Abstract:
This invention is a continuous variable transmission. This invention uses a mechanism known as “scotch yoke” principle to change the ratio of the input and output in the transmission. This invention uses a set of non-circular gears and circular gears to modify the input received from a system to deliver a steady and uniform output. It employs a unique way to change the ratio between the input and output of the transmission. Three very simple mechanisms are used to achieve changing the ratio. The option of reverse, park, and neutral gear mechanisms are integrated into this design. This invention offers a co-axial input to output feasibility.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The patents U.S. Pat. No. 5,603,240 and US 20100199805 use some of the features used in this design. The advantages in this invention include: 
         [0002]    The U.S. Pat. No. 5,603,240 does not have a co-axial input to output and therefore cannot be used for applications requiring this configuration. The output travels as the ratio is changed. Therefore, this design cannot be used when stationary output is required. The new invention offers a stationary and co-axial input and output shaft. The envelope used in this prior art is comparably larger. 
         [0003]    US 20100199805 offers a sinusoidal output and uses several modules just to minimize the “ripple” when a steady and uniform input is provided. Therefore, this design cannot be used when a steady and uniform output is desired. The new invention offers a steady and uniform output when the input is steady and uniform. This can be achieved with as low as three modules. 
       BRIEF SUMMARY OF THE INVENTION 
       [0004]    The main object of this invention is to provide a UNIFORM and STEADY output, when the input is uniform and steady, with the ability to transmit high torque without depending on friction or friction factor. Many of the continuous variable transmissions that is in the market today are friction dependent therefor lacks the ability to transmit high torque. Those continuous variable transmissions, which are non-friction dependent does not have a uniform and steady output when the input is uniform and steady. This design aids reduction in the overall size and economically mass produced. This design can be easily integrated into any system. This design is very versatile and can be used ranging from light duty to heavy duty. This design allows replacement of existing regular transmission, requiring very little modification. This design offers the option of stationary co-axial input and output. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0005]    FIG.  1 —CVT general assembly perspective view. 
           [0006]    FIG.  2 —CVT general assembly perspective view with frames made transparent showing general arrangements of internal sub-assembly of components. 
           [0007]    FIG.  3 —Frame—Main Housing—Two identical parts are bolted together to form one main housing:
       A. Perspective view showing details on one side of the main housing.   B. Perspective view showing details on the other side of the main housing.       
 
           [0010]    FIG.  4 —Frame—Telescopic Sleeve Guide perspective view. 
           [0011]    FIG.  5 —Frame—Cross-Rack Guide perspective view. 
           [0012]    FIG.  6 —Input Shaft perspective view. 
           [0013]    FIG.  7 —Intermediate Gear Shaft perspective view. 
           [0014]    FIG.  8 —Power Link Shaft perspective view. 
           [0015]    FIG.  9 —Carrier Shaft perspective view. 
           [0016]    FIG.  10 —Cross Rack Assembly showing two perspective views and orthographic views showing details of the input shaft slot and the crank pin slot, orientation of the racks and details of the prongs:
       A—Top view   B—Perspective view  1     C—Perspective view  2     D—Front view   E—Side view   F—Rear view G-Enlarged view showing details of the prong.       
 
           [0023]    FIG.  11 —Pinion:
       A—Front view   B—Side view   C—Top view   D—Perspective view       
 
           [0028]    FIG.  12 —Pinion Shaft:
       A—Front view   B—Side view   C—Perspective view       
 
           [0032]    FIG.  5 —Frame-Cross-Rack Guide perspective view. 
           [0033]    FIG.  6 —Input Shaft perspective view. 
           [0034]    FIG.  7 —Intermediate Gear Shaft perspective view. 
           [0035]    FIG.  8 —Power Link Shaft perspective view. 
           [0036]    FIG.  9 —Carrier Shaft perspective view. 
           [0037]    FIG.  10 —Cross Rack Assembly showing two perspective views and orthographic views showing details of the input shaft slot and the crank pin slot, orientation of the racks and details of the prongs:
       A—Top view   B—Perspective view  1     C—Perspective view  2     D—Front view   E—Side view   F—Rear view   G—Enlarged view showing details of the prong.       
 
           [0045]    FIG.  11 —Pinion:
       A—Front view   B—Side view   C—Top view   D—Perspective view       
 
           [0050]    FIG.  12 —Pinion Shaft:
       A—Front view   B—Side view   C—Perspective view       
 
           [0054]    FIG.  20 —Ratio Cam:
       A—Front view   B—Top view   C—Perspective view       
 
           [0058]    FIG.  21 —Non-circular Gear (Driven):
       A—Top view   B—Front view   C—Perspective view       
 
           [0062]    FIG.  22 —Non-circular Gear (Driving):
       A—Top view   B—Front view   C—Perspective view       
 
           [0066]    FIG.  23 —Dummy Crank Pin:
       A—Top view   B—Front view   C—Perspective view       
 
           [0070]    FIG.  24 —Crank Pin:
       A—Top view   B—Front view   C—Side view   D—Perspective view       
 
           [0075]    FIG.  25 —Intermediate Circular Gear C 2 -C 3 :
       A—Front view   B—Side view   C—Perspective view   FIG.  26 —Carrier Gear C 4   a -C 5   b:      A—Front view   B—Side view   C—Perspective view       
 
           [0083]    FIG.  27 —Intermediate Circular Gear C 4 -C 5 :
       A—Front view   B—Side view   C—Perspective view.       
 
           [0087]    FIG.  28 —Intermediate Circular Gear C 1 :
       A—Front view   B—Side view   C—Perspective view       
 
           [0091]      FIG. 29-Spacer :
       A—Front view   B—Top view   C—Perspective view         
           [0095]    FIG.  30 —Gear Changing Lever for Spiral flute mechanism:
       A—Front view   B—Side view   C—Top view   D—Perspective view       
 
           [0100]    FIG.  31 —Spiral Flute:
       A—Front view   B—Side view   C—Perspective view       
 
           [0104]    FIG.  32 —Stationary differential Collar:
       A—Front view   B—Side view   C—Section view   D—Perspective view       
 
           [0109]    FIG.  33 —Dynamic differential Collar:
       A—Front view   B—Side view   C—Section view   D—Perspective view       
 
           [0114]    FIG.  34 —Sleeve—Input-Bevel perspective view: 
           [0115]      FIG. 35  thru  43 —Views showing the movement/position on rack assembly, crank pin as input disk rotates: shown at various stages: 
           [0116]    FIG.  35 —Crankpin closer to the axis and input disk at 0° 
           [0117]    FIG.  36 —Crankpin closer to the axis and input disk at 45° 
           [0118]    FIG.  37 —Crankpin closer to the axis and input disk at 90° 
           [0119]    FIG.  38 —Crankpin at midpoint and input disk at 0° 
           [0120]    FIG.  39 —Crankpin at midpoint and input disk at 45° 
           [0121]    FIG.  40 —Crankpin at midpoint and input disk at 90° 
           [0122]    FIG.  41 —Crankpin farthest from the gear and input disk at 0° 
           [0123]    FIG.  42 —Crankpin farthest from the gear and input disk at 45° 
           [0124]    FIG.  43 —Crankpin farthest from the gear and input disk at 90° 
           [0125]    FIG.  44 —Exploded view describing Input Modification—perspective view. Details showing arrangements and gear train of non-circular gear and intermediate gears to input disk. 
           [0126]      FIG. 45  thru  46 —Perspective view of ratio cam, input disk and crankpin showing operation behind how the cam alters the pin location 
           [0127]    FIG.  45 —input disk side (for clarity the ratio cam and input disk are shown transparent). 
           [0128]    FIG.  46 —Ratio cam side. 
           [0129]      FIG. 47  thru  50  Views showing working of planetary gear changing mechanism: 
           [0130]    FIG.  47 —Planetary Gear Changing Mechanism perspective view. The main frame is made partially transparent for clarity. 
           [0131]    FIG.  48 —Perspective view showing planetary gear changing mechanism view and detail of the circular slot in the main frame. The main frame is made partially transparent for clarity. (close up) 
           [0132]    FIG.  49 —Front view showing planetary gear changing mechanism. The main frame is made transparent for clarity. 
           [0133]    FIG.  50 —Sideview showing planetary gear changing mechanism. The main frame is made transparent for clarity. 
           [0134]    FIG.  51 —Exploded view showing Differential Mechanism, showing component arrangements and working (perspective view). 
           [0135]      FIG. 52  thru  57 —Views describing the ratio changing operation of the differential mechanism at various stages-shown partially sectioned to explain the function and interior details: 
           [0136]    FIG.  52 —Differential Mechanism (partially sectioned) view  1 . 
           [0137]    FIG.  53 —Differential Mechanism (partially sectioned) view  2 . 
           [0138]    FIG.  54 —Differential Mechanism (partially sectioned) view  3 . 
           [0139]    FIG.  55 —Differential Mechanism (partially sectioned) view  4 . 
           [0140]    FIG.  56 —Differential Mechanism (partially sectioned) view  5 . 
           [0141]    FIG.  57 —Differential Mechanism (partially sectioned) view  6 . 
           [0142]    FIG.  58 —Assembly showing working of gear changing mechanism—Spiral Flute Mechanism (exploded). 
           [0143]    FIG.  59 —Top view explaining working of the telescopic guide. 
           [0144]    FIG.  60 —Details of telescopic mechanism. The primary and sectonday on one side made transparent to show details. 
           [0145]      FIG. 61  thru  62 —Assembly of input disk, cross rack assembly, crank pin and crank pin retainer to show the concept behind function of crankpin retainer. 
           [0146]      FIG. 61  Crank pin and the crank pin retainer when they are in the middle of input slot. 
           [0147]    FIG.  62 —Crank pin and the crank pin retainer as it exits the input slot. 
           [0148]    FIG.  63 —Exploded view of one-way bearing assembly (pinion partially sectioned showing interior details). 
           [0149]    FIG.  64 —One-way bearing assembly. 
           [0150]    FIG.  65 —Power link Assembly. 
           [0151]    FIG.  66 —Assembly showing concept of vibration cancelation. 
           [0152]    FIG.  67 —Vibration Cancelation Mechanism: sub-assembly. 
           [0153]    FIG.  68 —Complete CVT Assembly showing the orientation of modules and orientation of racks: explaining how the 4 modules are placed. 
           [0154]      FIG. 69  thru  72 —Options of placement of non-circular gears, when a common non-circular driving gear is used with two non-circular driven gears. 
           [0155]      FIG. 69  non-circular gear placed at 135° 
           [0156]      FIG. 70  non-circular gear placed at 45° 
           [0157]      FIG. 71  non-circular gear placed at (—45°) 
           [0158]      FIG. 72  non-circular gear placed at (—135°) 
           [0159]      FIG. 73  thru  75 —Details showing how constant and uniform output is achieved: 
           [0160]    FIG.  73 —Assembly orientation of individual modules. 
           [0161]    FIG.  74 —Graph showing individual output at each rack and combined total output showing constant and uniform output with overlaps. 
           [0162]    FIG.  75 —Graphical representation of output with overlaps and sequence of engagement for a complete cycle. 
           [0163]      FIG. 76  thru  79 —Miter gear assembly describing forward, reverse, neutral and park gears: 
           [0164]    FIG.  76 —Engagement of clutches for a Forward gear. 
           [0165]    FIG.  77 —Engagement of clutches for a Reverse gear. 
           [0166]    FIG.  78 —Engagement of clutches for a Neutral gear. 
           [0167]    FIG.  79 —Engagement of clutches for “Park”. 
           [0168]    FIG.  80 —Concept of using of intermediate gear to eliminate multiple contacts between non—circular gears:
       A—top view   B—front view       
 
           [0171]    FIG.  81 —Co-axial output element with internal gears:
       A—Front view   B—Section side view   C—Perspective view       
 
           [0175]    FIG.  82 —Detail showing arrangement of co-axial output member in the assembly. 
           [0176]    FIG.  83 —Formula used to calculated the radius of the non-functional portion of the driving gear 
           [0177]    FIG.  84 —Mathematical derivation of the shape of the non-circular gears such that the linear velocity of the rack  64  is constant 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Summary of the Invention 
       [0178]    To briefly describe this invention is a Continuously Variable Transmission (CVT). Unlike existing CVT designs, this particular design does NOT depend on friction to transmit power. Most of the CVTs that exist today depend on friction to transmit power and thereby cannot be used where there is a need to transmit high power at low speed. Due to this advantage, it is possible to use this invention where high torque transmission is required. Co-axial input and output can be achieved with this layout. 
         [0179]    The working of this CVT can be described by the following simple sequential operations. 
         [0000]    a) A crank pin ( FIG. 23 ), revolves around the axis of an input disk ( FIG. 14 ) at an offset distance, and this offset distance can be altered. [The concept described in this operation exists in another patent US 20100199805. However, here an entirely different approach is adapted on how this concept is used, how the offset is altered etc. in a much simpler, and compact envelop.]
 
b) This offset crank pin  42  is caged in a slot of a rack assembly ( FIG. 10 ), and the rack assembly is restricted such that the rack can move only in the direction parallel to the rack  64 . By orienting another slot normal to the direction of movement, the rotational movement of the crank pin  42  is translated to pure linear back and forth movement of the rack  64 . This mechanism is commonly known as “scotch yoke mechanism” in the industry. The distance of this linear back and forth movement (stroke) is directly proportional to the radial distance of the crank pin  42  from the axis of the input disk  16 .
 
c) The rack  64  is linked to a pinion ( FIG. 11 ) converting this linear movement of the rack  64  to rocking oscillation of the pinion  47 .
 
d) This rocking oscillation movement is converted to a unidirectional rotation, using a ratchet mechanism/one-way bearing/computer controlled clutch.
 
         [0180]    One main purpose of this invention is to achieve a CONSTANT AND UNIFORM output angular velocity when the input angular velocity is constant and uniform. However, using the steps described above, this is NOT achieved, as the output is sinusoidal. By modifying the rate of change of angular displacement of the input disk  16 , uniform steady output can be achieved. By using a set of non-circular gears, the driving ( FIG. 22 ) and the driven ( FIG. 21 ), the rate of change in angular displacement at the input disk  16  can be altered. The output from the driven non-circular gear  9  is then transferred to the input disk  16  via some intermediate circular gears. 
         [0181]    The profile of the driving non-circular gear  8  is given by the equation, when radius “r” expressed 
         [0182]    Call as a function of θ is 
         [0000]    
       
         
           
             
               
                 
                   r 
                   
                     v 
                     1 
                   
                 
                  
                 
                   ( 
                   θ 
                   ) 
                 
               
               = 
               
                 
                   R 
                   * 
                   K 
                   * 
                   CTR 
                 
                 
                   
                     R 
                     * 
                     K 
                   
                   + 
                   
                     f 
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                 
               
             
             , 
           
         
       
     
         [0000]    where “K” is a constant depends on radii of all constant gears and, “R” is the desired ratio between rate of change in angular displacement of the input at the driving non-circular gear  8  and the output at the input disk  16 , 
         [0183]    The ideal value for “R” is generally 1. “K” is derived from the radii of the intermediate gears and it is equal to the product of the radii of the driven gears divided by the product of the radii of the driving gears. The ideal value for “K” is generally 1. “CTR” is the center-to-center distance of the two non-circular gears  8 &amp; 9 . This is chosen based on the available envelop for the assembly. 
         [0184]    f (θ) can be either sin 0 or cos 0. Both the formulae will yield identical and interchangeable profile, except they are rotated 90°. 
         [0185]    The profile of the driven non-circular gear  9  is given by the formula 
         [0000]    
       
         
           
             
               
                 
                   r 
                   
                     v 
                     2 
                   
                 
                  
                 
                   ( 
                   θ 
                   ) 
                 
               
               = 
               
                 CTR 
                 - 
                 
                   
                     R 
                     * 
                     K 
                     * 
                     CTR 
                   
                   
                     
                       R 
                       * 
                       K 
                     
                     + 
                     
                       f 
                        
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                 
               
             
             , 
           
         
       
     
         [0186]    The derivation of these profile shapes and the parameters used are explained in detail in subsequent topics. 
         [0187]    To aid in comprehending the invention a CAD model is designed, created, and explained below. 
         [0188]    The features used here are: 
         [0189]    The chosen value for “R” is 1. 
         [0190]    The chosen value for “K” is 1. 
         [0191]    A common input shaft ( FIG. 6 ) and a driving non-circular gear  8  are used for all four modules. 
         [0192]    A common cross-rack assembly  44 , input disk  16 , driven non-circular gear  9 , intermediate circular gears, crank pin  42 , ratio cam ( FIG. 20 ), and ratio changing mechanism is used for two modules. 
         [0193]    Two racks  64  are placed on the cross-rack assembly  44  with a phase shift of 180° 
         [0194]    Another identical assembly of modules is placed such that the second assembly of module is a lateral inversion of the first assembly of module and rotated by 90°. 
       LIST OF COMPONENTS 
       [0000]    
       
         
           
             1) Frame—Main housing 
             2) Frame—Cross-rack guide 
             3) Frame—Telescopic guide 
             4) Input shaft 
             5) Input shaft bearing 
             6) Intermediate gear shaft 
             7) Intermediate gear shaft bearing 
             8) Non-circular gear (driving) 
             9) Non-circular gear (driven) 
             10) Intermediate circular gear C 1   
             11) Intermediate circular gears C 2 -C 3   
             12) Intermediate circular gears C 4 -C 5   
             13) Bearing—collar (stationary and dynamic) 
             14) Bearing—circular gear C 2 -C 3   
             15) Bearing—circular gear C 4 -C 5   
             16) Input disk 
             17) Bearing—input disk 
             18) Ratio cam 
             19) Bearing—ratio cam 
             20) Intermediate carrier circular gears C 4   a -C 5   a    
             21) Carrier shaft 
             22) Bearing—carrier shaft 
             23) Ratio changing lever—planetary mechanism 
             24) Sleeve—Input disk—bevel 
             25) Stationary differential collar 
             26) Stationary differential collar spur shaft bearing 
             27) Stationary differential collar spur gear shaft 
             28) a) Stationary differential collar small bevel gear
           b) Stationary differential collar large bevel gear   
         
             29) Stationary differential collar spur gear 
             30) Spacer 
             31) Dynamic differential collar 
             32) Dynamic differential collar spur shaft bearing 
             33) Dynamic differential collar spur gear shaft 
             34) a) Dynamic differential collar small bevel gear
           b) Dynamic differential collar large bevel gear   
         
             35) Dynamic differential collar spur gear 
             36) Universal joint 
             37) Spiral flute 
             38) Slotted disk—input disk 
             39) Compression spring 
             40) Thrust bearing 
             41) Ratio changing lever—spiral flute mechanism 
             42) Crank pin 
             43) Dummy crank pin 
             44) Cross-Rack assembly 
             45) Primary telescopic sleeve 
             46) Secondary telescopic sleeve 
             47) Pinion 
             48) Pinion shaft 
             49) Pinion bearing 
             50) One-way bearing 
             51) Output Sprocket/gear 
             52) Power link shaft 
             53) Power link shaft bearing 
             54) Power link Sprocket/gear 
             55) Dummy rack 
             56) Wheel—vibration cancellation 
             57) Collar—wheel-vibration cancellation 
             58) Input shaft for miter bevel gears 
             59) Miter bevel gear 
             60) Clutch—park/neutral/reverse 
             61) Output shaft 
             62) Intermediate gear—non-circular gear connector 
             63) Guide—intermediate gear-non-circular gear connector 
             64) Rack 
             65) Co-axial output element with internal gear
 
Description of Assembly, Sub-Assembly of Components and their Functions:
 
           
         
       
     
       Description of the General Construction: 
       [0262]    The input shaft ( FIG. 6 ) is mounted on two input shaft bearings  5  and placed in the center of the frame-main housing(s) ( FIG. 3 ). The input disk  16  is mounted on the input shaft  4  and sandwiched between the rack assembly ( FIG. 10 ) and the ratio cam ( FIG. 20 ) and the crank pin  42  is caged in the slot, The crank pin  42  has a body shaped like rectangular prism with circular prism extended on both sides. One of them functions as a cam-follower, made to engage with the ratio cam and other functions as a crank pin  42 , and made to engage with the rack  64  on the cross rack assembly  44 . Parallel to the input disk  16  the driving non-circular gear  8  is mounted on the input shaft  4 . 
         [0000]    The intermediate gear shaft ( FIG. 7 ) is mounted on two constant gear shaft bearings  7 , with one in each of main housing  1 . The intermediate gear shaft  6  is placed parallel to the input shaft  4  at a distance “CTR” that is used to derive the shape of the non-circular gears. The powertrain flow from the input shaft  4  to the input disk  16  is as per the table provided below. 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
               
                   
                   
                 Type of  
               
               
                 From 
                 To 
                 Connection 
               
               
                   
               
             
             
               
                 Input shaft 
                 Non-Circular  
                 Axial Rigid 
               
               
                   
                 Gear Driven 
                   
               
               
                 Non-Circular  
                 Non-Circular  
                 Radial 
               
               
                 Gear-Driven 
                 Gear-Driving 
                   
               
               
                 Non-Circular  
                 Intermediate gear 1 
                 Axial; Rigid 
               
               
                 Gear-Driving 
                   
                   
               
               
                 Intermediate gear 1 
                 Intermediate gear 2 
                 Radial 
               
               
                 Intermediate gear 2 
                 Intermediate gear 3 
                 Axial, Rigid 
               
               
                 Intermediate gear 3 
                 Intermediate gear 4 
                 Radial 
               
               
                 Intermediate gear 4 
                 Intermediate gear 5 
                 Axial, Rigid 
               
               
                 Intermediate gear 5 
                 Slotted disk 
                 Radial 
               
               
                   
               
             
          
         
       
     
         [0263]    The driven non-circular gear  9  and the intermediate gear C 2 -C 3  ( FIG. 25 ) are mounted on the input shaft  4  and the intermediate gear- 1  ( FIG. 28 ) and intermediate gear C 4 -C 5  ( FIG. 27 ) are mounted on the constant gear shaft  6 . The driving non-circular gear  8  is directly mounted on the input shaft  4 , and the driven non-circular gear  9  along with the intermediate gear-C 1   10  are mounted directly on the intermediate gear shaft  6 . The others are placed in a bearing and mounted on their respective shafts. 
         [0264]    The rack assembly  44  is free to move only along the direction of the rack  64  and its movement is restricted by the frame-rack guide  2 . A set of telescopic-sleeves, primary ( FIG. 18 ) and secondary ( FIG. 19 ), are placed on either side of the rack assembly  44 . This will decrease the overall size needed for the rack assembly  44  and the frame main housing  1 . A prong placed on either side of the rack assembly  44  and another on the secondary sleeve  46 , to pull and extend the telescopic sleeves and the telescopic sleeves are collapsed by the body of the rack assembly  44 . These telescopic-sleeves are caged-in by the frame telescopic-guide ( FIG. 4 ). 
         [0265]    The rack  64  is coupled with a one-way bearing assembly ( FIG. 64 ) that consists of a pinion  47  that is placed on a pinion shaft ( FIG. 12 ). This pinion shaft  48  is mounted on the frame telescopic-guide  3  with a pinion bearing  49 . A gear or a sprocket is mounted on this pinion shaft  48  through a one-way-bearing  50  and is placed parallel to the pinion  47 . A power link shaft assembly ( FIG. 65 ) is placed parallel to the one-way bearing assembly ( FIG. 64 ). The power link assembly consists of a power link shaft ( FIG. 8 ) that is mounted on two bearings that are placed on the frame-telescopic-guide  3 . A gear or sprocket is placed on the power link shaft&#39;s each ends. The power from the pinion shaft  48  is transmitted to the power link through this gear or sprocket. 
       The Working and the Concept of the Main CVT: 
       [0266]    When the input disk  16  rotates, by the ‘scotch yoke’ mechanism the crank pin  42  moves the cross rack assembly in the direction parallel to the rack  64 . The distance travel by such movement is directly proportional to the distance of the axis of the crank pin  42  from the axis of the input disk  16 . By altering this distance, the distance travelled by the rack assembly, this is termed as “stroke” can be altered. Since the work done is constant, which is a product of force applied multiplied by the distance traveled (F*stroke). For a smaller stroke, the force applied is greater and for a longer stroke, the force applied is smaller. However, the motion is back and forth oscillation. This force from the linear back and forth motion of the rack  64  is later transferred to a pinion  47  as a rocking motion. The torque generated by this rocking motion is directly proportional to the force applied from the rack  64 . This is transferred to an output sprocket/gear via a one-way bearing  50  or a computer controlled clutch or a ratchet mechanism to a unidirectional rotation. This unidirectional rotation is further delivered to the wheels. 
         [0000]    Arrangement of Transmission of Power from Engine/Power Source to Input Disk  16 : 
         [0267]    By using a set of non-circular gears, the driving ( FIG. 8 ) and the driven ( FIG. 9 ), the rate of change in angular displacement at the input disk  16  is altered. The output from the input shaft  4  is transferred through a set of non-circular gears and then transferred to the input disk  16  via five intermediate circular gears. The non-circular driving gear  8  is mounted directly on the input shaft  4 . The driven non-circular gear  9  is mounted on the intermediate gear shaft ( FIG. 7 ), which is mounted on two bearings  7  and placed on the two main housings  1 . 
         [0268]    The intermediate circular gear-C 1   10  is mounted on the intermediate gear shaft  6 , with a direct connection to the driven non-circular gear  9 . The intermediate gear C 2 -C 3  ( FIG. 25 ) is mounted on the input shaft  4 , free to spin with a bearing  14 . The intermediate gear C 4 -C 5  ( FIG. 26 ) is mounted on the intermediate gear shaft  6  that is free to spin with a bearing  15  and intermediate gear C 5  drives the input disk  16 . The radius of these intermediate gears are chosen such that the input disk  16  completes one revolution when the driving non-circular gear ( FIG. 22 ) completes one revolution. It should satisfy the conditions—rC2/rC1=n1, rC4/rC3=n2, and rdisc/rC5=n1*n2 and the K value will be 1. 
         [0000]    Reason Behind the Need for a Circular Gear Between the Non-Circular Gears when the Profile Interferes/Multiple Contacts at the Same Instant: 
         [0269]    Depending on the values chosen for the variables “R”, “K” and “CTR” the shape of the non-circular gears could have multiple contact points at any given point of time. From the equations for the non-circular gear profiles, it can be seen that the radius of the driven non-circular gear  9  is lower than the input shaft  4  it is mounted on over a wide region and reaches zero at two locations. In addition, there is a potential that, due to the shape of the profile, the driven non-circular gear  9  and the driving non-circular gear  8  may have multiple contact points at a given time. This can be eliminated by inserting an intermittent circular gear  62  between the two non-circular gears. This increases the distance between the two non-circular gears and eliminates the issue of multiple contact point at any given time. 
       Concept Behind Using Ratio-Changing Cam: 
       [0270]    In order to change the input to output ratio, the location of the crank pin  42  must be changed. This can be achieved by rotating the ratio cam plate  18  which has a slot with a certain profile. When the ratio cam plate  18  is rotated with respect to the input disk  16  this profile forces the crank pin  42  to move in radial direction of the disk axis. This is because the axis of the crank pin  42  intersects the slot input disk  16  and the slot in the ratio cam plate  18 . When the crank pin  42  is closer to the axis of the input disk  16  the stroke is shorter and since the work done is constant, the force is increased. Similarly with the crank pin  42  is farther from the axis of the input disk  16 , the stroke is longer and since the work done is constant, the force is decreased. The challenge here is to have the ratio cam plate  18  and the input disk  16  spinning synchronized during normal operation however, and when the ratio change is desired, the input disk  16  and the ratio cam plate  18  should have a relative angular velocity. By using one of the three mechanisms described below, a relative angular velocity between the input disk  16  and the ratio cam plate  18  can be achieved, when desired. 
       The Methods to Change Ratio: 
     1. Planetary Mechanism: 
       [0271]    A set of intermediate carrier circular gears, C 4   a , and C 5   a  ( FIG. 26 ) are axially connected and mounted on a common carrier shaft ( FIG. 9 ). C 4   a  is identical to the circular gear C 4  and C 5   a  is identical to the circular gear C 5 . The movement of this common axis is restricted to a circular slot/path, which is at a constant distance from the rotation axes of the input disk  16  and the ratio cam plate. The gear  4   a  is radially connected to gear C 3  and the gear C 5   a  is radially connected to the ratio cam plate  18 . A ratio-changing lever—planetary mechanism ( FIG. 37 ), pivoted on the frame enables the location of the carrier shaft  21  to move along the slot. While the location is being displaced, there is a relative angular displacement between the input disk  16  and the ratio cam plate  18 . 
       2. Spiral Flute Mechanism: 
       [0272]    A spiral fluted input disk collar ( FIG. 38 ) with twisted profile is axially attached to the input disk  16 . Slots matching the twisted profile of the spiral flute is broached on the ratio cam plate  18  and placed co-axial to the input disk  16 . When the distance between the ratio cam plate  18  and the input disk  16  remain unchanged, the input disk  16  and the ratio cam plate  18  spin synchronized. While the distance between the input disk  16  and the ratio cam plate  18  is being altered, the relative angular velocity between the input disk  16  and the ratio cam plate  18  changes as the ratio cam plate  18  is forced to rotate with respect to the input disk  16 . This axial translation is achieved with a ratio-changing lever-spiral flute mechanism ( FIG. 40 ) that pushes a thrust bearing  40  attached to the ratio cam plate  18  towards the input disk  16 . This is sprung back with a compression spring ( FIG. 39 ) placed between the input disk  16  and the ratio cam plate  18 . 
       3. Differential Mechanism: 
       [0273]    A stationary collar large bevel gear  28   b  is axially attached to the input disk  16  via a sleeve—input disk to bevel ( FIG. 32 ). A stationary differential collar ( FIG. 32 ), which is co-axially spaced to the large bevel gear  28   b , by a thrust bearing  40  is free to spin independently with respect to the large bevel gear  28   b . The stationary differential collar  25  is restricted to move axially with respect to the large bevel gear  28   b . A, free to spin stationary collar shaft  27  is placed normal to the axis of the stationary differential collar  25  in a bearing  26  placed in the stationary differential collar  25 . A stationary collar small bevel gear- 128   a  and a stationary differential collar spur gear  29  is axially and rigidly attached to the stationary differential collar shaft  27  and the stationary collar small bevel gear  28   a  is paired with the stationary collar large bevel gear  28   b.    
         [0274]    Similarly, 
         [0275]    A dynamic large bevel gear ( FIG. 17 ) is co-axially placed parallel to the ratio cam plate such that they spin synchronized but allowing displacement between them along the axis. A dynamic differential collar ( FIG. 33 ) which is co-axially placed to the dynamic collar large bevel gear  28   a  spaced by a thrust bearing  40  is free to spin independently with respect to the dynamic collar large bevel gear  34   b . The dynamic differential collar  31  is restricted to move axially with respect to the dynamic collar large bevel gear  34   a . A, free to spin dynamic collar shaft  33  with a universal joint  36  placed in its axis is placed normal to the axis of the dynamic differential collar in a bearing  32  placed in the dynamic differential collar  31 . A dynamic collar small bevel gear  34   a  and a dynamic collar spur gear  35  is axially and rigidly attached to the dynamic collar spur gear shaft  33  and the dynamic collar small bevel gear  34   a  is paired with the dynamic collar large bevel gear  34   b . The universal joint  36  is common to the dynamic collar spur gear shaft  33  and the small bevel gear shaft, allowing a small mismatch. 
         [0276]    A spacer keeps the two spur gears in contact. The spacer ( FIG. 29 ) is free to move axially with respect to dynamic collar spur gear shaft  33 . 
         [0277]    Here the stationary differential collar  25  and the dynamic differential collar  31  are identical and interchangeable. 
         [0278]    By this arrangement the dynamic flow train is as described below 
         [0000]    a. The stationary collar large bevel gear  28   a  spins stationary collar small bevel gear  28   b.  
 
b. The stationary collar small bevel gear  28  spins the stationary collar shaft  27 .
 
c. The stationary collar shaft  27  spins the stationary collar spur gear  29 
 
d. The stationary collar spur gear  29  spins dynamic collar spur gear  35 .
 
e. The dynamic collar spur gear  35  spins dynamic collar shaft  33 .
 
f. The dynamic collar shaft  33  thru the universal joint  36  spins the dynamic collar small bevel gear  34   a.  
 
g. The dynamic collar small bevel gear  34   a  spins the dynamic collar large bevel gear  34   b.  
 
h. The dynamic collar large bevel gear  34   b  spins the ratio cam plate  18 .
 
         [0279]    Since the two large bevel gears, the two small bevel gears, and the spur gears are identical and same size respectively, when the dynamic differential collar  31  is stationary, the angular velocity of the ratio cam plate  18  is synchronized with the input disk  16 . While the dynamic differential collar  31  is being rotated with respect to the stationary differential collar  25 , there will be a relative angular displacement between the input disk  16  and the ratio cam plate  18 . 
       Concept Behind Using Telescopic-Sleeve to Enable a Compact Design: 
       [0280]    For this design to work the length of the input slot of the rack assembly has to be a value equal to 2*stroke+input-shaft diameter+2*minimum material thickness+2*the distance to reach the rack guide. This entire length has to be guided by the rack guide. Since the rack guide also has to accommodate the travel of the rack  64 , the opening portion of the rack guide should have a width at least as the diameter of the input disk  16  or it will be out of reach when the rack  64  travels to one side to the extreme. The telescopic-guide extends the support and as a result, the overall length of the rack assembly can be reduced by the “distance to reach the rack guide.” This also makes it possible for the main housing  1  to be shorter by that distance. Prongs are provided in the design of the rack assembly and in the secondary sleeves to extend the telescopic-sleeves. The body of the rack assembly collapses the telescopic-sleeves. 
       Concept Behind Use/Working Function of Slider Guide: 
       [0281]    The crank pin is much smaller than the input-shaft  4 . Since both the slot cross each other, there is a potential that the crank pin can slip in to the input-shaft slot. This is eliminated by using a slider guide ( FIG. 13 ) that is larger than the input-shaft slot. This is made to float in the crank pin slot enclosing the crank pin  42 . 
       Overlap of Power Transmission, Design in Implementing the Concept: 
       [0282]    To ensure smooth transition from one module to the next, for a brief period both the modules are active and engage when the output from both of them reach a constant and uniform value. The first module disengages while it is still in the functional region and the second module is well in the functional region. 
         [0000]    Modules and their Assembly Layout and Constraints: 
         [0283]    All the four modules share one common input-shaft and one common non-circular driving gear. Two of the modules share a common input disk  16  and gear changing mechanism. The Racks are placed at 90° phase shift to the next. To accommodate this, the driven non-circular gear  9  is oriented at 45° with the driven non-circular gear  9  phased at 45° relative to the other non-circular driven gear. Also due to the fact the non-circular gears are symmetric it can be also oriented at 135°. This adds up to a 90° phase shift between racks. 
       Concept of Power Transfer/Link Between Modules: 
       [0284]    When the modules operate in sequence, they must be linked before the power is transferred to the wheels. This is achieved by using a power link shaft  52  that has gears or sprocket to link the output from each module such that it has a continuous power to the wheels. The power is also transferred in sequence. 
       Reverse Gear Mechanism: 
       [0285]    The output from the power link shaft  52  is coupled with input-shaft  4  of a miter bevel gear differential mechanism, The output of these miter gears will therefore revolve in opposite direction. The output shaft  61  if this differential mechanism is placed co-axial to the output miter bevel gears with clearance so that free to spin independently with respect to the output miter bevel gears. Two collars with a clutch are placed on the output shaft  61  allowing them to move axially. These can be made to link with either of the output miter bevel gears, which revolve in opposite direction. When one of the collars is made to link, by means of clutch, with a particular output miter bevel gear and the output shaft  61  will revolve is a particular direction. It will reverse its direction if the link is swapped to the other output miter gear. 
       Neutral Gear Mechanism: 
       [0286]    When the collars are not in link with any of the output miter bevel gears, the collar and the output shaft  61  are not restricted and, thus, they ares free to spin in any direction and function as a “neutral” gear. 
       Park Mechanism: 
       [0287]    When the collars are in link with both the output miter bevel gears, the collar is restricted from spinning and functions as a “parking” gear. 
       Feature and Mechanism to Compensate Vibration: 
       [0288]    1. Dummy crank pin: The crank pin is placed off-center when the input disk  16  revolves. This imbalance will result in vibration. To compensate this, a dummy crank pin is placed at same distance 180° apart. This is moved by the same ratio cam that moves the crank pin. This movement is identical to the movement of the crank pin. The cam slots are made identical at 180° apart. 
         [0289]    2. Dead weight for counter oscillation: As the input disk  16  rotates the cross rack assembly has a oscillatory motion which will result in vibration. It is cancelled by having an appropriate mass oscillating in the opposite direction. This is achieved by attaching a wheel in contact with the rack  64 , which will spin back and forth. Bringing an appropriate mass in contact with the wheel at 180° apart will compensate for this vibration. 
       Co-Axial Input and Output Option Feature: 
       [0290]    When co-axial input and output is desired, this can be achieved by adding a output member  65  which has an internal gear which is paired with the power link gear. A bearing is placed between input shaft  4  and the co-axial output member  65 , allowing them to spin independently. 
       Constraints: 
       [0291]    When K=1 and R=1, the Conditions that Apply are: 
         [0292]    The number of teeth on driving non-circular gear ( FIG. 22 ) should be same as number of teeth on driven non-circular gear ( FIG. 21 ), which means their perimeters are the same. i.e. they complete 1 revolution at the same time even though the instantaneous speeds may not be the same. Alternatively, the portion that does not follow the desired shape, i.e. the portion where minimum radius ‘r’ is used, 2nd set of non-circular gears can be used optionally in parallel to achieve the goal. 
         [0000]        rc 2/ rc=n 1, rc 4/ rc 3= n 2, and  r disc/ rc 5= n 1* n 2 apply. 
         [0293]    Desired but not mandatory (rv 1 +rv 2 )=(rc 3 +rc 4 )=(rc 5 +rdisc)=(rc 1 +rv 2 )=ctr. This will allow placing of all the driving and driven gears on two common shafts, of which one of them being the input-shaft  4 . 
       Mathematical Derivations: 
       [0294]    The main aim is to determine a mathematical formula for the shape of the non-circular gears such that v rack  (linear velocity of the rack  64 ) is constant. 
         [0000]    
       
         
           
             
               ω 
               INPUT 
             
             = 
             
               ω 
               
                 v 
                 1 
               
             
           
         
       
       
         
           
             
               
                 r 
                 
                   v 
                   1 
                 
               
               * 
               
                 ω 
                 
                   v 
                   1 
                 
               
             
             = 
             
               
                 r 
                 
                   v 
                   2 
                 
               
               * 
               
                 ω 
                 
                   v 
                   2 
                 
               
             
           
         
       
       
         
           
             
               ω 
               
                 v 
                 2 
               
             
             = 
             
               ω 
               
                 c 
                 1 
               
             
           
         
       
       
         
           
             
               
                 r 
                 
                   c 
                   1 
                 
               
               * 
               
                 ω 
                 
                   c 
                   1 
                 
               
             
             = 
             
               
                 r 
                 
                   c 
                   2 
                 
               
               * 
               
                 ω 
                 
                   c 
                   2 
                 
               
             
           
         
       
       
         
           
             
               ω 
               
                 c 
                 2 
               
             
             = 
             
               ω 
               
                 c 
                 3 
               
             
           
         
       
       
         
           
             
               
                 r 
                 
                   c 
                   3 
                 
               
               * 
               
                 ω 
                 
                   c 
                   3 
                 
               
             
             = 
             
               
                 r 
                 
                   c 
                   4 
                 
               
               * 
               
                 ω 
                 
                   c 
                   4 
                 
               
             
           
         
       
       
         
           
             
               ω 
               
                 c 
                 4 
               
             
             = 
             
               ω 
               
                 c 
                 5 
               
             
           
         
       
       
         
           
             
               
                 r 
                 
                   c 
                   5 
                 
               
               * 
               
                 ω 
                 
                   c 
                   5 
                 
               
             
             = 
             
               
                 r 
                 disk 
               
               * 
               
                 ω 
                 disk 
               
             
           
         
       
       
         
           
             
               v 
               rank 
             
             = 
             
               
                 ω 
                 disk 
               
               * 
               
                 r 
                 gear 
               
               * 
               
                 f 
                  
                 
                   ( 
                   θ 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 v 
                 rack 
               
               
                 r 
                 gear 
               
             
             = 
             
               ω 
               OUTPUT 
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 ω 
                 DISK 
               
               * 
               
                 r 
                 gear 
               
               * 
               
                 f 
                  
                 
                   ( 
                   θ 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 r 
                 disk 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 r 
                 disk 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   
                     c 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   
                     c 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 
                   r 
                   
                     c 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   
                     v 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 
                   r 
                   
                     c 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   
                     v 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     v 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 
                   r 
                   
                     v 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
             
           
         
       
       
         
           
             
               ω 
               OUTPUT 
             
             = 
             
               
                 
                   ω 
                   INPUT 
                 
                 * 
                 
                   r 
                   
                     v 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 
                   r 
                   
                     v 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
             
           
         
       
       
         
           
             
               
                 ω 
                 OUTPUT 
               
               
                 ω 
                 INPUT 
               
             
             = 
             R 
           
         
       
       
         
           
             R 
             = 
             
               
                 
                   r 
                   
                     v 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
                 * 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
               
                 
                   r 
                   
                     v 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
             
           
         
       
       
         
           
             K 
             = 
             
               
                 
                   r 
                   
                     c 
                     2 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     4 
                   
                 
                 * 
                 
                   r 
                   disk 
                 
               
               
                 
                   r 
                   
                     c 
                     1 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     3 
                   
                 
                 * 
                 
                   r 
                   
                     c 
                     5 
                   
                 
               
             
           
         
       
       
         
           
             
               
                 R 
                 * 
                 K 
               
               
                 f 
                  
                 
                   ( 
                   θ 
                   ) 
                 
               
             
             = 
             
               
                 r 
                 
                   v 
                   1 
                 
               
               
                 r 
                 
                   v 
                   2 
                 
               
             
           
         
       
       
         
           
             
               
                 r 
                 
                   v 
                   1 
                 
               
               + 
               
                 r 
                 
                   v 
                   2 
                 
               
             
             = 
             CTR 
           
         
       
       
         
           
             
               r 
               
                 v 
                 1 
               
             
             = 
             
               
                 R 
                 * 
                 K 
                 * 
                 CTR 
               
               
                 
                   ( 
                   
                     R 
                     * 
                     K 
                   
                   ) 
                 
                 + 
                 
                   f 
                    
                   
                     ( 
                     θ 
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
               r 
               
                 v 
                 2 
               
             
             = 
             
               CTR 
               - 
               
                 
                   R 
                   * 
                   K 
                   * 
                   CTR 
                 
                 
                   
                     ( 
                     
                       R 
                       * 
                       K 
                     
                     ) 
                   
                   + 
                   
                     f 
                      
                     
                       ( 
                       θ 
                       ) 
                     
                   
                 
               
             
           
         
       
       
         
           
             Where, 
             ω INPUT —Input angular velocity
           ω v     1   —Angular velocity of Non-circular gear-driving   ω v     2   —Angular velocity of Non-circular gear driven   ω c     1   —Angular velocity of constant gear  1     ω c     2   —Angular velocity of constant gear  2     ω c     3   —Angular velocity of constant gear  3     ω c     4   —Angular velocity of constant gear  4     ω c     5   —Angular velocity of constant gear  5     ω disk —Angular velocity of disk   ω OUTPUT —Output Angular Velocity at output
               r v     1   —radius of Non-circular gear-driving   
               
         
             r v     2   —radius of Non-circular gear driven 
             r c     1   —radius of constant gear  1   
             r c     2   —radius of constant gear  2   
             r c     3   —radius of constant gear  3   
             r c     4   —radius of constant gear  4   
             r c     5   —radius of constant gear  5   
             r disk  radius of disk 
             r offset —radial position of the crankpin 
             R—input to output angular velocity ratio 
             K—(ratio of the product of radii of driven gears to driving gears) 
             CTR—center to center distance between the 2 non-circular gears
           f (θ) −sin θ or cos θ