Abstract:
A gearbox for maximizing the number of torques produced with the least loss of energy by using a geometric sequence of terms of ratios for the gears and having the separation in the degree of the common ratio uniform for all the gearsets between the same two shafts. The gearbox has high number of useable torques to gears plus shafts ratio. The gearbox can be used for gearboxes in any types of machines where torques or speeds are used.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     1. Field of the Invention  
         [0002]     This invention relates to a gearbox with gearsets having degrees of constant ratios in a geometric sequence to provide an efficient ratio of torques or speeds to the number of gears and shafts in the gearbox.  
         [0003]     2. Description of the Related Art  
         [0004]     In the prior art, the efficiency of the gear ratios was not maximized for the most efficient transmission of power through a gearbox. The ratio of torque quantity to gears and shafts in the gearbox in U.S. Pat. No. 5,079,965 is 46%. It has three forward and three reverse torques provided by ten gears on three shafts. 6/(10+3)=46%. This is not an efficient ratio.  
         [0005]     In U.S. Pat. No. 5,388,472 there are seven forward torques and one reverse torque provided by 18 gears on 4 shafts. The ratio of torque quantity to gears and shafts in the gearbox is 8/(18+4)=36%. This is not an efficient ratio.  
         [0006]     In U.S. Pat. No. 5,735,175 there are five forward torques and one reverse torque provided by 13 gears on 4 shafts. The ratio of torque quantity to gears and shafts in the gearbox is 6/(13+4)=35%. This is not an efficient ratio.  
         [0007]     For energy efficiency, it is desired to provide a high ratio of torque quantity to gears and shafts in gearboxes and to have as many forward and reverse speeds as possible with as small of a small gearbox as possible.  
       SUMMARY OF THE INVENTION  
       [0008]     The gearbox produces a number of forward speeds or torques using gears whose sizes differ by degrees in a geometric sequence having a common ratio R. The gears used are selected by synchronized clutches having pinions meshing with gears to form gearsets in the gearbox.  
         [0009]     There can be any number of gearsets to select from between two shafts in the gearbox. Gearsets between the same two shafts are in the same unit in the gearbox. The total number of forward gears available to select from in the gearbox is the product calculated by multiplying the number of gearsets in the units. For example if there are two units, one with 3 gearsets and the other with 4 gearsets, then there are 12 combinations thereof for producing 12 forward speeds.  
         [0010]     The degrees of common ratio in the geometric sequences are different for each unit in the gearbox. Each unit in the gearbox has gearsets with the same degree of separation of the common ratio between the gearsets. For example if the degree of separation is 6 and there are three gearsets in the unit then the first gearset may have a ratio of R 6  the second gearset may have a ratio of 1 and the third gearset may have a ratio of 1/R 6 . The next unit will have a degree of separation other than six. Preferably all of the ratios have the number 1 in either the numerator or the denominator. The gearsets are formed between the pinions and gears or join gears in each unit.  
         [0011]     The degree of common ratio of the gearsets for each unit is calculated by dividing the number of forward speeds or torques produced by the gearbox by the number of gearsets in the unit. For example if the gearbox has 24 speeds and a unit with 4 gearsets then that unit has 6 degrees of difference between the geatsets in the unit. The degree of common ratio of the gearsets for the next unit in the gearbox is calculated by dividing the degree of common ratio of the gearsets in the previous unit by the number of gearsets in the next unit etc. until the degree of common ratio for all units is calculated.  
         [0012]     With the degree of difference in the common ratio of each gearset in the unit selected the designer may by design choice select any degree of the common ratio for the first gearset in the unit and then select the degree of the common ratio for the remaining gearsets in the unit.  
         [0013]     The gearbox may also have other features such as a unit having a split shaft with a clutch for producing additional torques in the gearbox. The gearbox may also have a reverse pinion to provide reverse speeds. A differential may be used on the drive shaft. The gears may have two faces, which may be switched as the gears wear down. Further, the gearbox may come in sections with different frame members, the shafts extending between the sections.  
         [0014]     Each unit in the gearbox may have a gearset with a 1 to 1 ratio such that the final gearbox output may also be selected to be 1 to 1. This may be achieved by combinations of ratios of gearsets of inverse values such as 1/R and R in the different units to provide a gearbox with an input to output ratio of 1 to 1.  
         [0015]     The combination of using degrees of a common ratio for the gear sizes in a gearbox with the same degree of common ration difference in each unit of the gearbox and using the ratio of the number speeds to shafts plus gears results in the most efficient gearbox.  
       OBJECTS OF THE INVENTION  
       [0016]     It is an object of the invention to provide a gearbox with the best number of torques to gears and shafts ratio.  
         [0017]     It is an object of the invention to provide the lowest energy loss gearbox.  
         [0018]     It is an object of the invention to provide a low weight gearbox.  
         [0019]     It is an object of the invention to provide the largest number of forward and reverse speeds on the least number of shafts with the least number of gears.  
         [0020]     It is an object of the invention to use gears varying in size by degrees of a common ratio in a geometric sequence.  
         [0021]     It is an object of the invention to provide a gearbox wherein the product gearsets in the units equals number of forward speeds or torques in the gearbox.  
         [0022]     It is an object of the invention to provide a gearbox having gearsets wherein the gear teeth ratios in each unit differ from each other by the same degree in the geometric sequence having a common ratio.  
         [0023]     It is an object of the invention to provide a gearbox having the same degree of common ratio of difference in the geometric sequences of all gearsets in the same unit.  
         [0024]     It is an object of the invention to have a join gear between two gearsets in two units between three shafts.  
         [0025]     It is the object of the invention to use addendum shifting to allow for two join gears on the same shaft wherein four gearsets, two in each of two units, have sufficient degrees of common ratios in the geometric sequences for equalizing the difference in distance between two shafts.  
         [0026]     It is an object of the invention for all gearsets to use both the left and right sides of the gear teeth.  
         [0027]     It is an object of the invention to use a differential affixed to output shaft.  
         [0028]     It is an object of the invention to provide a reverse pinion on any shaft to produce reverse speeds.  
         [0029]     It is an object of the invention to use split shafts with clutches to produce additional speeds or torques in the gearbox  
         [0030]     It is an object of the invention to provide multiple frame members for combinations of the gearset units to form a gearbox.  
         [0031]     It is an object of the invention to provide a gearbox with the most efficient use of a largest quantity of forward and reverse torques for saving energy.  
         [0032]     It is an object of the invention to provide gearbox with the largest quantity of forward and reverse torques for use in road or weather conditions.  
         [0033]     It is an object of the invention to provide a gearbox with the option of having a ratio of 1 to 1 in each unit for a final gearbox output ratio of 1 to 1.  
         [0034]     Other objects, advantages and novel features of the present invention will become apparent from the following description of the preferred embodiments when considered in conjunction with the accompanying drawings. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0035]      FIG. 1  is a schematic of a gearbox with 5 shafts having 4 units of gearsets therebetween with a 2, 2, 2, 3 gearset per unit arrangement.  
         [0036]      FIG. 1A  is a table of the possible combinations of selected pinions for engaging the gearsets shown in  FIG. 1  to produce forward and reverse speeds.  
         [0037]      FIG. 1B  is a table showing the gearsets and the associated degree of the common ratios in the geometric sequence of the gearsets in the four units shown in  FIG. 1 .  
         [0038]      FIG. 2  is a schematic of a gearbox with 5 shafts and 4 units of gearsets therebetween with a 1, 2, 3, and 4 gearset per unit arrangement, wherein the use of a split shaft provides two shafts in the gearbox, to produce forward and reverse speeds.  
         [0039]      FIG. 2A  is a table shown in  FIG. 2 .  
         [0040]      FIG. 2B  is a table showing the gearsets and the associated degree of the common ratios in the geometric sequence of the gearsets in the four units shown in  FIG. 2 .  
         [0041]      FIG. 2C  is a table of the possible combinations of selected pinions for engaging the gearsets when using the split shafts as shown in  FIG. 2 .  
         [0042]      FIG. 2D  is a table of ratios of the gearsets in the gearset units if join of two split shafts  
         [0043]      FIG. 2E  is a table of combinations of engageable pinions for a power take off on shaft  203 .  
         [0044]     ? FIG. 2F  is a table of ratios of the gearsets in the two units with the split shaft engaged.  
         [0045]      FIG. 2P  is a schematic showing the wear on the right side of gear tooth of the gears in  FIG. 2 .  
         [0046]      FIG. 2 . 1  is a schematic showing the turning over of the shafts in the gearbox as shown on  FIG. 2  to use the other side of the gears.  
         [0047]      FIG. 2 . 1 A is a table of selected pinions for providing gearsets shown in  FIG. 2 . 1 .  
         [0048]      FIG. 2 . 1 B is a table of ratios of the gearsets in the two units shown in  FIG. 2 . 1   
         [0049]      FIG. 2 . 1 E is a table of ratios of the gearsets in the two units if first split shaft join to working organ.  
         [0050]      FIG. 2 . 1 F is a table of ratios of the gearsets in the gearset units if first split shaft join to working organ.  
         [0051]      FIG. 2 . 1 P is a schematic showing the wear on the left side of gear tooth of the gears in  FIG. 2 . 1 .  
         [0052]      FIG. 3  is a schematic of a gearbox with 4 shafts with 3 units of gearsets therebetween having 2, 2, and 6 gearsets respectively in the units.  
         [0053]      FIG. 3A  is a table of the possible combinations of selected pinions for engaging the gearsets shown in  FIG. 3 .  
         [0054]      FIG. 3B  is a table showing the gearsets and the associated degree of the common ratios in the geometric sequence of the gearsets in the three units shown in  FIG. 3 .  
         [0055]      FIG. 4  is a schematic of a gearbox with 3 shafts and 2 units of gearsets therebetween having 4, 6 gearsets respectively in the units.  
         [0056]      FIG. 4A  is a table of the possible combinations of selected pinions for engaging the gearsets shown in  FIG. 4 .  
         [0057]      FIG. 4B  is a table showing the gearsets and the associated degree of the common ratios in the geometric sequence of the gearsets in the two units shown in  FIG. 4 .  
         [0058]      FIG. 5  is a schematic of a gearbox with 5 shafts and 4 units of gearsets therebetween having 1, 1, 3, and 8 gearsets respectively in the units.  
         [0059]      FIG. 5A  is a table of the possible combinations of selected pinions for engaging the gearsets shown in  FIG. 5 .  
         [0060]      FIG. 5B  is a table showing the gearsets and the associated degree of the common ratios in the geometric sequence of the gearsets in the two units shown in  FIG. 5 .  
         [0061]      FIG. 6  is a schematic of a gearbox with 4 shafts and 3 units of gearsets therebetween having 2, 3, and 4 gearsets respectively in the units. Three units A, B and D of gearsets having three-separated frames members.  
         [0062]      FIG. 6A  is a table of the possible combinations of selected pinions for engaging the gearsets shown in  FIG. 6 .  
         [0063]      FIG. 6B  is a chart ratios of the gearsets in the three units shown in  FIG. 6 . 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0064]     The gearboxes shown in the figures have pinions on clutches for engaging shafts and gears. The ratio of the diameters or numbers of teeth on pinions and gears determines the relative speeds of the shafts. All of the gears and pinions in the gearbox are related by degrees of a common ratio in a geometric progression. For example, if the common ratio is 1 to 1.20 then the common ratio of the first degree will be 1, a common ratio of the second degree will be 1 to 1.2, a common ratio of the third degree will be 1 to 1.44, a common ratio of the fourth degree will be 1 to 1.728, etc. The product of the number of gearsets in all the units (number of gearsets between pairs of shafts) equals the number of forward speeds or torques in the gearbox. Each unit has a fixed degree of common ratio difference between the gearsets of the unit. Each unit has a different degree in the geometric sequence from the other units. Each unit may have a gearset ratio of 1 such that the final output of the gearbox may be 1 to 1. One or more shafts may have one or more join gears. Shafts in the gearbox may have a split shaft with a clutch.  
         [0065]     In the embodiments shown there are generally 24 forward and 12 or 24 reverse gears available in gearboxes with 4 or 5 shafts and 6 reverse gears in gearbox with 3 shafts. A gearbox having split shaft with 5 shafts can produced 68 gears having 36 forward and 24 reverse gears, plus 2 forward and 2 reverse gears as a power take off. In the embodiment shown in  FIG. 2 . 1  the same gearbox as shown in  FIG. 2  is driven on the opposite side of the split shaft and the shaft has been turned over for use of the gears on the opposite side of the teeth to double the life of the gears in the gearbox. The gearbox in  FIG. 2 . 1  has as an addition 2 forward and 2 reverse gears for power take off compared to the gearbox in  FIG. 2 . The gearbox in  FIG. 2  produces 12 forward gears as does the gearbox in  FIG. 2 .  
         [0066]     For making the most efficient gearbox the gears in the gearsets should all be sized to be degrees of a common ratio in a geometric sequence and the ratio of torques to the number of gears and shafts should be maximized. In the embodiments shown herein there are between 14 and 22 gears in each gearbox for an average ratio of torques to gears and shafts of 189%.  
         [0067]     In the first embodiment, shown in  FIG. 1 , there are 24 gears of forward and 12 reverse speeds available from gearbox  100 . Gearbox  100  has frame members  101  supporting drive shaft  102 , first intermediate shaft  103 , second intermediate shaft  104 , third intermediate shaft  105 , and differential shaft  106  connected to differential  160 .  
         [0068]     Power may enter the gearbox  100  on the left side on outward end  171  of the drive shaft  102  or on opposite outward end  172  if the shaft  102  in gearbox  100  is turned over for using the opposed side of teeth on the gears. Power entering at outward end  171  enters double synchronizer clutch  114 . Pinion  110  and pinion  111  are in double synchronizer clutch  114  and may be separately selected. When pinion  110  is selected it engages drive shaft  102 , and engages and turns gear  115  on first intermediate shaft  103  to form gearset  112 . Gearset  112  connects drive shaft  102  and the first intermediate shaft  103  such that the first intermediate shaft  103  turns at a rate depending on the ratio of the gears in the gearset  112 . When pinion  111  is selected it engages drive shaft  102 , and engages and turns gear  116  on intermediate shaft  103  to form gearset  113 . The gearsets  112  and  113  between the drive shaft  102  and the first intermediate shaft  103  are unit C gearsets. Gearset  112  has ratio of 1 to 1 or zero degrees of difference in a geometric sequence. Gearset  113  has the ratio of 1/R 3  or three degrees of difference in a geometric sequence.  
         [0069]     Gear  115  meshes with pinion  119  to form gearset  117  having a ratio of 1 and turns second intermediate shaft  104  if pinion  119  is selected in double synchronizer clutch  121 .  
         [0070]     Gear  116  meshes with pinion  120  to form gearset  118  having a ratio of R 2 , when pinion  120  is selected in double synchronizer clutch  121  with R being the degree of common ratio in the geometric sequence. The gearsets  117  and  118 , between the first intermediate shaft  103  and second intermediate shaft  104 , are unit D gearsets. Four gearsets  112 ,  113 ,  117  and  118  of the two units C and D have two join gears  115  and  116  on the first intermediate shaft  103 . Gearset  118  has a ratio of 1/R 2  and has a difference in value of R from gearset  113 , which has a ratio of R 3 . In the embodiment shown the teeth of pinion  118  were addendum shifted to make the teeth mesh properly.  
         [0071]     When pinion  122  in single synchronizer clutch  124  is selected to engage first intermediate shaft  103  it turns second intermediate shaft  104  by meshing with gear  125  forming gearset  123  with a ratio of 1/R. Gearset  123  is a unit D gearset. Gear  125  also meshes with pinion  127  forming gearset  126  having ratio 1/R 2 . When single synchronizer clutch  128  is selected power is transmitted to third intermediate shaft  105  by pinion  127 .  
         [0072]     Second intermediate shaft  104  can also transmit power to third intermediate shaft  105  by use of single synchronizer clutch  135  having pinion  133  which meshes with gear  136  to form gearset  134  with having a ratio of 1 to 1/R 8 . Gearsets  126  and  134  are unit B gearsets.  
         [0073]     Third intermediate shaft  105  has two ways to transmit power to the differential shaft  106 . As the third intermediate shaft  105  is turned it turns gear  136  engaging and turning differential shaft  106  by pinion  138  on single synchronizer clutch  139  when pinion  138  is selected and engages differential shaft  106  to form gearset  137  having a ratio of 1. Third intermediate shaft  105  can also transmit power to the differential shaft  106  by way of single synchronizer clutch  131  having pinion  129  which meshes with gear  132  to form gearset  130  with a ratio of 1 to 1/R 12 . Gearsets  130  and  137  are unit A gearsets.  
         [0074]     A sliding reverse pinion  107  runs power from the drive shaft  102  to first intermediate shaft  103  by way of idler gear  108  and reverse gear  109 . By design choice, as can be readily seen in  FIG. 1 , the reverse mechanism may have 9 different locations between the 5 shafts to provide 1, 2, 4, 6, 8, or 12 reverse gears.  
         [0075]     When the various clutches in  FIG. 1  are selected to operate the combinations of gears in the gearbox, twenty-four forward and twelve reverse speeds may be selected from in a 2, 2, 2, 3 pattern from unit A, B, C and D gearsets.  
         [0076]     The table in  FIG. 1A  shows the combinations of pinions selected at the clutches to yield the twenty-four speeds. The speeds can be calculated from the ratios of the gears and pinions.  
         [0077]     In the gearbox depicted in  FIG. 1  there are 36 torques, 24 forward and 12 reverse, using 14 gears and 5 shafts for a torque to gears and shafts ratio of 36/(14+5)=1.9.  
         [0078]     As shown in the table of  FIG. 1B  the combinations of gears yield one gearset from the of two possibilities 1 or 1/R 12  in unit A, one gearset from the of two possibilities 1/R 2  or 1/R 8  in unit B, one gearset from the of two possibilities 1 or  1 /R 3  in unit C and one gearset from the of three possibilities 1, 1/R or  1 /R 2  in unit D for a total of 24 forward gear combinations and 12 reverse gears.  
         [0079]     There is a uniform separation in the degree of the common ratio of the gearsets in each unit. The degree of common ratios of separation is calculated based on the number of forward gears or torques in the gearbox divided by the number of gearsets in the unit. In gearbox  100  shown in  FIG. 1  there are 4 units A, B, C and D with 2, 2, 2, and 3 gearsets respectively. The common ratio degree of separation in the geometric sequence of the unit A is 12 degrees since there a 2 gearsets in unit A and 24 forward gears, (24/2=12). Therefore the separation in the common ratio of the geometric sequence is of the 12 th  degree in unit A. If one of the gearsets in unit A has a ratio of 1 the second gearset has ratio of 1/R 12  or R 12 . Here by design choice the gearsets have the ratios of 1 and 1/R 12 . Unit B has 2 gearsets with a separation of 6 degrees in the common ratio of the geometric sequence since there are remaining 12 combinations of gearsets that can be used and 2 gearsets in unit B, (12/2=6). If the first gearset in unit B has a ratio of 1/R 2 , then the second gearset has a ratio of 1/R 8 , which is a common ratio of 6 degrees different from the first gearset. The choice of 1/R 2  and 1/R 8  are a matter of design choice but the six degrees of separation is part of the gearbox formula. Since unit C has 2 gearsets with 6 remaining combinations of gearsets, out of the original 24 combinations, there are three degrees of separation in unit C (6/2=3). If the first gearset in unit C has a ratio in the geometric sequence of 1 by design choice, then the second gearset will have three degrees of separation such as R 3  or 1/R 3 . In gearbox  100  the ratio selected is 1/R 3  by design choice. The remaining 3 gearsets have one degree of separation in the common ratio of the geometric sequence. In gearbox  100  the ratios selected in unit D are 1, R and R 2  by design choice. In order for the gearbox to have an input to output ratio of 1 to 1 the gearbox can have a gearset ratio selection in the units of 1×1×1/R 2 ×R 2 =1.  
         [0080]     In the second embodiment, gearbox  200 , as shown in  FIG. 2  and  FIG. 2 . 1  there are 36 gears of forward speeds and 24 reverse speeds. Due to the split shaft ( 202 ,  204  connected by clutch  250 ) there can be 4 forward speeds and 4 reverse speeds available for a power take off on the split shaft.  
         [0081]     Gearbox  200  has a frame member  201  supporting drive shaft  202 , first intermediate shaft  203 , second intermediate shaft  204 , third intermediate shaft  205 , and differential shaft  206  connected to differential  260 . Drive shaft  202  is split with second intermediate shaft  204  with the shafts joined by synchronizer clutch  250 .  
         [0082]     Power can enter the gearbox  200  on the left side on outward end  271  of the drive shaft  202  or on opposed outward end  272  of the split second intermediate shaft  204 . The second intermediate shaft  204  can be turned over as shown in  FIG. 2 . 1  for using the opposed side of teeth on the gears as shown in  FIG. 2P  to extend the life of the gearbox particularly for the power take off feature of the addition of 4 gears.  
         [0083]     Power entering the gearbox  200  at outward end  271  first enters double synchronizer clutch  212 . Pinion  210  and reverse pinion  207  are in double synchronizer clutch  212  and may be separately selected. When pinion  210  is selected it engages drive shaft  202 , and engages and turns gear  213  on first intermediate shaft  203  to form gearset  211  with a ratio of 1/R 8 . Gearset  211  connects drive shaft  202  and the first intermediate shaft  203  such that the first intermediate shaft  203  turns at a rate depending on the ratio of the gears in the gearset  211  which here is 1/R 8 . The gearset  211  between the drive shaft  202  and the first intermediate shaft  203  is a unit S gearset.  
         [0084]     There are two possible ways to transmit power from the first intermediate shaft  203  to the second intermediate shaft  204 . Pinions  214  and  215  are in double synchronizer clutch  218  and may be separately selected. When pinion  214  on first intermediate shaft  203  is selected, it engages and turns gear  219  on second intermediate shaft  204  to form gearset  216  with gearset ratio of 1/R 12 . Gearset  216  is between first intermediate shaft  203  and the second intermediate shaft  204  such that the second intermediate shaft  204  turns at a rate 1 to R 12 . When pinion  215  on first intermediate shaft  203  is selected it engages and turns gear  220  on second intermediate shaft  204  to form gearset  217  with a gearset ratio of 1. Gearset  217  is between first intermediate shaft  203  and the second intermediate shaft  204  such that the second intermediate shaft  204  turns at a rate 1 compared to first intermediate shaft  203 . Gearsets  216  and  217  between the first intermediate shaft  203  and the second intermediate shaft  204  are unit A gearsets.  
         [0085]     There are four possible ways to transmit power from the second intermediate shaft  204  to the third intermediate shaft  205 . As the second intermediate shaft  204  is turned it turns gear  219  engaging and turning third intermediate shaft  205  by pinion  222  on single synchronizer clutch  223 . When pinion  222  is selected it engages third intermediate shaft  205  to form gearset  221  with ratio of R 7 . Gearset  221  connects the second intermediate shaft  204  such that the third intermediate shaft  205  turns at a rate of 1 to R 7 .  
         [0086]     When pinion  224  in single synchronizer clutch  226  is selected it engages second intermediate shaft  204  and turns third intermediate shaft  205  by meshing with gear  227  forming gearset  225  with a ratio of R 6 . Gearset  225  is between the second intermediate shaft  204  and the third intermediate shaft  205  such that the third intermediate shaft  205  turns at a rate of R 6  compared to second intermediate shaft  204 .  
         [0087]     Pinion  228  and pinion  229  are in double synchronizer clutch  232  and may be separately selected. When pinion  228  in double synchronizer clutch  232  is selected to engage second intermediate shaft  204  it turns third intermediate shaft  205  by meshing with join gear  233  forming gearset  230  with a ratio of R 8 . Gearset  230  is between second intermediate shaft  204  and third intermediate shaft  205  such that the third intermediate shaft  205  turns at a rate of R 8  compared to first intermediate shaft  203 .  
         [0088]     When pinion  229  in double synchronizer clutch  232  is selected to engage second intermediate shaft  204  it turns third intermediate shaft  205  by meshing with gear  234  forming gearset  231  with a ratio of R 5 . Gearset  231  is between second intermediate shaft  204  and third intermediate shaft  205  such that the third intermediate shaft  205  turns at a rate of R 5  compared to second intermediate shaft  203 .  
         [0089]     The gearsets  221 ,  225 ,  230  and  231  between the second intermediate shaft  204  third intermediate shaft  205  are unit D gearsets.  
         [0090]     There are three possible ways to transmit power from the third intermediate shaft  205  to the differential shaft  206 . Pinion  237  and pinion  238  are in double synchronizer clutch  239  and may be separately selected. As a third intermediate shaft  205  is turned it turns join gear  233  engaging and turning differential shaft  206  by pinion  237  on double synchronizer clutch  239  when pinion  237  is selected and engages differential shaft  206  to form gearset  235  with a ratio of 1/R 8 . Gearset  235  connects the third intermediate shaft  205  to the differential shaft  206  such that it turns at a rate of 1 to 1/R 8 . As second intermediate shaft  204  is turned it turns join gear  234  engaging and turning third intermediate shaft  205  by pinion  238  on double synchronizer clutch  239  when pinion  238  is selected and engages differential shaft  206  to form gearset  236  with a ratio of 1/R 4 . Gearset  236  connects the third intermediate shaft  205  such that the differential shaft  206  turns at a rate of 1 to R 4  compared to third intermediate shaft  205 .  
         [0091]     Four gearsets  230 ,  231 , 235  and  236  of the two units B and D have two join gears  233  and  234  on the third intermediate shaft  205 . For spacing of the shaft purposed gearset  236  with a ratio of 1/R 4  is pared with gearset  236  with a ratio of R 5  and gearset  230  with a ratio of R 8  and gearset  235  with a ratio of 1/R 8  are paired. By design choice the teeth of pinion  238  were addendum modification shifted to mesh with the teeth on join gear  234 .  
         [0092]     When pinion  240  in single synchronizer clutch  242  is selected to engage third intermediate shaft  205  it turns differential shaft  206  by meshing with gear  243  forming gearset  241  with a ratio of 1. Gearset  241  is between third intermediate shaft  205  and the differential shaft  206  such that the differential shaft  206  turns at a rate 1 to 1 compared to third intermediate shaft  205 .  
         [0093]     The gearsets  235 ,  236  and  241  between the third intermediate shaft  205  and differential shaft  206  are unit B gearsets.  
         [0094]     A reverse pinion  207  is in double synchronizer clutch  212 . When reverse pinion  207  is selected it engages drive shaft  202 , and engages and turns idle gear  208  and reverse gear  209  on first intermediate shaft  203 . As can be seen in  FIG. 2  the reverse mechanism may have 5 locations between 5 shafts where one shaft is split to provide 1, 3, 6, 8 or 12 reverse gears.  
         [0095]     When the various clutches are selected to operate the various combinations of gears in gearbox  200 , twenty-four forward and twenty-four reverse speeds, as shown in  FIG. 2A , may be selected from in a 1, 2, 3, 4 pattern of gearsets in unit S, A, B, and D respectively as shown in  FIG. 2B .  
         [0096]     Alternatively, second intermediate shaft  204  can receive power by engaging synchronizer clutch  250  on the split shaft when power is connected to outward end  271  of drive shaft  202  or by directly connecting second intermediate shaft  204  to the power source at outward end  272 . The power then flows through the gearbox  200  from second intermediate shaft  204  to third intermediate shaft  205  to the differential shaft  206  by use of the 4 gearsets in unit D and the 3 gearsets of unit B operated as described above. The ratios of the gearsets are shown in  FIG. 2D  which is a subset of the gearsets of  FIG. 2B . The output gear ratios are the combinations of the ratios in Unit B and Unit D which will produce ratios R 8 , R 7 , R 6 , R 5 , R 4 , R 3 , R 2 , R, 1, 1/R, 1/R 2  and 1/R 3  which overlap some of the results which can be obtained by using units A, B, D and S. The overlapping resultant ratios are 1, 1/R , 1/R 2  and 1/R 3  obtained by the use of gearset  211  with a ratio of 1/R 12  of unit S applied to the unit B and unit D results, so there are two ways to obtain these gear ratios using gearbox  200 .  
         [0097]      FIG. 2 . 1  shows a variation of  FIG. 2  with the shafts turned around such that the other side of the gear teeth are used as shown in  FIG. 2 . 1 P. Power enters the gearbox  200  from outward end  272  on split second intermediate shaft  204  and can be transferred to first intermediate shaft  203  then to split drive shaft  202  by use of pinion  214  and pinion  215  are in double synchronizer clutch  218  which may be separately selected. As a second intermediate shaft  204  is turned it turns gear  220  engaging and turning first intermediate shaft  203  by pinion  215  on double synchronizer clutch  218  when pinion  215  is selected and engages first intermediate shaft  203  to form gearset  217  with ratio of 1. Gearset  217  connects the second intermediate shaft  204  such that the first intermediate shaft  203  turns at a rate of 1 to 1. As a second intermediate shaft  204  is turned it turns gear  219  engaging and turning first intermediate shaft  203  by pinion  214  on double synchronizer clutch  218  when pinion  214  is selected and engages first intermediate shaft  203  to form gearset  216  with a ratio of R 12 . Gearset  216  connects the second intermediate shaft  204  such that the first intermediate shaft  203  turns at a rate of 1 to R 12 .  
         [0098]     The gearsets  216  and  217  between the drive shaft  202  and the first intermediate shaft  203  are unit A1 gearsets.  
         [0099]     As a first intermediate shaft  203  is turned it turns gear  213  engaging and turning drive shaft  202  by pinion  210  on double synchronizer clutch  212  when pinion  210  is selected and engages drive shaft  202  to form gearset  211  with ratio of R 12 . Gearset  211  connects the first intermediate shaft  203  to drive shaft  203  such that drive shaft  203  turns at a rate of 1 to R 12 . The gearset  211  between second intermediate shaft  204  and first intermediate shaft  203  is a unit S1 gearset.  
         [0100]     As first intermediate shaft  203  is turned it turns reverse gear  209  engaging and turning the idle gear  208  for engaging and turning drive shaft  202  when pinion  207  on double synchronizer clutch  212  is selected and engages drive shaft  202 .  
         [0101]     The split drive shaft  202  with 2 forward gears (ratios are R 12  and R 24 ) and 2 reverse gears may used as a power take off at outward end  271 .  
         [0102]     The tables in  FIG. 2A ,  FIG. 2C ,  FIG. 2E  show the combinations of pinions selected at the clutches to yield the thirty eight forward and twenty-six reverse speeds for output of the gearbox at the differential and for the power take off. The speeds can be calculated from the combinations of degrees of ratios of the gears and pinions.  
         [0103]     There are 68 torques of 36 forward and 24 reverse for movement and 4 forward and 4 reverse speeds for working organ on 17 gears and 5 shafts for a torque to gears and shafts ratio of 68/(17+5)=3.09.  
         [0104]     As shown the table in  FIG. 2B  the combinations of gears yield two ratios of gearsets from the of two possibilities 1 and 1/R 12  in unit A, three ratios of gearsets from the of two possibilities 1/R 4 , 1/R 8  and 1 in unit B, four ratios of gearsets from the of four possibilities R 5 , R 6,  R 7  and R 8  in unit D one ratio of gearset 1/R 12  unit S for a total of 24 forward gear combinations and 24 reverse gears.  
         [0105]     As shown the table in  FIG. 2D  the combinations of gears yield three ratios of gearsets from two possibilities R 4 , 1/R 4  and 1 in unit B, four ratios of gearsets from the of four possibilities R 5 , R 6 , R 7  and R 8  in unit D for a total of 12 forward gear combinations.  
         [0106]     As shown the table in  FIG. 2F  the combinations of gears yield two ratios of gearsets from the of two possibilities 1 and 1/R 12  in unit A, and one ratio in gearset 1/R 12  unit S for a total of 2 forward gear combinations and 2 reverse gears.  
         [0107]     The table in  FIG. 2 . 1 A,  FIG. 2 . 1 E shows the combinations of pinions selected at the clutches to yield the twelve forward for movement and two forward and two reverse speeds for a power take off. The speeds can be calculated from the combinations of degrees of common ratios of the gears and pinions.  
         [0108]     As shown the table in  FIG. 2 . 1 F the combinations of gears yield two ratios of gearsets from the of two possibilities 1 and R 12  in unit A1, and one ratio R 12  for the gearset in unit S1 for a total of 2 forward gear combinations and 2 reverse gears.  
         [0109]     In  FIG. 2  the degree of common ratio in the geometric sequence for the 1×2×3×4 gearbox of units S, A, B and D respectively having 24 forward gears and a direct gear, is 12 degrees for unit A, since there a 2 gearsets in unit A and 24 in all. 24/2=12, therefore the common ratio of gearsets in unit A has a ratio of 12 th  degree. If the first gearset is selected by design choice to have a ratio of 1 the second gearset will have 12 degrees of separation and has a ratio of 1/R 12 . There are 12 combinations of gearsets remaining. Unit B has three gearsets. 12/3=4, therefore the gearsets in unit B differ by four degrees of common ratio in the geometric sequence. Therefore, the degrees of common ratio by design choice can be R 4 , 1/R 4  and 1. In unit D there are four gearsets to choose from for one degree of common ratio in the geometric sequence between gearsets ratios. The degrees of common ratio by design choice can be R 8 , R 7 , R 6  and R 5 . The fixed gearset of unit S may have ratio of 1/R 8 , which is selected by design choice to provide the gearbox with the desired output torques. In order to have a 1 to 1 input to output ratio from the gearbox the gearset choices of 1×1×1/R 8 ×R 8 =1 can be made.  
         [0110]     In a third embodiment shown in  FIG. 3  there are 24 gears of forward and 12 reverse speeds available from gearbox  300 . Gearbox  300  has frame members  301  supporting drive shaft  302 , first intermediate shaft  303 , second intermediate shaft  304 , and differential shaft  305  connected to differential  360 .  
         [0111]     Power enters to left side of the gearbox  300  on outward end  371  of the drive shaft  302  or on opposed outward end  372  if the shaft is turned over for using the opposed side of teeth. The drive shaft  302  passes through double synchronizer clutch  313 . Pinion  309  and pinion  310  are in double synchronizer clutch  313  and may be separately selected. When pinion  309  is selected it engages drive shaft  302 , and engages and turns join gear  314  on first intermediate shaft  303  to form gearset  311  with a ratio of 1. Gearset  311  connects drive shaft  302  and first intermediate shaft  303  such that the first intermediate shaft  303  turns at a rate depending on the ratio of the gears in the gearset  311 . When pinion  310  is selected it engages drive shaft  302 , and engages and turns join gear  315  on first intermediate shaft  303  to form gearset  312  with a ratio of 1/R 6 . Gearset  312  is between drive shaft  302  and first intermediate shaft  303  such that the first intermediate shaft  303  turns at a rate of 1 to R 6 . The gearsets  311  and  312  between the drive shaft  302  and the first intermediate shaft  303  are unit B gearsets.  
         [0112]     When pinion  321  in double synchronizer clutch  325  is selected to engage first intermediate shaft  303  it turns second intermediate shaft  304  by meshing with gear  326  forming gearset  323  with a ratio of R 4 . Gearset  323  is between first intermediate shaft  303  and second intermediate shaft  304  such that the second intermediate shaft  304  turns at a rate of 1 to R 4  relative to the first intermediate shaft  303 . When pinion  322  in double synchronizer clutch  325  is selected to engage first intermediate shaft  303  it turns second intermediate shaft  304  by meshing with gear  327  forming gearset  324  with a ratio of R 3 . Gearset  324  is between first intermediate shaft  303  and second intermediate shaft  304  such that the second intermediate shaft  304  turns at a rate 1 to R 3  relative to first intermediate shaft  303 .  
         [0113]     When pinion  328  in double synchronizer clutch  332  is selected it engages first intermediate shaft  303 , and engages and turns gear  333  on second intermediate shaft  304  to form gearset  330  with a ratio of R 2 . Gearset  330  connects first intermediate shaft  303  and second intermediate shaft  304  such that the second intermediate shaft  304  turns at a rate of 1 to R 3  relative to first intermediate shaft  303 . When pinion  329  in double synchronizer clutch  332  is selected it engages first intermediate shaft  303 , and engages and turns gear  334  on second intermediate shaft  304  to form gearset  331  with a ratio of 1 to R. Gearset  331  connects first intermediate shaft  303  and second intermediate shaft  304  such that the second intermediate shaft  304  turns at a rate 1 to R relative to first intermediate shaft  303 .  
         [0114]     When pinion  318  is selected it engages second intermediate shaft  304 , and engages and is turned by join gear  314  on first intermediate shaft  303  to form gearset  316  with a ratio of 1 to 1. Gearset  316  connects first intermediate shaft  303  and second intermediate shaft  304  such that second intermediate shaft  304  turns at a rate 1 to 1 relative to first intermediate shaft  303 .  
         [0115]     When pinion  319  is selected it engages second intermediate shaft  304 , and engages and is turned by join gear  315  on first intermediate shaft  303  to form gearset  317  with a ratio of 1 to R 5 . Gearset  317  connects first intermediate shaft  303  and second intermediate shaft  304  such that second intermediate shaft  304  turns at rate 1 to R 5  relative to first intermediate shaft  303 .  
         [0116]     Gearset  316 ,  317 ,  323 ,  324 ,  330 ,  331  are unit D gearsets. Gearsets  311 ,  312 ,  316  and  317  of units B and D have join gears  315  and  316  on the first intermediate shaft  303 . Gearset  317  has a ratio of 1/R 6  and different by geometric ratio R from inverse ratio of R 5  of gearset  312  By design choice, teeth of pinion  319  are addendum shifted to adjust for the difference of the common ratio R between the two gearsets. Similarly the size R 5  of gearset  317  is different than the size of ratio 1/R 6  of gearset  312  of unit B by the geometric ratio R when it is installed with join gear  315 . For installing both gearsets together, it id necessary to do use addendum shifting og the teeth in pinion  319 .  
         [0117]     When pinion  338  in synchronizer clutch  340  is selected it engages second intermediate shaft  304 , and engages and turns gear  341  on differential shaft  305  to form gearset  339  with a ratio of 1/R 17 . Gearset  339  connects second intermediate shaft  304  and the differential shaft  305  such that the differential shaft  305  turns at a rate 1 to 1/R 17  compared to second intermediate shaft  304 . As second intermediate shaft  304  is turned it turns join gear  334  forming gearset  335  with a ratio of 1/R 5 . Join gear  334  also engages and turns pinion  336  in single synchronizer clutch  337  on differential shaft  305 . Gearset  335  connects second intermediate shaft  304  and the differential shaft  305  such that the differential shaft  305  turns at a rate 1 to R 5  compared to second intermediate shaft  304 . Gearset  335  and  339  are unit A gearsets.  
         [0118]     The differential shaft  305  may be run in reverse by engaging reverse pinion  306 , which connects to idler gear  307  and reverse gear  308  on differential  360 . As can be seen in  FIG. 3 , the reverse mechanism may have 5 different locations between the 4 shafts, where one shaft is split, providing 1, 2, 4, or 12 reverse gears.  
         [0119]     When the various clutches are selected to operate the various combinations of gears in gearbox  300 , twenty-four forward and twelve reverse speeds may be selected from in a 2, 2, 6 pattern using gearsets in unit A, B, and D respectively.  
         [0120]     The table in  FIG. 3A  shows the combinations of pinions selected at the clutches to yield the twenty-four forward and twelve reverse speeds. The speeds can be calculated from the combinations of degrees of common ratios of the gears and pinions.  
         [0121]     There are 36 torques, 24 forward and 12 reverse on 17 gears and 4 shafts for a torque to gears and shafts ratio of 36/(17+4)=1.7.  
         [0122]     As shown the table in  FIG. 3B  the combinations of gears yield two ratios of gearsets from the of two possibilities 1/R 5  and 1/R 17  in unit A, two ratios of gearsets from the of two possibilities 1/R 6  and 1 in unit B, six ratios of gearsets from the of six possibilities 1, R, R 2,  R 3 , R 4  and R 5  in unit D for a total of 24 forward gear combinations and 12 reverse gears.  
         [0123]     In  FIG. 3B  the degree of separation between the ratios in the gearsets for the ratio in the geometric sequence in the 2×2×6 gearbox having 24 gears, is 12 for unit A, since there a 2 gearsets in unit A and 24 in all. 24/2=12, therefore the difference in the a common ratio is of the 12 th  degree in unit A. If the first gearset is selected by design choice to have a ratio of 1/R 5  the second gearset will have 12 degrees of separation and has a ratio of 1/R 17 . There are 12 combinations of gearsets remaining. Unit B has two gearsets. 12/2=6, therefore the gearsets in unit B differ by six degrees of common ratio in the geometric sequence. Therefore the degrees of common ratio by design choice can be 1/R 6  and 1. In unit D are six gearsets and 6 remaining gears from the original 24 to choose from for a one degree of common ratio in the geometric sequence between gearsets. The degrees of common ratio by design choice can be 1, R, R 2 , R 3 , R 4 , R 5  in unit D. To obtain a 1 to 1 input to output in the gearbox the gearsets having rations of 1×1/R 5 ×R 5 =1 may be selected.  
         [0124]     In the fourth embodiment shown in  FIG. 4  there are 24 gears of forward and 6 reverse speeds available from gearbox  400 . Gearbox  400  has frame members  401  supporting drive shaft  402 , intermediate shaft  403  and differential shaft  404  connected to differential  460 .  
         [0125]     Power enters to left side of the gearbox  400  on outward end  471  of the drive shaft  402  or on opposed outward end  472  if the shafts are reversed for using the opposite side of the gear teeth. The drive shaft  402  passes through double synchronizer clutches  412 ,  420  and  427 . Pinion  408  and pinion  409  are in double synchronizer clutch  412  and may be separately selected. When pinion  408  is selected it engages drive shaft  402 , and engages and turns join gear  413  on intermediate shaft  403  to form gearset  410  with ratio of 1 to 1/R 11 . Gearset  410  connects drive shaft  402  and the intermediate shaft  403  such that the first intermediate shaft  403  turns at a rate depending on the ratio of the gears in the gearset  410 . When pinion  409  is selected it engages drive shaft  402 , and engages and turns join gear  414  on intermediate shaft  403  to form gearset  411  with ratio of 1 to 1/R 10 . Gearset  411  is between drive shaft  402  and first intermediate shaft  403  such that the intermediate shaft  403  turns at a rate 1 to 1/R 10 .  
         [0126]     Pinion  415  and pinion  416  are in double synchronizer clutch  420  and may be separately selected. When pinion  415  is selected it engages drive shaft  402 , and engages and turns join gear  421  on intermediate shaft  403  to form gearset  417  with a ratio of 1 to 1/R 9 . Gearset  417  connects drive shaft  402  and the intermediate shaft  403  such that the first intermediate shaft  403  turns at a rate depending on the ratio of the gears in the gearset  417 . When pinion  416  is selected it engages drive shaft  402 , and engages and turns join gear  422  on intermediate shaft  403  to form gearset  418  with a ratio of 1 to 1/R 8 . Gearset  418  is between drive shaft  402  and first intermediate shaft  403  such that the intermediate shaft  403  turns at a rate 1 to 1/R 8 .  
         [0127]     Pinion  423  and pinion  424  are in double synchronizer clutch  427  and may be separately selected. When pinion  423  is selected it engages drive shaft  402 , and engages and turns gear  428  on intermediate shaft  403  to form gearset  425  with a ratio of 1 to 1/R 7 . Gearset  425  connects drive shaft  402  and the intermediate shaft  403  such that the intermediate shaft  403  turns at a rate depending on the ratio of the gears in the gearset  425 . When pinion  424  is selected it engages drive shaft  402 , and engages and turns join gear  429  on intermediate shaft  403  to form gearset  426  with ratio of 1/R 6 . Gearset  426  is between drive shaft  402  and first intermediate shaft  403  such that the intermediate shaft  403  turns at a rate of 1 to 1/R 6 . Gearsets  410 ,  411 ,  417 ,  418 ,  425  and  426  between the drive shaft  402  and the first intermediate shaft  403  are unit D gearsets.  
         [0128]     When pinion  437  in double synchronizer clutch  441  is selected to engage intermediate shaft  403  it turns differential shaft  404  by meshing with gear  442  on the differential  460  to form gearset  439  having a ratio of 1 to R 6 . Gearset  439  is between intermediate shaft  403  and differential shaft  404  such that the differential shaft  404  turns at a rate 1 to R 6  relative to the intermediate shaft  403 . When pinion  438  in double synchronizer clutch  441  is selected to engage intermediate shaft  403  it turns the differential shaft  404  by meshing with gear  443  on the differential  460  to form gearset  440  with a ratio of 1 to 1/R 12 . Gearset  440  is between intermediate shaft  403  and the differential shaft  404  such that the differential shaft  404  turns at a rate of 1 to R 12  compared to intermediate shaft  403 .  
         [0129]     When pinion  433  in single synchronizer clutch  435  is selected it engages intermediate shaft  403 , and engages and turns gear  436  on the differential  460  to form gearset  434  with a ratio of 1 to 1. Gearset  434  connects intermediate shaft  403  and differential shaft  404  such that the differential shaft  404  turns at a rate 1 to 1 relative to intermediate shaft  403 . As intermediate shaft  403  is turned it turns gear  429  engaging and turning differential shaft  404  by pinion  431  on single synchronizer clutch  432  when pinion  431  is selected and differential shaft  404  to form gearset  430  with ratio of 1 to R 6 . Gearset  430  connects intermediate shaft  403  and differential shaft  404  such that the differential shaft  404  turns at a rate 1 to R 6  compared to intermediate shaft  403 .  
         [0130]     Gearset  430 .  434 ,  439  and  440  are unit A gearsets.  
         [0131]     The differential shaft  404  may be run in reverse by engaging reverse pinion  405 , which connects to idler gear  406  and reverse gear  407  on differential  460 . As can be seen in  FIG. 4  the reverse mechanism may have 2 locations between 3 shafts to provide 1, 4 or 6 reverse gears.  
         [0132]     When the various clutches are selected to operate the various combinations of gears in gearbox  400 , twenty-four forward and six reverse speeds may be selected from in a 4, 6 pattern from unit A, and D gearsets.  
         [0133]     The table in  FIG. 4A  shows the combinations of pinions selected at the clutches to yield the twenty-four forward and six reverse speeds. The speeds can be calculated from the combinations of degrees of ratios of the gears and pinions.  
         [0134]     There are 30 torques, 24 forward and 6 reverse on 19 gears and 3 shafts for a torque to gears and shafts ratio of 30/(19+3)=1.36.  
         [0135]     As shown the table in  FIG. 4B  the combinations of gears yield four ratios of gearsets from the of four possibilities R 6 , 1, 1/R 6  and 1/R 12  in unit A, six ratios of gearsets from the of six possibilities 1/R 6 , 1/R 7 , 1/R 8 , 1/R 9 , 1/R 10  and 1/R 11  in unit D for a total of 24 forward gear combinations and 6 reverse gears.  
         [0136]     In  FIG. 4B  the degree of separation for the ratio in the geometric sequence for the 4×6 gearbox having 24 gears, is 6 for unit A, since there a 4 gearsets in unit A and 24 in all. 24/4=6, therefore the ratios of gearsets in unit A has a separation in the common ratio of 6 th  degree. If the first gearset is selected by design choice to have a ratio of R 6  the second gearset will have 6 degrees of separation and have a ratio of 1, the third gearset will have 6 degrees of separation and have a ratio of 1/R 6 , the fourth gearset will have 6 degrees of separation and have a ratio of 1/R 12 . There are 6 combinations of gearsets remaining. Unit D has six gearsets. 6/6=1, therefore the gearsets in unit D differ by one degree of common ratio in the geometric sequence. In unit D are six gearsets and 6 remaining gears from the original 24 to choose from for a one degree of common ratio in the geometric sequence between ratios of gearsets. Therefore the degrees of common ratio by design choice can be 1/R 6 , 1/R 7 , 1/R 8 , 1/R 9 , 1/R 10  and 1/R 11 . To provide a gearbox with a 1 to 1 input to output gearsets can be chosen having values 1/R 6 ×R 6 =1.  
         [0137]     In the fifth embodiment, shown in  FIG. 5 , gearbox  500  has 24 gears of forward and 24 reverse speeds available. Gearbox  500  has a frame members  501  supporting drive shaft  502 , first intermediate shaft  503 , second intermediate shaft  504 , third intermediate shaft  505 , and differential shaft  506  connected to differential  560 .  
         [0138]     Power enters the left side of gearbox  500  on outward end  571  of the drive shaft  502  or on opposite outward end  572  if the shafts are reversed for using the opposite side of the gears teeth. Drive shaft  502  passes through double synchronizer clutch  510 . Pinion  511  and reverse pinion  507  are in double synchronizer clutch  510  and may be separately selected. When pinion  511  is selected it engages drive shaft  502 , and engages and turns gear  513  on first intermediate shaft  503  to form gearset  512  with ratio 1 to of R 3 . Gearset  512  connects drive shaft  502  and the first intermediate shaft  503  such that the first intermediate shaft  503  turns at a rate depending on the ratio of the gears in the gearset  512 . When reverse pinion  507  is selected it engages drive shaft  502 , and engages and turns idle gear  508  and reverse gear  509  on intermediate shaft  503 .  
         [0139]     The gearset  512  between the drive shaft  502  and the first intermediate shaft  503  is a unit S1 gearset.  
         [0140]     There are three possible ways to transmit power from the first intermediate shaft  503  to the second intermediate shaft  504 . As first intermediate shaft  503  is turned it turns join gear  513  engaging and turning second intermediate shaft  504  by pinion  515  on single synchronizer clutch  516  when pinion  515  is selected and engages second intermediate shaft  505  to form gearset  514  with a ratio of 1 to 1/R 8 . Gearset  514  connects the first intermediate shaft  503  such that the second intermediate shaft  504  turns at a rate of 1 to 1/R 8 . Pinions  517  and  518  are in double synchronizer clutch  521  and may be separately selected. When pinion  517  on first intermediate shaft  503  is selected, it engages and turns join gear  522  on second intermediate shaft  504  to form gearset  519  with ratio of R 8 . Gearset  519  is between first intermediate shaft  503  and the second intermediate shaft  504  such that the second intermediate shaft  504  turns at a rate depending on the ratio of the gears in the gearset  519 . When pinion  518  on first intermediate shaft  503  is selected, it engages and turns gear  523  on second intermediate shaft  504  to form gearset  520  with ratio of 1 to 1. Gearset  520  is between first intermediate shaft  503  and the second intermediate shaft  504  such that the second intermediate shaft  504  turns at a rate 1 to 1 compared to first intermediate shaft  503 .  
         [0141]     Gearsets  519 ,  520  and  514  between the first intermediate shaft  503  and the second intermediate shaft  504  are unit A gearsets.  
         [0142]     There are eight possible ways to transmit power from the second intermediate shaft  504  to the third intermediate shaft  505 . Pinion  526  and pinion  527  are in double synchronizer clutch  528  and may be separately selected. As a second intermediate shaft  504  is turned it turns join gear  522  engaging and turning third intermediate shaft  505  by pinion  526  on double synchronizer clutch  528 . When pinion  526  is selected it engages third intermediate shaft  505  to form gearset  524  with ratio of 1/R. Gearset  524  connects the second intermediate shaft  504  such that the third intermediate shaft  505  turns at a rate of 1 to R. As a second intermediate shaft  504  is turned it turns join gear  523 , which engages and turns second intermediate shaft  504  by pinion  527  on double synchronizer clutch  528  when pinion  527  is selected and engages third intermediate shaft  505  to form gearset  525  with ratio of R 8 . Gearset  525  connects the second intermediate shaft  504  such that the third intermediate shaft  505  turns at a rate of 1 to R 8  compared to second intermediate shaft  504 .  
         [0143]     Four gearsets  519 ,  520 ,  524  and  525  of the two units B and D have two join gears  522  and  523  on the second intermediate shaft  504 . Gearset  520  with a ratio of 1 is different by geometric ratio R from ratio of 1/R of gearset  525 . By design choice, teeth of pinion  527  were addendum modification shifted to make the gear teeth mesh due to the difference in gear size.  
         [0144]     Pinions  529  and  530  are in double synchronizer clutch  533  and may be separately selected. When pinion  529  in double synchronizer clutch  533  is selected to engage second intermediate shaft  504  it turns third intermediate shaft  505  by meshing with join gear  534  forming gearset  531  with a ratio of 1 to 1/R 2 . Gearset  531  is between second intermediate shaft  504  and third intermediate shaft  505  such that the third intermediate shaft  505  turns at a rate 1 to 1/R 2  compared to first intermediate shaft  503 .  
         [0145]     When pinion  530  in double synchronizer clutch  533  is selected to engage second intermediate shaft  504  it turns third intermediate shaft  505  by meshing with join gear  535  forming gearset  532  with a ratio of 1 to 1/R 3 . Gearset  532  is between second intermediate shaft  504  and third intermediate shaft  505  such that the third intermediate shaft  505  turns at a rate 1 to 1/R 3  compared to second intermediate shaft  503 .  
         [0146]     Pinions  536  and  537  are in double synchronizer clutch  540  and may be separately selected. When pinion  536  in double synchronizer clutch  540  is selected to engage second intermediate shaft  504  it turns third intermediate shaft  505  by meshing with gear  541  forming gearset  538  with a ratio of 1 to 1/R 4 . Gearset  538  is between second intermediate shaft  504  and the third intermediate shaft  505  such that the third intermediate shaft  505  turns at a rate 1 to 1/R 4  compared to second intermediate shaft  504 .  
         [0147]     When pinion  537  in double synchronizer clutch  540  is selected to engage second intermediate shaft  504  it turns third intermediate shaft  505  by meshing with join gear  542  forming gearset  539  with a ratio of 1/R 5 . Gearset  539  is between second intermediate shaft  504  and third intermediate shaft  505  such that the third intermediate shaft  505  turns at a rate 1 to 1/R 5  compared to second intermediate shaft  503 .  
         [0148]     Pinions  543  and  544  are in double synchronizer clutch  547  and may be separately selected. When pinion  543  in double synchronizer clutch  547  is selected to engage second intermediate shaft  504  it turns third intermediate shaft  505  by meshing with gear  548  forming gearset  545  with a ratio of 1/R 6 . Gearset  545  is between second intermediate shaft  504  and third intermediate shaft  505  such that the third intermediate shaft  505  turns at a rate 1 to R 6  compared to second intermediate shaft  503 .  
         [0149]     When pinion  544  in double synchronizer clutch  540  is selected to engage second intermediate shaft  504  it turns third intermediate shaft  505  by meshing with gear  549  forming gearset  546  with a ratio of 1/R 7 . Gearset  546  is between second intermediate shaft  504  and the third intermediate shaft  505  such that the third intermediate shaft  505  turns at a rate 1 to R 7  compared to second intermediate shaft  503 .  
         [0150]     The gearsets  524 ,  525 ,  531 ,  532 ,  538 ,  539 ,  545  and  546  between the second intermediate shaft  504  and the third intermediate shaft  505  are unit D gearsets.  
         [0151]     As third intermediate shaft  505  is turned it turns join gear  535  engaging and turning differential shaft  506  by gear  551  on differential  560  engaging differential shaft  506  to form gearset  550  with a ratio of 1 to 1/R 10 . Gearset  550  connects the third intermediate shaft  505  such that the differential shaft  506  turns at a rate of 1 to R 10  compared to third intermediate shaft  504 . Gearset  550  is a unit S2 gearset.  
         [0152]     A sliding reverse pinion  507  is also available by design choice to run power from the drive shaft  502  to first intermediate shaft  503  by way of idler gear  508  and reverse gear  509 . As can be seen in  FIG. 5 , the reverse mechanism may have 9 different locations between the 5 shafts to provide 1, 3, 8, or 24 reverse gears.  
         [0153]     When the various clutches are selected to operate the various combinations of gears in gearbox  500 , twenty-four forward and twenty-four reverse speeds may be selected from in a 1, 1, 3, 8 pattern from unit S1, A, D, and S2 gearsets.  
         [0154]     The table in  FIG. 5A  shows the combinations of pinions selected at the clutches to yield the twenty-four forward and twenty-four reverse speeds. The speeds can be calculated from the combinations of degrees of ratios of the gears and pinions.  
         [0155]     There are 48 torques 24 forward and 24 reverse on 22 gears and 5 shafts for a torque to gears and shafts ratio of 48/(22+5)=1.78.  
         [0156]     As shown the table in  FIG. 5B  the combinations of gears yield one gearset R 3  in unit S1, three ratios of gearsets from the of three possibilities R 8 , 1/R 8  and 1 in unit A, eight ratios of gearsets from the of eight possibilities 1/R, 1/R 2 , 1/R 3 , 1/R 4 , 1/R 5 , 1/R 6 , 1/R 7 , 1/R 8  in unit D, and one gearset 1/R 10  in unit S2 for a total of 24 forward gears and 24 reverse gears.  
         [0157]     In gearbox  500  the degree of common ratio in the geometric sequence for the 1×1×3×8 gearbox having 24 gears, is 8 for unit A, since there 3 gearsets in Unit A and 24 in all. 24/3=8, therefore the common ratio of gearsets in unit A is a common ratio of 8 th  degree in the geometric sequence. If the first gearset is selected by a ratio of R 8  the second gearsets can have a ratio of 1, and the third gearset can have a ratio of 1/R 8 . There are 8 combinations of gearsets remaining and unit D has eight gearsets. 8/8=1, so the gearsets in unit D differ by 1 degree of the common ratio in the geometric sequence. The degrees of common ratio in the geometric sequence were selected by design choice to be 1/R, 1/R 2 , 1/R 3 , 1/R 4 , 1/R 5 , 1/R 6 , 1/R 7 , and 1/R 8  in unit D. The standard of fixed gearsets S1 and S2 we selected by design choice to be 1/R 3  and 1/R 10 . In order to provide a 1 to 1 input to output ratio of the gearbox the units can be selected as R 3 ×1/R×1/R 10 ×R 8 =1.  
         [0158]     In the sixth embodiment shown in  FIG. 6  there are 24 gears of forward and 12 reverse speeds available from gearbox  600 . Gearbox  600  has 4 frames members  645 ,  601 ,  611  and  625 . Supported split drive shaft  646  in frame member  645  is connected by clutch  651  to split drive shaft  602  in frame member  601 . First split intermediate shaft  647  in frame member  645  is connected by clutch  652  to first split intermediate shaft  603  in frame member  601 , which is connected by clutch  653  to first split intermediate shaft  612  in frame member  611 . Second split intermediate shaft  613  in frame member  611  is connected by clutch  654  to second split intermediate shaft  626  i frame member  625 . Differential shaft  627  is affixed to differential  660  in frame member  625 .  
         [0159]     Frame member  645  encompasses split drive shaft  646  supporting reverse pinion  648  engaging idle gear  649  for turning reverse gear  650 , fixed to first split intermediate shaft  647 . Frame members  601  encompasses split drive shaft  602 , first split intermediate shaft  603  and gearsets  606  and  607  as unit A gearsets. Frame member  611  encompasses first split intermediate shaft  612 , second split intermediate shaft  613  and gearsets  616 ,  617  and  622  which are unit B gearsets. Frame member  625  encompasses second split intermediate shaft  626 , differential shaft  627  and gearsets  630 ,  631 ,  637  and  638  which are unit D Gearsets.  
         [0160]     A split drive shaft  646  and first split intermediate shaft  647  have outward ends extending from frame member  645  which are connected by two clutches  651  and  652  to two outward ends of split drive shaft  602  and first split intermediate shaft  603  supported by frame members  601 .  
         [0161]     The first split intermediate shaft  603  has an outward end extending from frame member  611  connected by clutch  653  to the outward end of first split intermediate shaft  612  in frame member  611 . Second split intermediate shaft  613  has an outward end extending from frame members  611  connected by clutch  654  to other outward end of the second split intermediate shaft  626  supported by frame member  625   
         [0162]     The power source can be connected to the left side of the gearbox  600  on outward end  671  of the drive shaft  646  or to the right side on outward end  672  of split drive shaft  602 . The shafts can be turned around to use the teeth on the opposite side of the gears  
         [0163]     Split drive shaft  646  is connected by clutch  651  to split drive shaft  602 . Split drive shaft  646  passes through reverse pinion  648  and split drive shaft  602  passes through pinions  604 ,  605  are in double synchronizer clutch  608 . Pinions  604 ,  605  and may be separately selected for engaging split drive shaft  602 . When reverse pinion  648  is selected it engages turns split first intermediate shaft  647  connected by clutch  652  to split first intermediate shaft  603 . As can be seen in  FIG. 6  the reverse mechanism may have 2 locations between 4 shafts supported by 4 frame members having 3 split shafts to provide 4 or 8 reverse gears.  
         [0164]     When pinion  604  is selected it engages and turns join gear  609  on split first intermediate shaft  603  to form gearset  606  with a ratio of 1 to R 6 . When pinion  605  is selected it engages and turns join gear  610  on split first intermediate shaft  603  to form gearset  607  with a ratio of 1 to 1/R 6 . Gearsets  606  and  607  are unit A gearsets.  
         [0165]     The outward end of first split intermediate shaft  603  is connected by clutch  653  to the outward end of split intermediate shaft  612 .  
         [0166]     Frame member  611  encompasses split first intermediate shaft  612  and split second intermediate shaft  613 . When pinion  614  on double synchronizer clutch  618  is selected it engages and turns join gear  619  on split second intermediate shaft  613  to form gearset  616  with ratio of 1 to 1. When pinion  615  on double synchronizer clutch  618  is selected it engages and turns join gear  620  on split first intermediate shaft  613  to form gearset  617  with ratio of 1 to 1/R 4 . When pinion  621  on single synchronizer clutch  624  is selected it engages and turns join gear  623  on split first intermediate shaft  613  to form gearset  622  with ratio of 1 to 1/R 8 .  
         [0167]     Gearsets  616 ,  617  and  622  are unit B gearsets.  
         [0168]     The outward end of split second intermediate shaft  613  is connected by clutch  654  to the outward end of split second intermediate shaft  626 . The frame member  625  encompasses split second intermediate shaft  626 , and differential shaft  627  having affixed differential  660 .  
         [0169]     When pinion  628  on double synchronizer clutch  632  is selected it engages and turns join gear  633  to form gearset  630  with a ratio of 1 to 1/R 9 . When pinion  629  on double synchronizer clutch  632  is selected it engages and turns join gear  634  on differential shaft  627  to form gearset  631  with a ratio of 1 to 1/R 8 .  
         [0170]     When pinion  635  on double synchronizer clutch  639  is selected it engages and turns join gear  640  on differential shaft  627  to form gearset  637  with a ratio of 1 to 1/R 7 . When pinion  636  on double synchronizer clutch  639  is selected it engages and turns join gear  641  on differential shaft  627  to form gearset  638  with a ratio of 1 to 1/R 6 .  
         [0171]     Gearsets  630 ,  631 ,  637  and  638  are unit D gearsets.  
         [0172]     When the various clutches are selected to operate the various combinations of gears in the gearbox, twenty-four forward and twenty-four reverse speeds may be selected from in a 2, 3, 4 pattern from unit A, B, and D gearsets.  
         [0173]     The table in  FIG. 6A  shows the combinations of pinions selected at the clutches to yield the twenty-four forward and twelve reverse speeds. The speeds can be calculated from the combinations of degrees of ratios of the gears and pinions.  
         [0174]     There are 36 torques 24 forward and 12 reverse on 18 gears and 4 shafts having 3-split shafts supported by 4 frames members for a torques to gears and shafts ratio of 36/(18+5)=1.5.  
         [0175]     As shown the table in  FIG. 6B  the combinations of gears yield two ratios of gearsets from the of two possibilities R 6  and 1/R 6  in unit A, three ratios of gearsets from the of three possibilities R 8 , 1/R 4  and 1 in unit B, and four ratios of gearsets from the of four possibilities 1/R 6 , 1/R 7 , 1/R 8  and 1/R 9  in unit D.  
         [0176]     In  FIG. 6  the degree of the common ratio in the geometric sequence for the 2×3×4 gearbox having 24 gears, is 12 for unit A, since there a 2 gearsets in unit A and  24  in all. 24/2=12, therefore the common ratio of gearsets in the unit A is a common ratio of 12 th  degree in the geometric sequence. If the first gearset is selected by a ratio of R 6  the second gearset can have a ratio of 1/R 6 .  
         [0177]     There are 3 combinations of gearsets remaining and unit B has three gearsets. 12/3=4, so the gearsets in the unit B differ by 4 degree of the common ratio in the geometric sequence. The degrees of common ratio in the geometric sequence were selected by design choice to be 1, 1/R 4  and 1/R 8  in unit B.  
         [0178]     There are 4 combinations of gearsets remaining and unit D has four gearsets. 4/4=1, so the gearsets in the unit D differ by 1 degree of common ratios in the geometric sequence. The degrees of common ratio in the geometric sequence were selected by design choice to be 1/R 6 , 1/R 7 , 1/R 8  and 1/R 9  in unit D. In order to provide a 1 to 1 input to output in gearbox  600  the unit values of 1×1/R 6 ×R 6 =1 may be selected.