EMBODIMENT DESIGN OF NOVEL 5-SPEED REAR DRIVE HUBS FOR BICYCLES
Yi-Chang Wu and Tze-Cheng Wu
Department of Mechanical Engineering, National Yunlin University of Science and Technology,
Douliou, Yunlin, Taiwan, R.O.C.
E-mail: wuyc@yuntech.edu.tw
ICETI-2014 J1038_SCI
No. 15-CSME-22, E.I.C. Accession 3797
ABSTRACT
This paper presents embodiment design of 5-speed rear drive hubs for bicycles. A 7-link, 2-degrees of
freedom (DOF) compound planetary gear train as the main body of a rear drive hub is introduced. The
relationship between the number of coaxial links of a planetary gear train and the number of gear stages that
a drive hub can provide with is discussed. By means of kinematic analysis, four speed ratios of the planetary
gear train are derived, which represents four forward gears of the rear drive hub. By adding a direct-drive
gear, five forward gears can be provided and two feasible clutching sequence tables are synthesized. Manual
translational-type gear-shifting mechanisms are further designed to incorporate with the planetary gear train
for appropriately controlling the gear stage. The power-flow path at each gear stage is checked to verify the
feasibility of the proposed design. Finally, two novel 5-speed bicycle rear drive hubs are presented.
Keywords: embodiment design; rear drive hub; translational-type gear-shifting mechanism.
RÉALISATION D’UN CONCEPT INNOVATEUR DE MOYEU ARRIÈRE
À CINQ VITESSES POUR BICYCLETTES
RÉSUMÉ
Cet article présente la réalisation d’un concept de moyeu arrière à cinq vitesses pour bicyclette. Un lien à
7 maillons et deux degrés de liberté, et une transmission à train d’engrenage planétaire composé comme
corps principal d’un moyeu arrière est présenté. La relation entre le nombre de maillons axiaux d’un train
d’engrenage planétaire et le nombre de stade d’engrenages que le moyeu peut générer est débattue. Par le
moyen d’analyse cinématique, un moyeu de quatre vitesses de train d’engrenage est dérivé, ce qui représente
quatre engrenages avant du moyeu arrière. En ajoutant un engrenage d’entraînement direct, cinq engrenages
de marche avant peuvent être dérivés, et deux tables de séquence d’embrayage possibles sont synthétisées.
De plus, des mécanismes manuels de type translationnel et de changement de vitesse sont conçus pour
incorporer avec l’engrenage planétaire une commande appropriée du stade d’engrenage. La trajectoire de
la chaîne cinématique à chaque stade de l’engrenage est contrôlée pour vérifier la faisabilité du concept.
Finalement, deux nouveaux concepts de moyeu arrière de cinq vitesses pour bicyclette sont présentés.
Mots-clés : réalisation d’un concept; moyeu arrière; mécanisme de changement de vitesse de type translationnel.
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
431
NOMENCLATURE
k
m
Zi
number of coaxial links of a planetary gear train
maximum number of gear stages of a planetary gear train
number of teeth on gear i
Greek symbols
γ
ωi
gear ratio of a meshed gear set
angular velocity of gear i (rad/s)
Subscripts
DOF
SR
degree of freedom
speed ratio
1. INTRODUCTION
A bicycle is usually equipped with a mechanical transmission to provide several forward gears so as to
adjust the driving speed of a bike and the pedaling force of a cyclist. A rear drive hub is a manual speedchanging device stored within the hub of the rear wheel of a bicycle for torque multiplication. Because the
rear drive hub is enclosed inside the hub shell of the rear wheel, it is more reliable and longevous requiring
much less maintenance than the conventional rear derailleur. A bicycle’s rear drive hub mainly consists of
a gear mechanism to change the angular speed of the rear wheel and a manual gear-shifting mechanism to
incorporate with the gear mechanism and properly control the gear stage. A cyclist manipulates a thumbshifter installed on the handle bar to activate a bell crank mechanism mounted on the rear fork using a
shifter cable, in order to determine the gear stage of the rear drive hub. The multi-speed rear drive hub
overcomes an inherent problem of gear-jumping that the existing rear derailleur usually has. One unique
feature of the rear drive hub is the ability to shift gears when the bicycle is stopped. A bicycle equipped
with a rear drive hub is more suitable for use in stop-and-go urban traffic than one with an existing rear
derailleur.
Because the transmission system typically represents about half of the production cost of a bicycle [1],
corresponding researches and developments on rear drive hubs are always important issues for bicycle manufacturing companies. In 1976, two European companies, Fichtel & Sachs A.G. [2] and Raleigh [3], proposed
3-speed rear drive hubs for bicycles. The gear mechanism of a 3-speed drive hub is a 5-link, 2-degrees of
freedom (DOF) basic planetary gear train, which provides three forward gears, including a low-speed gear,
a direct-drive gear and a high-speed gear. A coaster brake was designed and added to the 3-speed rear drive
hub manufactured by the Fichtel & Sachs A.G. company [4]. In 1979, the Shimano company presented a
mechanical control device [5], i.e., a bell crank mechanism to be incorporated with the gear-shifting mechanism of a 3-speed rear drive hub. The bell crank mechanism is used to translate the angular displacement of
the thumb-shifter into the translational movement of the gear-shifting mechanism. In order to provide more
gear stages, the Fichtel & Sachs A.G. company proposed a 5-speed epicyclic-type rear drive hub in 1975
[6]. This drive hub comprised a 7-link, 2-DOF planetary gear train with a compound sun gear. In 1987,
the Fichtel & Sachs A.G. company further presented a 5-speed rear drive hub that consisted of a 6-link,
2-DOF planetary gear train with a compound planet gear [7]. In 1998, the Sturmey-Archer company also
proposed a 5-speed rear drive hub using an identical 6-link, 2-DOF planetary gear train [8] but with a different gear-shifting mechanism. From then on, rear drive hubs with up to 12 speeds [9], 14 speeds [10] and 16
speeds [11] for bicycles were developed progressively. Some studies further discuss about the integration of
electric motors and rear drive hubs for electric bicycles [12, 13]. However, most of the R&D documents and
technical reports for rear drive hubs are classified. A complete design process for guiding the embodiment
design of multi-speed rear drive hubs of bicycles is not available, which limits their development.
432
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
Fig. 1. A 7-link, 2-DOF compound planetary gear train using in a 5-speed bicycle rear drive hub.
This study presents the embodiment design of 5-speed planetary-type rear drive hubs with novel gear
mechanisms and gear-shifting mechanisms for bicycles. First, the relationship between the number of coaxial links of a planetary gear train and the number of gear stages that a drive hub can provide with is derived.
Next, a 7-link, 2-DOF planetary gear train with a compound ring gear is selected as the main body of a rear
drive hub. With the aid of kinematic analysis, the speed ratio formula at each gear stage of the planetary
gear train is determined. Feasible clutching sequence tables are then synthesized for the presented planetary
gear train. Manual translational-type gear-shifting mechanisms are developed to be incorporated with the
planetary gear train for properly controlling the gear stages of rear drive hubs. The power-flow path at each
gear stage of each rear drive hub is analyzed and checked. Finally, the embodiment design of two novel
5-speed rear drive hubs for bicycles are presented.
2. A COMPOUND PLANETARY GEAR TRAIN
Most bicycles’ rear drive hubs use planetary gear trains to achieve required forward gears. The number of
forward gears that a rear drive hub can provide is mainly governed by the kinematic structure of a planetary
gear train. For a planetary gear train used in a rear drive hub, only coaxial links adjacent to the frame, i.e.,
the stationary hub axle, can be selected as the fixed link, input link and output link. In engineering practice,
only sun gears of a planetary gear train are convenient to assign as fixed links for a rear drive hub. For a
planetary gear train with k coaxial links, a sun gear can be arbitrarily assigned as the fixed link, then, the
rest (k-1) coaxial links can be selected as the input and output links. There are a total of (k-1)(k-2) different
arrangements. Each arrangement of the input, output and fixed links generates a specific output angular
speed, which represents a gear stage that a planetary gear train possesses. By adding a direct-drive gear, the
maximum number of gear stages m of a planetary gear train with k coaxial links can be expressed as follows:
m = (k − 1)(k − 2) + 1.
(1)
To provide five forward gears, a planetary gear train should have at least four coaxial links. Based on the
atlas of 2-DOF planetary gear trains with up to seven links [14], one 6-link and twenty-five 7-link planetary
gear trains satisfy the design requirement that the gear train has at least four coaxial links. The only one
6-link, two-DOF planetary gear train had been used in an existing 5-speed rear drive hub patented by the
Fichtel & Sachs A.G. company [7]. Unlike an existing rear drive hub using a 7-link, 2-DOF planetary gear
train with a compound sun gear [6], a 7-link, 2-DOF planetary gear train with a compound ring gear, as
shown in Fig. 1, is selected as the gear mechanism to be used in the design of 5-speed rear drive hubs.
The presented planetary gear train consists of a stationary hub axle (frame) 0 mounted on the rear fork, a
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
433
Table 1. Specifications of the speed ratio range for multi-speed rear drive hubs of bicycles.
SR range
3-speed 5-speed 7-speed
1.50 < SR ≤ 2.00
–
–
G-1
1.33 < SR ≤ 1.50
–
G-1
G-2
1.00 < SR ≤ 1.33
G-1
G-2
G-3
SR = 1.00
G-2
G-3
G-4
0.75 ≤ SR < 1.00
G-3
G-4
G-5
0.67 ≤ SR < 0.75
–
G-5
G-6
0.50 ≤ SR < 0.67
–
–
G-7
Table 2. Four arrangements for the fixed, input and output links for the planetary gear train shown in Fig. 1.
Fixed link Input link Output link Speed ratio (SR) formula SR range
3
1
2
(γ53 − γ51 )/γ53
SR > 1
3
2
1
γ53 /(γ53 − γ51 )
0 < SR < 1
4
1
2
(γ64 − γ61 )/γ64
SR > 1
4
2
1
γ64 /(γ64 − γ61 )
0 < SR < 1
compound ring gear 1, a carrier 2, sun gears 3 and 4 and planet gears 5 and 6. As can be seen in Fig. 1, there
are four fundamental circuits [15]: (1,5)(2), (1,6)(2), (3,5)(2) and (4,6)(2); the related fundamental circuit
equations are listed as:
ω1 − γ51 ω5 + (γ51 − 1)ω2 = 0.
(2)
ω1 − γ61 ω6 + (γ61 − 1)ω2 = 0.
(3)
ω3 − γ53 ω5 + (γ53 − 1)ω2 = 0.
(4)
ω4 − γ64 ω6 + (γ64 − 1)ω2 = 0.
(5)
where ωi is the angular speed of link i, γ ji = ±Z j /Zi represents the gear ratio of a meshed gear set and Zi is
the number of teeth on gear i. The positive sign of the gear ratio is for an internal gear pair; the negative for
an external gear pair.
For a gear train, the speed ratio (SR) is the ratio of the input shaft speed to the output shaft speed. A
bicycle’s multi-speed rear drive hub usually provides several low-speed gears (SR > 1), several high-speed
gears (0 < SR < 1) and a direct-drive gear (SR = 1) for different applications, such as climbing, level-ground
riding, downhill riding, etc. All of these gears are forward gears. Table 1 shows the specifications of the
speed ratio range for 3-speed, 5-speed and 7-speed bicycles’ rear drive hubs. For the presented planetary
gear train shown in Fig. 1, sun gears 3 or 4 can be assigned as the fixed link, while ring gear 1 or carrier
2 can be assigned as the input link or the output link. There are four arrangements for the fixed, input and
output links for this planetary gear train. The speed ratio formula of each arrangement can be derived based
on Eqs. (2)–(5) and these are listed in Table 2. It is found that the planetary gear train provides two lowspeed gears when ring gear 1 is the input link, and two high-speed gears when carrier 2 is the input link. By
adding a direct-drive gear, the planetary gear train shown in Fig. 1 totally provides five forward gears, which
satisfies the specifications of the speed ratio range of the 5-speed bicycle rear drive hub shown in Table 1.
3. SYNTHESIS OF CLUTCHING SEQUENCE
For a bicycle’s rear drive hub, the activations of fixed, input and output links of a planetary gear train at
each gear stage are achieved by controlling mechanical clutches adjacent to these links through a manual
gear-shifting mechanism. Because sun gears 3 and 4 are determined as fixed links, two locking clutches,
434
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
Table 3. Two sets of feasible clutching sequences for the planetary gear train shown in Fig. 1.
Gear
Case I
Case II
Fixed link Input link Output link Fixed link Input link Output link
G-1
3
1
2
4
1
2
G-2
4
1
2
3
1
2
G-3
4
1
1
3
1
1
G-4
4
2
1
3
2
1
G-5
3
2
1
4
2
1
Table 4. Clutching sequence table for Case I.
Gear
Clutches
Ci1 Co1 Ci2 Co2 Cf3 Cf4
G-1
X
X
X
G-2
X
X
X
G-3
X
X
X
G-4
X
X
X
G-5
X
X
X
Table 5. Clutching sequence table for Case II.
Gear
Clutches
Ci1 Co1 Ci2 Co2 Cf3 Cf4
G-1
X
X
X
G-2
X
X
X
G-3
X
X
X
G-4
X
X
X
G-5
X
X
X
Cf3 and Cf4, should be arranged in the rear drive hub. Ring gear 1 and carrier 2 are simultaneously assigned
as the input and output links; two input clutches Ci1 and Ci2 as well as two output clutches Co1 and Co2 are
arranged in the rear drive hub. When synthesizing the clutching sequence of a multi-speed transmission, it
is an important rule that only one clutch is engaged while another is simultaneously disengaged during gear
stage changes. Such a kind of operation is called a single clutch-to-clutch shift [15]. This is an important
feature for a rear drive hub to shift smoothly from one gear stage to another and also reduce the complexity
of the gear-shifting mechanism. Based on this rule and the speed ratio range shown in Table 2, two sets of
feasible clutching sequences, i.e., Case I and Case II, can be synthesized, as presented in Table 3. Gears
G-1 and G-2 are low-speed gears, gear G-3 is a direct-drive gear and gears G-4 and G-5 are high-speed
gears. The corresponding clutching sequence tables for Case I and Case II are shown in Tables 4 and 5,
respectively. The symbol ‘X’ shown in Tables 4 and 5 shows that the related clutch is engaged.
4. MANUAL TRANSLATIONAL-TYPE GEAR-SHIFTING MECHANISMS
When the clutching sequence of a rear drive hub is synthesized, a manual gear-shifting mechanism is then
designed to operate with the planetary gear train and guide the transmitted power from the rear sprocket
through the rear drive hub to the rear wheel. Here, a translational-type gear-shifting mechanism [16] is
employed to manually control the activations of locking clutches Cf3 and Cf4, input clutches Ci1 and Ci2
and output clutches Co1 and Co2, based on the related clutching sequence table. The one-way pawl-andratchet clutches are used as the input and output clutches. The engagement of the one-way pawl-and-ratchet
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
435
Fig. 2. Two different configurations of one-way pawl-and-ratchet clutch used as the output clutch Co1.
Fig. 3. The key and key way assemblies used as the locking clutch.
clutch can be governed by either the angular speed or the axial position of the driving pawl. When the
angular speed of the driving pawl is greater than that of the ratchet wheel, the one-way pawl-and-ratchet
clutch is engaged. Otherwise, it is disengaged. In this study, two different configurations of one-way pawland-ratchet clutches are applied to the output clutch Co1 connected to ring gear 1. For the configuration
shown in Fig. 2(a), the engagement of the one-way pawl-and-ratchet clutch depends on the axial position
of the driving pawl on an axially moveable member. For the other configuration, shown in Fig. 2(b), the
engagement of the one-way pawl-and-ratchet clutch is controlled by the axial position of a drive member.
A torsion spring stored on a pin (not shown in the figure) of the driving pawl allows the driving pawl to
engage with the ratchet wheel. When the flange of the drive member touches the driving pawl, the pawl
rotates an angle about the pin axle and then is in the disengagement state. Besides, the key and key way
assemblies are used as the locking clutches Cf3 and Cf4 as depicted in Fig. 3. The key portion is integrated
within the central hollow space of the sun gear, while the key way is integrated on an axially moveable
control lever. Here, the clutching sequence table of Case I, shown in Table 4, is taken as an example
to explain the embodiment design of the manual translational-type gear-shifting mechanism. Due to two
different configurations of the output clutch Co1 as shown in Fig. 2, two schematic diagrams of novel 5436
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
Fig. 4. Two schematic diagrams of novel 5-speed rear drive hubs using the proposed compound planetary gear train.
Fig. 5. Embodiment design of a 5-speed rear drive hub shown in Fig. 4(a).
speed rear drive hubs using the proposed compound planetary gear train are presented in Figs. 4(a) and 4(b),
respectively.
Figures 5 and 6 demonstrate the embodiment designs of 5-speed rear drive hubs shown in Figs. 4(a) and
4(b), respectively. Except for the input clutches Ci1 and Ci2, output clutches Co1 and Co2 as well as
locking clutches Cf3 and Cf4, the presented translational-type gear-shifting mechanism also comprises a
drive member 7 to govern the activation of the output clutch Co1 and the input clutch Ci2, a control lever
8 to govern the engagement of the locking clutch Cf3 and Cf4, a control sleeve 9 connected to a bell crank
mechanism by a shifter cable to handle the gear stage and also to push the drive member 7 and the control
lever 8, a retaining ring 11, and four torsion springs 10, 12, 13 and 14.
5. ANALYSIS OF POWER-FLOW PATH
In order to validate the feasibitity of the proposed 5-speed rear drive hubs, the power-flow path analysis is
adopted to check the transmission path at each gear stage. The embodiment design shown in Fig. 5 is taken
as an example to explain. At high-speed gear G-5, the rear wheel has the highest angular speed. As can be
seen in Fig. 7(a), control sleeve 9 and drive member 7 are at their extreme left position on the stationary hub
axle 0. Sun gears 3 and 4 and control lever 8 are also at their extreme left position in this gear stage. Since
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
437
Fig. 6. Embodiment design of a 5-speed rear drive hub shown in Fig. 4(b).
the key ways of sun gear 3 are engaged with the keys of control lever 8, locking clutch Cf3 is activated.
The angular speed of ring gear 1 is greater than those of the sprocket and carrier 2 at gear G-5. Hence,
the angular speeds of the ratchet wheels of input clutch Ci1 and output clutch Co2 are greater than those
of the driving pawls of these two clutches, which leads to the disengagement of clutches Ci1 and Co2. On
the other hand, clutches Ci2 and Co1 are engaged at this gear stage. The input power from the sprocket is
transmitted from drive member 7 via input clutch Ci2 to carrier 2, planet gear 5, ring gear 1, output clutch
Co1 and finally, to the hub shell, as shown in Fig. 7(a). As control sleeve 9 pushes drive member 7 and
simultaneously shifts to the next right position, the rear drive hub is at high-speed gear G-4. A compression
spring 13 exerts a thrust force on sun gear 4 and axially shifts sun gears 3 and 4 to the right-side position.
Because control lever 8 stays in the same axial position (left-side position) as gear stage G-5, the keys of
control lever 8 depart from the key ways of sun gear 3 and are engaged with the key ways of sun gear 4.
Hence, locking clutch Cf3 is disengaged. At this gear stage, input clutch Ci2, outout clutch Co1 and locking
clutch Cf4 are engaged. As seen in Fig. 7(b), the input power from the sprocket is transmitted from drive
member 7, via input clutch Ci2 to carrier 2, planet gear 6, ring gear 1, output clutch Co1 and finally, to the
hub shell at gear stage G-4. At direct-drive gear G-3, control sleeve 9 drives drive member 7 to the next
right position on stationary hub axle 0. The driving pawl of input clutch Ci2 on drive member 7 separates
from the ratchet wheel integrated on carrier 2, so that input clutch Ci2 is disengaged. Because the angular
speed of ring gear 1 is greater than that of carrier 2, output clutch Co2 is still disengaged. The input power
from the sprocket is transmitted via input clutch Ci1 to ring gear 1, output clutch Co1 and finally, to the hub
shell at gear stage G-3, as illustrated in Fig. 7(c). When control sleeve 9 and drive member 7 are moved
to the next right position, i.e., the low-speed gear G-2, the flange of drive member 7 touches the driving
pawl of output clutch Co1 which disengages output clutch Co1. At this gear stage, input clutch Ci1, output
clutch Co2 and locking clutch Cf4 are engaged. As shown in Fig. 7(d), the input power from the sprocket is
transmitted to ring gear 1 via input clutch Ci1, planet gear 6, carrier 2 and finally, to the hub shell via output
clutch Co2. At the low-speed gear G-1, the rear wheel has the lowest angular speed. Control sleeve 9 drives
drive member 7 axially moving to the extreme right position on stationary hub axle 0. Control sleeve 9 also
pushes control lever 8 to its right-side position. The keys of control lever 8 depart from the key ways of sun
gear 4 and are engaged with the key ways of sun gear 3. So, locking clutch Cf3 is activated again, while
locking clutch Cf4 is disengaged. The flange of drive member 7 still restricts the driving pawl to disengage
output clutch Co1. As can be seen in Fig. 7(e), the input power from the sprocket is transmitted to ring gear
438
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
Fig. 7. Power-flow path analysis at each gear stage of the developed 5-speed rear drive hub shown in Fig. 5.
1 via input clutch Ci1, planet gear 5, carrier 2 and finally, to the hub shell via output clutch Co2. From the
above analysis, it can be seen that the proposed 5-speed rear drive hub, shown in Fig. 5, provides a proper
power-flow path at each gear stage.
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
439
Fig. 8. Exploded view for the embodiment design of the 5-speed rear drive hub shown in Fig. 5.
Fig. 9. Exploded view for the embodiment design of the 5-speed rear drive hub shown in Fig. 6.
Figures 8 and 9 present the exploded views of the developed rear drive hubs shown in Figs. 5 and 6, repectively. These two 5-speed bicycle rear drive hubs are totally new designs and successfully avoid the patent
right. From the structural and operational point of view, the planetary gear mechanisms, gear sequences,
clutching sequences and gear-shifting control mechanisms are totally different between the presented 5speed rear drive hubs and the 3-speed rear drive hubs proposed by Wu and Chang [17].
6. CONCLUSIONS
The embodiment design of 5-speed rear drive hubs for bicycles is presented step-by-step in this paper. For
a 5-speed rear drive hub, the planetary gear train should have at least four coaxial links. Two clutching
440
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
sequence tables, which satisfy the operation of a single clutch-to-clutch shift during gear stage changes,
are synthesized to provide five forward gears, including two high-speed gears, a direct-drive gear and two
low-speed gears. Two novel 5-speed rear drive hubs composed of comound planetary gear trains and manual
translational-type gear-shifting mechanisms are developed based on the clutching sequence table of Case I.
The power-flow path at each gear stage is analized to demostrate the validity of the developed rear drive
hubs. The design process can be applied to the embodiment designs of novel 5-speed rear drive hubs based
on the clutching sequence table of Case II shown in Table 5. The remaining twenty-four 7-link, 2-DOF
planetary gear trains with four coaxial links mentioned in Section 2 can also be assigned as the main bodies
of 5-speed rear drive hubs to generate new design concepts based on the presented design process.
ACKNOWLEDGEMENT
The authors are grateful to the Ministry of Science and Technology, Taiwan, R.O.C. for the financial support
of this research under Grant No. 102-2221-E-224-016-MY2.
REFERENCES
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
Tsai, M.C. and Su, H.Y., “Speed change mechanism”, U.S. Patent No. 8,226,517, 2012.
Schulz, H., “Multi-speed hub”, U.S. Patent No. 3,995,503, 1976.
Munn, D.C., “Epicyclic change-speed hubs”, U.S. Patent No. 3,955,444, 1976.
Schulz, H., Flosser, J., Kessler, R., Schmidt, K., Eisend, E., Hild, E., Loffler, K. and Steuer, W., “Multiple speed
hub with coaster brake”, U.S. Patent No. 4,059,028, 1977.
Hanada, M. and Fukui, S, “Gear transmission control device for multiple-speed hub for bicycles”, U.S. Patent
No. 4,179,953, 1979.
Hillyer, A.W., “Epicyclic change speed hubs”, U.S. Patent No. 3,886,811, 1975.
Bergles, E., “Multi-speed gear hub for a bicycle”, U.S. Patent No. 4,651,853, 1987.
Rickels, S.T., “Epicyclic change speed gear hubs”, U.S. Patent No. 5,813,937, 1998.
Meier-Burkamp, G., “Multi-speed hub for bicycles”, U.S. Patent No. 5,527,230, 1996.
Rohloff, B., “Multispeed bicycle gear systems”, U.S. Patent No. 6,048,287, 2000.
Wu, Y.C. and Ren, P.W., “Design and analysis of a multispeed transmission hub”, INFORMATION: An International Interdisciplinary Journal, Vol. 16, No. 9(B), pp. 7003–7014, 2013.
Wu, Y.C. and Sun, Z.H., “Design and analysis of a novel speed-changing wheel hub with an integrated electric
motor for electric bicycles”, Mathematical Problems in Engineering, Vol. 2013, Article ID 369504, pp. 1–8,
2013.
Wu, Y.C. and Lin, B.W., “Design of a six-speed transmission hub with an integrated brushless permanent-magnet
motor used for electric bicycles”, Engineering Computations, Vol. 31, No. 2, pp. 160–176, 2014.
Hsu, C.H. and Wu, Y.C., “Enumeration of planetary gear trains for multi-speed bicycle drive hubs”, Proceedings
of National Science Council (Taiwan), Part A, Vol. 22, No. 5, pp. 670–676, 1998.
Tsai, L.W., Mechanism Design: Enumeration of Kinematic Structures According to Function (1st ed.), CRC
Press LLC, 2001.
Chen, L.A., Ren, P.W. and Wu, Y.C., “Design of a gear-shifting control mechanism for 8-speed bicycle drive
hubs”, Smart Science, Vol. 1, No. 2, pp. 94–98, 2013.
Wu, Y.C. and Chang, C.W., “Development of 3-speed rear hub bicycle transmissions with gear-shifting mechanisms”, Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015.
Transactions of the Canadian Society for Mechanical Engineering, Vol. 39, No. 3, 2015
441