Abstract:
This invention is directed to a novel amphibious surface vehicle ( 10 ) having a hull like chassis ( 11 ) with a plurality of rotary engagement devices ( 14 ) adapted for travel over various surface terrains and fluidic substances ( 17 ). Each engagement device includes rotors ( 16 ) having a multi-lobular periphery that provides improved tractive and propulsive attributes. The rotors are coupled through a driven eccentric hub ( 30 ) and phased by a non-circular internal gear pair ( 27, 37 ) so as to provide synchronized linear motion upon a weight bearing surface ( 15 ). The rotors with an overlapping contact ratio which produces increased traction and bearing area translating to improved overall performance upon a planar surfaces ( 15 ). This overlapping action becomes more paddle like when surface penetration occurs or by adjusting lever ( 19 ) aggressively changing the phasing incidence of the rotors ( 16 ), which is conducive to fluidic propulsion on water or other low shear strength substances ( 17 ).

Description:
CROSS-REFERENCED TO RELATED APPLICATIONS 
     None. 
     FEDERALLY SPONSORED RESEARCH 
     None. 
     SEQUENCE LISTING 
     None. 
     BACKGROUND OF THE INVENTION 
     1. Field of Invention 
     This invention relates to engagement devices for amphibious surface vehicles, particularly for such devices to be operated in tractive and/or propulsive modes over varying terrain attributes, surface conditions, and though substances exhibiting high fluidity characteristics. 
     2. Prior Art 
     The current art of surface transport vehicles utilized numerous types of engagement devices such as, wheels, endless tracks, steppers, articulating members, and rails. Such transport devices perform adequately within their respective surface domains, however struggle and become cumbersome when transitioning to other surfaces beyond their intended operational envelopes. 
     For example, this is typical of conventionally wheeled vehicles transitioning from a developed road bed to dry sand, loose gravel, or moisture saturated soils resulting in the shear failure of the surface, thus penetrating therein. This usually results in the loss of forward momentum and available traction, thus becoming completely immobilized within the surface encountered. A method to alleviate this problem as found in the construction, mining, agriculture and timber industries which commonly utilize large wheel diameters and widths to increase the contact area or footprint to aforesaid unimproved surfaces. This approach reduces the ground pressure exerted therefore lowering the shearing forces imposed to the underlying terrain. 
     The efficient mobility of a wheeled surface vehicle is dependant on several factors: slope of the surface (grade), internal wheel friction, contact friction (grip) and rolling resistance. The latter is directly related to the amount of deformation of the wheel and the load bearing surface when in contact, thus creating this additional resistance. Rolling resistance is analogous to ascending a constant positive slope and when this slope is combined to the actual grade, it can overcome the provided traction (grip), thus spinning occurs. Also, rolling resistance requires additional power and torque to overcome due to continuously traversing this added slope thus more fuel consumption and the loss of available pulling force. To reduce rolling resistance by distributing the load to a greater contact area thus increasing traction and decreasing penetration into the ground surface results in greater efficiency and effective pulling power. This is the rationale in the industries mention above, but a scalability limit is soon reached with very large diameter wheels, by sacrificing torque or rotational leverage (rim-pull), thus insufficient power to pull or haul a payload over yielding surface conditions. 
     Another terrain engagement device that brings the surface along with it, such as a track laying vehicle, which nearly negates rolling resistance by providing a large contact area, thus limiting penetration. Also, track laying vehicles are very agile in steep terrain more so than conventionally wheeled devices by generating large amounts of traction and leverage or drawbar pull which is analogous to wheel rimpull mentioned above. They can negotiate low ground pressure areas due to low downward forces exerted by employing wide tracks thus reduce yielding effects of the underlying surface. A critical tradeoff occurs though, with tracked vehicles in performance in speed, therefore not an effective conveyance on improved, hard or paved surfaces where higher velocities can be attained by wheeled vehicles. Albeit, tracks are very robust, they have other major drawbacks such as a very short service life, a high maintenance schedule, continual part replacement, and prohibitive energy consumption. Also, a multi-linked track or chain is as strong as its weakest link and this is the ‘Achilles Heel’ of track laying or endless track vehicles were redundancy is paramount, such as with military, search rescue, and remote operations. 
     However, the vehicle performance envelope can be expanded by combining various terrain engagement systems in complimentary configurations. This usually is impractical and creates unneeded complexity and expenses with the same inherent disadvantages mentioned above. Several prior art vehicles utilize such methods and have only found limited success. Also, amphibious vehicles may utilize auxiliary propulsion devices when waterborne. These propulsion devices range from screw propellers, water jets, paddle wheels, or ducted fans such as with hovercraft. By just utilizing a single propulsive drive device to do both surface engagement and to impel thrust, would greatly simplify the operation and cost of the vehicle. 
     The following prior art will described several of the numerous innovations to overcome some of the disadvantages mentioned above 
     Harvey, in U.S. Pat. No. 5,881,831 teaches a multi-terrain amphibious vehicle adapted for travel across various types and attributes. The vehicle includes a chassis assembly which extends in a longitudinal direction; a plurality of propulsion members rotatably coupled to the chassis assembly for propelling the vehicle across a given surface; and, a control mechanism for controlling the rotational velocities and phases of the propulsion members. Each propulsion member essentially resembles a mutilated circular wheel where the mutilated portion of perimeter segment is used to engage or ‘pushes off’ of the underlying surface. However, the propulsion members require a complicated control mechanism to collectively cooperate so as to operate effectively over various terrains. Also, the use of a circular perimeter segment for the propulsion members creates the same disadvantages aforementioned for wheeled vehicles. 
     Reid, in U.S. Pat. No. 4,102,423 shows a ground traction device which is non-circular in its periphery and each member containing a three lobed tire, preferably constructed of rubber. The periphery containing three individual arcs arranged in the form of an equilateral triangle. Members may be situated adjacent or axially spaced apart and have peripheries of any other suitable shape, such as two or four sided. It is intended to operate and tramp over soft ground and when transitioning to a hard surface, the ground engaging member behaves as a circular wheel of constant radius by compressing the rubber tire portion. However, this adaptation could create excessive amount of heat buildup in the rubber tire due to constant compression and rebound cycle when operated on a hard surface. The rubber or other flexible material under these conditions would eventually fail and de-vulcanize or delaminate, thus rendering a vehicle equipped with ground traction devices inoperative. Also, pressure sensitive soft terrain would be adversely affected by the penetrating ‘digging’ lobes when not compressed by the underlying surface. 
     Sfredda, in U.S. Pat. No. 2,786,540 illustrates a non-circular wheeled vehicle with similar phasing of the ground contacting wheels as with Harvey&#39;s patent where a set is “out of phase”. This relationship contributes to good traction, so as to permit differently shaped edge portions of different wheels to simultaneously contact the ground at all times. This achieved by vertically reciprocating the axis of rotation within a slot so as to limit its travel, and to permit smooth contact with a horizontal plane. Other, non-circular, multi-sided configurations (polygons) as a hexagon, octagon or the like may be employed. Sfredda teaches the use of a roller and a cam disk to urge or float the axle within a limiting slot as it rotates by a driven geared pinion. However, two or three sided (lobed) configurations seem excluded due to gear interference or impracticality with a cam system. Also, the device contemplated is limited to a pair of non-circular wheels per wheel site. This would also cause ‘digging’ within pressure sensitive terrain since each corner edge portion would contact the surface simultaneously. 
     OBJECTS AND ADVANTAGES 
     It is a primary object of the present invention is to provide an improved amphibious surface vehicle which is adapted to effectively traverse various terrain types and fluidic substances. 
     Another object of the present invention is to provide a vehicle which can be easily adjusted for a range of surfaces; tractive mode across land and/or propulsive mode on fluidic surfaces. 
     Another object of the present invention is to provide a vehicle which is adapted with built-in gear reduction in its engagement devices. 
     Another object of the present invention is to provide a vehicle which minimizes impact to the underlying terrain or pressure sensitive substances. 
     According to the invention, the object is accomplished by providing a plurality of engagement devices mounted on a vehicle, which overcomes the above-mentioned disadvantages of the heretofore-known devices and methods of this general type and which is generally improved in its operation and efficiency. 
     SUMMARY 
     This invention relates to amphibious surface vehicles, particularly to the engagement or propulsion drive devices to be operated over varying load bearing (shear strength) surfaces, terrain attribute, traction conditions, and/or to impel thrust within low shear strength soils or highly fluidic substances. The invention disclosed herein amphibious surface vehicle with synchro-phased rotary engagement devices is applicable to a plurality of vehicles or structures desiring greater mobility and maneuverability to a variety of surfaces. 
     With the foregoing and other objects in view there is provided, in accordance with the invention, synchro-phased rotary engagement devices, the invention will now be described by way of example only and with reference to the accompanying drawings. 
    
    
     
       DRAWINGS 
       Figures 
         FIG. 1  is a perspective view of one preferred embodiment of the present invention; 
         FIG. 2  is an enlarged perspective view, partially cut-away, of a portion the embodiment shown in  FIG. 1  of the present invention; 
         FIG. 3  is an exploded perspective view of the embodiment shown in  FIG. 2  of the present invention; 
         FIG. 4  is a side elevation view of which the right being schematic and the left illustrating a detailed view of the preferred embodiment of the present invention; 
         FIG. 5   a  is side elevation of one preferred embodiment engaging a planar surface; 
         FIG. 5   b  is side elevation of one preferred embodiment engaging a partially yielding surface; 
         FIG. 5   c  is side elevation of one preferred embodiment propelling forward within a fluidic substance; and 
         FIG. 6  is an exploded perspective view of an alternate embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     FIGS.  1 - 5   
     Preferred Embodiment 
     Referring now to the drawings, in which like alpha-numeric characters of reference denote like elements, and particularly to  FIG. 1  which illustrates a perspective view of one preferred embodiment of the instant invention. A self-propelled amphibious surface vehicle  10  which generally includes, a navicular-shaped hull or chassis assembly  11 , a passenger cabin  12 , a plurality of synchro-phased rotary engagement or propulsion devices  14 , each mated distally and operatively to an axle housing  13  positioned near the waterline of each longitudinal side, thereon. 
     As shown in  FIG. 1 , there are preferably three engagement devices  14  located on one longitudinal side of chassis assembly  11  with an equal number coaxially disposed on the opposite side (partially shown) supporting and propelling vehicle  10  on a weight bearing surface  15 . Although, substantially secured coaxially, engagement devices  14  of the preferred embodiment, may be operatively independent with a suitable mechanism known in prior art such as a differential (not shown) to decouple the coaxially paired propulsion devices  14  so as to permit independent rotation and phasing. 
     In  FIG. 2  which depicts a close-up perspective view of engagement device  14  mounted distally to axle housing  13 . The engagement device  14  generally includes two rotor assemblies  16   a ,  16   b  each preferably clad by a treaded tire  18  mounted on a wheel  20  supported rotatably and secured to an eccentrically driven hub  30 . Drive hub  30  is operatively connected to a drive axle  60  (partially shown) situated within axle housing  13 . To position axle housing  13  angularly by use of an actuable lever  19  secured thereon and shown in solid in the I position (high contact mode). Preferably, actuable lever  19  is housed within chassis assembly  11  to limit the amount of hull penetrations and for protection from external impacts and to limit environmental exposure. 
     Referring again to  FIG. 1 , hull chassis assembly  11 , which preferably encloses below deck, typical onboard components necessary for automotive transport such as a; motive force, power train, fuel storage, skid-steer/braking device (not shown). The superstructure, a passenger cabin  12  situated near the bow/front of chassis assembly  11  which houses driver controls, monitoring gauges, and occupant seating (not shown) typically needed to be effectively driven and operated. Also, another feature of the forward located passenger cabin  12  which has a facetted shape helpful to deflecting water spray and waves from entering the rear deck area of chassis assembly  11 . This is especially applicable when transitioning from land to waterborne operations where high approach angles may be presented. If desired, the incorporation of self-bailing devices to the deck area such as scuppers (not shown) to passively evacuate water may be used when afloat. 
     If desired, other suitable techniques known in prior art to prevent, displace, remove, and/or seal from water intrusion, to safeguard buoyancy, may be utilized so as not to hinder the effectiveness of amphibious surface vehicle  10 . Also, other steering systems may be incorporated as found on conventionally equipped automotive vehicles. The specific configuration and construction of the chassis assembly  11  and passenger cabin  12  are not important to the present invention and will not be described in any further detail within this specification. 
     However, one particular feature of the chassis assembly  11  is to provide housing and structural support for an actuable control device (not shown) to position lever  19  for each propulsion devices  14  which will be described later in the following paragraphs. 
     The details of each similar engagement device  14  of  FIGS. 1 ,  2  are shown in  FIGS. 3 and 4 . Each engagement device  14  generally includes a pair of coaxially adjacent and in slightly spaced relation, an inner and outer lobed rotor assemblies,  16   a  and  16   b  respectively. Both  16   a , and  16   b  are arranged 180° out of phase and revolve about a single axis Z, radially offset by a distance e, to urge cycloidal motion. In the art, the distance e is referred to as the eccentricity of the rotor, or alternately stated, the distance of the geometric center of a revolving body from an axis of rotation. 
     Although dissimilar in spatial relation, the identically structured rotor assemblies  16   a  and  16   b , will be described as one for brevity in the following paragraphs. 
     Referring to  FIGS. 3 and 4 , particularly to an exploded isometric view of one engagement device  14 , each rotor assembly  16   a ,  16   b  is comprised of resilient tire  18  mounted and fixed to a substantially tri-lobular shaped wheel  20   a ,  20   b  in a conventional manner. Tire  18 , preferably with a wide aggressive tread and constructed of solid molded rubber, partially overlaps a flange like rim  24  along the peripheral edge an integral of each wheel  20   a ,  20   b . Also, generally included on one side of each wheel  20   a ,  20   b  a castellated recess  21 , a shoulder  22  within, and a multiplicity of threaded apertures for fasteners are disposed opposite rim  24 . 
     The preferred embodiment comprises solid rubber tire  18  of suitable hardness, and the remainder of engagement device  14  generally consists essentially of low carbon steel, preferably alloyed to resist corrosion in marine environments and to minimize material by providing high-strength to weight properties. The tire may be constructed if desired in other known structural forms such as pneumatic, foam, or airless similar to Michelin&#39;s “T-wheel” to minimize weight and material. To provide the hollow structure of wheel  20   a ,  20   b  which can comprise of several fitments joined together by conventional fasteners with associated gaskets, it is preferably fusion welded to provide a sealed durable unit thus creating additional needed buoyancy. 
     Referring again to  FIG. 3 , disposed oppositely of rim  24  of each wheel  20   a ,  20   b  a bifurcated, non-circular, internal gear assembly  27   a ,  27   b  is attached and revolves therewith. The gear assembly  27   a ,  27   b  is mechanically fixed with a plurality of locating dowel pins  42  and flush head bolts  52  to their appropriate apertures within castellated recess  21  of wheel  20   a ,  20   b . The interior half of internal gear assembly  27   a ,  27   b  is keyed within recess  21 , and comprises a, tri-cusped shape, internal gear segment  26   a ,  26   b  and now completing the exterior half, a tri-lobed shape, internal gear segment  28   a ,  28   b  with a periphery substantially the same as rim  24 . 
     DETAILED DESCRIPTION 
     FIGS.  1 - 5   
     Preferred Embodiment 
     Collectively, internal gear segment halves  26   a  and  28   a  complete a closed pitch curve but laterally offset to overcome mechanical interference with a bifurcated, non-circular, pinion gear assembly  37   a ,  37   b . If desired an integral unit may be utilized by combining each gear half into one thus reducing additional components and manufacturing costs, but for clarity the bifurcated assemblies are shown in the  FIGS. 3 ,  5 , and  6 . The internal gear assemblies  27   a ,  27   b , which rolls without slipping and conjugates with a stationary pinion assemblies  37   a ,  37   b , thus urging rotational phasing of rotor assembly  16   a ,  16   b , as it revolves about axis Z. The particular design criteria of the non-circular pitch curves S and Q, with a plurality of teeth formed thereon  44 ,  45 , respectfully will be discussed in more detail later in this specification. 
     In addition to controlling the phase of rotor assembly  16   a ,  16   b , each internal gear segments  26   a ,  26   b  may be utilized to laterally retain cylindrical hub  30   a ,  30   b  within a bore  32 , which is geometrically centered about axis O of  FIG. 4  to wheel  20   a ,  20   b . Also, internal gear segment  28   a ,  28   a  may be used as the compliment to rim  24  in laterally securing tire  18  to the peripheral surface of wheel  20   a ,  20   b.    
     Referring again to  FIG. 3 , to hub  30   a ,  30   b  with a diameter substantially equal to its depth, includes a concentric retaining ring  23  on one extremity to be disposed within shoulder  22  of wheel  20   a ,  20   b . Also included, a hexed or splined aperture  33 , eccentrically located within to receive one half of a similarly shaped coupling collar  31 , an anti-friction means (not shown) supported thereon. Preferably, appropriate contact seals may accompany the roller element bearing(s), disposed between the hub  30   a  and the interior surface of cylindrical bore  32 , to prohibit the incursion of water and foreign contaminates. 
     As shown in  FIGS. 2 and 3 , isometric views of one engagement device  14  situated between two adjacent similar devices and operatively connected to chassis assembly  11  of  FIG. 1  via axle housing  13 . Aforementioned, each propulsion device  14 , generally comprises a pair of rotor assemblies  16   a  and  16   b . Each rotor assembly  16  describe in detail are now joined via the coupling collar  31  and slightly separated axially by a spacer  41 , preferably integral thereto. 
     The coupling collar  31  depicted allows differing radial configurations of the hubs  30   a  and  30   b  inherent to the symmetrical geometrical shape of a polygon. It is preferred with a pair of rotor assemblies  16   a  and  16   b , to maintain a near mass-balance, to be spatially situated in the 180° opposing configuration. An additional rotor, so as three rotors utilized would benefit by having the spacing in the 120° configuration. Additionally, other prior art techniques to counter-balance the engagement device  14  may be utilized to mitigate vibration and wobbling effects especially at high rotational velocities. 
     Also, if desired, the coupling collar  31  may be fitted with at least one anti-friction means (not shown), either sleeve or roller element bearing within. The coupling collar  31  is rotationally mounted and concentric with rotational axis Z on a journal portion of a flanged tubular spindle  35 . 
     The flanged tubular spindle  35 , substantially cylindrical in shape, generally includes a pair of splined or keyed portions adjacent to the journal portion and a distal portion with threads  46  formed thereon. The hollow portion preferably comprises a sleeve bearing(s) (not shown) within to rotatably support the rotational driven means. The phasing pinion gear assemblies  27   a  and  27   b  are adapted and secured vertically (traction mode I) in the rotational plane to inner and outer splined portions  34  and  36 , respectively. 
     Referring again to  FIG. 3 , it best can be seen the details of pinion assemblies  27   a  and  27   b . The interior (relative to rotor assembly) half of pinion gear assemblies  27   a  and  27   b  comprises an, eye shaped, lower external sector gear  38   a ,  38   b  to conjugate with cusped internal gear segment  26   a ,  26   b . Now completing the exterior half of pinion gear assemblies  37   a  and  37   b , comprises a partially mutilated external gear  40   a ,  40   b  so as not to interfere while conjugating with lobed internal gear segment  28   a ,  28   b . The halves are preferably mechanically fastened with a pair of dowel pins  42 , in face to face relation, to provide additional torsional support when mounted to there respective splined portions on spindle  35 . 
     The pair of pinion gear assemblies  37   a  and  37   b  each comprises splined apertures within to coincide with there respective mounting splines which exhibit slightly different inside spatial parameters. This is to allow pass through to mounting splines  34  for gear assembly  37   a  and refusal of gear assembly  37   b , thus retaining it to mounting splines  36  on spindle  35 . Preferably, securing means such as a set screw(s)  53  or other appropriate fastener(s) within threaded aperture(s) to allow lateral adjustments in position of pinion gear assemblies  37   a  and  37   b.    
     Also, to maintain the correct coplanar relationship with corresponding mating gears a shim or spacing washer(s)  48  inserted between the rotating assembly and pinion faces may be employed. A retaining hex nut  50  with associated lock washer  48  fastened to distal threads  46  supporting pinion gear assembly  27   b  to spindle  35 , thus laterally securing coupling collar  31  and rotor assemblies  16   a  and  16   b  mounted thereon. 
     In designing and constructing the gear assemblies  27   a ,  27   b  and  37   a ,  37   b  conjugating pitch curves and the exterior profile shape of rotor assemblies  16   a ,  16   b  of the preferred embodiment described above. First, the gears pitch curves are an imaginary line that allows for positioning of the teeth, second the two meshing gears pitch curves contact at a line of tangency to operate effectively. It can best be seen within the schematic portion of  FIG. 4  depicting the non-circular pitch curves Q, S and rotor profile P which will be parametrically derived. 
     For clarity, a hypotrochoid plane curve generating method may be used to determine the rectangular coordinates used for the creation of a three lobed peripheral contacting curve P. A hypotrochoidal curve is formed by first selecting a fixed circle and a generating circle having a radius less than the fixed circle. The generating circle is placed within the fixed circle so that the generating circle is able to roll along the circumference without slipping. The hypotrochoidal curve is defined by the locus of points traced (a generatrix) by the distal portion of a curtate line segment radial fixed to the center of the generating circle, as the generating circle is rolled within the circumference of the fixed circle. 
     The parametric equations to calculate the pair of rectangular coordinate points for the profile curve P are provided by the following: 
     
       
         
           
             
               X 
               P 
             
             = 
             
               
                 
                   ( 
                   
                     R 
                     - 
                     r 
                   
                   ) 
                 
                 ⁢ 
                 
                   sin 
                   ⁡ 
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               - 
               
                 e 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   sin 
                   ⁡ 
                   
                     ( 
                     
                       
                         
                           ( 
                           
                             R 
                             - 
                             r 
                           
                           ) 
                         
                         ⁢ 
                         θ 
                       
                       r 
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
               Y 
               P 
             
             = 
             
               
                 
                   ( 
                   
                     R 
                     - 
                     r 
                   
                   ) 
                 
                 ⁢ 
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               + 
               
                 e 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     
                       
                         
                           ( 
                           
                             R 
                             - 
                             r 
                           
                           ) 
                         
                         ⁢ 
                         θ 
                       
                       r 
                     
                     ) 
                   
                 
               
             
           
         
       
     
     Wherein:
         R=is the fixed (outer) circle radius   r=is the generating (inner) circle radius   θ=is the angle to the center of generating circle   e=eccentric and/or length of radial line segment       

     The equation above is one of many that can be utilized by those skilled in the art for determining appropriate non-circular curve coordinates. Any mathematical function that does not reverse its slope, have discontinuities, excessive ratios or cause mechanical interference may be used. Also, the level of accuracy and acceptable tolerances may justify which method one is likely to employee in the design and construction process. 
     In designing the synchro-phased rotary engagement devices  14 , in accordance to the preferred embodiment shown in  FIGS. 1-5 , firstly by determining an adequate ground clearance and also providing sufficient thrust when waterborne. A height h of 34 inches perpendicularly measured between a horizontal surface  15  to a rotational axis Z was obtained experimentally. Now to select the appropriate curvature of the profile curve P while providing ample propulsion (lobes) without sacrificing radial contact area so as not to be to abrupt or concave. This is found to be generally 30 percent in variation of the rotor radii, thus 10 inches of range, therefore 39 inches at the lobe apices and 29 inches at mid transition, respectfully. If desired, other percentages of variation may be selected to increase or decrease the degree of lobe curvature of the rotor assemblies  16   a  and  16   b  although this will slightly alter the constant velocity output function to a plane surface  15 . 
     Now with the above criteria, other design parameters can be mathematically derived such as e which equates to 5 inches or one half the throw of eccentric hub  30  which equals the difference in the rotor periphery radii. This is also the length of the curtate line segment to generate the three lobes and three transitions on the contact profile curve to maintain a constant h to axis Z. Now to determine the remaining parameters R and r, which share a 3:1 geometric relationship a numerical integer to be a closed algebraic curve with three lobes. Hence, R=r3 and from  FIG. 4  we see that h=R−r and substituting r with R/3, combining and arranging like terms, derives a formula R=3h/2. Consequently, solving with a value of 34 inches for h, the fixed circle radius R equates to 51 inches and by the 3:1 relationship aforementioned, thus obtaining the generating circle radius r of 17 inches. 
     Returning to the parametric equations provided above, and inputting the design values for curve P along with a range of angular intervals for θ from 0° to 360° into each simultaneously, thus resulting in a multiplicity coordinate pairs which create the generatrix. If desired to reduce the number of calculated point pairs used, they may be plotted or placed in a computer aided drafting (CAD) program and preferably interconnected by arc or line segments to interpolate and fill between the generated point coordinates. Also, utilizing another technique available within a CAD program containing a mirroring sub-routine, this can replicate the graphical inverse of a selected segment of the profile curve P, to efficiently complete the remaining curve segments. 
     The parametric equations provided above produce coordinates beginning from the positive Y-axis and progressing in a clockwise direction starting from 0° and ending at 360°. This modification helps allows mirroring about the Y-axis if generated to 180° or one half the range of a complete circle. Again, the number of points calculated depends on the level of accuracy desired and for the preferred embodiment is one quarter of a degree resulting in 1,440 points connected by arc segments were used in its creation. In the schematic portion of  FIG. 4 , the fixed and generating circles with the curtate line segment can be seen as it proceeds clockwise from C-C′ as it rolls A-A′ and B-B′ thus creating the generatrix of contact curve P as it rolls within the fixed circle. 
     Before moving on to non-circular curves Q and S, a brief explanation to the rationale of each three lobed rotor assemblies  16   a , 16   b  and their unique feature in providing continuous contact without varying h while rolling T and transmitting a near constant velocity tangentially as it revolves upon surface  15 . Conventional circular internal gear arrangement that provides phasing found on rotary trochoid displacement devices (Wankel type) may be used, if desired, but the input rotation velocity would need to be varied to maintain both a simultaneous contact and constant tangential velocity. This would be problematic if more than one rotor assembly  16  were desired for engagement device  14  due to spatial limitations of providing a varying rotational input for each separate rotor assembly  16 . Although, the use of this adaptation may be devised as to function but with increasing difficulty with each additional rotor assembly  16  desired for engagement device  14 . Therefore, by converting constant angular velocity to variable angular velocity via a non-circular internal gear system taught herein is far superior in providing positional phasing to a plurality of rotor assemblies  16   a  and  16   b  or more if desired from a single rotational input source while transmitting a near constant tangential velocity output to a plane surface  15 . It will be apparent that the present invention will greatly reduce the mechanical complexity of such devices and permits its adaptation to conventional vehicles and implements with no farther modifications. 
     Now that the formation of three lobed contact curve P is complete, the phasing gear pitch curves Q and S, external (pinion) and internal respectfully, may now be mathematically obtained utilizing the coordinate point data from contact curve P. Aforementioned, for brevity and familiarity, the hypotrochoid non-circular curves which are known to those skilled in the art have also derived other mathematical formulas such as the tangential vector angle to any point located on the hypotrochoid when the angle θ to the generating circle is known. The tangential vector angle φ will be used to compute both internal and pinion phasing gear parameters in polar coordinate form which are as follows. 
     
       
         
           
             ϕ 
             = 
             
               
                 θ 
                 ⁡ 
                 
                   ( 
                   
                     1 
                     - 
                     
                       R 
                       
                         2 
                         ⁢ 
                         r 
                       
                     
                   
                   ) 
                 
               
               + 
               
                 
                   cot 
                   
                     - 
                     1 
                   
                 
                 ⁡ 
                 
                   [ 
                   
                     
                       
                         r 
                         - 
                         e 
                       
                       
                         r 
                         + 
                         e 
                       
                     
                     ⁢ 
                     
                       cot 
                       ⁡ 
                       
                         ( 
                         
                           
                             R 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             θ 
                           
                           
                             2 
                             ⁢ 
                             r 
                           
                         
                         ) 
                       
                     
                   
                   ] 
                 
               
             
           
         
       
       
         
           
             β 
             = 
             
               
                 
                   tan 
                   
                     - 
                     1 
                   
                 
                 ⁡ 
                 
                   ( 
                   
                     y 
                     x 
                   
                   ) 
                 
               
               - 
               ϕ 
             
           
         
       
     
     Wherein:
         φ=tangential vector angle (slope m)   β=angle at contact with horizontal surface       

               θ   Q     =           cos     -   1       ⁡     (       h   -           x   2     +     y   2         ⁢     cos   ⁡     (   β   )           e     )       ⁢           ⁢     R   Q       =               x   2     +     y   2         ⁢     sin   ⁡     (   β   )           sin   ⁡     (     θ   Q     )         -   e             θ S =θ Q   −φ R   S =R Q   +e    
     To convert from polar form to rectangular coordinate form to plot curve Q and S:
 
 X   Q   =R   Q  sin(θ Q ),  Y   Q   =R   Q  cos(θ Q )+ e  
 
 X   S   =R   S  sin(θ S ),  Y   S   =R   S  cos(θ S )
 
     If desired, the hypotrochoid or other non-circular profile curves used for the rotor assembly  16  periphery may utilize another method to approximate the tangent slope m. For example, by finding the mathematical difference between each of the Y P  and X P  values immediately adjacent to the coordinate point in question. Then by dividing the ΔY by ΔX thus obtaining the tangent slope m which can now be inputted into curve Q and S equations after converting to angle φ. 
     As with periphery curve P, the two curves Q and S can be completed using the same technique by joining the arc or line segments and mirroring about the Y-axis in a CAD program. Although, the mirroring of pitch curve P requires an additional axis k located 120° positive of the Y-axis to correctly reflect the curve for a three lobed contact curve. Also, an additional step to extrapolate the 0° and 120° portion may done by extending the adjacent arc to the Y and k axis again by using CAD extend line or arc sub-routine. 
     DETAILED DESCRIPTION 
     FIGS.  1 - 5   
     Preferred Embodiment 
     In designing and constructing other multi-lobed engagement devices  14 , with four lobes for example, the mirroring axis k would be located at 135° to correctly generate the internal gear pitch curve. This relationship can best be seen in  FIG. 4  where if pitch curve S is conjugated upon pitch curve Q showing 120° and 180° of total arc respectfully, resulting in the rotational displacement of 60° for the contact curve P of rotor assemblies  16   a  and  16   b . A two-lobed rotor would require a mirroring axis k at 90° and result in the rotational displacement of 90° for the contact curve P. 
     It should be noted, the use of a hypotrochoid contact curve other than three lobes, renders a tangential velocity that is significantly variable with a constant rotational input, thus requires an alternative design method to remedy, if desired. This technique is as follows. 
     To determine fixed pinion curve Q without complete coordinate parameters for the rotor peripheral curve P except for the max/min radii desired and the number of lobes to be spaced equal-distant are known or selected. The following method may be utilized to generate the pitch and contact curves and is disclosed herein. 
     First, multiply the geometric mean of the rotor radii maximum and minimum values by the desired lobe module. For example, four lobes would require 90 degrees or revolution to complete a cycle, thus 270 degrees of conjugation per 360 degrees of input rotation. The module then would be 0.75 to output the required 90 degrees to complete a cycle. 
     This product is found to be equal to the perpendicular distance from the near foci to the directrix of a conical curve or ellipse with the major axis being situated vertically. 
     Several geometric properties of the ellipse are exploited to provide the unique kinematic relationships such as the constant ratio between the radial distance from the focus and the normal distance between that point on the curve to the directrix, and to those skilled in the art, the eccentricity E of the ellipse. 
     Secondly, eccentricity E can be derived of the ellipse curve or pitch curve Q, by dividing the difference of the arithmetic mean of the rotor radii or h and the directrix value above by the throw of the eccentric e and inversing the resultant. 
     Thirdly, the product of the eccentricity E and the directrix value defines the semi-latus rectum of the ellipse and the semi-major axis can now be found by dividing the semi-latus rectum by one minus the square of eccentricity E. 
     Finally, the distance to the near foci axis can be found by multiplying eccentricity E by the semi-major axis which now defines the ellipse that will become the pitch curve Q of the pinion phasing gear with axis Z located at its near focus. 
     To develop the conjugate or internal pitch curve S to mate with the pinion curve Q, the Law of Cosines preferably may be used to yield a locus of points when connected by lines or arcs have a length equal to the ellipse perimeter. The radial distances are greater by the distance of the throw or e and for a four-lobed rotor which results in 270 degrees of cumulative arc. To connect and complete the curve S use techniques mentioned above. 
     Now with both conjugating curves Q and S defined, the contact curve P can now be generated. Begin by dividing the radial distances of each point on curve S by E to find the normal distance when in contact with a horizontal surface  15 . Then by placing the constant ratio pairings at the center of rotor  16  O and to the curve S while maintaining there angular and length relationships, thus generating a locus points that create curve P. 
     Now to the placement of gear teeth  44 ,  45  on both internal and external pitch curve segments, which may be done prior to the mirroring procedure. The involute generation of the gear tooth profiles utilized 20 degree pressure angle with a 0.23 inch positive profile shift to alleviate interference. For the preferred embodiment, a virtual cutter rack laid out for segment length and iterated in a CAD program to produce highly accurate teeth which may use a computer numerically controlled milling machine for construction. 
     Although, gears of this type may be produced for instance with a reciprocating cutter of fellows type, whose pitch circle is made to roll slowly on the curved pitch line of a non-circular gear. Alternate methods to produce the gear profiles of various types may be utilized and to those skilled in the art, to numerous for description in this specification. 
     The preferred embodiment as shown in  FIGS. 3 and 4  contains 32 teeth for each of the external pinion gear assemblies  37   a  and  37   b  and 96 teeth for each of internal gear assemblies  27   a  and  27   b . It has been found that with, at a minimum, a difference of 15 teeth reduces interference while conjugating in the high contact ratio lobe portions. When the gears are bifurcated, as with the three lobe rotor, the internal gear teeth located at 60°, 180°, and 300° as shown in  FIG. 3  are trimmed so as not to interfere and bind during operation. This is one method utilized in design process and constructing the various non-circular curves utilized in preferred embodiment with three lobes. 
     Now returning to  FIG. 3  where it can best be seen the proximal portion of spindle  35  which comprises a symmetrically shaped mounting flange  51  with, at least one, preferably four apertures equally spaced and adapted to accept flush head bolts  52 . Also, a shoulder  53  concentrically formed thereon to provide a supporting journal for a two piece mechanical cover,  54  and  55 , which are substantially congruent to flange  23  and rim  24  in profile, respectfully. 
     The cover member  54  eccentrically disposed on the shoulder  53  also rotates within cover member  55  which is fastened to and revolves with inner rotor assembly  16   a ,  16   b . Preferably, thin section bearing(s) and appropriate contact seal(s) mention above and accompanying wheel  20  and hub  30  bearing(s) may be used between the rotating members of the cover members  54 , and  55 . 
     Alternatively, to house the exposed internal gear assembly  27   b  and pinion gear assembly  37   b  an outwardly convex drive plate  57 , is secured with a plurality bolts  52 , covers and revolves with rotor assembly  16   b . Preferably, drive plate  57  has a periphery and central thickness similar to internal gear  28   b  to adequately support a bearing cup  59  (dotted lines) which is geometrically centered within. This is to urge revolving motion to rotor assemblies  16   a  via coupler  31  and  16   b  (direction arrows) a circular journal  56  is eccentrically supported distally on a drive axle  60  integral thereto. Preferably, a roller element bearing (not shown) mounted between eccentric journal  56  and bearing cup  57  to efficiently transmit torque. Now to axle  60  with a proximal splined portion  58  formed thereon, pass through the hollow portion of spindle  35  and operatively connected to the motive force rotational means (not shown) within chassis assembly  11 . 
     In the preferred embodiment, in  FIGS. 1-5 , supporting spindle  35  is similar to prior art in the operational sense, such as with floating drive axle means found on extreme duty off-road vehicles. One inherent advantage for example is easy access to components to inspect, repair, and or replace without the complete disassembly of engagement device  14 . Also, for instance, disconnecting the motive means such as the removal of drive axle  60 , would not render engagement device  14  inoperable as a support idler, therefore still functional to amphibious surface vehicle  10  in a load carrying role. This built-in redundancy is particularly critical in harsh remote environments where mechanical failure may occur while still allowing amphibious surface vehicle  10  to be effectively operated by the other fully functioning engagement devices  14 . 
     In operation of the particularly configured and constructed amphibious surface vehicle  10  as described herein, which provides mobility, agility, and versatility over a wide variety of terrain an aquatic realms. Traversing with the present invention retains the benefits of a circular wheel for operation over hard or improved surfaces and exhibits much improved tractive and pressure properties when operating over yielding and deforming substrates, thus increasing its efficiency. The engagement devices  14  of the present invention overcomes this problem since, as it does not rely on a tread pattern to produce tractive effort, the surfaces can be relatively smooth and flat, thus can provide a paddle like action. This, together with a relatively good operating speed, also minimizes degradation of the ground surface that is a common problem with conventional wheeled devices. 
     It can best be seen in  FIG. 5   a , a side view depicting one novel feature of the present invention, amphibious surface vehicle  10  supported by a plurality of synchro-phased rotary engagement devices  14  which comprise of a pair of rotor assemblies  16   a ,  16   b  each. The preferred embodiment is operating in an overlapping contact ratio mode (position I) engaging simultaneous and continuously with a non-yielding planar surface  15 . 
     Now to  FIG. 5   b , another side view depicting a second novel feature of the present invention amphibious surface vehicle  10  propelled by a plurality of synchro-phased rotary engagement devices  14  which comprise of a pair of rotor assemblies  16   a ,  16   b  each. The preferred embodiment is shown operating in the traction/propulsion mode (position II), providing traction, floatation, and imparting forward thrust to a pliable yielding surface found between hard surface  15  and substance  17  exhibiting high fluidity. 
     Turning to  FIG. 5   c , yet another side view depicting a third novel feature of the present invention amphibious surface vehicle  10  propelled by a plurality of synchro-phased rotary engagement devices  14  which comprise of a pair of rotor assemblies  16   a ,  16   b  each. The preferred embodiment is shown operating in the waterborne propulsion mode (position III), imparting forward thrust within substance  17  exhibiting high fluidity. 
     DETAILED DESCRIPTION 
     FIG.  6   
     Alternate Embodiment 
     The details of an alternative form of engagement device  14  are illustrated in  FIG. 6  an exploded isometric view. Essentially the same in operation, a engagement device  114  comprises of rotor assemblies  16   a ,  16   b  as described above, except the phasing gear assemblies  27 ,  37  are situated in face to face relation instead of outwardly as with engagement device  14 . This spatial relationship requires an actuating lever  119  to be operatively connected between rotor assemblies  16   a ,  16   b . This alternative is due to the omission of the driven means such as axle  60  in lieu of a solid live spindle  135  to provide both support and to urge rotation (direction arrow) to eccentric hubs  130   a  and  130   b . Also, engagement device  114  requires an additional mechanical cover member  54 ,  55  without the need of drive plate  25  for its operation. 
     The actuating lever  119  preferably integral to a hexed mounting collar  140  which supports both pinion assemblies  37   a ,  37   b  in a vertically secured position (high contact mode shown solid) to phase rotor assemblies  16   a , 16   b . The hexed mounting collar  140  may be integral and spaced axially by a central member  141 . Both mounting collar  140  and central member  141  with a bore  142  which allow pass though of spindle  130 , may also contains two support shoulders  153  for both mechanical covers. Seals and anti-friction means aforementioned for the preferred embodiment may be used if desired. 
     Alternate embodiment shown in  FIG. 6  utilizes live spindle  135  to transmit torque to the rotor assemblies  16   a ,  16   b  instead of a fixed spindle means as shown in  FIGS. 2 and 3 . The cylindrical hubs  130   a  and  130   b  are similar to hubs  30   a  and  30   b  except for mounting apertures  133  which are shown splined. These hubs  30   a ,  30   b  are mated to there respective mounting splines  134 ,  136  to solid live spindle  135  and secured by washer  48  and retaining nut  50 . 
     The live axle arrangement may be adapted for use on many vehicle drive systems such as an agricultural type tractor or an automotive type wheel hub. Varying the different propulsion modes is accomplished utilizing actuating lever  119  (arrow) which is shown situated between rotor assemblies  16   a  and  16   b . The device to position lever  119  may be actuated from the 3-way hitch system typically found on the tractor mentioned above. Also, if desired, the lever  119  could be fixed so as not change the traction mode from one to another when consistently operating within one type of terrain. 
     In its particular application to the movement of an amphibious surface vehicle as hereinbefore described, the present invention provides a further significant advantage over conventionally wheeled vehicles. The synchro-phased rotary engaging device  14  exhibits a profile that is less than one third that of a circular wheel, with a comparable operating diameter, therefore a significant reduction in mass while providing a greater torque transfer. 
     Alternatively, those skilled in the art will readily recognize that a wide variety of other support structures and various other design configurations may be used while still enjoying the benefits and advantages of the invention as taught herein. While the description above contains much specificity, these should not be construed as limitations on the scope of the invention, but as exemplifications of the presently preferred embodiments thereof. Many other ramifications and variations are possible within the teachings of the invention. For example, if desired, the rotor assemblies  16   a ,  16   b  may be axially separated further so as to be essential one rotor per device  14 . The use of a fixed roller chain in the shape of the internal pitch curve S and sprocket(s) as a substitute to gearing for one or more of the fixed pinions having the periphery essentially the same as pitch curve Q. Without motive means or from human power means as with a wheel-chair like device for off-road use or steep inclines. This large overlapping contact area is especially useful where tipping may occur due the inherent stability of engagement device  14 . 
     Thus the scope of the invention should be determined by the appended claims and their legal equivalents, and not by the examples given.