Lepelletier gear mechanism

In 1992, Lepelletier proposed three degrees of freedom epicyclic gear mechanisms.^[1] These are now called Lepelletier gear mechanisms.^[2] The Lepelletier gearbox is constructed by connecting a planetary gear to a Ravigneaux gear.^[3]

The transmission was the first of its kind to offer additional gear ratios by combining serial and parallel power flow without increasing the complexity of the design.

Due to these advantages, this gearset concept became widely used in automatic vehicle transmissions. ZF was the first to start series production in 2000. Aisin/Toyota, Ford, and GM followed in 2005. For the first time, the construction costs could be reduced compared to the respective predecessor models.

The main objective in replacing the predecessor model was to improve vehicle fuel economy with extra speeds and a wider gear span to allow the engine speed level to be lowered (downspeeding). The layout brings the ability to shift in a non-sequential manner – going from gear 6 to gear 2 in extreme situations simply by changing one shift element (actuating clutch E and releasing brake A).

In order to increase the number of ratios, all major manufacturers has abandoned the conventional design method of limiting themselves to pure in-line epicyclic gearing and extended it to a combination with parallel epicyclic gearing. The 6HP from ZF is the first transmission designed according to this new paradigm. After gaining additional gear ratios only with additional components, this time the number of components has to decrease while the number of ratios still increase. The progress is reflected in a much better ratio of the number of gears to the number of components used compared to existing layouts.

Gearset concept: cost-effectiveness^[a]

With Assessment	Output: Gear Ratios	Innovation Elasticity[b] Δ Output : Δ Input	Input: Main Components
			Total	Gearsets	Brakes	Clutches
6HP Ref. Object	${\displaystyle n_{O1}}$ ${\displaystyle n_{O2}}$	Topic[b]	${\displaystyle n_{I}=n_{G}+}$ ${\displaystyle n_{B}+n_{C}}$	${\displaystyle n_{G1}}$ ${\displaystyle n_{G2}}$	${\displaystyle n_{B1}}$ ${\displaystyle n_{B2}}$	${\displaystyle n_{C1}}$ ${\displaystyle n_{C2}}$
Δ Number	${\displaystyle n_{O1}-n_{O2}}$		${\displaystyle n_{I1}-n_{I2}}$	${\displaystyle n_{G1}-n_{G2}}$	${\displaystyle n_{B1}-n_{B2}}$	${\displaystyle n_{C1}-n_{C2}}$
Relative Δ	Δ Output ${\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}$	${\displaystyle {\tfrac {n_{O1}-n_{O2}}{n_{O2}}}:{\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}$ ${\displaystyle ={\tfrac {n_{O1}-n_{O2}}{n_{O2}}}}$·${\displaystyle {\tfrac {n_{I2}}{n_{I1}-n_{I2}}}}$	Δ Input ${\displaystyle {\tfrac {n_{I1}-n_{I2}}{n_{I2}}}}$	${\displaystyle {\tfrac {n_{G1}-n_{G2}}{n_{G2}}}}$	${\displaystyle {\tfrac {n_{B1}-n_{B2}}{n_{B2}}}}$	${\displaystyle {\tfrac {n_{C1}-n_{C2}}{n_{C2}}}}$
6HP 5HP 24/30[c]	6[d] 5[d]	Progress[b]	8 9	3[e] 3	2 3	3 3
Δ Number	1		-1	0	-1	0
Relative Δ	0.200 ${\displaystyle {\tfrac {1}{5}}}$	−1.800[b] ${\displaystyle {\tfrac {1}{5}}:{\tfrac {-1}{9}}={\tfrac {1}{5}}}$·${\displaystyle {\tfrac {-9}{1}}={\tfrac {-9}{5}}}$	−0.111 ${\displaystyle {\tfrac {-1}{9}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$	−0.333 ${\displaystyle {\tfrac {-1}{3}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$
6HP 5HP 18/19[c]	6[d] 5[d]	Progress[b]	8 10	3[e] 3[e]	2 3	3 4
Δ Number	1		-2	0	-1	-1
Relative Δ	0.200 ${\displaystyle {\tfrac {1}{5}}}$	−1.000[b] ${\displaystyle {\tfrac {1}{5}}:{\tfrac {-1}{5}}={\tfrac {1}{5}}}$·${\displaystyle {\tfrac {-5}{1}}={\tfrac {-1}{1}}}$	−0.200 ${\displaystyle {\tfrac {-1}{5}}}$	0.000 ${\displaystyle {\tfrac {0}{3}}}$	−0.333 ${\displaystyle {\tfrac {-1}{3}}}$	−0.250 ${\displaystyle {\tfrac {-1}{4}}}$
6HP 3-Speed[f]	6[d] 3[d]	Market Position[b]	8 7	3[e] 2	2 3	3 2
Δ Number	3		1	1	-1	1
Relative Δ	1.000 ${\displaystyle {\tfrac {1}{1}}}$	7.000[b] ${\displaystyle {\tfrac {1}{1}}:{\tfrac {1}{7}}={\tfrac {1}{1}}}$·${\displaystyle {\tfrac {7}{1}}={\tfrac {7}{1}}}$	0.143 ${\displaystyle {\tfrac {1}{7}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$	−0.333 ${\displaystyle {\tfrac {-1}{3}}}$	0.500 ${\displaystyle {\tfrac {1}{2}}}$
^ Progress increases cost-effectiveness and is reflected in the ratio of forward gears to main components. It depends on the power flow: parallel: using the two degrees of freedom of planetary gearsets to increase the number of gears with unchanged number of components serial: in-line combined planetary gearsets without using the two degrees of freedom to increase the number of gears a corresponding increase in the number of components is unavoidable ^ a b c d e f g h Innovation elasticity classifies progress and market position Automobile manufacturers drive forward technical developments primarily in order to remain competitive or to achieve or defend technological leadership. This technical progress has therefore always been subject to economic constraints Only innovations whose relative additional benefit is greater than the relative additional resource input, i.e. whose economic elasticity is greater than 1, are considered for realization The required innovation elasticity of an automobile manufacturer depends on its expected return on investment. The basic assumption that the relative additional benefit must be at least twice as high as the relative additional resource input helps with orientation negative, if the output increases and the input decreases, is perfect 2 or above is good 1 or above is acceptable (red) below this is unsatisfactory (bold) ^ a b Direct predecessor To reflect the progress of the specific model change ^ a b c d e f plus 1 reverse gear ^ a b c d of which 2 gearsets are combined as a compound Ravigneaux gearset ^ Reference standard (benchmark) 3-speed transmissions with torque converters have established the modern market for automatic transmissions and thus made it possible in the first place, as this design proved to be a particularly successful compromise between cost and performance It became the archetype and dominated the world market for around 3 decades, setting the standard for automatic transmissions. It was only when fuel consumption became the focus of interest that this design reached its limits, which is why it has now completely disappeared from the market What has remained is the orientation that it offers as a reference standard (point of reference, benchmark) for this market for determining progressiveness and thus the market position of all other, later designs All transmission variants consist of 7 main components Typical examples are Turbo-Hydramatic from GM Cruise-O-Matic from Ford TorqueFlite from Chrysler Detroit Gear from BorgWarner for Studebaker BW-35 from BorgWarner and as T35 from Aisin 3N 71 from Nissan/Jatco 3 HP from ZF Friedrichshafen W3A 040 and W3B 050 from Mercedes-Benz

The Lepelletier gearset concept actually provides 7 forward gears. However, the 5th gear, which is configured as a direct gear (ratio 1.00) in this configuration, requires a releaseable brake for S₁ (sun gear of the first gearset, which is the simple one) and thus a 6th shifting element without any corresponding benefit: with ratios of approximately 1.15 and 0.85, the 4th and 6th gears are so close together that the 5th gear can easily be dispensed with. This means that all manufacturers can manage with 5 shifting elements and all transmissions built have 6 gear ratios instead of the possible 7.

In the illustrations, the Ravigneaux gearset is shown vertically mirrored, contrary to actual practice, for the sake of clarity.

• Reverse gear
• Neutral
• 1st gear
• 2nd gear
• 3rd gear
• 4th gear
• 5th gear: not used in actual existing gearboxes
• 6th gear: 5th gear in actual existing gearboxes
• 7th gear: 6th gear in actual existing gearboxes

The ratios of the 6 gears are nicely evenly distributed in all versions. Exceptions are the large step from 1st to 2nd gear and the almost geometric steps from 3rd to 4th to 5th gear. They cannot be eliminated without affecting all other gears. As the large step is shifted due to the large span to a lower speed range than with conventional gearboxes, it is less significant. As the gear steps are smaller overall due to the additional gear(s), the geometric gear steps are still smaller than the corresponding gear steps of conventional gearboxes. Overall, therefore, the weaknesses are not overly significant. As the selected gearset concept saves up to 2 components compared to 5-speed transmissions, the advantages clearly outweigh the disadvantages.

In combination with a torque converter lock-up clutch, the gearset largely closes the gap between vehicles with automatic and manual transmissions in terms of fuel efficiency.

Gear ratio analysis^[a][b]

In-Depth Analysis[c] With Assessment And Torque Ratio[d] And Efficiency Calculation[e]		Planetary Gearset: Teeth[f] Lepelletier Gear Mechanism			Count	Nomi- nal[g] Effec- tive[h]	Cen- ter[i]
		Simple	Ravigneaux				Avg.[j]
Make[k] Model	Version First Delivery	S1[l] R1[m]	S2[n] R2[o]	S3[p] R3[q]	Brakes Clutches	Ratio Span	Gear Step[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	${\displaystyle {i_{R}}}$[c]	${\displaystyle {i_{1}}}$[c]	${\displaystyle {i_{2}}}$[c]	${\displaystyle {i_{3}}}$[c]	${\displaystyle {i_{4}}}$[c]	${\displaystyle {i_{5}}}$[c]	${\displaystyle {i_{6}}}$[c]
Step[r]	${\displaystyle -{\frac {i_{R}}{i_{1}}}}$[s]	${\displaystyle {\frac {i_{1}}{i_{1}}}}$	${\displaystyle {\frac {i_{1}}{i_{2}}}}$[t]	${\displaystyle {\frac {i_{2}}{i_{3}}}}$	${\displaystyle {\frac {i_{3}}{i_{4}}}}$	${\displaystyle {\frac {i_{4}}{i_{5}}}}$	${\displaystyle {\frac {i_{5}}{i_{6}}}}$
Δ Step[u][v]			${\displaystyle {\tfrac {i_{1}}{i_{2}}}:{\tfrac {i_{2}}{i_{3}}}}$	${\displaystyle {\tfrac {i_{2}}{i_{3}}}:{\tfrac {i_{3}}{i_{4}}}}$	${\displaystyle {\tfrac {i_{3}}{i_{4}}}:{\tfrac {i_{4}}{i_{5}}}}$	${\displaystyle {\tfrac {i_{4}}{i_{5}}}:{\tfrac {i_{5}}{i_{6}}}}$
Shaft Speed	${\displaystyle {\frac {i_{1}}{i_{R}}}}$	${\displaystyle {\frac {i_{1}}{i_{1}}}}$	${\displaystyle {\frac {i_{1}}{i_{2}}}}$	${\displaystyle {\frac {i_{1}}{i_{3}}}}$	${\displaystyle {\frac {i_{1}}{i_{4}}}}$	${\displaystyle {\frac {i_{1}}{i_{5}}}}$	${\displaystyle {\frac {i_{1}}{i_{6}}}}$
Δ Shaft Speed[w]	${\displaystyle 0-{\tfrac {i_{1}}{i_{R}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{1}}}-0}$	${\displaystyle {\tfrac {i_{1}}{i_{2}}}-{\tfrac {i_{1}}{i_{1}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{3}}}-{\tfrac {i_{1}}{i_{2}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{4}}}-{\tfrac {i_{1}}{i_{3}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{5}}}-{\tfrac {i_{1}}{i_{4}}}}$	${\displaystyle {\tfrac {i_{1}}{i_{6}}}-{\tfrac {i_{1}}{i_{5}}}}$
Torque Ratio[d]	${\displaystyle \mu _{R}}$[d]	${\displaystyle \mu _{1}}$[d]	${\displaystyle \mu _{2}}$[d]	${\displaystyle \mu _{3}}$[d]	${\displaystyle \mu _{4}}$[d]	${\displaystyle \mu _{5}}$[d]	${\displaystyle \mu _{6}}$[d]
Efficiency ${\displaystyle \eta _{n}}$[e]	${\displaystyle {\frac {\mu _{R}}{i_{R}}}}$[e]	${\displaystyle {\frac {\mu _{1}}{i_{1}}}}$[e]	${\displaystyle {\frac {\mu _{2}}{i_{2}}}}$[e]	${\displaystyle {\frac {\mu _{3}}{i_{3}}}}$[e]	${\displaystyle {\frac {\mu _{4}}{i_{4}}}}$[e]	${\displaystyle {\frac {\mu _{5}}{i_{5}}}}$[e]	${\displaystyle {\frac {\mu _{6}}{i_{6}}}}$[e]
2000: first manufacturer to use the Lepelletier gearset mechanism: ZF 6HP 1st generation
ZF 6HP 26[x] ZF 6HP 19[x] ZF 6HP 32[x]	600 N⋅m (443 lb⋅ft) 400 N⋅m (295 lb⋅ft)[y] 750 N⋅m (553 lb⋅ft)[4] 2000 (all)	37 71	31 38	38 85	2 3	6.0354 4.9236 [h][s]	1.6977
							1.4327[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	−3.4025[s][h] ${\displaystyle -{\tfrac {4,590}{1,349}}}$	4.1708 ${\displaystyle {\tfrac {9,180}{2,201}}}$	2.3397[t] ${\displaystyle {\tfrac {211,140}{90,241}}}$	1.5211 ${\displaystyle {\tfrac {108}{71}}}$	1.1428 [v][w] ${\displaystyle {\tfrac {9,180}{8,033}}}$	0.8672 ${\displaystyle {\tfrac {4,590}{5,293}}}$	0.6911 ${\displaystyle {\tfrac {85}{123}}}$
Step	0.8158[s]	1.0000	1.7826[t]	1.5382	1.3311	1.3178	1.2549
Δ Step[u]			1.1589	1.1559	1.0101[v]	1.0502
Speed	-1.2258	1.0000	1.7826	2.7419	3.6497	4.8096	6.0354
Δ Speed	1.2258	1.0000	0.7826	0.9593	0.9078[w]	1.1599	1.2258
Torque Ratio[d]	–3.3116 –3.2665	4.0186 3.9436	2.2837 2.2559	1.5107 1.5055	1.1359 1.1325	0.8633 0.8613	0.6867 0.6845
Efficiency ${\displaystyle \eta _{n}}$[e]	0.9733 0.9600	0.9635 0.9455	0.9761 0.9642	0.9931 0.9897	0.9939 0.9910	0.9955 0.9932	0.9937 0.9905
2007: ZF 6HP 2nd generation
ZF 6HP 28[x] ZF 6HP 21[x] ZF 6HP 34[x]	600 N⋅m (443 lb⋅ft) 450 N⋅m (332 lb⋅ft)[z] 750 N⋅m (553 lb⋅ft)[aa] 2007 (all)	37 71	31 38	38 85	2 3	6.0354 4.9236 [h][s]	1.6977
							1.4327[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	−3.4025[s][h]	4.1708	2.3397[t]	1.5211	1.1428 [v][w]	0.8672	0.6911
Other manufacturer using the Lepelletier gear mechanism
Aisin AWTF-80 SC	450 N⋅m (332 lb⋅ft)[7] 2005	50 90	36 44	44 96	2 3	6.0494 4.9495 [h][s]	1.6865
							1.4333[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	−3.3939[s][h] ${\displaystyle -{\tfrac {112}{33}}}$	4.1481 ${\displaystyle {\tfrac {112}{27}}}$	2.3704[t] ${\displaystyle {\tfrac {64}{27}}}$	1.5556 ${\displaystyle {\tfrac {14}{9}}}$	1.1546[v] ${\displaystyle {\tfrac {112}{97}}}$	0.8593 ${\displaystyle {\tfrac {336}{391}}}$	0.6857[w] ${\displaystyle {\tfrac {24}{35}}}$
Step	0.8182[s]	1.0000	1.7500[t]	1.5238	1.3472	1.3436	1.2532
Δ Step[u]			1.1484	1.1311	1.0027[v]	1.0722
Speed	-1.2222	1.0000	1.7500	2.6667	3.5926	4.8272	6.0494
Δ Speed	1.2222	1.0000	0.7500	0.9167	0.9259	1.2346	1.2222[w]
Torque Ratio[d]	–3.3023 –3.2568	3.9956 3.9204	2.3127 2.2841	1.5444 1.5389	1.1471 1.1434	0.8553 0.8532	0.6813 0.6791
Efficiency ${\displaystyle \eta _{n}}$[e]	0.9730 0.9596	0.9632 0.9451	0.9757 0.9636	0.9929 0.9893	0.9935 0.9903	0.9953 0.9928	0.9936 0.9904
Ford 6R 60 6R 80	600 N⋅m (443 lb⋅ft) 800 N⋅m (590 lb⋅ft) 2005 (all)	37 71	31 38	38 85	2 3	6.0354 4.9236 [h][s]	1.6977
							1.4327[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	−3.4025[s][h]	4.1708	2.3397[t]	1.5211	1.1428 [v][w]	0.8672	0.6911
Ford 6R 140	1,400 N⋅m (1,033 lb⋅ft) 2005	49 95	37 47	47 97	2 3	5.8993 4.6441 [h][s]	1.6361
							1.4261[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	−3.1283[s][h] ${\displaystyle -{\tfrac {13,968}{4,485}}}$	3.9738 ${\displaystyle {\tfrac {13,968}{3,515}}}$	2.3181 [t][v] ${\displaystyle {\tfrac {8,148}{3,515}}}$	1.5158 ${\displaystyle {\tfrac {144}{95}}}$	1.1492 [v][w] ${\displaystyle {\tfrac {13,968}{12,155}}}$	0.8585 ${\displaystyle {\tfrac {13,968}{16,271}}}$	0.6736 ${\displaystyle {\tfrac {97}{144}}}$
Step	0.7872[s]	1.0000	1.7143[t]	1.5293	1.3190	1.3389	1.2744
Δ Step[u]			1.1210[v]	1.1594	0.9854[v]	1.0504
Speed	-1.2703	1.0000	1.7143	2.6216	3.4580	4.6290	5.8993
Δ Speed	1.2703	1.0000	0.7143	0.9073	0.8364[w]	1.1710	1.2703
Torque Ratio[d]	–3.0449 –3.0035	3.8290 3.7576	2.2615 2.2333	1.5055 1.5003	1.1419 1.1383	0.8543 0.8522	0.6692 0.6669
Efficiency ${\displaystyle \eta _{n}}$[e]	0.9733 0.9601	0.9635 0.9456	0.9756 0.9635	0.9932 0.9898	0.9937 0.9906	0.9952 0.9927	0.9934 0.9900
GM 6L 45 6L 50	500 N⋅m (369 lb⋅ft) 2006	49 89	37 47	47 97	2 3	6.0346 4.7507 [h][s]	1.6548
							1.4326[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	−3.2001[s][h] ${\displaystyle -{\tfrac {13,386}{4,183}}}$	4.0650 ${\displaystyle {\tfrac {13,386}{3,293}}}$	2.3712 [t][v] ${\displaystyle {\tfrac {15,617}{63586}}}$	1.5506 ${\displaystyle {\tfrac {138}{89}}}$	1.1567 [v][w] ${\displaystyle {\tfrac {13,386}{11,573}}}$	0.8532 ${\displaystyle {\tfrac {13,386}{15,689}}}$	0.6736 ${\displaystyle {\tfrac {97}{144}}}$
Step	0.7872[s]	1.0000	1.7143[t]	1.5293	1.3406	1.3557	1.2662
Δ Step[u]			1.1210[v]	1.1408	0.9889[v]	1.0703
Speed	-1.2703	1.0000	1.7143	2.6216	3.5144	4.7643	6.0346
Δ Speed	1.2703	1.0000	0.7143	0.9073	0.8928[w]	1.2499	1.2703
Torque Ratio[d]	–3.1138 –3.0710	3.9156 3.8421	2.3127 2.2826	1.5396 1.5340	1.1490 1.1453	0.8490 0.8468	0.6692 0.6692
Efficiency ${\displaystyle \eta _{n}}$[e]	0.9730 0.9597	0.9633 0.9452	0.9753 0.9630	0.9929 0.9893	0.9934 0.9902	0.9951 0.9925	0.9934 0.9900
GM 6L 80 6L 90	800 N⋅m (590 lb⋅ft) 2005	50 94	35 46	46 92	2 3	6.0401 4.5957 [h][s]	1.6384
							1.4329[r]
Gear	R	1	2	3	4	5	6
Gear Ratio[c]	−3.0638[s][h] ${\displaystyle -{\tfrac {144}{47}}}$	4.0267 ${\displaystyle {\tfrac {6,624}{1,645}}}$	2.3635 [t][v] ${\displaystyle {\tfrac {3,888}{1,645}}}$	1.5319 ${\displaystyle {\tfrac {72}{47}}}$	1.1522 [v][w] ${\displaystyle {\tfrac {6,624}{5,749}}}$	0.8521 ${\displaystyle {\tfrac {144}{169}}}$	0.6667 ${\displaystyle {\tfrac {2}{3}}}$
Step	0.7609[s]	1.0000	1.7037[t]	1.5429	1.3296	1.3522	1.2781
Δ Step[u]			1.1043[v]	1.1604	0.9832[v]	1.0580
Speed	-1.3143	1.0000	1.7037	2.6286	3.4948	4.7258	6.0401
Δ Speed	1.3143	1.0000	0.7037	0.9249	0.8662[w]	1.2310	1.3143
Torque Ratio[d]	–2.9817 –2.9410	3.8794 3.8068	2.3048 2.2756	1.5213 1.5160	1.1448 1.1412	0.8478 0.8456	0.6622 0.6599
Efficiency ${\displaystyle \eta _{n}}$[e]	0.9732 0.9599	0.9634 0.9454	0.9751 0.9628	0.9931 0.9896	0.9936 0.9904	0.9950 0.9924	0.9932 0.9898
Actuated Shift Elements[ab]
Brake A[ac]		❶	❶	❶	❶
Brake B[ad]	❶			❶		❶
Clutch C[ae]			❶				❶
Clutch D[af]	❶	❶
Clutch E[ag]					❶	❶	❶
Geometric Ratios: Speed Conversion
Gear Ratio[c] R & 3 & 6 Ordinary[ah] Elementary Noted[ai]	${\displaystyle i_{R}=-{\frac {R_{3}(S_{1}+R_{1})}{R_{1}S_{3}}}}$		${\displaystyle i_{3}={\frac {S_{1}+R_{1}}{R_{1}}}}$		${\displaystyle i_{6}={\frac {R_{3}}{S_{3}+R_{3}}}}$
	${\displaystyle i_{R}=-\left(1+{\tfrac {S_{1}}{R_{1}}}\right){\tfrac {R_{3}}{S_{3}}}}$		${\displaystyle i_{3}=1+{\tfrac {S_{1}}{R_{1}}}}$		${\displaystyle i_{6}={\tfrac {1}{1+{\tfrac {S_{3}}{R_{3}}}}}}$
Gear Ratio[c] 1 & 2 Ordinary[ah] Elementary Noted[ai]	${\displaystyle i_{1}={\frac {R_{2}R_{3}(S_{1}+R_{1})}{R_{1}S_{2}S_{3}}}}$			${\displaystyle i_{2}={\frac {R_{3}(S_{1}+R_{1})(S_{2}+R_{2})}{R_{1}S_{2}(S_{3}+R_{3})}}}$
	${\displaystyle i_{1}=\left(1+{\tfrac {S_{1}}{R_{1}}}\right){\tfrac {R_{2}R_{3}}{S_{2}S_{3}}}}$			${\displaystyle i_{2}={\tfrac {\left(1+{\tfrac {S_{1}}{R_{1}}}\right)\left(1+{\tfrac {R_{2}}{S_{2}}}\right)}{1+{\tfrac {S_{3}}{R_{3}}}}}}$
Gear Ratio[c] 4 & 5 Ordinary[ah] Elementary Noted[ai]	${\displaystyle i_{4}={\frac {R_{2}R_{3}(S_{1}+R_{1})}{R_{2}R_{3}(S_{1}+R_{1})-S_{1}S_{2}S_{3}}}}$			${\displaystyle i_{5}={\frac {R_{3}(S_{1}+R_{1})}{R_{3}(S_{1}+R_{1})+S_{1}S_{3}}}}$
	${\displaystyle i_{4}={\tfrac {1}{1-{\tfrac {\tfrac {S_{2}S_{3}}{R_{2}R_{3}}}{1+{\tfrac {R_{1}}{S_{1}}}}}}}}$			${\displaystyle i_{5}={\tfrac {1}{1+{\tfrac {\tfrac {S_{3}}{R_{3}}}{1+{\tfrac {R_{1}}{S_{1}}}}}}}}$
Kinetic Ratios: Torque Conversion
Torque Ratio[d] R & 3 & 6	${\displaystyle \mu _{R}=-\left(1+{\tfrac {S_{1}}{R_{1}}}\eta _{0}\right){\tfrac {R_{3}}{S_{3}}}\eta _{0}}$		${\displaystyle \mu _{3}=1+{\tfrac {S_{1}}{R_{1}}}\eta _{0}}$		${\displaystyle \mu _{6}={\tfrac {1}{1+{\tfrac {S_{3}}{R_{3}}}\cdot {\tfrac {1}{\eta _{0}}}}}}$
Torque Ratio[d] 1 & 2	${\displaystyle \mu _{1}=\left(1+{\tfrac {S_{1}}{R_{1}}}\eta _{0}\right){\tfrac {R_{2}R_{3}}{S_{2}S_{3}}}{\eta _{0}}^{\tfrac {3}{2}}}$			${\displaystyle \mu _{2}={\tfrac {\left(1+{\tfrac {S_{1}}{R_{1}}}\eta _{0}\right)\left(1+{\tfrac {R_{2}}{S_{2}}}\eta _{0}\right)}{1+{\tfrac {S_{3}}{R_{3}}}\cdot {\tfrac {1}{\eta _{0}}}}}}$
Torque Ratio[d] 4 & 5	${\displaystyle \mu _{4}={\tfrac {1}{1-{\tfrac {{\tfrac {S_{2}S_{3}}{R_{2}R_{3}}}{\eta _{0}}^{\tfrac {3}{2}}}{1+{\tfrac {R_{1}}{S_{1}}}\cdot {\tfrac {1}{\eta _{0}}}}}}}}$			${\displaystyle \mu _{5}={\tfrac {1}{1+{\tfrac {{\tfrac {S_{3}}{R_{3}}}\cdot {\tfrac {1}{\eta _{0}}}}{1+{\tfrac {R_{1}}{S_{1}}}\eta _{0}}}}}}$
^ The 6HP-transmission is the first one to use the Lepelletier gear mechanism ^ Revised 14 January 2026 Nomenclature ${\displaystyle S_{n}=}$ sun gear: number of teeth ${\displaystyle R_{n}=}$ ring gear: number of teeth ${\displaystyle \color {gray}{C_{n}=}}$ carrier or planetary gear carrier (not needed) ${\displaystyle s_{n}=}$ sun gear: shaft speed ${\displaystyle r_{n}=}$ ring gear: shaft speed ${\displaystyle c_{n}=}$ carrier or planetary gear carrier: shaft speed With ${\displaystyle n=}$ gear is ${\displaystyle i_{n}=}$ gear ratio or transmission ratio ${\displaystyle \omega _{1;n}=\omega _{t}=}$ shaft speed shaft 1: input (turbine) shaft ${\displaystyle \omega _{2;n}=}$ shaft speed shaft 2: output shaft ${\displaystyle T_{1;n}=T_{t}=}$ torque shaft 1: input (turbine) shaft ${\displaystyle T_{2;n}=}$ torque shaft 2: output shaft ${\displaystyle \mu _{n}=}$ torque ratio or torque conversion ratio ${\displaystyle \eta _{n}=}$ efficiency ${\displaystyle i_{0}=}$ stationary gear ratio ${\displaystyle \eta _{0}=}$ (assumed) stationary gear efficiency ^ a b c d e f g h i j k l m n o p q r s Gear ratio (transmission ratio) ${\displaystyle i_{n}}$ — speed conversion — The gear ratio ${\displaystyle i_{n}}$ is the ratio of input shaft speed ${\displaystyle \omega _{1;n}}$ to output shaft speed ${\displaystyle \omega _{2;n}}$ and therefore corresponds to the reciprocal of the shaft speeds ${\displaystyle i_{n}={\frac {1}{\frac {\omega _{2;n}}{\omega _{1;n}}}}={\frac {\omega _{1;n}}{\omega _{2;n}}}={\frac {\omega _{t}}{\omega _{2;n}}}}$ ^ a b c d e f g h i j k l m n o p q Torque ratio (torque conversion ratio) ${\displaystyle \mu _{n}}$ — torque conversion — The torque ratio ${\displaystyle \mu _{n}}$ is the ratio of output torque ${\displaystyle T_{2;n}}$ to input torque ${\displaystyle T_{1;n}}$ minus efficiency losses and therefore corresponds (apart from the efficiency losses) to the reciprocal of the shaft speeds too ${\displaystyle \mu _{n}=i_{n}\eta _{n;\eta _{0}}={\frac {\omega _{1;n}\eta _{n;\eta _{0}}}{\omega _{2;n}}}={\frac {T_{2;n}\eta _{n;\eta _{0}}}{T_{1;n}}}}$ whereby ${\displaystyle \eta _{n;\eta _{0}}}$ may vary from gear to gear according to the formulas listed in this table and ${\displaystyle 0\leq \eta _{n;\eta _{0}}\leq 1}$ ^ a b c d e f g h i j k l m n Efficiency The efficiency ${\displaystyle \eta _{n}}$ is calculated from the torque ratio in relation to the gear ratio (transmission ratio) ${\displaystyle \eta _{n}={\frac {\mu _{n}}{i_{n}}}}$ Power loss for single meshing gears is in the range of 1 % to 1.5 % helical gear pairs, which are used to reduce noise in passenger cars, are in the upper part of the loss range spur gear pairs, which are limited to commercial vehicles due to their poorer noise comfort, are in the lower part of the loss range Corridor for torque ratio and efficiency in planetary gearsets, the stationary gear ratio ${\displaystyle i_{0}}$ is formed via the planetary gears and thus by two meshes for reasons of simplification, the efficiency for both meshes together is commonly specified there the efficiencies ${\displaystyle \eta _{0}}$ specified here are based on assumed efficiencies for the stationary ratio ${\displaystyle i_{0}}$ of ${\displaystyle \eta _{0}=0.9800}$ (upper value) and ${\displaystyle \eta _{0}=0.9700}$ (lower value) for both interventions together The corresponding efficiency for single-meshing gear pairs is ${\displaystyle {\eta _{0}}^{\tfrac {1}{2}}}$ at ${\displaystyle 0.9800^{\tfrac {1}{2}}=0.98995}$ (upper value) and ${\displaystyle 0.9700^{\tfrac {1}{2}}=0.98489}$ (lower value) ^ Layout Input and output are on opposite sides Planetary gearset 1 is on the input (turbine) side Input (turbine) shafts are R1 and, if actuated, C2/C3 (the common carrier of the compound Ravigneaux gearset) Output shaft is R3 (ring gear of outer Ravigneaux gearset) ^ Total ratio span (total gear ratio/total transmission ratio) nominal ${\displaystyle {\frac {\omega _{2;n}}{\omega _{2;1}}}={\frac {\frac {\omega _{2;n}}{\omega _{2;1}\omega _{2;n}}}{\frac {\omega _{2;1}}{\omega _{2;1}\omega _{2;n}}}}={\frac {\frac {1}{\omega _{2;1}}}{\frac {1}{\omega _{2;n}}}}={\frac {\frac {\omega _{t}}{\omega _{2;1}}}{\frac {\omega _{t}}{\omega _{2;n}}}}={\frac {i_{1}}{i_{n}}}}$ A wider span enables the downspeeding when driving outside the city limits increase the climbing ability when driving over mountain passes or off-road or when towing a trailer ^ a b c d e f g h i j k l m n o Total ratio span (total gear ratio/total transmission ratio) effective ${\displaystyle {\frac {\omega _{2;n}}{max(\omega _{2;1};|\omega _{2;R}|)}}={\frac {min(i_{1};|i_{R}|)}{i_{n}}}}$ The span is only effective to the extent that the reverse gear ratio matches that of 1st gear see also Standard R:1 Digression Reverse gear is usually longer than 1st gear the effective span is therefore of central importance for describing the suitability of a transmission because in these cases, the nominal spread conveys a misleading picture which is only unproblematic for vehicles with high specific power Market participants Manufacturers naturally have no interest in specifying the effective span Users have not yet formulated the practical benefits that the effective span has for them The effective span has not yet played a role in research and teaching Contrary to its significance the effective span has therefore not yet been able to establish itself either in theory or in practice. End of digression ^ Ratio span's center ${\displaystyle (i_{1}i_{n})^{\frac {1}{2}}}$ The center indicates the speed level of the transmission Together with the final drive ratio it gives the shaft speed level of the vehicle ^ Average gear step ${\displaystyle \left({\frac {\omega _{2;n}}{\omega _{2;1}}}\right)^{\frac {1}{n-1}}=\left({\frac {i_{1}}{i_{n}}}\right)^{\frac {1}{n-1}}}$ There are ${\displaystyle n-1}$ gear steps between ${\displaystyle n}$ gears with decreasing step width the gears connect better to each other shifting comfort increases ^ Make ${\displaystyle =}$ manufacturer ^ Sun 1: sun gear of gearset 1 ^ Ring 1: ring gear of gearset 1 ^ Sun 2: sun gear of gearset 2: inner Ravigneaux gearset ^ Ring 2: ring gear of gearset 2: inner Ravigneaux gearset ^ Sun 3: sun gear of gearset 3: outer Ravigneaux gearset ^ Ring 3: ring gear of gearset 3: outer Ravigneaux gearset ^ a b c d e f g h i Standard 50:50 — 50 % is above and 50 % is below the average gear step — With steadily decreasing gear steps (yellow highlighted line Step) and a particularly large step from 1st to 2nd gear the lower half of the gear steps (between the small gears; rounded down, here the first 2) is always larger and the upper half of the gear steps (between the large gears; rounded up, here the last 3) is always smaller than the average gear step (cell highlighted yellow two rows above on the far right) lower half: smaller gear steps are a waste of possible ratios (red bold) upper half: larger gear steps are unsatisfactory (red bold) ^ a b c d e f g h i j k l m n o p q r s t Standard R:1 — reverse and 1st gear have the same ratio — The ideal reverse gear has the same transmission ratio as 1st gear no impairment when maneuvering especially when towing a trailer a torque converter can only partially compensate for this deficiency Plus 11.11 % minus 10 % compared to 1st gear is good Plus 25 % minus 20 % is acceptable (red) Above this is unsatisfactory (bold) see also Total ratio span (total gear ratio/total transmission ratio) effective ^ a b c d e f g h i j k l m Standard 1:2 — gear step 1st to 2nd gear as small as possible — With continuously decreasing gear steps (yellow marked line Step) the largest gear step is the one from 1st to 2nd gear, which for a good speed connection and a smooth gear shift must be as small as possible A gear ratio of up to 1.6667 : 1 (5 : 3) is good Up to 1.7500 : 1 (7 : 4) is acceptable (red) Above is unsatisfactory (bold) ^ a b c d e f Δ Step: from large to small gears (from right to left) ^ a b c d e f g h i j k l m n o p q r s Standard STEP — from large to small gears: steady and progressive increase in gear steps — Gear steps should increase: Δ Step (first green highlighted line Δ Step) is always greater than 1 As progressive as possible: Δ Step is always greater than the previous step Not progressively increasing is acceptable (red) Not increasing is unsatisfactory (bold) ^ a b c d e f g h i j k l m Standard SPEED — from small to large gears: steady increase in shaft speed difference — Shaft speed differences should increase: Δ shaft speed (second line marked in green Δ (shaft) speed) is always greater than the previous one 1 difference smaller than the previous one is acceptable (red) 2 consecutive ones are a waste of possible ratios (bold) ^ a b c d e f for Rear-wheel drive cars ^ 400 N⋅m (295 lbf⋅ft) or 400 N⋅m (295 lbf⋅ft) ^ produced in the PRC,[5] alternatively known as 6HP 19tu and 6HP 19z ^ planned, but never went into production[6] ^ Permanently coupled elements Apart from Ravigneaux couplings, there are no permanent couplings ^ Blocks R2 and S3 ^ Blocks C2/C3 (the common carrier of the compound Ravigneaux gearset) ^ Couples C1 and S2 ^ Couples C1 with R2 and S3 ^ Couples R1 with C2/C3 (the common carrier of the compound Ravigneaux gearset) ^ a b c Ordinary noted For direct determination of the ratio ^ a b c Elementary noted Alternative representation for determining the transmission ratio Contains only operands With simple fractions of both central gears of a planetary gearset Or with the value 1 As a basis For reliable And traceable Determination of the torque conversion rate and efficiency

The limitations of the Lepelletier gearset lie in the number of gear ratios provided and in the efficiency issues that Ravigneaux gearsets always contend with. Therefore, starting in 2008 with the ZF 8HP, the Lepelletier gearset was replaced by gearset concepts with even more gears and largely dispensing with the use of Ravigneaux gearsets. This was followed later by the GM 8L, Aisin-Toyota 8-speed transmission, and the Ford-GM 10-speed transmission, for example.