Abstract:
A family of power transmissions which are utilized in a powertrain include three planetary gearsets and five torque-transmitting mechanisms. The torque-transmitting mechanisms are engaged in combinations of three to provide a reverse drive ratio and six forward speed ratios. The torque-transmitting mechanisms will include at least four rotating type torque-transmitting mechanisms and, in some instances, one stationary type torque-transmitting mechanism. The planetary gearsets are of either the single pinion type or of the double pinion type of planetary gearsets.

Description:
TECHNICAL FIELD 
     The present invention relates to power transmissions and, more particularly, to a family of transmissions having three planetary gearsets that are controlled by five torque-transmitting mechanisms to provide six forward speed ratios and one reverse speed ratio. 
     BACKGROUND OF THE INVENTION 
     Passenger vehicles include a powertrain that is comprised of an engine, multi-speed transmission, and a differential or final drive mechanism. The multi-speed transmission increases the overall operating range of the vehicle by permitting the engine to operate through its torque range a number of times as the transmission ratios are interchanged. The number of forward speed ratios that are available in a transmission determines the number of ratio interchanges that can occur and therefore the number of times the engine torque range can be repeated. 
     Early automatic transmissions had two speed ranges. This severely limited the overall speed range of the vehicle and therefore required a relatively large engine that could produce a wide speed and torque range. This resulted in the engine operating at a specific fuel consumption point, during cruising, other than the most efficient point. Therefore, manually shifted (countershaft transmissions) were the most popular. 
     With the advent of three and four speed automatic transmissions, the automatic shifting (planetary gear) transmission increased in popularity with the motoring public. These transmissions improve the operating performance and fuel economy of the vehicle. The increased number of speed ratios reduces the step size between ratios and therefore improves the shift quality of the transmission by making the ratio interchanges substantially imperceptible to the operator under normal vehicle acceleration. 
     It has been suggested that the number of forward speed ratios be increased to five and even six speeds. This has been accomplished in many heavy truck powertrains. Six speed transmissions are disclosed in U.S. Pat. No. 4,070,927 issued to Polak on Jan. 31, 1978; U.S. Pat. No. 6,071,208 issued to Koivunen on Jun. 6, 2000; U.S. Pat. No. 5,106,352 issued to Lepelletier on Apr. 21, 1992; and U.S. Pat. No. 5,599,251 issued to Beim and McCarrick on Feb. 4, 1997. 
     Six speed transmissions offer several advantages over four and five speed transmissions, including improved vehicle acceleration and improved fuel economy. While many trucks employ six-speed transmissions, such as Polak, passenger cars are still manufactured, for the main part, with three and four speed automatic transmissions, and relatively few five or six speed devices due to the size and complexity of these transmissions. The Polak transmission provides six forward speed ratios with three planetary gearsets, two clutches, and three brakes. The Koivunen and Beim patents utilize six torque transmitting devices including four brakes and two clutches to establish the six forward speed ratios and one reverse ratio. The Lepelletier employs three planetary gearsets, three clutches and two brakes to provide six forward speed ratios and one reverse ratio. One of the planetary gearsets in Lepelletier is positioned and operated to establish two fixed speed input members for the remaining two planetary gearsets. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide an improved family of transmissions operating in a powertrain and being capable of providing at least six forward speed ratios and one reverse speed ratio. 
     In one aspect of the present invention, each family member has three planetary gearsets each consisting of a sun gear member, a ring gear member, and a planet carrier assembly member. In another aspect of the present invention, each family member includes five torque-transmitting mechanisms that are operable to control the speed ratios of the planetary gearsets. In yet another aspect of the present invention, a fixed interconnecting member continuously interconnects a first member of the second planetary gearset with a first member of the third planetary gearset. In yet still another aspect of the present invention, a second member of the third planetary gearset is continuously connected with a stationary member such as a transmission housing. 
     In still another aspect of the present invention, the input shaft is continuously connected with a member of the first or second planetary gearset, and the output shaft is continuously connected with a member of the first or second planetary gearset. In yet still another aspect of the present invention, the five torque-transmitting mechanisms are comprised of either five clutches, or four clutches and one brake. In a further aspect of the present invention, a first of the torque-transmitting mechanisms selectively connects a member of the first planetary gearset with either the input shaft, the fixed interconnecting member, or a member of the second or third planetary gearset. 
     In a yet further aspect of the present invention, a second of the torque-transmitting mechanisms selectively interconnects a member of the second planetary gearset with either the input shaft, the output shaft, the fixed interconnecting member, or a member of the first or third planetary gearsets. In a still further aspect of the present invention, a third of the torque-transmitting mechanisms selectively connects a member of the third planetary gearset with either the input shaft, the output shaft, the fixed interconnecting member, or a member of the&amp; first or second planetary gearsets. 
     In yet still a further aspect of the present invention, a fourth of the torque-transmitting mechanisms selectively interconnects a member of the first, second or third planetary gearset with either the fixed interconnecting member or another member of the first, second or third planetary gearsets. In yet another aspect of the present invention, a fifth torque-transmitting mechanism selectively connects a member of the first, second or third planetary gearset with either another member of the first, second or third planetary gearset, or connects a member of the first, second or third planetary gearset with a stationary member of the transmission. In still another aspect of the present invention, the five torque-transmitting mechanisms are selectively actuated or engaged in combinations of three to establish at least six forward speed ratios and one reverse speed ratio between the input and output shafts of the transmission. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a schematic representation of a powertrain having a transmission family member incorporating the present invention. 
     FIG. 2 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  1 . 
     FIG. 3 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 4 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  3 . 
     FIG. 5 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 6 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  5 . 
     FIG. 7 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 8 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  7 . 
     FIG. 9 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 10 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  9 . 
     FIG. 11 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 12 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  11 . 
     FIG. 13 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 14 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  13 . 
     FIG. 15 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 16 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  15 . 
     FIG. 17 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 18 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  17 . 
     FIG. 19 is a schematic representation of a powertrain having another transmission family member incorporating the present invention. 
     FIG. 20 is a truth table and chart describing some of the operating characteristics of the powertrain depicted in FIG.  19 . 
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Referring to the drawings, wherein like characters represent the same or corresponding parts throughout the several views, there is seen in FIG. 1 a powertrain  10  that includes a conventional engine and torque converter  12 , a planetary transmission  14 , and a conventional final drive mechanism  16 . The planetary transmission  14  includes an input shaft  17 , a planetary gear arrangement  18 , and an output shaft  19 . The planetary gear arrangement  18  includes three planetary gearsets  20 ,  30 , and  40 . 
     The planetary gearset  20  includes a sun gear member  22 , a ring gear member  24 , and a planet carrier assembly member  26  which includes a plurality of pinion gears  27  rotatably mounted on a carrier  29  and disposed in meshing relationship with both the sun gear member  22  and the ring gear member  24 . 
     The planetary gearset  30  includes a sun gear member  32 , a ring gear member  34 , and a planet carrier assembly member  36  which includes a plurality of pinion gears  37  rotatably mounted on a carrier  39  and disposed in meshing relationship with both the sun gear member  32  and the ring gear member  34 . 
     The planetary gearset  40  includes a sun gear member  42 , a ring gear member  44 , and a planet carrier assembly member  46  which includes a plurality of pinion gears  47  rotatably mounted on a carrier  49  and disposed in meshing relationship with both the sun gear member  42  and the ring gear member  44 . 
     The planetary gear arrangement  18  also includes five torque-transmitting mechanisms  50 ,  52 ,  54 ,  56 , and  58 . The torque-transmitting mechanisms are conventional selectively engaged fluid-operated devices. The torque-transmitting mechanisms are preferably controlled by a conventional electro-hydraulic system, not shown, that includes a preprogrammed digital computer. 
     The input shaft  17  is continuously connected with the engine and torque converter  12  and the ring gear member  24 . The output shaft  19  is continuously connected with the final drive mechanism  16  and the planet carrier assembly member  26 . The sun gear members  32  and  42  are continuously interconnected by an interconnecting member  70 . The ring gear member  44  is continuously connected with a transmission housing  60  that is a stationary member in the transmission and serves to ground the ring gear member  44 . 
     The ring gear member  24  and input shaft  17  are selectively connectable with the planet carrier assembly member  46  through the torque-transmitting mechanism  50 . The output shaft  19  and planet carrier assembly member  26  are selectively connectable with the ring gear member  34  through the torque-transmitting mechanism  52 . The sun gear member  22  is selectively connectable with the sun gear members  32  and  42  and therefore the interconnecting member  70  through the torque-transmitting mechanism  54 . The sun gear member  22  is also selectively connectable with the planet carrier assembly member  36  through the torque-transmitting mechanism  56 . The planet carrier assembly member  36  and planet carrier assembly member  46  are selectively connectable together through the torque-transmitting mechanism  58 . 
     The torque-transmitting mechanisms  50 ,  52 ,  54 ,  56 , and  58  are selectively connectable in combinations of three, as shown in FIG. 2, to provide six forward speed ratios and one reverse speed ratio. 
     To establish the reverse speed ratio, the torque-transmitting mechanisms  50 ,  52 , and  58  are engaged. With this combination of engagements, the output shaft  19  is selectively connected with the ring gear member  34 , and the input shaft  17  is selectively connected with both the planet carrier assembly member  46  and the planet carrier assembly member  36 . The sun gear members  42  and  32  are driven forwardly at a speed determined by the speed of the planet carrier assembly member  46  and the ring gear/sun gear tooth ratio of the planetary gearset  40 . The ring gear member  34  and therefore output shaft  19  is driven in reverse at a speed determined by the speed of sun gear member  32 , the speed of the planet carrier assembly member  36 , and ring gear/sun gear tooth ratio of the planetary gearset  30 . The overall numerical value of the reverse speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  30  and  40 . 
     As noted in FIG. 2, the torque-transmitting mechanisms  52  and  58  are also engaged in the first forward speed ratio as well as the torque-transmitting mechanism  54 . Therefore, the torque-transmitting mechanisms  52  and  58  can remain engaged through the neutral condition thereby simplifying the forward/reverse shift sequence. 
     During the first forward speed ratio, the sun gear members  22 ,  32 , and  42  are driven in reverse at a speed determined by the speed of the ring gear member  24 , the speed of the planet carrier assembly member  26 , and the ring gear/sun gear tooth ratio of the planetary gearset  20 . Planet carrier assembly members  46  and  36  are driven in reverse at a speed determined by the speed of the sun gear member  42  and the ring gear/sun gear tooth ratio of the planetary gearset  40 . Ring gear member  34 , planet carrier assembly member  26 , and output shaft  19  are driven forwardly at a speed determined by the speed of the sun gear member  32 , the speed of planet carrier assembly member  36 , and the ring gear/sun gear tooth ratio of the planetary gearset  30 . The overall numerical value of the first forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  20 ,  30 , and  40 . 
     The second forward speed ratio is determined by the engagement of the torque-transmitting mechanisms  52 ,  56 , and  58 . The first to second ratio interchange is a single transition shift. The sun gear member  22 , planet carrier assembly member  36 , and the planet carrier assembly member  46  are driven in reverse at a speed determined by the speed of the ring gear member  24 , the speed of the planet carrier assembly member  26  and the ring gear/sun gear tooth ratio of the planetary gearset  20 . The sun gear members  42  and  32  are driven in reverse at a speed determined by the speed of the planet carrier assembly member  46  and the ring gear/sun gear tooth ratio of the planetary gearset  40 . The ring gear member  34 , the planet carrier assembly member  26 , and the output shaft  19  are driven forwardly at a speed determined by the speed of the sun gear member  32 , the speed of the planet carrier assembly member  36 , and the ring gear/sun gear tooth ratio of the planetary gearset  30 . The overall numerical value of the second forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  20 ,  30 , and  40 . 
     To establish the third forward speed ratio, the torque-transmitting mechanisms  54 ,  56 , and  58  are engaged. With this combination of engagements, the planetary gearsets  40  and  30  are held stationary as well as the sun gear member  22 . The planet carrier assembly member  26  and the output shaft  19  are driven forwardly at a reduced speed ratio determined by the speed of the ring gear member  24  and the ring gear/sun gear tooth ratio of the planetary gearset  20 . The overall numerical value of the third forward speed ratio is determined by the ring gear/sun gear tooth ratio of the planetary gearset  20 . 
     The fourth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  50 ,  56 , and  58 . The third to fourth ratio interchange is a single transition shift. During the fourth forward speed ratio, the sun gear member  22  is driven at the same speed as the input shaft  17  and therefore ring gear member  24 . The output shaft  19  and planet carrier assembly member  26  are also rotated at the speed of the input shaft  17  such that the fourth forward speed ratio is a 1:1 drive. 
     The fifth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  50 ,  52 , and  56 . During the fifth forward speed ratio, the sun gear members  42  and  32  are driven forwardly at an increased speed ratio determined by the speed of the planet carrier assembly member  46  and the ring gear/sun gear tooth ratio of the planetary gearset  40 . The sun gear member  22  is driven at a speed determined by the speed of the ring gear member  24 , the speed of the planet carrier assembly member  26 , and the ring gear/sun gear tooth ratio of the planetary gearset  20 . The ring gear member  34 , planet carrier assembly member  26 , and output shaft  19  are driven forwardly at an increased speed ratio determined by the speed of the sun gear member  32 , the speed of the planet carrier assembly member  36 , and the ring gear/sun gear tooth ratio of the planetary gearset  30 . The overall numerical value of the fifth forward speed ratio is determined by the planetary gearsets  20 ,  30 , and  40 . 
     The sixth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  50 ,  54 , and  56 . The ratio interchange from fifth to sixth is a single transition shift. During the sixth forward speed ratio, the sun gear members  42 ,  32 , and  22  are rotated forwardly at an increased speed ratio determined by the speed of the planet carrier assembly member  46  and the ring gear/sun gear tooth ratio of the planetary gearset  40 . The planet carrier assembly member  46  and the output shaft  19  are driven forwardly at a speed determined by the speed of the ring gear member  24 , the speed of the sun gear member  22 , and the ring gear/sun gear tooth ratio of the planetary gearset  20 . The overall numerical value of the sixth forward speed ratio is determined by the planetary gearsets  20  and  40 . 
     The truth table of FIG. 2 describes the interchange sequence of the torque-transmitting mechanisms  50 ,  52 ,  54 ,  56 , and  58  for the forward speed ratios and the reverse speed ratio as described above. The truth table gives an example of numerical values that can be utilized with the planetary transmission  14 . These numerical values are computed from the ring gear/sun gear tooth ratios of the planetary gearsets  20 ,  30 , and  40  that actively transmit torque during the respective gear ratios. The ring gear/sun gear tooth ratios are also given as examples in FIG.  2 . FIG. 2 further has a chart which provides the ratio steps between adjacent forward speed ratios and between the forward/reverse speed ratios. For example, the first to second step ratio is 1.79 when the given ring gear/sun gear tooth ratios examples are employed. 
     A powertrain  110 , shown in FIG. 3, includes the conventional engine and torque converter  12 , a planetary transmission  114 , and a conventional final drive mechanism  16 . The planetary transmission  114  includes an input shaft  17 , a planetary gear arrangement  118 , and the output shaft  19 . The planetary gear arrangement  118  includes three planetary gearsets  120 ,  130 , and  140 . 
     The planetary gearset  120  includes a sun gear member  122 , a ring gear member  124 , and a planet carrier assembly member  126  which includes a plurality of pinion gears  127  rotatably mounted on a carrier  129  and disposed in meshing relationship with both the sun gear member  122  and the ring gear member  124 . 
     The planetary gearset  130  includes a sun gear member  132 , a ring gear member  134 , and a planet carrier assembly member  136  which includes a plurality of pinion gears  137  rotatably mounted on a carrier  139  and disposed in meshing relationship with both the sun gear member  132  and the ring gear member  134 . 
     The planetary gearset  140  includes a sun gear member  142 , a ring gear member  144 , and a planet carrier assembly member  146  which includes a plurality of pinion gears  147  rotatably mounted on a carrier  149  and disposed in meshing relationship with both the sun gear member  142  and the ring gear member  144 . 
     The planetary gear arrangement  118  also includes five torque-transmitting mechanisms  150 ,  152 ,  154 ,  156 , and  158 . The torque-transmitting mechanisms are conventional selectively engaged fluid-operated devices. The torque-transmitting mechanisms are preferably controlled by a conventional electro-hydraulic system, not shown, that includes a preprogrammed digital computer. 
     The input shaft  17  is continuously connected with the engine and torque converter  12  and the planet carrier assembly member  126 . The output shaft  19  is continuously connected with the final drive mechanism  16  and the sun gear member  122 . The sun gear member  142  and the ring gear member  134  are continuously interconnected by an interconnecting member  170 . The ring gear member  144  is continuously connected with the stationary transmission housing  60 . 
     The planet carrier assembly member  126  and input shaft  17  are selectively connectable with the interconnecting member  170  through the torque-transmitting mechanism  150 . The output shaft  19  and the sun gear member  122  are selectively connectable with the sun gear member  132  through the torque-transmitting mechanism  154 . The ring gear member  124  is selectively connectable with the planet carrier assembly members  136  through the torque-transmitting mechanism  152 . The sun gear member  132  is also selectively connectable with the planet carrier assembly member  146  through the torque-transmitting mechanism  156 . The planet carrier assembly member  136  and planet carrier assembly member  146  are selectively connectable together through the torque-transmitting mechanism  158 . 
     The torque-transmitting mechanisms  150 ,  152 ,  154 ,  156 , and  158  are selectively connectable in combinations of three, as shown in FIG. 2, to provide six forward speed ratios and one reverse speed ratio. 
     The truth table of FIG. 4 describes the engagement schedule for the torque-transmitting mechanisms  150 ,  152 ,  154 ,  156 , and  158  which are engaged in combinations of three to provide the six forward speed ratios and the one reverse speed ratio. 
     To establish the reverse speed ratio, the torque-transmitting mechanisms  150 ,  154 , and  158  are engaged. During the reverse speed ratio, the ring gear member  134  and sun gear member  142  are driven by the input shaft  17 . The planet carrier assembly member  146  and planet carrier assembly member  136  are driven forwardly at a speed determined by the speed of the sun gear member  142  and the ring gear/sun gear tooth ratio of the planetary gearset  140 . The sun gear member  132  and therefore output shaft  19  are driven in reverse at a speed determined by the speed of the ring gear member  134 , the speed of the planet carrier assembly member  136 , and the ring gear/sun gear tooth ratio of the planetary gearset  130 . The overall numerical value of the reverse speed ratio is determined by the ring gear/sun gear tooth ratio of the planetary gearsets  130  and  140 . 
     The first forward speed ratio is established by the engagement of the torque-transmitting mechanisms  150 ,  154 , and  156 . It should be noted that the torque-transmitting mechanisms  150  and  154  remain engaged through the neutral condition thereby simplifying the forward/reverse shift sequence. During the first forward speed ratio, the sun gear member  140  is driven by the input shaft  17 . The planet carrier assembly member  146 , sun gear member  132 , and output shaft  19  are driven at the speed determined by the speed of the sun gear member  142  and the ring gear/sun gear tooth ratio of the planetary gearset  140 . 
     To establish the second forward speed ratio, the torque-transmitting mechanisms  152 ,  154 , and  156  are engaged. The first to second ratio interchange is a single transition shift. During the second forward speed ratio, the ring gear member  124  and planet carrier assembly member  136  are driven forwardly at a speed determined by the speed of the planet carrier assembly member  126 , the speed of the sun gear member  122 , and the ring gear/sun gear tooth ratio of the planetary gearset  120 . The ring gear member  134  and sun gear member  142  are driven forwardly at a speed determined by the speed of the planet carrier assembly member  136 , the speed of the sun gear member  132 , and the ring gear/sun gear tooth ratio of the planetary gearset  130 . The planet carrier assembly member  146 , sun gear member  132 , and output shaft  19  are driven forwardly at a speed determined by the speed of the sun gear member  142  and the ring gear/sun gear tooth ratio of the planetary gearset  140 . The overall numerical value of the second forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  120 ,  130 , and  140 . 
     To establish the third forward speed ratio, the torque-transmitting mechanisms  150 ,  152 , and  154  are engaged. The second to third ratio interchange is a single transition ratio shift. With this combination of torque-transmitting mechanisms engaged, the ring gear member  124  and planet carrier assembly member  136  rotate in unison, the input shaft  17 , planet carrier assembly member  126 , and ring gear member  134  rotate in unison, and the sun gear member  132 , sun gear member  122 , and output shaft  19  rotate in unison. Since the members of the planetary gearsets  120  and  130  all rotate in unison, the drive is a 1:1 ratio with the output shaft  19  being driven at the same speed as the input shaft  17 . 
     The fourth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  150 ,  152 , and  156 . The third to fourth interchange is a single transition shift. During the fourth forward speed ratio, the planet carrier assembly member  146  and the sun gear member  132  are driven forwardly at a speed determined by the speed of the sun gear member  142  and the ring gear/sun gear tooth ratio of the planetary gearset  140 . The planet carrier assembly member  136  and ring gear member  124  are driven at a speed determined by the speed of the sun gear member  132 , the speed of the ring gear member  134 , and the ring gear/sun gear tooth ratio of the planetary gearset  130 . The sun gear member  122  and output shaft  19  are driven forwardly at a speed determined by the speed of the planet carrier assembly member  126 , the speed of the ring gear member  124 , and the ring gear/sun gear tooth ratio of the planetary gearset  120 . The overall numerical value of the fourth forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  120 ,  130 , and  140 . 
     The fifth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  150 ,  152 , and  158 . The planet carrier assembly member  146 , planet carrier assembly member  136 , and the ring gear member  124  are driven at a speed determined by the speed of the sun gear member  142  and the ring gear/sun gear tooth ratio of the planetary gearset  140 . The sun gear member  122  and therefore output shaft  19  are driven at a speed determined by the speed of the planet carrier assembly member  126 , the speed of the ring gear member  124 , and the ring gear/sun gear tooth ratio of the planetary gearset  120 . The overall numerical value of the fifth forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  120  and  140 . 
     The sixth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  152 ,  156 , and  158 . With this combination of engagements, the planetary gearset  140  and the ring gear member  124  are held stationary. The sun gear member  122  and therefore output shaft  19  is driven forwardly at an increased speed ratio determined by the speed of the planet carrier assembly member  126  and the ring gear/sun gear tooth ratio of the planetary gearset  120 . The overall numerical value of the sixth forward speed ratio is determined by the ring gear/sun gear tooth ratio of the planetary gearset  120 . 
     A powertrain  210 , shown in FIG. 5, includes the conventional engine and torque converter  12 , a planetary transmission  214 , and the conventional final drive mechanism  16 . The planetary transmission  214  includes an input shaft  17 , a planetary gear arrangement  218 , and the output shaft  19 . The planetary gear arrangement  218  includes three planetary gearsets  220 ,  230 , and  240 . 
     The planetary gearset  220  includes a sun gear member  222 , a ring gear member  224 , and a planet carrier assembly member  226  which includes a plurality of pinion gears  227  rotatably mounted on a carrier  229  and disposed in meshing relationship with both the sun gear member  222  and the ring gear member  224 . 
     The planetary gearset  230  includes a sun gear member  232 , a ring gear member  234 , and a planet carrier assembly member  236  which includes a plurality of pinion gears  237  rotatably mounted on a carrier  239  and disposed in meshing relationship with both the sun gear member  232  and the ring gear member  234 . 
     The planetary gearset  240  includes a sun gear member  242 , a ring gear member  244 , and a planet carrier assembly member  246  which includes a plurality of pinion gears  247  rotatably mounted on a carrier  249  and disposed in meshing relationship with both the sun gear member  242  and the ring gear member  244 . 
     The planetary gear arrangement  218  also includes five torque-transmitting mechanisms  250 ,  252 ,  254 ,  256 , and  258 . The torque-transmitting mechanisms are conventional selectively engaged fluid-operated devices. The torque-transmitting mechanisms are preferably controlled by a conventional electro-hydraulic system, not shown, that includes a preprogrammed digital computer. 
     Input shaft  17  is continuously connected between the engine and torque converter  12  and the planet carrier assembly member  226 . The output shaft  19  is continuously connected with the ring gear member  224 . The sun gear members  232  and  242  are continuously interconnected by an interconnecting member  270 , and the ring gear member  244  is continuously connected with the transmission housing  60 . The input shaft  17  is selectively connectable with the planet carrier assembly member  246  through the torque-transmitting mechanism  250 . The output shaft  19  and ring gear member  224  are selectively connectable with the ring gear member  234  through the torque-transmitting mechanism  252 . The ring gear member  234  and sun gear member  222  are selectively interconnectable through the torque-transmitting mechanism  254 . The sun gear member  222  and planet carrier assembly member  236  are selectively interconnectable through the torque-transmitting mechanism  256 , and the planet carrier assembly member  236  and planet carrier assembly member  246  are selectively interconnectable through the torque-transmitting mechanism  258 . 
     The truth table of FIG. 6 illustrates the engagement sequence of the torque-transmitting mechanisms  250 ,  252 ,  254 ,  256 , and  258  to establish the reverse drive ratio and the forward drive ratios. The reverse drive ratio is established with the engagement of the torque-transmitting mechanisms  250 ,  254 , and  256 . With the engagement of the torque-transmitting mechanisms  254  and  256 , the planetary gearset  230  will rotate as a single unit. The sun gear members  232  and  242  are rotated forwardly at a speed determined by the speed of the planet carrier assembly member  246  and the ring gear/sun gear tooth ratio of the planetary gearset  240 . The sun gear member  222  is rotated forwardly at a speed equal to the speed of the sun gear members  232  and  242 . The ring gear member  224  and therefore output shaft  19  are rotated in reverse at a speed determined by the speed of the sun gear member  222 , the speed of the planet carrier assembly member  226 , and the ring gear/sun gear tooth ratio of the planetary gearset  220 . The overall numerical ratio of the reverse speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  240  and  220 . 
     The first forward speed ratio is established with the engagement of the torque-transmitting mechanisms  250 ,  252 , and  258 . During the first forward speed ratio, the planet carrier assembly member  246  and planet carrier assembly member  236  are driven forwardly at a speed equal to the speed of the input shaft  17 . The sun gear members  242  and  232  are driven at a speed determined by the speed of the planet carrier assembly member  246  and the ring gear/sun gear tooth ratio of the planetary gearset  240 . The ring gear member  234  and output shaft  19  are driven at a speed determined by the speed of the sun gear member  232 , the speed of the planet carrier assembly member  236 , and the ring gear/sun gear tooth ratio of the planetary gearset  230 . The overall numerical value of the first forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  230  and  240 . 
     The second forward speed ratio is established with the engagement of the torque-transmitting mechanisms  252 ,  256 , and  258 . The first to second ratio interchange is a single transition shift. The sun gear member  222 , planet carrier assembly member  236 , planet carrier assembly member  246  are driven at a speed determined by the speeds of the planet carrier assembly member  226  and the ring gear member  224 , and the ring gear/sun gear tooth ratio of the planetary gearset  220 . The sun gear members  242  and  232  are driven at a speed determined by the speed of the planet carrier assembly member  246  and the ring gear/sun gear tooth ratio of the planetary gearset  240 . The ring gear member  234 , ring gear member  224 , and output shaft  19  are driven at a speed determined by the speed of the planet carrier assembly member  236 , the speed of the sun gear member  232 , and the ring gear/sun gear tooth ratio of the planetary gearset  230 . The overall numerical value of the second forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  220 ,  230 , and  240 . 
     The third forward speed ratio is established with the engagement of the torque-transmitting mechanisms  250 ,  252 , and  256 . The second to third ratio interchange is a single transition shift. During the third forward speed ratio, the sun gear members  242  and  232  are driven at a speed determined by the speed of the planet carrier assembly member  246  and the ring gear/sun gear tooth ratio of the planetary gearset  240 . The planet carrier assembly member  236  and sun gear member  222  are driven at a speed determined by the speed of the sun gear member  232 , the speed of the ring gear member  234 , and the ring gear/sun gear tooth ratio of the planetary gearset  230 . The ring gear member  224  and ring gear member  234  are driven at a speed determined by the speed of the sun gear member  222 , the speed of the planet carrier assembly member  226 , and the ring gear/sun gear tooth ratio of the planetary gearset  220 . The overall numerical value of the third forward speed ratio is determined by the ring gear/sun gear tooth ratio of all three planetary gearsets  220 ,  230 , and  240 . 
     The fourth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  250 ,  252 , and  254 . The third to fourth ratio interchange is a single transition shift. The engagement of the torque-transmitting mechanisms  252  and  254  selectively interconnect two members of the planetary gearset  220  such that when the planet carrier assembly member  226  is driven at the speed of the input shaft  17 , the output shaft  19  will also rotate at the same speed. The fourth forward speed ratio is a direct drive, or 1:1 ratio. 
     The fifth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  250 ,  254 , and  258 . The fourth to fifth ratio interchange is a single transition shift. During the fifth forward speed ratio, the sun gear members  242  and  232  are driven at a speed determined by the speed of the planet carrier assembly member  246  and the ring gear/sun gear tooth ratio of the planetary gearset  240 . The ring gear member  234  and sun gear member  222  are driven at a speed determined by the speed of the sun gear member  232 , the speed of the planet carrier assembly member  236 , and the ring gear/sun gear tooth ratio of the planetary gearset  230 . The ring gear member  224  and therefore output shaft  19  are driven at a speed determined by the speed of the sun gear member  222 , the speed of the planet carrier assembly member  226 , and ring gear/sun gear tooth ratio of the planetary gearset  220 . The overall numerical value of the fifth forward speed ratio is determined by the ring gear/sun gear tooth ratios of all three planetary gearsets  220 ,  230 , and  240 . 
     The sixth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  254 ,  256 , and  258 . The fifth to sixth ratio interchange is a single transition shift. This combination of torque-transmitting mechanisms effectively hold the planetary gearsets  240  and  230 , as well as the sun gear member  222 , stationary. The ring gear member  224  and output shaft  19  are driven forwardly at an increased speed ratio determined by the speed of the planet carrier assembly member  226  and the ring gear/sun gear tooth ratio of the planetary gearset  220 . The overall numerical value of the sixth forward speed ratio is determined by the ring gear/sun gear tooth ratio of the planetary gearset  220 . 
     The truth table and chart of FIG. 6, as suggested above, describe the interchange sequence of the torque-transmitting mechanisms necessary to establish the forward and reverse speed ratios. The truth table also presents an example of the speed ratio numbers that are available with the embodiment shown in FIG.  5 . These ratio numbers are determined utilizing the ring gear/sun gear tooth ratios given as examples in FIG.  6 . Also given in FIG. 6 is a chart of the ratio steps between adjacent forward speed ratios and the ratio step between the forward first gear and reverse ratios. For example, the step ratio between the first and second ratios is 1.73 when the example tooth ratios are employed. 
     A powertrain  310 , shown in FIG. 7, includes the conventional engine and torque converter  12 , a planetary transmission  314 , and the conventional final drive mechanism  16 . The planetary transmission  314  includes an input shaft  17 , a planetary gear arrangement  318 , and the output shaft  19 . The planetary gear arrangement  318  includes three planetary gearsets  320 ,  330 , and  340 . 
     The planetary gearset  320  includes a sun gear member  322 , a ring gear member  324 , and a planet carrier assembly member  326  which includes a plurality of pinion gears  327  rotatably mounted on a carrier  329  and disposed in meshing relationship with both the sun gear member  322  and the ring gear member  324 . 
     The planetary gearset  330  includes a sun gear member  332 , a ring gear member  334 , and a planet carrier assembly member  336  which includes a plurality of pinion gears  337  rotatably mounted on a carrier  339  and disposed in meshing relationship with both the sun gear member  332  and the ring gear member  334 . 
     The planetary gearset  340  includes a sun gear member  342 , a ring gear member  344 , and a planet carrier assembly member  346  which includes a plurality of pinion gears  347  rotatably mounted on a carrier  349  and disposed in meshing relationship with both the sun gear member  342  and the ring gear member  344 . 
     The planetary gear arrangement  318  also includes five torque-transmitting mechanisms  350 ,  352 ,  354 ,  356 , and  358 . The torque-transmitting mechanisms are conventional selectively engaged fluid-operated devices. The torque-transmitting mechanisms are preferably controlled by a conventional electro-hydraulic system, not shown, that includes a preprogrammed digital computer. 
     The input shaft  17  is continuously connected with the ring gear member  324  and selectively connectable with the planet carrier assembly member  346  through the torque-transmitting mechanism  350 . The output shaft  19  is continuously connected with the planet carrier assembly member  326  and selectively connectable with the ring gear member  334  through the torque-transmitting mechanism  352 . The sun gear members  332  and  342  are continuously interconnected through an interconnecting member  370  and are selectively connectable with the sun gear member  322  through the torque-transmitting mechanism  354 . The ring gear member  344  is continuously connected with the transmission housing  60 . The planet carrier assembly member  336  is selectively connectable with the sun gear member  322  through the torque-transmitting mechanism  356 , and with the planet carrier assembly member  346  through the torque-transmitting mechanism  358 . 
     The truth table of FIG. 8 describes the engagement and interchange sequence of the torque-transmitting mechanisms  350 ,  352 ,  354 ,  356 , and  358  to establish the reverse speed ratio and six forward speed ratios which are possible with the planetary gear arrangement  318 . 
     To establish the reverse speed ratio, the torque-transmitting mechanisms  350 ,  352 , and  358  are engaged. During the reverse speed ratio, the sun gear members  342  and  332  are driven forwardly at speed determined by the speed of the planet carrier assembly member  346  and the ring gear/sun gear tooth ratio of the planetary gearset  340 . The ring gear member  334  and therefore output shaft  19  are driven in reverse at a speed determined by the speed of the sun gear member  332 , the speed of the planet carrier assembly member  336 , and the ring gear/sun gear tooth ratio of the planetary gearset  330 . The overall numerical value of the reverse speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  330  and  340 . 
     The first forward speed ratio is established with the engagement of the torque-transmitting mechanisms  352 ,  354 , and  358 . The torque-transmitting mechanisms  352  and  358  may remain engaged through the neutral condition thereby simplifying the forward/reverse interchange. During the first forward speed ratio, the sun gear members  322 ,  332 , and  342  are driven at a speed determined by the speed of the ring gear member  324 , the speed of the planet carrier assembly member  326 , and the ring gear/sun gear tooth ratio of the planetary gearset  320 . The planet carrier assembly member  346  and the planet carrier assembly member  336  are driven at a speed determined by the speed of the sun gear member  342  and the ring gear/sun gear tooth ratio of the planetary gearset  340 . The ring gear member  334  and output shaft  19  are driven at a speed determined by the speed of the sun gear member  322 , the speed of the planet carrier assembly member  336 , and the ring gear/sun gear tooth ratio of the planetary gearset  330 . The overall numerical value of the first forward speed ratio is determined by the ring gear/sun gear tooth ratios of all three planetary gearsets  320 ,  330 , and  340 . 
     The second forward speed ratio is established with the engagement of the torque-transmitting mechanisms  352 ,  356 , and  358 . The first to second interchange is a single transition shift. During the second forward speed ratio, the sun gear member  322 , planet carrier assembly member  336 , and planet carrier assembly member  346  are driven at a speed determined by the speed of the ring gear member  324 , the speed of the planet carrier assembly member  326 , and the ring gear/sun gear tooth ratio of the planetary gearset  320 . The sun gear members  342  and  332  are driven at a speed determined by the speed of the planet carrier assembly member  346  and the ring gear/sun gear tooth ratio of the planetary gearset  340 . The ring gear member  334 , planet carrier assembly member  326 , and output shaft  19  are driven at a speed determined by the speed of the sun gear member  332 , the speed of the planet carrier assembly member  336 , and the ring gear/sun gear tooth ratio of the planetary gearset  330 . The overall numerical value of the second forward speed ratio is determined by the ring gear/sun gear tooth ratio of all three planetary gearsets  320 ,  330 , and  340 . 
     The third forward speed ratio is established with the engagement of the torque-transmitting mechanisms  354 ,  356 , and  358 . This combination of engagements holds the planetary gearsets  340  and  330 , and the sun gear member  322 , stationary. The output shaft  19  and planet carrier assembly member  326  are driven at a speed determined by the speed of the ring gear member  324  and the ring gear/sun gear tooth ratio of the planetary gearset  320 . The overall numerical value of the third forward speed ratio is determined by the ring gear/sun gear tooth ratio of the planetary gearset  320 . 
     The fourth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  350 ,  356 , and  358 . The third to fourth interchange is a single transition shift. With this combination of engagements, the sun gear member  322  is driven by the input shaft  17 , such that a 1:1 drive ratio is provided during the fourth forward speed ratio. 
     The fifth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  350 ,  352 , and  356 . This is a single transition interchange. During the fifth forward speed ratio, the sun gear members  342  and  332  are driven forwardly at a speed determined by the speed of the planet carrier assembly member  346  and the ring gear/sun gear tooth ratio of the planetary gearset  340 . The planet carrier assembly member  336  and the sun gear member  322  are driven at a speed determined by the speed of the sun gear member  332 , the speed of the ring gear member  334 , and the ring gear/sun gear tooth ratio of the planetary gearset  330 . The planet carrier assembly member  326 , ring gear member  334 , and output shaft  19  are driven at a speed determined by the speed of the sun gear member  322 , the speed of the ring gear member  324 , and the ring gear/sun gear tooth ratio of the planetary gearset  320 . The overall numerical value of the fifth forward speed ratio is determined by the ring gear/sun gear tooth ratios of all three planetary gearsets  320 ,  330 , and  340 . 
     The sixth forward speed ratio is established with the engagement of the torque-transmitting mechanisms  350 ,  352 , and  354 . This is a single transition ratio interchange. The sun gear members  342 ,  332 , and  322  are driven at a speed determined by the speed of the planet carrier assembly member  346  and the ring gear/sun gear tooth ratio of the planetary gearset  340 . The planet carrier assembly member  326  and output shaft  19  are driven at a speed determined by the speed of the sun gear member  322 , the speed of the ring gear member  324 , and the ring gear/sun gear tooth ratio of the planetary gearset  320 . The overall numerical value of the sixth forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  320  and  340 . 
     A powertrain  410 , shown in FIG. 9, includes the conventional engine and torque converter  12 , a planetary transmission  414 , and the conventional final drive mechanism  16 . The engine and torque converter  12  are connected with the planetary transmission  414  through the input shaft  17 , and the final drive mechanism  16  is connected with the transmission  414  through the output shaft  19 . The planetary transmission  414  includes a planetary gear arrangement  418  that has three planetary gearsets  420 ,  430 , and  440 , and five torque-transmitting mechanisms  450 ,  452 ,  454 ,  456 , and  458 . Each of the planetary gearsets is a simple type planetary gearset and each of the torque-transmitting mechanisms are of the rotating type, commonly termed clutches. 
     The planetary gearset  420  includes a sun gear member  422 , a ring gear member  424 , and a planet carrier assembly member  426  which includes a plurality of pinion gears  427  rotatably mounted on a carrier  429  and disposed in meshing relationship with both the sun gear member  422  and the ring gear member  424 . 
     The planetary gearset  430  includes a sun gear member  432 , a ring gear member  434 , and a planet carrier assembly member  436  which includes a plurality of pinion gears  437  rotatably mounted on a carrier  439  and disposed in meshing relationship with both the sun gear member  432  and the ring gear member  434 . 
     The planetary gearset  440  includes a sun gear member  442 , a ring gear member  444 , and a planet carrier assembly member  446  which includes a plurality of pinion gears  447  rotatably mounted on a carrier  449  and disposed in meshing relationship with both the sun gear member  442  and the ring gear member  444 . 
     The planet carrier assembly member  426  is continuously connected with the input shaft  17 . The planet carrier assembly member  436  is continuously connected with the output shaft  19 . The ring gear member  434  and sun gear member  442  are continuously interconnected by an interconnecting member  470 , and the ring gear member  444  is continuously connected with the transmission housing  60 . The input shaft  17  is selectively connectable with the ring gear member  424  through the torque-transmitting mechanism  450 . The output shaft  19  is selectively connectable with the planet carrier assembly member  446  through the torque-transmitting mechanism  458 . The interconnecting member  470  is selectively connectable with the ring gear member  424  through the torque-transmitting mechanism  452 . The ring gear member  424  is selectively connectable with the planet carrier assembly member  446  through the torque-transmitting mechanism  454 . The sun gear members  422  and  432  are selectively interconnectable through the torque-transmitting mechanism  456 . 
     The truth table and chart shown in FIG. 10 define the torque-transmitting mechanism engagement sequence required for each of the forward speed ratios and the reverse speed ratio  450 ,  452 ,  454 ,  456 , and  458 . The truth table also indicates that the torque-transmitting mechanisms  450  and  458  can remain engaged through the neutral condition thereby simplifying the forward/reverse interchange. The examples of ratios for the various speeds are calculated utilizing the ring gear/sun gear tooth ratios, also given by way of example in FIG.  10 . As is evident from the truth table of FIG. 10, all of the single step forward ratio interchanges are of the single transition type. Also, the double step interchanges, such as first to third and second to fourth, are of the single transition interchange type. The chart of FIG. 10 illustrates the step ratios between adjacent speed ratios that are accomplished with the given ratio numbers. For example, the first to second step ratio is 1.64. 
     Those skilled in the art will recognize that the numerical value of the reverse speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  430  and  440 . The numerical value of the first forward speed ratio is determined by the ring gear/sun gear tooth ratio of the planetary gearset  440 . The numerical of the second forward speed ratio is determined by the ring gear/sun gear tooth ratios of all the planetary gearsets  420 ,  430 , and  440 . The third forward speed ratio is a direct drive ratio, or a 1:1 ratio. The numerical value of the fourth forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  420  and  430 . The numerical value of the fifth forward speed ratio is determined by the ring gear/sun gear tooth ratios of the planetary gearsets  430  and  440 . The numerical value of the sixth forward speed ratio is determined by the ring gear/sun gear tooth ratios of all of the planetary gearsets  420 ,  430 , and  440 . 
     A powertrain  510 , shown in FIG. 11, includes the conventional engine and torque converter  12 , a planetary transmission  514 , and the conventional final drive mechanism  16 . The engine and torque converter  12  are drivingly connected with the planetary transmission  514  through the input shaft  17 , and the transmission  514  is drivingly connected with the final drive mechanism  16  through the output shaft  19 . The planetary transmission  514  includes a planetary gear arrangement  518  that is comprised of the three planetary gearsets  520 ,  530 , and  540 , and five torque-transmitting mechanisms  550 ,  552 ,  554 ,  556 , and  558 . The torque-transmitting mechanisms  550 ,  552 ,  554 , and  556  are rotating type torque-transmitting mechanisms, commonly termed clutches. The torque-transmitting mechanism  558  is a stationary type torque-transmitting mechanism, commonly termed a brake. 
     The planetary gearset  520  includes a sun gear member  522 , a ring gear member  524 , and a planet carrier assembly member  526  which includes a plurality of pinion gears  527  rotatably mounted on a carrier  529  and disposed in meshing relationship with both the sun gear member  522  and the ring gear member  524 . 
     The planetary gearset  530  includes a sun gear member  532 , a ring gear member  534 , and a planet carrier assembly member  536  which includes a plurality of pinion gears  537  rotatably mounted on a carrier  539  and disposed in meshing relationship with both the sun gear member  532  and the ring gear member  534 . 
     The planetary gearset  540  includes a sun gear member  542 , a ring gear member  544 , and a planet carrier assembly member  546  which includes a plurality of pinion gears  547  rotatably mounted on a carrier  549  and disposed in meshing relationship with both the sun gear member  542  and the ring gear member  544 . 
     The input shaft  17  is continuously connected with the sun gear member  532  and selectively connectable with the planet carrier assembly member  526  through the torque-transmitting mechanism  550 . The output shaft  19  is continuously connected with the sun gear member  522 . The planet carrier assembly member  526  is selectively connectable with the ring gear member  544  through the torque-transmitting mechanism  552 . The ring gear member  524  is selectively connectable with the planet carrier assembly member  536  through the torque-transmitting mechanism  554 . The ring gear member  524  is also selectively connectable with the ring gear member  544  through the torque-transmitting mechanism  556 . The ring gear member  534  and planet carrier assembly member  546  are continuously interconnected by an interconnecting member  570 , and are selectively connectable with the transmission housing  60  through the torque-transmitting mechanism  558 . The sun gear member  542  is continuously connected with the transmission housing  60 . 
     The truth table and chart shown in FIG. 12 define the engagement sequence and combination of the torque-transmitting mechanisms  550 ,  552 ,  554 ,  556 , and  558  that are utilized to establish the reverse drive ratio and the six forward speed ratios. It should be noted that the torque-transmitting mechanisms  552  and  554  are engaged through the neutral condition which simplifies the forward/reverse shift. The numerical values given for the speed ratios, by way of example, have been established utilizing the ring gear/sun gear tooth ratios given in FIG.  12 . The R 1 /S 1  value is the ring gear/sun gear tooth ratio of the planetary gearset  520 ; the R 2 /S 2  value is the ring gear/sun gear tooth ratio of the planetary gearset  530 ; and the R 3 /S 3  value is the ring gear/sun gear tooth ratio of the planetary gearset  540 . 
     Those skilled in the art will recognize that the combination of torque-transmitting mechanism engagement shown for reverse will provide the numerical value of the reverse ratio to be determined from the planetary gearsets  520  and  530 . The numerical value of the first forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  530  and  540 . The numerical value of the second forward speed ratio is one or a direct drive. The, numerical values of the third forward speed ratio and the fourth forward speed ratio are determined utilizing the ring gear/sun gear tooth ratios of all three planetary gearsets  520 ,  530 , and  540 . The numerical value of the fifth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  520  and  530 . The numerical value of the sixth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratio of the planetary gearset  520 . 
     It can also be determined from the truth table of FIG. 12 that all of the single step forward ratio interchanges are of the single transition variety, as are all of the double step ratio interchanges. The chart of FIG. 12 describes the ratio steps of the first through sixth forward speed ratios as well as the reverse to first ratio step. For example, the ratio step from first to second is 1.75. 
     A powertrain  610 , shown in FIG. 13, includes the conventional engine and torque converter  12 , a planetary transmission  614 , and the conventional final drive mechanism  16 . The engine and torque converter  12  are drivingly connected with the planetary transmission  614  through the input shaft  17 , and the transmission  614  is drivingly connected with the final drive mechanism  16  through the output shaft  19 . The planetary transmission  614  includes a planetary gear arrangement  618  that is comprised of the three planetary gearsets  620 ,  630 , and  640 , and five torque-transmitting mechanisms  650 ,  652 ,  654 ,  656 , and  658 . The torque-transmitting mechanisms  650 ,  652 ,  654 , and  656  are rotating type torque-transmitting mechanisms, commonly termed clutches. The torque-transmitting mechanism  658  is a stationary type torque-transmitting mechanism, commonly termed a brake. 
     The planetary gearset  620  includes a sun gear member  622 , a ring gear member  624 , and a planet carrier assembly member  626  which includes a plurality of pinion gears  627  rotatably mounted on a carrier  629  and disposed in meshing relationship with both the sun gear member  622  and the ring gear member  624 . 
     The planetary gearset  630  includes a sun gear member  632 , a ring gear member  634 , and a planet carrier assembly member  636  which includes a plurality of pinion gears  637  rotatably mounted on a carrier  639  and disposed in meshing relationship with both the sun gear member  632  and the ring gear member  634 . 
     The planetary gearset  640  includes a sun gear member  642 , a ring gear member  644 , and a planet carrier assembly member  646  which includes a plurality of pinion gears  647  rotatably mounted on a carrier  649  and disposed in meshing relationship with both the sun gear member  642  and the ring gear member  644 . 
     The input shaft  17  is continuously connected with the sun gear member  632 , and selectively connectable with the planet carrier assembly member  626  through the torque-transmitting mechanism  654 . The output shaft  19  is continuously connected with the sun gear member  620 . The planet carrier assembly member  646  is continuously interconnected with the ring gear member  634  through a interconnecting member  670 . The sun gear member  642  is continuously connected with the transmission housing  60 . The planet carrier assembly member  626  is selectively connectable with the ring gear member  644  through the torque-transmitting mechanism  656 . The ring gear member  624  is selectively connectable with the planet carrier assembly member  636  through the torque-transmitting mechanism  650 , and selectively connectable with the ring gear member  644  through the torque-transmitting mechanism  652 . The ring gear member  644  is selectively connectable with the transmission housing  60  through the torque-transmitting mechanism  658 . 
     The truth table shown in FIG. 14 defines the torque-transmitting mechanism engagement sequence required for each of the forward speed ratios and the reverse speed ratio. The truth table also indicates that the torque-transmitting mechanisms  650  and  656  can remain engaged through the neutral condition thereby simplifying the forward/reverse shift interchange. The numerical values given by way of example in the truth table have been determined utilizing the ring gear/sun gear tooth ratios also given by way of example in FIG.  14 . The R 1 /S 1  value is the ring gear/sun gear tooth ratio of the planetary gearset  620 ; the R 2 /S 2  value is the ring gear/sun gear tooth ratio of the planetary gearset  630 ; and the R 3 /S 3  value is the ring gear/sun gear tooth ratio of the planetary gearset  640 . It can be readily determined from the truth table that each of the single step and double step interchanges in the forward direction are of the single transition variety. The chart of FIG. 14 describes the ratio steps between adjacent forward speed ratios and between the reverse and first forward speed ratio. For example, the first to second step ratio is 1.75. 
     Those skilled in the art, upon reviewing the truth table, will recognize that the numerical value of the reverse speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  620  and  630 . The numerical value of the first forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  630  and  640 . The second forward speed ratio is a direct drive, or 1:1 ratio. The numerical values of the third forward speed ratio and the fourth forward speed ratio are determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  620 ,  630 , and  640 . The numerical value of the fifth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  620  and  630 . The numerical value of the sixth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratio of the planetary gearset  620 . 
     A powertrain  710 , shown in FIG. 15, includes the conventional engine and torque converter  12 , a planetary transmission  714 , and the conventional final drive mechanism  16 . The planetary transmission  714  includes a planetary gear arrangement  718 , the input shaft  17 , and output shaft  19 . The planetary gear arrangement  718  includes three planetary gearsets  720 ,  730 , and  740 , and five rotating torque-transmitting mechanisms, or clutches,  750 ,  752 ,  754 ,  756 , and  758 . The torque-transmitting mechanisms are engaged as described in the truth table of FIG. 16, in combinations of three to establish six forward speed ratios and one reverse speed ratio. 
     The planetary gearset  720  includes a sun gear member  722 , a ring gear member  724 , and a planet carrier assembly member  726  which includes a plurality of pinion gears  727  rotatably mounted on a carrier  729  and disposed in meshing relationship with both the sun gear member  722  and the ring gear member  724 . 
     The planetary gearset  730  includes a sun gear member  732 , a ring gear member  734 , and a planet carrier assembly member  736  which includes a plurality of pinion gears  737  rotatably mounted on a carrier  739  and disposed in meshing relationship with both the sun gear member  732  and the ring gear member  734 . 
     The planetary gearset  740  includes a sun gear member  742 , a ring gear member  744 , and a planet carrier assembly member  746  which includes a plurality of pinion gears  747  rotatably mounted on a carrier  749  and disposed in meshing relationship with both the sun gear member  742  and the ring gear member  744 . 
     The input shaft  17  is continuously connected with the planet carrier assembly member  736 , and selectively connectable with the planet carrier assembly member  746  through the torque-transmitting mechanism  758 . The output shaft  19  is continuously connected with the ring gear member  724 , and selectively connectable with the ring gear member  734  through the torque-transmitting mechanism  754 . The sun gear members  742  and  732  are continuously interconnected through an interconnecting member  770 , and selectively connectable with the sun gear member  720  through the torque-transmitting mechanism  750 . The ring gear member  744  is continuously connected with transmission housing  60 . The planet carrier assembly member  746  is selectively connectable with the sun gear member  722  through the torque-transmitting mechanism  752 . 
     The truth table of FIG. 16, as mentioned above, describes the engagement sequence of the torque-transmitting mechanisms that are utilized to provide the speed ratios of the transmission  714 . The truth table also provides a numerical value for each of the speed ratios by way of example. The numerical values were determined utilizing the ring gear/sun gear tooth ratios also given FIG.  16 . The R 1 /S 1  value is the ring gear/sun gear tooth ratio of the planetary gearset  720 ; the R 2 /S 2  value is the ring gear/sun gear tooth ratio of the planetary gearset  730 ; and the R 3 /S 3  value is the ring gear/sun gear tooth ratio of the planetary gearset  740 . Also given in FIG. 16 is a chart showing the step ratio between adjacent forward steps and the reverse to first step. For example, the first to second step ratio is 1.67. 
     Those skilled in the art will recognize that the numerical value of the reverse speed ratio is determined utilizing the ring gear/sun gear tooth ratios of all three planetary gearsets  720 ,  730 , and  740 . The numerical value of the first forward speed ratio is also determined utilizing the ring gear/sun gear tooth ratios of all three planetary gearsets  720 ,  730 , and  740 . The numerical values of the second and third forward speed ratios are determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  730  and  740 . The numerical value of the fourth forward speed ratio is one, or a direct drive ratio. The numerical value of the fifth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratio of the planetary gearset  730 . The numerical value of the sixth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  720  and  730 . 
     A powertrain  810 , shown in FIG. 17, includes the conventional engine and torque converter  12 , a planetary transmission  814 , and the final drive mechanism  16 . The planetary transmission  814  includes a planet carrier assembly member  818  that is comprised of the input shaft  17 , the output shaft  19 , and three planetary gearsets  820 ,  830 , and  840 , as well as five torque-transmitting mechanisms  850 ,  852 ,  854 ,  856 , and  858 . The torque-transmitting mechanisms  850 ,  852 ,  854 , and  856  are rotating type torque-transmitting mechanisms, commonly termed clutches. The torque-transmitting mechanism  858  is a stationary type torque-transmitting mechanism, or brake. 
     The planetary gearset  820  includes a sun gear member  822 , a ring gear member  824 , and a planet carrier assembly member  826  which includes a plurality of pinion gears  827  rotatably mounted on a carrier  829  and disposed in meshing relationship with both the sun gear member  822  and the ring gear member  824 . 
     The planetary gearset  830  includes a sun gear member  832 , a ring gear member  834 , and a planet carrier assembly member  836  which includes a pair of intermeshing of pinion gears  837  and  838  rotatably mounted on a carrier  839  and meshing with the sun gear member  832  and the ring gear member  834 , respectively. 
     The planetary gearset  840  includes a sun gear member  842 , a ring gear member  844 , and a planet carrier assembly member  846  which includes a plurality of pinion gears  847  rotatably mounted on a carrier  849  and disposed in meshing relationship with both the sun gear member  842  and the ring gear member  844 . 
     The truth table shown in FIG. 18 describes the torque-transmitting mechanism engagement sequence utilized to provide a reverse drive ratio and six forward speed ratios in the planetary gear arrangement  818 . The truth table also indicates that the torque-transmitting mechanisms  850  and  852  can remain engaged through the neutral condition thereby simplifying the forward/reverse interchange. The numerical values set forth in the truth table are given by way of example and are calculated from the example tooth ratios also given in FIG.  18 . The R 1 /S 1  value is the ring gear/sun gear tooth ratio of the planetary gearset  820 ; the R 2 /S 2  value is the ring gear/sun gear tooth ratio of the planetary gearset  830 ; and the R 3 /S 3  value is the ring gear/sun gear tooth ratio of the planetary gearset  840 . The chart of FIG. 18 provides the ratio steps that are present between adjacent forward speed ratios and between the reverse and first speed ratio. For example, the first to second step ratio is 1.53. 
     Those skilled in the art will recognize that the numerical value of the reverse speed ratio is determined utilizing the ring gear/sun gear tooth ratio of the planetary gearset  830 . The numerical value of the first and second forward speed ratios is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  830  and  840 . The third forward speed ratio is a direct drive, or a value of one. The numerical value of the fourth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of all three planetary gearsets  820 ,  830 , and  840 . The numerical value of the fifth and sixth forward speed ratios is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  820  and  830 . 
     A powertrain  910 , shown in FIG. 19, includes the conventional engine and torque converter  12 , a planetary transmission  914 , and the final drive mechanism  16 . The planetary transmission  914  includes a planetary gear arrangement  918 , the input shaft  17 , and output shaft  19 . The planetary gear arrangement  918  includes three planetary gearsets  920 ,  930 , and  940 , and five rotating torque-transmitting mechanisms, or clutches,  950 ,  952 ,  954 ,  956 , and  958 . The torque-transmitting mechanisms are engaged as described in the truth table of FIG. 20, in combinations of three to establish six forward speed ratios and one reverse speed ratio. 
     The planetary gearset  920  includes a sun gear member  922 , a ring gear member  924 , and a planet carrier assembly member  926  which includes a pair of intermeshing pinion gears  927  and  928  rotatably mounted on a carrier  929  and meshingly engage the sun gear member  922  and the ring gear member  924 , respectively. 
     The planetary gearset  930  includes a sun gear member  932 , a ring gear member  934 , and a planet carrier assembly member  936  which includes a plurality of pinion gears  937  rotatably mounted on a carrier  939  and disposed in meshing relationship with both the sun gear member  932  and the ring gear member  934 . 
     The planetary gearset  940  includes a sun gear member  942 , a ring gear member  944 , and a planet carrier assembly member  946  which includes a plurality of pinion gears  947  rotatably mounted on a carrier  949  and disposed in meshing relationship with both the sun gear member  942  and the ring gear member  944 . 
     The input shaft  17  is continuously connected with the ring gear member  924 , and selectively connectable with the ring gear member  934  and sun gear member  942  through the torque-transmitting mechanism  950 . The ring gear member  934  and sun gear member  942  are continuously interconnected by an interconnecting  970 . The output shaft  19  is continuously connected with the sun gear member  922 , and selectively connectable with the sun gear member  932  through the torque-transmitting mechanism  954 . The ring gear member  944  is continuously connected with the transmission housing  60 . The sun gear member  932  and planet carrier assembly member  946  are selectively interconnectable through the torque-transmitting mechanism  956 . The planet carrier assembly member  936  is selectively connectable with the planet carrier assembly member  946  through the torque-transmitting mechanism  958 , and selectively connectable with the planet carrier assembly member  926  through the torque-transmitting mechanism  952 . 
     The truth table and chart shown in FIG. 20, as explained above, describe the engagement sequence of the torque-transmitting mechanisms that establish the speed ratios. The truth table also provides an example of a ratio value for each of the speed ratios. These example values are determined utilizing the example ring gear/sun gear tooth ratios, also given in FIG.  20 . The R 1 /S 1  value is the ring gear/sun gear tooth ratio of the planetary gearset  920 ; the R 2 /S 2  value is the ring gear/sun gear tooth ratio of the planetary gearset  930 ; and the R 3 /S 3  value is the ring gear/sun gear tooth ratio of the planetary gearset  940 . Also shown in FIG. 20 are the ratio steps provided between the forward speed ratios and between the reverse and first speed ratio. For example, the first to second ratio step is 1.61. 
     Those skilled in the art will recognize that the numerical value for the reverse speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  930  and  940 . The numerical value of the first forward speed ratio is determined utilizing the ring gear/sun gear tooth ratio of the planetary gearset  940 . The numerical value of the second forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of all three planetary gearsets  920 ,  930 , and  940 . The third forward speed ratio is a one, which is a direct drive. The numerical value of the fourth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of all three planetary gearsets  920 ,  930 , and  940 . The numerical value of the fifth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratios of the planetary gearsets  920  and  940 . The numerical value of the sixth forward speed ratio is determined utilizing the ring gear/sun gear tooth ratio of the planetary gearset  920 . Those skilled in the art will also recognize that all of the forward single step ratio interchanges and all of the double step ratio interchanges are of the single transition variety. 
     From the foregoing presentation it should be obvious that each planetary gearset has at least one member that is non-continuously interconnected with another member of the transmission. The torque transmitting mechanisms are effective to provide a selective interconnection for those non-continuously interconnected members to establish a connection between them and other members of the transmission or between continuously interconnected members of the transmission such as the input shaft  17 , the output shaft  19 , or the interconnecting members.