13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
IMD-123
The Design of Three-speed Front Internal Gear Hub for A Bicycle
*
Long-Chang Hsieh *
Hsiu-Chen Tang †
Dept. of Power Mechanical Engineering, National Formosa University,
†
Institute of Mechanical & Electro- Mechanical Engineering
64 Wun Hua Rd., Huwei, Yunlin 63208, Taiwan
Planetary gear trains are commonly used in various
transmissions due to the reason of compact size,
lightweight, and multi-degrees of freedom.In the past, the
kinematic analysis of planetary gear trains has been the
subject of a number of studies [1-4]. Some studies [5-10]
focused on the kinematic design of planetary gear trains
for specific purpose.
The characteristics of the transmission systems are
the important factors for bicycles. The transmission
systems of the bicycles can be the external changingspeed systems or internal multi-speed gear systems. The
internal multi-speed gear system is also called as multispeed gear hub. The multi-speed transmission system of a
bicycle includes multi-speed gear unit, control device of
changing speed, and operating device for steering control
device to change speed. Figure 1 shows the multi-speed
transmission system of a bicycle.
Conventionally, the multi-speed gear hub is used in
the rear axle of bicycle.This paper explores the kinematic
design of multi-speed gear hub for axle of bottom bracket.
The purpose of this work is to propose a systematic
approach for the kinematic design of three-speed front
internal gear hub for a bicycle.
Abstract—The transmission system of a bicycle can
be the external changing-speed system or internal multispeed gear system. The internal multi-speed gear system
is also called as multi-speed gear hub. The gears of the
internal multi-speed gear system are inside the gear hub,
it has the advantage of low pollution of chain and chainwheels. It also has the advantage of high transmission
efficiency and low maintaining cost. Recently, the
internal multi-speed gear systems are used in city bikes,
sport bikes, folding bikes, and electric bikes.
Traditionally, the multi-speed gear hub of a bicycle is
used in the rear axle not in axle of bottom bracket.
Recently, some three-speed gear hubs for the axle of
bracket are proposed. The multi-speed internal gear hub
for the axle of bottom bracket of a bicycle is called multispeed front internal gear hub. The purposed of this paper
is to propose a design methodology for the design of
three-speed front internal gear hubs with planetary gear
trains for bicycles under the condition of not changing
the shape of the tube on bottom bracket. Based on the
concept of train value equation and the kinematic
relationship of the members of the train circuit, we
propose a design methodology for the kinematic design of
three-speed front internal gear hubs. Three three-speed
front internal gear hubs are designed to illustrate the
design methodology. And, one engineering drawing for
case II is carried out to verify the design methodology.
Based on the proposed methodology, all three-speed
front gear hubs with planetary gear trains can be
synthesized. 1
Keywords: Front internal gear hub, kinematic design, planetary gear
train, train value equation.
I. Introduction
The bicycle is invented so far more than 200 years.
Early bicycles are mankind's main tool to ride instead of
walk. Recently, because of having the advantages of light
weight, cheap and pollution-free, bicycles become the
most popular traffic vehicles. They can be used as
exercising machines and traffic vehicles.
Figure 1 Multi-speed transmission system of a bicycle.
II. Gear Train
The gear train of a power system can be ordinary
gear train or planetary gear train. An ordinary gear train is
a gear train which all gears rotate above its own axis, and
a planetary train is a gear train contains at least one gear
(planet) which is required to rotate above its own axis
and another axis. Figures 2(a) and 2(b) show the ordinary
gear train and planetary gear train, respectively.
*
[email protected]
[email protected]
13th World Congress in Mechanism and Machine Science, Guanajuato,
México, 19-25 June, 2011
†
1
1
13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
(a) Ordinary gear train
(b) Planetary train
Figure 2 Gear Trains
IMD-123
(a) Structure
(b) Kinematicskelton
Figure 6 Apparatus for Actuating a Switching Shaft
Operatively Connected with a Switchable
Bottom Bracket Bearing Gear [14]
III. Existing Front Internal Gear Hubs
The front internal gear hub of a bicycle can be
classified as: (1) ordinary gear train, and (2) planetary
gear train. Figure 3 shows a front internal gear hub with
ordinary gear train [11]. Figures 4 and 5 show front
internal gear hubs with planetary gear trains [12-13].
(a) Structure
(b) Control device
Figure 3 Front internal gear hub with ordinary gear train
(Nicolai) [11]
Figure 7
(c) Kinematic skelton
Shiftable drive mechanism for a bicycle or the
bike[15]
Figure 4 Front internal gear hub with planetary gear train
(SRAM) [12]
(a) Structure
(b) Kinematic skelton
Figure 5 Front gear hub with planetary gear train
(Schlumpf) [13]
Figure 6 shows a U.S. patent [14] “Apparatus for
Actuating a Switching Shaft Operatively Connected with
a Switchable Bottom Bracket Bearing Gear” which is
two-speed front internal gear hub. Figure 7 shows
another U.S. patent [15] “Shiftable drive mechanism for a
bicycle or the bike” which are three types of two-speed
front internal gear hubs. Figure 8 shows another U.S.
patent [16] “Mounting system for an internal bicycle
transmission” which is also two-speed front internal gear
hub. There are many other patents [17-21] about front
internal gear hubs for bicycles can be used as our design
references.
(c) Structure of axle of bottom bracket
Figure 8 Mounting system for an internal bicycle
transmission [16]
IV. Planetary Gear Trains
There are numerous design concepts of planetary
gear trains [22], from which this paper has chosen the
non-coupled planetary gear train to act as the reference
basis for our design of the two-speed front gear hub for a
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13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
IMD-123
bicycle. Figures 9(a) and 9(b) are five-bar planetary gear
trains with two degrees of freedom, and Figure 9(c), 9(d),
9(e), and 9(f) are six-bar planetary gear trains with two
degrees of freedom.
(a) Carrier k is fixed
(b) Sun gear i is fixed
(c) Sun gear j is fixed
Figure 10 Planetary gear train with one train circuit
(a)
(b)
(c)
Rr 
  ji
in i


  ji
 out  j
1
(4)
If sun gear i is adjacent to input shaft (ωi=ωin), and sun
gear j is adjacent to output shaft (ωj=ωout), the reduction
ratio (Rr) can be written as:
Rr 
(d)
(e)
(f)
Figure 9 Five design concepts of planetary gear trains[22]
For a train circuit of a planetary gear train, if it
contains first sun gear i , last sun gear j , and carrier k ,
the relationship of ωi , ωj , and ωk can be expressed as :
Rr 
(1)
 ji
  ji
in k



out  j
( ji  1) ( ji  1)
(6)
If sun gear j is adjacent to input shaft (ωj=ωin), and carrier
k is adjacent to output shaft (ωk=ωout), the reduction ratio
(Rr) can be written as:
Where ξji is the train value of sun gear j to sun gear i.
The train value ξji be positive sign, if positive rotation of
ωik produces positive rotation of ωjk; and ξji be negative
sign, otherwise.
For the planetary gear train shown in figure 2(b),
train circuit 2-3-5-4-2 contains sun gear 2, sun gear 3,
and carrier 4. Its train value equation and train value ξ32
can be expressed as:
 2   32  3  ( 32  1) 4  0
 32  ( Z 3  Z 5 ) /( Z 5  Z 2 )  0
(5)
According to Figure 10(b), if carrier k is adjacent to
input shaft (ωk=ωin), and sun gear j is adjacent to output
shaft (ωj=ωout), the reduction ratio (Rr) can be written as:
V. Train Value Equation
i   ji j  ( ji  1)k  0
in  j
1
1



 out i
  ji  ji
Rr 
( ji  1) ( ji  1)
in  j



 out  k
 ji
  ji
(7)
According to Figure 10(c), if carrier k is adjacent to
input shaft (ωk=ωin), and sun gear i is adjacent to output
shaft (ωi=ωout), the reduction ratio (Rr) can be written as:
(2)
(3)
Rr 
For a planetary gear train with one train circuit,
there are three members (i, j, and k) can be adjacent to
input shaft, output shaft, and frame. If carrier k, sun gear
i, sun gear j are adjacent to frame, ωk=0, ωi =0, ωj =0
respectively and the kinematic relationship can be drawn
as figure 10(a), figure 10(b), and figure 10(c) respectively.
According to figure 10(a), if sun gear i is adjacent to
input shaft (ωi=ωin), and sun gear i is adjacent to output
shaft (ωj=ωout), the reduction ratio (Rr) can be written as:
in  k
1
1



 out i
( ji  1)
( ji  1)
(8)
If sun gear i is adjacent to input shaft (ωi=ωin), and carrier
k is adjacent to output shaft (ωk=ωout), the reduction ratio
(Rr) can be written as:
Rr 
3
( ji  1)
in i


 ( ji  1)
1
 out  k
(9)
13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
IMD-123
VI. Kinematic Design
After deciding the planetary gear train, the
kinematic design can be carried out on the three-speed
front internal gear hub. On conceiving the feasible
design concept, the design constrains of the three-speed
front internal gear hub should be taken into consideration,
so as to make the composed mechanism to meet
requirements. The three-speed front internal gear hub in
this paper has the following design constrains:
(1) It needs to possess three-speed shift function.
(2) its foot-board axle can be connected with the shift
mechanism’s input axle.
(3) The relationship of reduction ratios of three-speed
front gear hub is : 1.2< Rr1/ Rr2 ≒ Rr2/ Rr3<1.65.
(a) Kinematic skelton
【Example 1】
Table 1 shows the reduction ratio, equations (4)~(9)
of planetary gear train shown in figure 9(a).
(b) First speed
(c)Second speed
(c) Third speed
Figure 11 Three-speed front internal gear hub (Case I)
Table 1 Reduction ratios of planetary gear train 9(a)
Table 2 The Reduction ratios of example 1
Clutch
Reduction
ratio
C3
C4
OWC3
OWC4
1
Control not
Rr1=1.2875
◎
◎
to engage
2
Rr2=1
◎
◎
3
Rr3=0.7777
◎
◎
◎：Engage
Speed
No
1
2
3
4
5
6
7
ξ32<0
In. Fixed Out. Reduction ratio Value Dir.
2
4
3
ξ32
-2.5
3
4
2
1/ξ32
-0.4
4
2
3
-ξ32/(1-ξ32)
0.7143 +
3
2
4
-( 1-ξ32)/ ξ32
1.4
+
4
3
2
1/(1 -ξ32)
0.287
+
2
3
4
(1-ξ32)
3.5
+
Direct drive
1
1
+
【Example 2】
Table 3 shows the reduction ratio, equations (4)~(9)
of planetary gear train shown in figure 9(d).
Table 3 Reduction ratios of planetary gear train 9(d)
For a planetary gear train shown in figure 9(a), the
train value ξ32<0. According to table 1, using No.4, No.7,
and No.3, the three reduction ratios (Rr1, Rr2, and Rr32) of
the planetary gear trains can be expressed as:
Rr1 = - ( 1-ξ32) / ξ32
Rr2 = 1
Rr3 = - ξ32 / (1-ξ32)1
(10)
(11)
(12)
No.
1
2
3
4
5
6
7
8
9
Based on equations (10)-(12), if ξ32=-3.5 then Rr1 =
1.2857, Rr2=1, Rr3 =0.7777, and Rr1/Rr2=Rr2/Rr3 =1.2857.
For the planetary gear train shown in figure 11, if Z2=24,
Z5=30, and Z3=84, then ξ32=-3.5. Figure 11 shows the
corresponding three gear positions for bicycle. Table 2
shows the clutch sequence of the corresponding threespeed front internal gear hub.
4
in fixed out
2
3
5
2
3
6
2
5
3
2
5
6
2
6
3
2
6
5
3
2
5
3
2
6
3
5
2
ξ62<0 and ξ63<0
Reduction ratio Value Dir.
-(ξ32 -1)
0.571
+
(ξ62 -ξ63)/ (1-ξ63) 0.464
+
ξ32
0.428
+
ξ62
-1.857
(1 -ξ62)/ (1-ξ63)
0.536
+
1 -ξ62
2.857
+
(ξ32–1)/ ξ32
-1.333
(ξ63 –ξ62)/ (1-ξ62) -0.866
1/ξ32
2.333
+
13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
3
5
6
3
6
2
3
6
5
5
2
3
5
2
6
5
3
2
5
3
6
5
6
2
5
6
3
6
2
3
6
2
5
6
3
2
6
3
5
6
5
2
6
5
3
Direct drive
ξ63
(1 –ξ63)/ (1 –ξ62)
ξ63
ξ32/ (ξ32 –1)
ξ62/(ξ62-1)
-1/(ξ32-1)
ξ63/(ξ63-1)
1/(1-ξ62)
1/(1-ξ63)
(1 –ξ62)/ (ξ63-ξ62)
(ξ62-1)/ξ62
(1 –ξ63)/ (ξ62-ξ63)
(ξ63-1)/ξ63
1/ξ62
1/ξ63
1
-4.333
1.866
4.333
-0.75
0.65
1.75
0.813
0.35
0.188
-1.154
1.538
2.154
1.231
-0.538
-0.231
1
IMD-123
Table 4 The Reduction ratios of example II
Clutch
Reduction
Speed
ratio
C2
C3
OWC 5
◎
1
Rr1=1
◎
2
Rr2=0.7942
◎
3
Rr3=0.5956
◎：Engage
+
+
+
+
+
+
+
+
+
+
-
【Example 2】
Table 5 shows the reduction ratio, equations (4)~(9)
of planetary gear train shown in figure 9(f).
Table 5 Reduction ratios of planetary gear train 9(f)
For a planetary gear train shown in figure 9(d), the
train value ξ62<0 and ξ63<0. According to table 3, using
No.16, and No.14, the three reduction ratios (Rr1, Rr2 and
Rr3) of the planetary gear trains can be expressed as:
Rr1 = 1
Rr2 = ξ63 / (ξ63-1)
Rr3 = ξ62 / (ξ62-1)
(13)
(14)
(15)
No.
1
2
3
4
5
6
7
Based on equations (13)-(15), if ξ63=-3.8571 and
ξ62=-1.4727 then Rr1=1, Rr1=0.7942, Rr3 =0.5956, and
Rr1/Rr2=1.26≒Rr2/Rr3 =1.33. For the planetary gear train
shown in figure 12, if Z2=33, Z3=21, Z4=18, Z4’=30, and
Z6=81, thenξ63=-3.8571 and ξ62=-1.4727. Figure 12
shows the corresponding three gear positions for bicycle.
Table 4 shows the clutch sequence of the corresponding
three-speed front internal gear hub.
in fixed out
2
5
6
2
6
5
5
2
6
5
6
2
6
2
5
6
5
2
Direct drive
ξ62>0
Reduction ratio
ξ62
(1-ξ62)
ξ62/(ξ62-1)
1/(1 -ξ62)
(ξ62-1)/ξ62
1/ξ62
1
Value
2.667
-1.667
1.6
-0.6
0.625
0.375
1
Dir.
+
+
+
+
For a planetary gear train shown in figure 9(e), the
train value ξji>0. According to table 5, using No.1, No.3,
and No.7, the three reduction ratios (Rr1, Rr2 and Rr3) of
the planetary gear trains can be expressed as:
(a) Kinematic skelton
Rr1 = ξ62
Rr2 = ξ62/(ξ62-1)
Rr3 = 1
(b) First speed
(16)
(17)
(18)
Based on equations (16)-(18), If ξ62= 2.6667 then
Rr1 = 2.6667, Rr2 =1.6, Rr3 = 1, and Rr1/Rr2 =Rr2/Rr3 =1.6.
For the planetary gear train shown in figure 13, if Z2=36,
Z3=Z4=21, and Z6=9, then ξ62=2.6667. Figure 13 shows
the corresponding three gear positions for bicycle. Table
6 shows the clutch sequence of the corresponding threespeed front internal gear hub.
(c)Second speed
(c) Third speed
Figure 12. Three-speed front internal gear hub (Case II)
5
13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
(a) Kinematic skelton
IMD-123
(a) Section diagram
(b) First speed
(b) Chain wheel and housing
(c) Planetary gear train
(d) Sun gears
Figure 15 Engineering drawing of planetary gear train
for Case II
(c)Second speed
(c) Third speed
Figure 13. Three-speed front internal gear hub (Case III)
Table 6 The Reduction ratios of example III
Clutch
Reduction
Speed
ratio
B2
B5
C2
C5
◎
◎
1
Gr1=2.667
◎
◎
2
Gr2=1.6
◎
◎
3
Gr3=1
◎：Engage
Figure 16 Control device of Case I
VII. Engineering Drawing
Using the solid works, the engineering drawing for
case II are shown as figures 14, 15, and 16. Figure 17
shows the three-speeds engineering drawings.
(a) First speed
(a) Isometric diagram
(b) Section diagram
(b) Second speed
© Third speed
Figure 17 Three speeds of front internal gear hub
(Case II)
(c) Explode diagram
Figure 14 Engineering drawing of Case II
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13th World Congress in Mechanism and Machine Science, Guanajuato, México, 19-25 June, 2011
VIII. Conclusions
In this paper, we propose a design methodology for
the design of three-speed front internal gear hubs with
planetary gear trains for bicycles. Based on the design
concepts proposed and train value equation of planetary
gear train, we derive the reduction ratio equations of
three-speed front internal gear hubs with planetary gear
train for bicycle. Three three-speed front internal gear
hubs are designed to illustrate the design methodology.
And, one engineering drawing for case II is carried out to
verify the design methodology. According to the
proposed methodology, all three-speed front internal gear
hubs with planetary gear trains for bicycles can be
synthesized. The design approach can also be used to
design the three-speed front internal gear hubs for bicycle,
electric motorcycle, and electric scooter.
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
Acknowledgments
[18]
The authors are grateful to the Chuan Wei Industrial
Co., Ltd. of taiwan for supporting this research.
[19]
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[20]
H.H. Mabie and C.F.Reinholtz, Mechanisms and
Dynamics of Machinery, John Wiley and Sons, new
York, 1987.
L.W. Tsai, An algorithm for the kinematic analysis of
epicyclic gear trains, Proc. 9th Applied Mechanisms
Conference, Kansas City, Missouri, Vol.1,pp 1-5,
1985.
L.C. Hsieh, H.S. Yan, & L.I. Wu, An algorithm for
the automotive kinematic analysis of planetary gear
trains by fundamental circuit method, Journal of the
Chinese Society of Mechanical Engineers, Vol.10,
No.2, pp.153-158, 1989.
L.C. Hsieh and H.S. Yan, “Generalized Kinematic
Analysis of Planetary Gear Trains”, International
Journal of Vehicle Design, Vol.13, No.5/6, pp.494504, 1992.
C. Bagei, Efficient method for the synthesis of
compound planetary differential gear trains for
multiple speed ratio generation, and constant direction
pointing chariots, Proc.10th Applied Mechanisms
Conference, New Orleans, Louisiana, 1987.
L.C. Hsieh and H.S. Yan, ”On the Kinematic Design
of Differential Devices for Heavy-Duty Vehicles,”
Journal of Applied Mechanisms and Robotics, Vol.3,
No.1, pp.7-16,1996.
L.C. Hsieh, ”An Efficient Method for the Kinematic
Design of coupled Gear Differentials for
Automobiles,” Journal of Applied Mechanisms and
Robotics, Vol.4, No.1, pp.7-12,1997.
L.C. Hsieh, H. S. Lee, and T.H. Chen, “An Algorithm
For The Kinematic Design Of Gear Transmissions
With High Reduction Ratio,” Materials Science
Forum, Vols.505-507, pp.1003-1008, 2006.(SCI)
L.C. Hsieh, M.H. Hsu, and T.H. Chen, “The Design
of Six-speed Gear hub for A Bicycle,” Journal of
[21]
[22]
7
IMD-123
Machine Design and Research, Vol.22, No.4, pp.303307, 2006.(EI)
L.C. Hsieh, T.H. Chen, and X.C.Tang, “The Invention
of Automatic Four-Speed Gear Hubs for Bicycles,”
Journal of machine design and research, Vol.25, No.4,
pp.102-108, 2009. (EI)
http://www.nicolai.net/products/e-products.htm
(2009/07/12).
http://www.schlumpf.ch/sd_engl.htm (2009/07/12).
http://www.sicklines.com/2008/08/21/previewtruvativ- hammerschmidt (2009/07/12).
Florian, S., “Apparatus for Actuating a Switching
Shaft Operatively Connected with a Switchable
Bottom Bracket Bearing Gear,” U.S. Patent, patent
No. 6123639, 2000.
Florian, S., “Shiftable Drive Mechanism for a Bicycle
or the Bike,” U.S.Patent,Pub.2006/0112026, 2006.
Kevin, W., Christopher S., Brian J., “Mounting
System for an Internal Bicycle Transmission,”
U.S.Patent,Pub.2008/0252037, 2008.
Fernand, S., “Bicycle Transmission,” U.S.Patent
No.4419905, 1983.
Kenji, M., hinya M., Naoki I., Yoshiaki T., “Bicycle
with speed change gear,” U.S.Patent, Pub. No.
2003/0080529, 2003.
James, A., “Transmission,” U.S.Patent,Pub.No.
2006/0058131, 2006.
Karlheinz, N., “Multiple gear transmission for a
bicycle,” U.S.Patent ,Pub.No. 2007/0210552, 2007.
Karlheinz, N, “Multiple gear transmission with
magnetic control,” U.S.Patent No. 0234090, 2008.
H.S. Yan and L.C. Hsieh, Conceptual design of gear
differentials for automotive vehicles, ASME
Transactions, Journal of Mechanical Design, Vol.116,
565-570, 1994.