the number of free-planetary gears. In circumnavigating their latitude the phase lag of each free-planetary gear relative to the lobe&#39;s nadir subsequent to it will increment uniformly. (increment uniformily, if the number of lobes had been chosen to be 1 less than the number of free-planetary gears; decrement uniformly, if the number of lobes had been chosen to be 1 more than the number of free-planetary gears.) Additionally, all phase lags will advance with advancing time. Thus entrained the Nutating Member will be enjoined to execute perfect geometrical rotations and simultaneous precessions relative to the Rotator. 
   This motion will occasion the inter-planetary volumes to suffer expansions and contractions thus defining them as combustion chambers. 
   According to another aspect of the instant invention, the Nutating Member can be counterweighted to relocate its center of mass to that of the sphere whence the entire apparatus be imparted with a reverse-English about the Rotator&#39;s axis thus endowing the formerly mere geometrical precession with a natural-physical (as per Euler) character. Adding the observation that both the Rotator and the free-planetary gears describe but circles the overall result is an extremely stress-free, lightweight, easily sealed, and easily milled device. Finally, while the cavitation provided by the gearing will yield a high burn efficiency, the insertion of “butterflies” into the inter-planetary volumes will coax the compression ratio to well within the Diesel regime. 
   OBJECTS AND ADVANTAGES 
   The instant invention utilizes not a cusped but a lobed curve called the polaricider which demarcates the Nutating Member, the main displacement element. This plus a Rotator and not fixed cams, but a sequence of free-planetary gears define the combustion chambers. 
   So, one object of the proposed invention is to lay to rest the sealing problem: the tighter the entrainment of rotating elements the greater the seal integrity. 
   A much greater object is to render all of the combustion elements with a completely natural, stress-free motion, as will be seen infra. This will allow an unbelievably light-weight construction. 
   A third object is to reduce wear, tear, and maintenance to levels commensurate with those of electric motors. 
   Several other objects and advantages will become apparent in the succeeding argument. 

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       FIG. 1  is an exploded isometric view showing all of the systems except for the electrical, exhaust, and charge distribution systems. 
       FIG. 2  and  FIG. 3  are details of a free-planetary gear and a left “butterfly” wing respectively. 
       FIG. 4  is an external elevation with the spherical cover, the “butterflies”, and two of the drive chains removed. Additionally, the curved arrows indicate the rotation as well as the precession of the Nutating Member under the condition of a stationary Rotator. 
       FIG. 5  is an elevation identical in orientation to  FIG. 4  except with the spherical cover and drive chains replaced. Again, the curved arrows indicate the rotation and precession of the Nutating Member after submitting the entire engine to reverse-English. 
       FIG. 6  is an orthogonal cutaway from  FIG. 5  of the device excluding the Nutating Member, free-planetary gears, “butterflies”, and drive chains. 
       FIG. 7  is an overhead conical cutaway from  FIG. 5  at the level of the pushrods. The pusbrods themselves, their springs, and the intake cam are not cutaway. The curved arrows indicate the motion of the free-planetary gears and the rotation of the cams relative to the spherical covers. 
       FIG. 8  is a highly schematicized depiction of the intake cam indicating the less-tight septagranimic intake regimen. The curved arrow indicates the rotation of the cam relative to the spherical covers. 
       FIG. 9  is an external elevation of an alternate embodiment with the spherical cover and the (inverted) “butterflies” removed. The curved arrows indicate the rotation and precession of the 
       FIG. 10  is a highly schematized depiction of a disk-like object spinning and simultaneously precessing at a small angle of inclination. 
   

   REFERENCE NUMERALS IN DRAWINGS 
   
       
         1  Nutating Member 
         2  Rotator 
         3 A-E Free Planetary Gears 
         4 A-E “Butterfly” Left Wings 
         5 A-E “Butterfly” Right Wings 
         6 A-E “Butterfly” Left Wing Slots 
         7 A-E “Butterfly” Right Wing Slots 
         8 A-E “Butterfly” Springs (compressive) 
         9  Inner Spherical Cover 
         10  Outer Spherical Cover 
         11 A, B Counterweights and Arms without Pivots 
         12 A, B Counterweights and Arms with Pivots 
         13 A-D Gimbal Pintles 
         14  Inner Gimbal Ring 
         15  Outer Gimbal Ring with Sprocket Gear 
         16  Gimbal Drive Chain 
         17  Fixed Shaft 
         18  Rotator Shaft 
         19  Rotator Shaft Sprocket Gear 
         20  Rotator Shaft Drive Chain 
         21  Support Lip for Rotator Shaft 
         22  Cam Shaft 
         23  Cam Shaft Sprocket Gear 
         24  Cam Shaft Drive Chain 
         25  Support Lip for Cam Shaft 
         26  Upper Slip Ring for Distributor 
         27  Lower Slip Ring for Distributor 
         28  Cam and Distributor Canister Top Cover 
         29  Cam and Distributor Canister Lateral Cover 
         30  Cam and Distributor Canister Bottom Cover 
         31  Intake Valve Cam 
         32  Exhaust Valve Cam 
         33 A-D Spider Legs 
         34  Spinnable Seal 
         35  Charge Spiracle 
         36  Main Charge Distribution Hose 
         37 A-G Atrial Distribution Hoses 
         38 A-G Charge Atria 
         39 A-G Intake Valve Heads and Pushrods 
         40 A-G Exhaust Valve Heads and Pushrods 
         41 A-N Valve Springs (compressive) 
         42 A-G Spark Plugs 
         100 - 700  (by  100 &#39;s) Schematic Valve and Spark Plug Stations 
         901  Nutating Member in Alternate Embodiment 
         902  Stator (only in Alternate Embodiment) 
         915  Outer Gimbal Ring with Sprocket Gear in Alternate Embodiment 
         916  Gimbal Drive Chain in Alternate Embodiment 
         917  Fixed Shaft in Alternate Embodiment 
         922  Cam Shaft in Alternate Embodiment 
         923  Cam Shaft Sprocket Gear in Alternate Embodiment 
         924  Cam Shaft Drive Chain in Alternate Embodiment 
         925  Support Lip for Cam Shaft in Alternate Embodiment 
         942  Spark Plug in Alternate Embodiment 
     
  
   DETAILED DESCRIPTION OF THE INVENTION 
   It is acknowledged at the outset that the description offered of the instant invention together with certain unavoidable philosophical digressions is far more complicated than its operation which is really no different than a rotary version of a four-stroke piston engine. On the other hand this complexity is completely canonical in the sense that it flows freely from the main engendering principle: to exploit as combustion chambers the varying volumes associated with a completely stress-free precessional process. 
   STATIC DESCRIPTION OF A PREFERRED EMBODIMENT 
   The composition of the engine divides itself naturally into two main assemblies: the spherical (in this preferred embodiment: upper) and the strictly rotating (in this preferred embodiment: lower). 
   As for the former, what immediately follows (see  FIG. 1 ) takes place in the geometrical milieu located between the outside surface of an inner spherical cover  9  and the inside surface of an outer spherical cover  10  whence all other surfaces are ruled surfaces whose rulings originate at the sphere&#39;s center. So, for instance, the therein confined  5  identical free-planetary gears  3 A-E are each defined not by a “pitch circle” but by a “pitch cone” the apex of which coincides with the center of the sphere. The actual surfaces of their teeth are similarly ruled. This applies exactly to a large substantially circular gear  2 , the Rotator which is welded to the inner and outer spherical covers. And this applies to a 4-lobed (in this embodiment) gear  1 , the Nutating Member. 
   Geometrical Digression 
   The Nutating Member is a novel structure. The pitch surface which demarcates it is called a polaricider. It is defined primarily almost tautologically as that curve which will roll without slipping over the pitch cone of a free-planetary gear, itself rolling without slipping over the pitch cone of the Rotator as the latter executes a perfect geometrical rotation and simultaneous precession relative to the Nutating Member. In particular the polaricider is a mathematical curve whose exact shape is predetermined by a specification of it five parameters discussed infra. Just the definition, however, induces on the polaricider a number of symmetries: Each projecting lobe must be identical to every other and must possess in itself perfect mirror symmetry. The same is true of each interjacent arch. Any Nutating Member can be gauged by the angle subtended at the sphere&#39;s center between the Nutating Member&#39;s pole (see  FIG. 4 ) and the nadir of any one of its lobes. For our engineering purposes the polaricider must meet a second condition namely that its periodicity be such that self-intersections are precluded. A third is that the curvature at the apex of an arch be somewhat less than that of a free-planetary gear. 
   In that the free-planetary gears are indeed free and doubly engaged the polaricider bears relationship to neither a cycloid, nor any involute, evolute, nor any spherical analogue thereof. 
   By “rotation and simultaneous precession” is meant the lay notion of an object spinning uniformly about its symmetry axis as this axis uniformly rotates about a secondary (in this emodiment: verticle) axis (see  FIGS. 4 and 5 ) rather than the more exacting notion of an object&#39;instantaneous angular velocity {right arrow over (ω)}′(of constant magnitude ω′) itself precessing about a fixed (in this embodiment:verticle) axis with angular velocity {right arrow over (ω)} (of constant magnitude ω). 
   Any prospective machine which tightly spans the surface of the sphere may be specified by five freely chosen parameters. They are the subtended angles at the sphere&#39;s center of a free-planetary gear, the Rotator, and the Nutating Member; an integer parameter equal to the number of free-planetary gears; and a binary parameter + or −, indicating whether the Nutating Member possesses a number of lobes equal to one more or one less than the number of free-planetary gears. It is generally noted that the polaricider will both exist and be a uniquelly predetermined mathematical curve following a specification of these five parameters, as could be attested to by one skilled in the Art of Dynamic Systems. 
   Once the existence and uniqueness of the polaricider is apprehended it seems amazing that some number of free-planetary gears can be simultaneously entrained between the Rotator and the Nutating Member. Actually it is trivial: On the surface of the inner spherical cover entrain a single free-planetary gear with the Rotator and initially, say, the nadir of a lobe of the Nutating Member therewith tilting that lobe maximally away from the Rotator. Now let the entrainment run its course according to the design criterion. As subsequent lobes arrive at their maximal distance from the Rotator entrain yet another free-planetary gear. When all of the free-planetary gears have been so entrained the resulting configuration will be as in  FIG. 4 . Here we can think of the far left free-planetary gear which is in profile as possessing, relative to its engaged lobe, a phase equal to zero. The free-planetary gear to its right bears an absolutely symmetric position, relative to its engaged lobe, as the free-planetary gear which is occluded behind it. Its phase relative to its entrained lobe on the other hand should be thought of as equal but opposite to its occluded partner. Exactly the same two observations hold for the free-planetary gear visible on the far right. Equivalently, for this and all configurations, as their latitude is circumnavigated the phase lag of each free-planetary gear relative to the lobe&#39;s nadir subsequent to it (not necessarily the nadir of that lobe with which it is engaged) will uniformly increment. 
   This more exacting, less lay notion, is illustrated in  FIG. 10 .  FIG. 10  depicts all of the parameters that specify a stress-free motion of a disk-like object at a small inclination angle. The primed coordinate system (x′,z′) is attatched to the body (and body cone) and is depicted at a moment of maximal declination. I Z′Z′  and I X′X′  are moments of inertia about the axis of symmetry and a perpendicular axis, respectively. {right arrow over (L)} is the angular momentum. β and α are the half-apex angles of the (larger) body cone and the (smaller) inertial-space cone. The former rolls without slipping over the latter with instantaneous velocity {right arrow over (ω)}′ which precesses about the vertical with angular velocity {right arrow over (ω)}. 
   Two formulae are immediately apparant:
 
tan β=ω′ X′ /ω′ Z′  and tan(β−α)=( I   X′X′ ω′ X′ )/( I   Z′Z′ ω′ Z′ )
 
   By considerring the curvilinear speed of any point on the axis of the body cone it can be seen that
 
ω′ sin β=ω sin (β−α)
 
   These three formulae suffice to solve for any configuration. It is the third formula which is crucial in making obvious the claim that for a stress-free motion of a disk-like object at small inclination angles ω/ω′≈2. Therefore, the disk efficiency, e, is defined by ω/ω′=2 e.    
   An example will suffice to illustrate the role e plays in the design process: Suppose, in the preferred embodiment (angle of inclination =β−α=14 degrees, see  FIG. 10  in which all rotations and precessions are mirror-reversed for clarity) it is anticipated that the Nutating Member will conduct itself with the inertial characteristics of a U.S. penny while its rotatable linkage ratifies upon it a perfectly stress-free motion. Then,
 
 I   X′X′ =[(1/4)( M (0.95 cm)(0.95 cm)+(1/12) M (0.146 cm)(0.146 cm)]/(1/2) M (0.95 cm)(0.95 cm)=[(1/4)(0.90)+(1/12)(0.02)]/(1/2)(0.90)=((0.225+0.0017)/0.45=0.227/0.45=0.504
 
tan(β−α)=tan(14 degrees)=0.2493, ω′ x′ /ω′ x′ =0.2493/0.504=0.495=tan β, β=26.32 degrees, α=12.32 degrees
 
   finally, ω/ω′=sin β/sin(β−α)=0.443/0.242=1.83=2e, e=92% 
   simply put, for a given spin rate, this Nutating Member will precess at 92% the rate it would have, had it been a perfectly flat disk at a vanishingly small angle of inclination. 
   Static Description (Cont.) 
   Thus far the physics of the Nutating Member is anything but stress-free. To achieve half that goal counterweight arms  11 A,  11 B,  12 A, and  12 B are affixed to the Nutating Member well free of the outer sphereical cover. Their primary function is to relocate the Member&#39;s center of mass to that of the sphere. This will result in the nullification of the Newtonian stress, i.e. no net force is necessary to direct the motion of the Nutating Member. Still, the rotational motion will be unnatural: For most reasonable configurations (but not all; see the alternate embodiment infra) the Nutating Member&#39;s precession will have the opposite sense as its rotation (see  FIG. 4 ). This is precluded by Euler&#39;s analysis and it is this circumstance that necessitates the entire device be imparted with a reverse-English. Before turning to the rotating assembly it should be noted that a secondary function of the counterweights is to sculpt the Nutating Member&#39;s elipsoid of inertia to one more disk-like and less rod-like. This will result in the nullification of the Eulerian stress, i.e. no net torque is necessary to direct the motion of the Nutating Member. A third function of counterweight arms  12 A and  12 B is to cradle via gimbal pintles  13 D and  13 B an inner gimbal ring  14  which in turn cradles via gimbal pintles  13 C and  13 A an outer gimbal ring and sprocket gear  15  (see  FIG. 1 ). 
   The entire rotational assembly is built on three hollow concentric lumena (see  FIG. 6 ). An innermost shaft  17  is stationary. Next out, a shaft  18  serves as axis for the Rotator to which it is attached via the inner spherical cover and ultimately struts or spider legs  33 A-D which in turn support a top cannister cover  28 . This along with a lateral cannister cover  29  and a bottom cannister cover  30  completely encloses the cam and distributor assembly. The Rotator shaft constrains the axis in three dimensional space, in this embodiment, of not just the Rotator but both the inner and outer spherical covers (not to mention the cam and distributer cannister). 
   Rotator shaft  18  is sustained upon stationary shaft  17  on an inward projecting lip  21  the lower surface of which comprises a seal  34  which in spite of its spinning prevents loss of charge as it passes up through stationary shaft  17  before exiting towards a combustion chamber via a spiracle  35 . The Rotator shaft is is also affixed with a sprocket gear  19 . 
   An outermost hollow shaft  22  governs the cams and distributor. Its lower region is affixed with a sprocket gear  23  and sustained upon Rotator shaft  18  on an outward projecting lip  25 . Its upper region extends as far as the cam and distributor canister whose inner workings are responsible for exhausting, charging, and igniting the inter-planetary combustion chambers. Though electrical slip rings  26  and  27  are depicted at the base of the Rotator shaft, the electrical system including any cams and/or microprocessors that might be utilized in the ignition process is assumed to be a well understood art, reside completely within the confines of the canister and is completely suppressed from the drawings. 
   Although the rotation and simultaneous precession of the Nutating Member relative to the Rotator in  FIG. 5  is precisely the same as in  FIG. 4 , as subjected to reverse-English the rotation and simultaneous precession depicted in  FIG. 5  can be seen to approach, in three dimensional inertial space, a ratio of 1:2 as demanded by Euler for a disk-like object. To facillitate the reverse-English, the rotational rates of sprocket gears  15  and  19  must be held in strict ratio. The means by which their motion are conveyed, in this embodiment, are linkages in the form of drive chains  16  and  20  engaged with two sprocket gears on a common drive shaft (not shown). This is also the means by which torque and energy are conveyed from the engine. The cams and distributor are sychronized with a similar motion-conveying linkage embodied by sprocket gear  23 , drive chain  24  and a third unseen sprocket gear on a common drive shaft. The relative diameters of all three sprocket gears  15 ,  19 , and  23  are propotioned under the assumption that the three engaged unseen sprocket gears on the common drive shaft are of the same diameter as each other. 
   The only place place besides the common drive shaft where the two assemblies communicate with each other is via the components that oversee the functioning of any including the instant internal combustion engine. Hence, the top cam shaft  22  is affixed via struts to an exhaust valve cam  32  and this to an intake valve cam  31 . Each cam shaft has a central circular cut-out to make way for Rotator shaft  18  which was previously described as affixed to the cannister with which it rotates. Turning to  FIG. 7  the cannister has (in this embodiment) 14 bores to provide egress for 7 pushrods with exhaust valve heads  40 A-G and 7 pushrods with intake valve heads  39 A-G as well as certain devices (not shown, as previously mentioned) to actuate the means of ignition, in this embodiment, the 7 spark plugs  42 A-G. The outer convex surface of all 14 valve heads are normally pulled flush with the outside surface of inner spherical cover 9 by their respective compressive springs  41 A-N. Looking down upon these proceedings the charge exits spiracle  35  to a hose  36  then chooses one of 7 distribution hoses  37 A-G and their corresponding atria  38 A-G before being loaded into one of 5 inter-planetary volumes. These are the means by which the charge or fluid is controlled prior to compression and ignition. 
   Design Considerations 
   To reiterate: thus far each engine can be specified by five freely chosen parameters. They are the subtended angles at the sphere&#39;s center of a free-planetary gear, the Rotator, and the Nutating Member; the integer number of lobes; and the binary parameter + or −. In point of fact one of the three continuous parameters must be absorbed to facilitate the condition that the compression ratio be fixed at a relatively high value, i.e. that each lobe have approximately the same (though somewhat less) extent than a free-planetary gear. (see  FIG. 1  and  FIG. 4 ) Fullfilling this condition still yields two dimensions of parameters to finesse forth another relationship which, though not critical may yield certain benefits: By a judicious choice of the ratio of the total number of gear teeth possessed by the Nutating Member to the total number of gear teeth possessed by the Rotator a periodicity can be induced upon the latter vis-a-vis the locations of maximal compression of the inter-planetary volumes. In this embodiment the ratio was chosen as 8:7 and thereby the number of positions of maximal compression occurring around the Rotator was fixed at 7: only 7 stations of spark plug, exhaust valve, and intake valve are necessary (see  FIG. 7 ). This fixing has certain advantages regarding the efficacy of the camming but a much greater relevance to the optimal placement of the sparkplugs, a process which in the history of automotive engineering has always proved to be most empirical. 
   Static Description (Cont.) 
   To further boost the compression ratio plugs can be optionally inserted into the inter-planetary volumes (see  FIG. 1 ). The purpose of these plugs is to displace a fixed amount of deadvolume from both the maximal and minimal inter-planetary volumes. As the compression ratio is=(MAX-DEAD)/(MlN-DEAD) it is easily perceived that as the deadvolume approaches the minimal volume, the compression ratio can be appreciably increased; certainly to a level comparable to that of the modern internal combustion engine of approximately 10, i.e., to about one order of magnitude. These could easily be adorned with various friction reducing rollers or gears but in this embodiment are mere sliding components consisting of left “butterfly” wings  4 A-E linked via compressive springs  8 A-E to right “butterfly” wings  5 A-E. It is important to note in so much as the “butterflies” reside within the inter-planetary volumes that their inside surfaces possess slots  6 A-E, and  7 A-E lest there be collision with the valve heads as they are sequentially actuated by their respective cams (see  FIG. 3 ). 
   Operation 
   As promised the operation is trivial. As each inter-planetary volume becomes bounded (in this embodiment: from above) sequentially by a lobe, an arch, a lobe, an arch, and a lobe, that volume undergoes the familiar cycling of the four-stroke piston engine: intake, compression, power, and exhaust. It only remains to say with respect to the 5 inter-planetary volumes that successive, say, ignitions follow a pentagrammic pattern while with respect to the 7 spark plug stations the ignitions follow a less-tight septagrammic pattern. (I.e., if I may hearken back to high school: not the more-tight septagrammic pattern of successive multiples of 3 modulo 7, but the less-tight septagrammic pattern of successive multiples of 2 modulo 7; or equivalently, successive multiples of 200 modulo 700.) In other words, in this embodiment the ignition is completely even-tempered with respect to both the inter-planetary volumes and the spark plug stations. 
   It is somewhat amazing that this latter regimen can be effected with just a three-pointed cam but consultation with the highly schematicized  FIG. 8  will allay all doubts. 
   DESCRIPTION AND OPERATION OF ONE ALTERNATE EMBODIMENT 
   As will be posited in the succeeding section there are numerous variations that can be played on this preferred theme. One alternate embodiment which simultaneously incorporates several of these is for the two main gear elements to take each other&#39;s place: 
   In  FIG. 9  it is seen that the Nutating Member,  901 , has been rendered substantially circular while what had been the Rotator, now a stator,  902 , has been endowed with lobes. The number of these lobes has been altered from 4 to 2, the number of free-planetary gears reduced from 5 to 3 while their general latitude has been made less equatorial and more polar. This latter variation admits to some alteration in the ratio of the total number of teeth of the lobed element to the total number of teeth of the substantially circular element. The upshot of these modifications is that the Nutating Member will execute stress-free rotations and simultaneous precessions absent any application of reverse-English. That is, if properly counterweighted, the now substantially circular Nutating Member will execute Eulerian motion relative to a stationary lobed element. This may have certain advantages. For instance, the spinable seal may be dispensed with. Another is that only one sparkplug,  942 , one intake valve head and one exhaust valve head arraigned about the inside spherical cover, welded now to the lobed element, are required. An outer gimbal ring with sprocket gear,  915 , a gimbal ring drive chain,  916 , a fixed shaft,  917 , a somewhat skinnier cam shaft,  922 , a cam shaft sprocket gear,  923 , a cam shaft drive chain,  924 , and a somewhat skinnier support lip,  925 , for the cam shaft have completely analogous functions. 
   Additional Scope 
   There are many variations that may prove advantageous. One, in the realm of hydro- or especially aero-dynamics, is that instead of conveying torque to a common remote drive shaft that there might be certain advantages in affixing a propeller or an impeller directly to the Nutating Member. Another is that the previously mentioned ratio of rotations of the Nutating Member and the Rotator Shaft (not to mention the Cam Shaft) should not be thought to be constrained to non-zero and non-infinite values: Certainly one or more may be frozen with respect to the engine&#39;s reference frame. Indeed, this was the case of the “Rotator” in the alternate embodiment. 
   Furthermore, the means by which this ratio is held fixed need not be sprocket gears linked to a common drive shaft. Various pinion gears, conical gears, belts, and such could easily be substituted. 
   In addition it might be, as in the case of the modern bicycle, that certain advantages may be reaped in certain departures from perfect roundness in regards to the sprocket gears. This may also be true of the free-planetary gears especially if coordinated with some periodicity as they traverse around the Nutating Member and substantially circular Rotator. Even the latter might absorb some of the precessional duties by assuming a lobedness. In this case, the second number of lobes will be determined by a second freely chosen binary parameter + or − and might not be equal to the number of lobes on the lobed Nutating Member. However, both numbers must be different by unity to the number of free-planetary gears. In this case both polariciders will be uniquelly mathematically predetermined curves as could be attested to by one skilled in the Art of Dynamic Systems. (Or, as in the case of the alternative embodiment, the Nutating Element may be unlobed.) 
   There are an infinitude of variations possible so the essence of the instant invention must be attributed to not the two embodiments nor these recent musings but strictly to the claims.