Dan Zhang, Senior Member, IEEE, Mike Reed, Beizhi Li, Zhen Gao, Yunjian Ge

1. Abstract—The Geneva mechanism has been used for timing
applications such as clocks, watches and film projectors so using
the great timing features it possesses would be ideal. This
research explores a totally different internal combustion design
in automotive industry which revolves around the Geneva
mechanism. The pins and slots of the mechanism form the
combustion chambers which are utilized to drive the Geneva
wheels to convert linear motion into rotary motion which can
power automobiles or even be used in small engine applications.
Firstly, there is an extensive analysis of the feasibility of this
type of engine design where parameters such as maximum
torque, internal pressure and efficiency are compared to a
similar displacement reciprocating internal combustion engine.
Then detailed optimization is conducted where necessary
changes can be made to the Geneva engine design to improve the
performance to be competitive with the reciprocating engine
design.
I. INTRODUCTION
HERE have been many innovations within the
automotive industry since the first automobile was
invented. From interior amenities such as heated seats
and climate control, to more mechanical advancements such
as hybrid engines or even hydrogen fuel cells, the automobile
has seen many improvements over the years. With the
exception of the Wankel (rotary) engine, the current
reciprocating piston engine design has dominated the
automotive industry as the central layout that all engine
designs are based upon. The Wankel engine was the most
significant and dramatic change from the traditional
reciprocating design in the sense that it did not use a linkage
to convert linear motion to rotary motion which can hinder
the engine’s efficiency. The Wankel engine used a rotary
piston which harnessed the combustion of fuel in a rotary
manner which seemed to be a much more efficient design.
But that design also had a major drawback due to its high
emission output which didn’t allow it to compete with the low
emission reciprocating engine designs.
Manuscript received January 15, 2009.
Dan Zhang (corresponding author) is with the University of Ontario
Institute of Technology, Oshawa, ON, Canada and the Donghua University,
Shanghai, China (phone: +1905.721.8668*2965, Fax: +1905.721.3370;
e-mail: Dan.Zhang@ uoit.ca).
Mike Reed is with the University of Ontario Institute of Technology.
Beizhi Li is with the Donghua University, Shanghai, China (email:
lbzhi@dhu.edu.cn)
Zhen Gao is with the Department of Automation, University of Science
and Technology of China (e-mail: zgao@mail.ustc.edu.cn).
Yunjian Ge is with the Institute of Intelligent Machines, Chinese Academy
of Sciences (e-mail: yjge@iim.ac.cn).
Researchers have done some related investigations [1-4].
Bereiter used the development of the reciprocating internal
combustion engine as the example of how many small
innovations can turn an inferior design into the dominating
design over a possibly better design. The reciprocating
internal combustion engine, through many small innovations
in its design, slowly became more efficient, reliable and
durable which allowed it to become the current dominating
design [5].
Jazar [6] discussed the four slot Geneva mechanism. He
described the geometry fully with mathematical formulae for
all important dimensions such as the radius of the journal
surfaces (the sliding surfaces of each wheel used for locating
purposes), the diameter of both the driving wheel and driven
wheel, the center to center distance for each wheel and the
location of the pin. Since changing one of these dimensions
affected most of the other dimensions, knowing these
formulae is quite important in the kinematics of the Geneva
mechanism.
Joskowicz [7] discussed the kinematic tolerance analysis
while using the Geneva mechanism as an example to test the
effects of tolerances on the kinematic function of the
mechanism. He showed how varying tolerances in a
mechanism could lead to improper function, jamming and
interference.
There have been many new ideas implemented into the
internal combustion engine to make them more efficient like
newer fuel types such as ethanol blends, bio-diesel, and
higher octane gasoline. Better fuel delivery systems and
enhanced valve train design have made engines more
efficient by gaining all the available horsepower and torque
that is available. Electric/ gasoline hybrid engines have made
the emission output of vehicles much less due to their dual
power source. However, very few total design changes have
been made to the actual internal combustion engine design.
One major change in the internal combustion engine is the
rotary, or Wankel, engine. This engine design does not use a
typical linkage system to convert linear motion into rotary
motion as the conventional internal combustion engines do.
This design has a rotary combustion chamber where its piston
rotates inside almost like a vane pump. So rather than trying
to convert linear motion into rotary motion, there is only
rotary motion which results in a very compact design.
The study’s main focus, however, will revolve around the
investigation of one possible solution to the development of a
new internal combustion engine design which uses the layout
of a Geneva mechanism. The advantages to this type of layout
will be discussed in detail and also, an engineering analysis of
Design Optimization of a Geneva Mechanism for Internal Combustion
Engine Application
Dan Zhang, Senior Member, IEEE, Mike Reed, Beizhi Li, Zhen Gao, Yunjian Ge
T
978-1-4244-3608-8/09/$25.00 © 2009 IEEE. 649
Proceedings of the 2009 IEEE
International Conference on Information and Automation
June 22 -25, 2009, Zhuhai/Macau, China

2. the design will be done to examine its per
will be a comparison to the standard rec
design to test whether this design would b
that can be competitive to the reciprocating
The comparison will calculate the maxi
average torque output of both the recip
combustion engine as well as the Genev
important to note that both engines will
displacement to ensure an accurate com
design. Ideally, the main objective to this pr
feasibility of the Geneva engine and hopef
itself worthy to be a competitive design and
a new engine design seen in industry in the
II. GENEVA MECHANISM
A. History
The Geneva mechanism was originally
watchmaker in Geneva, Switzerland some
century as a timing device to accurately adva
a watch (Tiamina). The mechanism allow
consistent angular movements which was
timing applications like clocks and watch
was not the only application of the Gen
Another popular application of this inventi
the advancement of the film reel in a movie p
movie projector needs to allow maximum
individual frames and minimum exposure o
these frames, a Geneva mechanism is the pe
to drive a projector.
B. Geometry
As illustrated in Figure 1, the layout
mechanism is fairly simple. First there is
which consists of a flat circular disk with
cutout from one of the sides. This circular
driven wheel to rotate intermittently during i
driving wheel also holds a pin which eng
equally spaced slots in the driven wheel
wheel a partial rotation.
Fig.1. Geneva Wheel
rformance. There
ciprocating piston
e a viable design
design.
imum torque and
procating internal
va engine. It is
be of equivalent
mparison of each
roject is to test the
fully it will prove
d possibly become
future.
y invented by a
etime in the 15th
ance the hands on
wed precise and
very desirable in
es. However this
neva mechanism.
ion is controlling
projector. Since a
m exposure of the
of the changing of
erfect mechanism
t of the Geneva
a driving wheel
a circular section
cutout allows the
its operation. The
gages one of the
which turns the
C. Operation
The operation of the Geneva mech
as its appearance. Figure 2 illustrates
it engages the pin (R) into one of the
(B). The radial cutout in the driving
of the driven wheel while the cutouts
along the outer surface of the driving
wheel in place to allow true intermit
Fig.2. Geneva Mechanism
As shown in Figure 2, one full c
driving wheel will result in 4 interm
the driven wheel with a period of
rotation. The driven wheel stays
design of the radial cutouts, until t
side and engages one of the ot
mechanism is a very useful design w
and precise angular position and timi
project, the mechanism will be u
combustion engine design which
features.
III. DESIGN PRO
A. Problem Statement
The problem to be resolved in thi
combustion engine design which
mechanism. The conventional
combustion engine has dominated
since the introduction of the first a
design however, has a very complic
and moving parts used to harness th
convert its linear motion into ro
complex system of moving parts
purposes such as the opening and
exhaust valves necessary for this com
extra parts add size, and subsequentl
engine reducing its overall effective
There is a current need for a new
more compact with fewer moving
demands while still maintaining c
values, such as average torque, wi
presently. The aim of this research i
completely new engine design based
in hopes to eliminate the need for co
and do away with the conventional s
current reciprocation design uses.
B. Design Requirements
Physical Requirements
hanism is just as graceful
s the driving wheel (A) as
e slots in the driven wheel
wheel allows the rotation
s of the driven wheel slide
g wheel to keep the driven
ttent motion.
m Operation
ontinuous rotation of the
mittent rotation events of
f dwell in between each
stationary, thanks to the
the pin reaches the other
ther driving slots. This
where intermittent motion
ing are concerned. In this
used as a novel internal
utilizes these important
OCESS
is study is a new internal
is based on the Geneva
reciprocating internal
the automotive industry
automobile. This type of
cated system of linkages
he combustion power and
otary motion. Also this
is also used for timing
d closing of intake and
mbustion cycle. All these
ly, the total weight of the
eness to move a vehicle.
w engine design which is
parts to improve weight
competitive performance
ith current designs used
is to prove the merit of a
d on a Geneva mechanism
omplex timing apparatus’
slider crank approach the
650

3. Physical requirements of this design, although limited, are
still quite important to note for this design. The new engine
design must use geometry synonymous to a Geneva
mechanism. The materials used in this design are unimportant
at this time because it is only the concept of the design that is
to be proven. Also, other details such as the electrical
components, fuel delivery system, as well as the intake and
exhaust system are not going to be explored because it is
outside the scope of this study. Therefore, the main
requirement is that this design will utilize the Geneva
mechanism as the primary element of the engine.
Functional Requirements
The functional requirements of this design revolve more
around the actual performance of the engine. This design
must be a very compact unit, and consequently, it should also
have a significantly fewer number of moving parts. The
design would also need to be more lightweight than the
reciprocating design it will be compared to. This design must
also be able to produce a competitive amount of torque output
compared to the reciprocating engine design.
C. Application
This type of engine design would likely be used in
applications where a smaller sized reciprocating engine
would be replaced. This engine would be used for
applications such as engines to power hydraulic pumps,
generators, lawn equipment or even smaller vehicles such as
motorcycles or ATV’s. This type of engine design would
likely not be seen in more large scale purposes like
automotive or marine applications due to the fact that very
large heavy disks would be used which have a large moment
of inertia that would take a lot of power to rotate.
IV. DESIGN SOLUTION
This section will discuss all the details behind the
generation of the Geneva engine concept from initial idea to
the final model. An in-depth discussion of the thought process
behind this design as well as important dimensions and
properties will be clearly illustrated throughout. Several
different parameters of each engine design will be shown as
well as all the dimensions of each component. This section
will also show all the calculations and data obtained during
the complete analysis of the Geneva engine design. Also
similar calculations will be done to the comparably sized
reciprocating engine so a full comparison can be established
to see if the final design satisfied the design requirements.
A. Concept Generation
The first decision would be whether the Geneva engine
would have a single pin wheel or a double pin wheel in its
design. To get the same volume of a compression chamber in
a single pin wheel design, the diameter of the pins and the
stroke length would have to be almost doubled in size which
would make the entire unit much larger. Also, the forces on
the slot wheel would only be in one direction for the single
pin wheel design. This could possibly cause the slot wheel to
deflect which would cause the precision fits to be not as
accurate. A dual pin wheel design was chosen in this project
because a firing event will occur on both sides at the same
time which would improve the effective space of the slot
wheel and also balance out the high forces applied to it during
the firing events.
Fig.3. CAD Model of the Geneva Engine Design [8]
The next decision revolves around the size of each
component. For the initial design a general arbitrary size was
made up to compute the values and the theoretical
reciprocating design used for comparison was based on those
dimensions. A spreadsheet was created to compute all the
necessary values such as combustion chamber volume,
combustion pressure, applied force and applied torque at
varying crank angles for both engine types. Then the
optimization of those parameters will take place to maximize
the performance and results of the Geneva engine.
B. Design Specifications
Geneva Engine Specifications
This Geneva engine design (Figure 3) [8] uses an eight pin
setup which uses four pins each pin wheel and the slot wheel
has four slots. This geometry creates a total of eight firing
events per revolution. The pin diameter and pin height were
both made to be 40mm and the total stroke is 60mm. This
results in a total compression chamber volume of 100cc and
800cc of power per revolution.
Reciprocating Engine Specifications
The reciprocating engine used for comparison purposes
was made to be equivalent in engine capacity. This was done
by making the energy output per revolution, which means the
same volume of fuel/air mixture is used, is equal in both
engine types. For the Geneva engine design, each combustion
chamber equates to approximately 100cc of displacement.
Since there are 4 pins per wheel, this makes 800 cc of power
for each revolution. So for the reciprocating engine, the
power for each revolution must also be equal to 800cc.
However, in a four stroke cycle in a reciprocating engine, one
full cycle consists of two full revolutions which equates to a
total displacement of 1600cc. This makes each combustion
chamber volume equal to 400cc (Note that only two chambers
are firing in each 360° revolution).
Figure 4 illustrates the instantaneous torque across the
entire 360° rotation of the cycle. The average torque
throughout the cycle is 73.65Nm while the maximum torque
in the cycle is 787.77Nm which occurs at 15° past top dead
centre.
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4. Fig.4. Reciprocating Engine Torque per Revolution
Figure 5 illustrates the instantaneous torque across the
entire 360° rotation of the Geneva engine’s cycle. The
average torque throughout the cycle is 70.44Nm while the
maximum torque in the cycle is 454.78Nm which occurs at
7.5° past top dead centre.
Fig.5. Geneva Engine Torque per Revolution
The average torque produced in the Geneva engine is
significantly close to the reciprocating design, only falling
short by approximately 12Nm.
V. OPTIMIZATION WITH GENETIC ALGORITHMS
Since only a few geometric parameters can be handled due
to the lack of convergence, this arises from the fact that
traditional optimization methods use a local search by a
convergent stepwise procedure, e.g. gradient, Hessians,
linearity, and continuity, which compares the values of the
next points and moves to the relative optimal points. Global
optima can be found only if the problem possesses certain
convexity properties which essentially guarantee that any
local optima are a global optimum. In other words,
conventional methods are based on a point-to-point rule; it
has the danger of falling in local optima.
The genetic algorithms [9-11] are based on the
population-to-population rule; it can escape from local
optima. Genetic algorithms have the advantages of robustness
and good convergence properties, i.e.
• they require no knowledge or gradient information about
the optimization problems; only the objective function and
corresponding fitness levels influence the directions of
search.
• Discontinuities present on the optimization problems
have little effect on the overall optimization performance.
• They are generally more straightforward to introduce,
since no restrictions for the definition of the objective
function exist.
• use probabilistic transition rules, not deterministic ones.
• They perform well for large-scale optimization problems.
Genetic algorithms have been shown to solve linear and
nonlinear problems by exploring all regions of state space and
exponentially exploiting promising areas through mutation,
crossover, and selection operations applied to individuals in
the population. Therefore, a genetic algorithm is adopted for
the optimization problems discussed in this paper. Figure 6
shows the general procedure of the algorithms.
Although a single population genetic algorithm is powerful
and performs well on a wide variety of problems. However,
better results can be obtained by introducing multiple
subpopulations.
Fig. 6. The procedure of Genetic Algorithms
A. Determination of parameter settings for Genetic
Algorithms
In order to use genetic algorithms properly, several
parameter settings have to be determined, they are:
chromosome representation, selection function, genetic
operators, the creation of the population size, mutation rate,
crossover rate, and the evaluation function. They are
described in more detail as follows:
• Chromosome representation: This is a basic issue for the
GA representation, it is used to describe each individual
in the population of interest. For the problem studied
here, the chromosomes consist of the architecture
parameters (coordinates of the attachment points,
Reciprocating Engine Torque per Revolution
-200.00
-100.00
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
-180 -150 -120 -90 -60 -30 0 30 60 90 120 150 180
Crank Angle (deg)
Torque(Nm)
Instantaneous Torque Average Torque
Geneva Engine Torque per Revolution
-200.00
-100.00
0.00
100.00
200.00
300.00
400.00
500.00
600.00
700.00
800.00
-45.00 -11.25 22.50 56.25 90.00 123.75 157.50 191.25 225.00 258.75 292.50
Crank Angle (deg)
Torque(Nm)
Instantaneous Torque Average Torque
652

5. coordinates of the moving platform, vertex distributions
at base and moving platform, platform height, etc.) and
behavior parameters (actuator stiffness, actuated link
stiffness, etc.) of the mechanisms.
• Selection function: This step is a key procedure to
produce the successive generations. It determines which
of the individuals will survive and continue on to the next
generation. In the paper, the roulette wheel approach is
applied.
• Genetic operators: The operators are used to create new
children based on the current generation in the
population. Basically, there are two types of operators:
crossover and mutation. Crossover takes two individuals
and produces two new individuals while mutation alters
one individual to produce a single new solution.
• Population size: The population size represents the
number of individuals or chromosomes in the population.
• Mutation rate: The mutation rate is defined as the
percentage of the total number of genes in the population,
it determines the probability that a mutation will occur.
The best mutation rate is application dependent but for
most applications is between 0.001 and 0.1 [23]. In the
case studied, mutation rate is 0.1.
• Crossover rate: The best crossover rate is application
dependent but for most applications is between 0.80 and
0.95 [23]. For the case studied, crossover rate is 0.85.
• Evaluation functions: Evaluation functions are subject to
the minimal requirement that the function can map the
population into a partially ordered set.
B. Optimization Parameters
For this design problem, the output torque of the Geneva
engine must be optimized (maximized) by altering all the
given design parameters. These parameters must be changed
within reasonable limits so the design is still realistic because
the genetic algorithm could possibly create an optimized
result that cannot possibly work in real life (such as having a
compression ration that is too low for combustion of fuels).
The important parameters of the Geneva engine that can be
manipulated to produce different torque values are: the radius
of the journal surfaces, the distance from the center of the
driving wheel to the drive pin, the diameter and height of the
pin/ slot as well as the center to center distance of the driving
and driven wheels.
There should be a specific list of criteria and boundaries
that should be implemented into the genetic algorithm for the
best optimization of the output torque of the Geneva engine
design. The compression ratio must stay above 9 units to stay
consistent with most internal combustion engines and also to
make sure combustion will still take place. The Center to
center distance for the driving and driven wheel must be equal
to the radius from the center of the pin to the center of the
driving wheel multiplied by a factor of ¥2. This value should
also lie somewhere between 80-110mm. The diameter of the
pin/ slot must be in the range of 30-50mm and the slot length
or the stroke of the pin must be between 50-70mm. Also, the
stroke/ diameter ratio must stay 60/40.
C. Optimization Results
The formulas and bounds for each parameter are:
barPP
mmHmmHPF
radiansradiansFF
mmRmmRFT
MAX
SPSp
CACA
50
50,30)1(
785.00cos/'
11080'*
==
≤≤→−=
≤≤→=
≤≤→=
θθ
αα (1)
Therefore, the final characteristic equation is:
α
θ
cos
)1( CASP RHP
T
−
= (2)
This formula along with the bounds for each parameter is
then applied to the genetic algorithm which finds the best
combination of values to maximize the output torque.
The optimized parameters to attain the maximum torque in
this optimization problem are as follows:
50
50
50
110
0.785
1.943
P
S
CA
P bar
mm
H mm
R mm
radians
T KNm
θ
α
=
=
=
=
=
=
(3)
With the above parameters used, the torque will be at a
maximum value of 1.943kNm which is much higher than the
original torque value obtained in the comparison.
VI. CONCLUSIONS
The Geneva engine proposed in this study could be another
design to challenge the reciprocating design. Due to its
compact design and it uses very few moving parts, the
Geneva engine is a simple yet elegant piece of machinery that
should perform very well. The fact that it has a lower surface
to volume ratio than a reciprocating engine means more heat
will be transformed into power rather than lost heat. Also, the
results obtained in the torque output analysis showed that the
Geneva engine is a design that can be competitive with
current internal combustion engine designs.
ACKNOWLEDGMENT
The first author gratefully acknowledges the support of
K.C.Wong Education Foundation, Hong Kong.
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