02e7e5284f777d06ed000000

Journal of Mechanical Science and Technology 27 (1) (2013) 207~214
www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-012-1207-8
Design of a slider-crank leg mechanism for mobile hopping robotic platforms†
Doyoung Chang1,♦
, Jeongryul Kim1,♦
, Dongkyu Choi1
, Kyu-Jin Cho1
, TaeWon Seo2,*
and Jongwon Kim1
1
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Korea
2
School of Mechanical Engineering, Yeungnam University, Gyeongsan, Korea
(Manuscript Received August 19, 2011; Revised March 9, 2012; Accepted August 13, 2012)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract
Legged locomotion has been widely researched due to its effectiveness in overcoming uneven terrains. Due to previous efforts there
has been much progress in achieving dynamic gait stability and as the next step, mimicking the high speed and efficiency observed in
animals has become a research interest. The main barrier in developing such a robotic platform is the limitation in the power efficiency of
the actuator: the use of pneumatic actuators produce sufficient power but are heavy and big; electronic motors can be compact but are
disadvantageous in producing sudden impact from stall which is required for high speed legged locomotion. As a new attempt in this
paper we suggest a new leg design for a mobile robot which uses the slider-crank mechanism to convert the continuous motor rotation
into piston motion which is used to impact the ground. We believe this new mechanism will have advantage over conventional leg
mechanism designs using electronic motors since it uses the continuous motion of the motor instead of sudden rotation movements from
stall state which is not ideal to draw out maximum working condition from an electronic motor. In order to control impact timing from
the periodic motion of the piston a mechanical passive clutch trigger mechanism was developed. Dynamic analysis was performed to
determine the optimal position for the mechanical switch position of the clutch trigger mechanism, and the results were verified through
simulation and experiment. Development of a legged locomotion with two degrees of freedom, slider-crank mechanism for impact and
additional actuation for swing motion, is proposed for future work.
Keywords: Slider-crank mechanism; Hopping locomotion; Legged robot; SLIP model
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction
Legged robots have a significant advantage over wheeled
robots in overcoming obstacles in uneven terrain. Wheeled
robots may be more efficient on flat terrain; however, their
mobility is very limited on irregular terrain. Therefore,
mechanisms that adopt a combination of wheels and legs have
been suggested (e.g., the rocker-bogie and the shrimp [1], the
tread-leg mechanism [2], and the Wheg mechanism [3]).
These are still limited because they require at least three con-
tacts on the ground at all times to maintain stability. State-of-
the art legged robots such as the quadruped BigDog [4] and
the biped humanoids [5] have greater abilities than wheel or
wheel-leg robots.
The gait of legged robots can be classified into two catego-
ries: static gaits and dynamic gaits. A static gait uses one step
at a time to ensure the stability of a robot by maintaining the
center of mass (CM) in the polygon created by the feet con-
tacting the ground. Therefore, in the case of a quadruped, at
least three feet should be in contact with the ground at all
times. On the contrary, a dynamic gait has a flight state in
which no foot has contact with ground. The kinetic energy of
the flight state is conserved as potential energy in the spring
during touch down, and increases the kinetic energy at lift-off.
The dynamic gait has disadvantages in terms of stability;
however, the dynamic gait has been widely researched due to
its advantages of power efficiency and high locomotion speed.
There have been several studies of robots that achieve a dy-
namic gait. Raibert introduced a balancing strategy for a
legged robot during dynamic gaits using the virtual leg con-
cept [6]. Recent research by Boston Dynamics (Waltham, MA,
USA) examines a state-of-the-art dynamic gait control for a
quadruped and biped [7]. On the other hand, there are several
dynamic gait robots that achieve stability with a simple con-
trol concept using passive dynamics; these include Scout2 [8]
and PAW [9]. Also, a simple open loop control strategy for a
hexapod mechanism with compliant legs was suggested, and
the good performance was demonstrated by the prototypes of
I-Sprawl [10] and RHex [11].
In this paper, we propose a new robot leg design for dy-
namic gaits. The robot leg consists of two components: a
slider-crank mechanism to generate linear actuation, and a
♦
These authors made equal contributions as first author.
*
Corresponding author. Tel.: +82 53 810 2442, Fax.: +82 53 810 4726
E-mail address: taewon_seo@yu.ac.kr
†
Recommended by Associate Editor Junzhi Yu
© KSME & Springer 2013

208 D. Chang et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 207~214
spring damping system to conserve and release potential en-
ergy. As the robot leg contacts the ground, the slider-crank
mechanism compresses the spring against the ground, and the
compressed spring makes the whole body achieve high hop-
ping motion. This procedure is repeated when the leg bounces
on the ground; therefore, the hopping motion can be repeated.
We believe there are two main advantages of the proposed
mechanism compared to conventional leg mechanisms. First,
the leg is relatively lighter than the legs of dynamic gait robots
actuated by pneumatic actuators. The weight of the leg can be
reduced since the mechanism uses an electric rotary actuator
rather than the pneumatic actuator that is widely used in dy-
namic gait robots such as the Raibert mechanisms [6, 7].
While the main issue of using an electric rotary motor is the
difficulty in generating high impact, the mechanism dedicates
its effort to producing relatively high impact by taking advan-
tage of the continuous rotation of the motor rather than servo
control from stall by using a slider-crank mechanism. Second,
the proposed leg design can store more potential energy than
the leg designs of other dynamic gait robots [8-11]. By using
the conserved potential energy to generate hopping motion,
we expect the proposed robot leg mechanism to be more en-
ergy conservative, thus enabling development of a compact
but highly locomotive dynamic gait robot.
This paper is organized as follows. Section 2 explains the
basic concepts and purpose of developing the proposed slider-
crank leg mechanism which has been inspired by the spring-
loaded inverted pendulum (SLIP) model. In Section 3, we
introduce the actual prototype and address the design issues.
To obtain constant jumping motion which is necessary for
stable locomotion a clutch trigger mechanism has been devel-
oped. To find the optimal design for the trigger, in the follow-
ing Section 4, we derive the dynamic model for the prototype
to determine the optimal design for the clutch trigger. Also,
discussion about the experimental results with the prototype is
presented. Concluding remarks are given in Section 5.
2. Slider-crank leg mechanism
The main barrier in developing a compact legged robotic
platform that is able to achieve high speed is the limitation in
the power efficiency of the actuator. That is, pneumatic actua-
tors used in legged robots are advantageous in generating a
large amount of force to impact the ground in a very short
time, but has disadvantages when used on a fully contained
mobile robot due to its large size, heavy weight, and signifi-
cant noise.
For this reason, mobile-legged robots that use motors for lo-
comotion have been suggested. Electronic motors can be
compact, but they are disadvantageous in producing sudden
impact from stall due to the actuation characteristics which is
required for high speed legged locomotion since. That is, in
terms of power output, rotary electric motors are advantageous
for continuous rotation rather than sudden movement from
stall. Linear electric motors have benefits in this aspect, but
they are also relatively large and heavy compared to rotary
motors with similar power output. A slider-crank mechanism
was applied for the actuation of I-Sprawl [9], but it used open-
loop passive control for a statically stable hexapod rather than
to generate large impact used in a dynamic gait.
As a new attempt in this paper we suggest a new leg design
for a mobile robot which uses the slider-crank mechanism to
convert the continuous motor rotation into piston motion
which is used to impact the ground. Fig. 1 shows the proposed
leg design. The leg consists of a rotational actuator, a slider-
crank mechanism, and a linear spring at the end of the slider.
The leg is operated as follows. The rotational actuator on the
main body rotates in one direction. Then, the slider-crank
mechanism converts the rotation to linear motion along to the
slider, which is the y-direction shown in Fig. 1(a). As a result,
the slider repeatedly moves upward and downward in the y-
direction. The linear momentum of the slider generates an
active impact on the ground, and the leg hops using the con-
served potential energy in the spring. The prototype design is
shown in Fig. 1(b).
The proposed leg mechanism was inspired by the SLIP
model, which has been suggested as a canonical model of
running animal dynamics [12]. The SLIP model describes the
running of animals as a repeated sequence of conservation and
release of potential energy using a linear spring. That is, when
the animal lands on the ground, the kinetic energy is con-
served as potential energy in the muscular system as if a
spring were compressed. The potential energy is used to pro-
duce a larger impact in the next jump. Adopting the basic
concept of the SLIP model is important for a mobile robot.
The model improves energy efficiency by reducing kinetic
energy loss, and helps to produce a larger impact for sufficient
jumping with limited actuation.
The slider-crank mechanism [13] helps the leg to generate
an active impact during locomotion according to the SLIP
Fig. 1. (a) Schematic of the slider-crank leg mechanism (l1: crank arm
length, l2: connecting rod length, l3: slider length, ls: spring length, M:
body mass, m1: crank arm mass, m2: connecting rod mass, m3: slider
mass, k: spring constant, c: damping coefficient, θ1: angle between the
body and the crank arm, θ2: angle between the crank arm and connect-
ing rod, and φ: transmission angle of the crank); (b) 3-D modeling of
the prototype.
(a) (b)

D. Chang et al. / Journal of Mechanical Science and Technology 27 (1) (2013) 207~214 209
model. The slider-crank mechanism converts the rotation of a
rotary motor to linear motion of the slider, which then gener-
ates an active impact of the foot against the ground. The foot
moves up and down, repeatedly actuated by the rotary motor.
When the foot lands on the ground, the spring is compressed
due to body inertia, and the slider starts to push against the
ground, thereby compressing the spring even more. High hop-
ping motion is achieved as the conserved potential energy in
the spring is released.
Now that we have explained the basic concepts, we investi-
gate design issues in designing and manufacturing an actual
prototype in the following section.
3. Prototype design and manufacturing
3.1 Specification of the prototype
A prototype of the slider-crank hopping leg was built as
shown in Fig. 2. The design parameters of the prototype leg
have been determined to satisfy the size and weight require-
ments for a compact legged robot which we target to build
which will weigh less than 20 kg and is able to achieve 5 m/s.
The dimensions of the prototype are 370 (L) x 200 (W) x
560 (H) mm3
, and the net weight is 2.7 kg. Detailed specifica-
tions are summarized in Table 1. A brushless direct current
(DC) motor (Maxon, Switzland) was used to rotate the crank.
The length of the connecting rod l2 was designed to be twice
the length of the crank arm l1. Different hopping heights are
achieved by controlling the rotation speed of the rotary motor.
The prototype was connected to a 1.5 m-long link that was
fixed on the ground via a universal joint to restrict the motion
of the hopping leg in one direction.
3.2 Clutch trigger mechanism
While the crank enables to draw out maximum working
condition of the motor, since the slider continuously repeats a
periodic motion it is difficult to obtain stable hopping motion.
That is, the achieved jumping is determined by the crank angle
at landing impact which we define as the transmission angle φ.
Thus, the transmission angle should be maintained as a fixed
value to achieve repeated hopping locomotion.
In order to control impact timing of the piston a mechanical
passive clutch trigger mechanism was developed as shown in
Fig. 3(a) to maintain a constant transmission angle and thus
achieve stable hopping motion. The mechanism consists of an
electromagnetic clutch that connects the crank with the motor
shaft, and a switch with an elastic stopper which is triggered
as the crank shaft rotates and pushes the switch as seen in Fig.
3(b). When the leg contacts the ground, the piston will be
pushed upwards resulting in rotating the crank and disengag-
ing with the elastic switch.
Table 1. Specification of the hopping leg prototype.
Name Size (mm) Weight (kg)
Body 55 (L) x 110 (W) x 560 (H) 1.1
Crank arm (mm) 45 (l1) 0.05
Connecting rod (mm) 90 (l2) 0.08
Slider (mm) 200 (l3) 0.5
Motor (mm) Ф35 x 108 0.52
Clutch (mm) Ф45.3 x 39.4 0.3
Trigger (mm) 40 (L) x 8 (W) x 75 (H) 0.01
Linear spring (mm) Ф36 x 245 0.4
Total 2.96
Fig. 2. Prototype of the proposed slider-crank hopping leg.
(a)
(b)
Fig. 3. (a) Electromagnetic clutch and trigger with elastic stopper; (b)
Clutch trigger mechanism.

The sequence of the mechanism is shown in Fig. 4. After a
successful jump, the crank keeps rotating in the clockwise
(CW) direction until it touches the switch and disconnects the
clutch. The elastic switch now acts as a mechanical stopper to
hold the crank at a constant transmission angle. As the foot
lands on the ground and the impact is transferred through the
connecting rod, the crank starts rotating and disengages with
the switch turning it off, and the clutch is re-connected so that
the actuation of the motor is transferred to the crank again.
Now, the motor drives the crank arm and as the foot touches
the ground the slider connected with the crank arm makes an
impact and the hopping leg makes a jump. After the leg jumps,
the crank arm rotates and pushes the switch again and the
crank arm is held at the transmission angle. Through this
mechanism a fixed transmission angle can be maintained dur-
ing a series of continuous hopping motions while maintaining
the advantage of continuous rotation of the motor.
The maximum output of the slider at impact is related to the
transmission angle φ of the crank link. Therefore, it is neces-
sary to obtain the optimal transmission angle and install the
elastic switch at this angle. In the following section we derive
the dynamic model of the hopping leg prototype to find the
optimal design for maximum performance and address the
design limitations.
4. Parametric design and experiment
The transmission angle in a slider-crank mechanism is de-
fined as the angle between the connecting rod and the axis
normal to the slider axis, which is denoted as φ in Fig. 1. Since
hopping height is affected by the transmission angle when the
foot leaves the ground in the take-off sequence, finding the
optimal transmission angle is required for efficient hopping
motion. For this, first dynamic modeling of the hopping mo-
tion is derived based on the force and momentum equation.
Then, the optimal transmission angle is determined through an
exhaustive search of the full range of transmission angles.
Verification using RecurDyn commercial dynamic simulation
software was also performed.
4.1 Modeling
We derived a model for hopping leg motion during the
landing and take-off sequence. In order to analyze the hopping
motion, we assumed that the initial state occurs when the foot
touches the ground, and the final state occurs when the hop-
ping leg totally loses contact with the ground. From a different
point of view, the motion could be interpreted according to the
compression and expansion of the spring. As the leg contacts
the ground the spring begins to be compressed due to gravita-
tional force and force applied by the slider. The spring con-
tacts the ground until the spring fully expands and recovers its
initial state, thus applying no force against the leg. We defined
the slider-crank model as shown in Fig. 5(a) and then simpli-
fied it as a two body mass-spring system, where the force
generated by the slider-crank mechanism is expressed as the
force acting on the two bodies to push each other away as
shown in Fig. 5(b). Note, that the crank shaft position moves
as the piston applies force to the ground making the analysis
different from the classical slider-crank dynamic analysis. The
focus of the analysis is to find the net impact the leg is able to
apply against the ground with respect to the crank angle at
impact or the transmission angle. The analysis is performed in
two steps. First the kinematics of the slider-crank is reviewed
and then based on the result dynamic analysis of the two body
system is performed to find the achieved jumping height for a
given transmission angle. The result for every angle is calcu-
lated to find the optimum trigger installation point.
First the position, velocity, and acceleration of the end of
the slider were derived (point B in Fig. 3) with respect to the
motion of the rotary actuator (point O in Fig. 3). The position
of the end of the slider was determined by the angle between
the crank arm and the slider θ1, the angle between the crank
arm and the connecting rod θ2 (see Fig. 1), and the length of
(a) (b)
Fig. 5. Free body diagram of the simplified leg mechanism model: (a)
Initial schematic; (b) Simplified schematic as a two body mass-spring
system.Fig. 4. Sequence of the passively-triggered clutch mechanism.

the crank arm l1 and connecting rod l2, as follows:
1 1 2 1 2cos( ) cos( )S l lθ θ θ= + + . (1)
We assumed that the rotary motor ran with constant angular
velocity ω; therefore, θ1 and θ2 are expressed as
1
1 0 2 1 1
2
, arcsin( sin( ))
l
t
l
θ ω θ θ θ θ= + =− + − (2)
where θ0 is the angle between the crank arm and the slider in
the initial state. The acceleration of the end is derived in a
straightforward manner by differentiating the position twice.
The acceleration is given as follows:
3
2
2
2
1
2
1
2
2
2
2
1
24
1
2
2
2
1
2
1
2
2
2
22
1
2
2
2
1
2
1
2
2
1
22
1
2
2
12
2
111








−
−
−
−
−
+−=
l
l
l
l
l
l
l
l
l
l
l
l
l
dt
Sd
σ
σσω
σ
σω
σ
σω
σω
(3)
where 1 0sin( )tσ ω θ= + and 2 0cos( ).tσ ω θ= +
Since the resulting acceleration is unnecessarily compli-
cated, we ignored the high-order term to assume that
2 2
1 1
2 22
2
1
l
l l
l
σ
− ≅ . (4)
The resulting acceleration can be simplified as follows:
2 22
2 1 0
1 02
2
cos(2( ))
cos( ) .
l td S
l t
ldt
ω ω θ
ω ω θ
+
= − + − (5)
Next, we calculate the force the hopping leg applies against
the ground. The force is proportional to the deformation of the
spring that is located at the end of the slider. For simplification,
the force applied through the crank mechanism is thought as
linear actuation. That is, a slider with mass m3 is being linearly
accelerated by a mass M. Also, the inertia effects of link m1
and m2 are neglected since the mass is relatively small. There-
fore, the free body diagram of the simplified leg mechanism
could be represented as a system composed of two rigid bod-
ies where the two bodies apply force against each other. Here,
the slider is a mass-spring system applying force against the
ground. It should be noted that the spring contacts the ground
and pushes the whole system away from ground until it recov-
ers its natural length and stops applying force.
The dynamics equation for M and m3 is derived in Eqs. (6)
and (7) respectively. The relative distance of the two masses
are as in Eq. (8), where d2
S/dt2
denotes the relative accelera-
tion of m3 with respect to M derived in Eq. (5).
2
1
2
,s
d y
M F Mg
dt
= − (6)
2
2
3 3 22
( ),s s
d y
m F m g k l y
dt
= − + + − (7)
2 2 2
1 2
2 2 2
.
d y d y d S
dt dt dt
− = (8)
By simultaneously solving the three equations the dynamics
equation of the whole system is derived as follows:
2 2
2
3 2 32 2
( ) ( ) 0.s
d y d S
M m ky kl M m g M
dt dt
+ + − + + + =
(9)
Adding the damping term to the equation, we now obtain
2 2
2 2
3 2 32 2
( ) ( ) 0s
d y dy d S
M m C ky kl M m g M
dtdt dt
+ + + − + + + =
(10)
where the damping coefficient c is experimentally measured.
Now, the height profile y2 could be obtained by substituting
d2
S/dt2
from Eq. (5) and solving Eq. (10). The net force gener-
ated by the spring against the ground is given by the following
equation:
2( ).sF k l y= − (11)
Assuming that momentum is conserved, the take-off veloc-
ity vout is first calculated, and then the achievable hopping
height is calculated using the landing velocity vin at the next
sequence, as follows:
1 2 3( ) ( ( ) ) ,out inm v v F M m m m g dt− = − + + +
∫ (12)
Fig. 6. Example of hopping trajectory derived by the dynamic model.
The blue dashed line and red solid line denote the hopping trajectory of
the system and the profile of the spring while it contacts ground, re-
spectively. The properties of the prototype are used as parameters
which are given as follows: l1 = 45 mm, l2 = 90 mm, l3 = 200 mm, ls =
100 mm, k = 15 kN/m, M = 1.875 kg, m1 = 0.050 kg, m2 = 0.075 kg, m3
= 0.478 kg, ω =180 rpm, vin = 2.42 m/s, c = 23.9 kg/s, and φ = 270º.

2
1
( ) ,out in sv v k l y dt
m
= + −
∫ (13)
21
maximum jump height .
2
outv
g
= (14)
Fig. 6 shows the result of the motion when the hopping leg
starts free-falling from 0.4 m above the ground to 0.1 m, re-
sulting vin = 2.42 m/s. We observed that during the bouncing
phase, the spring conserved potential energy and used the
energy to hop again. Due to damping energy loss, the hopping
height must reduce as after a few series of hopping. However,
with a slider-crank mechanism, the hopping leg is able to
maintain constant hopping height.
4.2 Comparison to simulation
Simulation of the hopping sequence was performed using
RecurDyn commercial dynamics simulation software (Func-
tionBay Inc., http://functionbay.co.kr) to verify the dynamics
modeling. The simulation results of the hopping sequence
using the same parameters as shown in Fig. 5 are shown in Fig.
7. The difference between the maximum hopping height from
the dynamics modeling results and the simulation results is
2.9%. Therefore, we assumed that the dynamics modeling was
reliable.
4.3 Transmission angle optimization for maximum hopping
height
Fig. 8 shows the corresponding hopping height obtained for
a given transmission angle. The blue line and red star denote
the results of the dynamics model and the dynamics simula-
tion, respectively. The optimum transmission angle φ was
270◦. The maximum height achieved at this angle was 0.42 m.
Note that since from 0◦ to 90◦, the slider is accelerating up-
wards while the leg is falling the slider does not contact the
ground at this angle and therefore the result between our dy-
namic model and the simulation is slightly different due to
calculation uncertainty.
However, due to physical constraints of the trigger mecha-
nism, it is impossible to install the trigger at the optimal
transmission angle. That is, in order for the mechanism to
work the crank should be disengaged from the trigger switch
as the slider is pushed in when the leg contacts the ground.
However, if the trigger is located in the right half of the angle
that is from 180◦ to 360◦ the crank will escape from the trigger
in the opposite direction of the crank rotation and thus the
mechanism will not work. Observing the results, the maxi-
mum height achieved increases as the transmission angle ap-
proaches the optimal angle. Therefore, we have designed the
trigger to be located as close as possible to 180◦. Experiment
results are discussed in the next section.
4.4 Experiment results
The maximum hopping height predicted by the dynamics
model was 0.42 m where the actual maximum hopping height
achieved without the clutch trigger mechanism, thus among
random transmission angle and hopping, was 0.35 m. With the
trigger installed at 135◦ the prototype was able to achieve
constant hopping height of 0.30 m as shown in Fig. 9. The
difference between the prototype with the predicted value and
randomly achieved maximum was 0.12 m (28.5%) and 0.05 m
(14.3%) respectively. We believe the prototype was able to
achieve similar jumping height compared to the randomly
achieved maximum although the trigger was not installed at
the optimal position due to the time delay of the crank to reach
maximum rotation speed when the clutch is engaged. Thus,
the actual transmission angle gets closer to the optimal value.
Fig. 7. Simulated hopping motion using RecurDyn.
Fig. 8. Maximum hopping height obtained for a given crank angle and
transmission angle by dynamic modeling (blue line) and dynamic
simulation (red star).
Fig. 9. Result of the hopping leg experiment.
Fig. 10. Hopping leg with swing motion.

Meanwhile, the causes of error between the randomly
achieved maximum height and predicted maximum was
mainly due to energy loss from mechanical resistance in the
slider mechanism, and difficulty in aligning the impact so as
to be perfectly normal to the ground causing loss of driving
force.
5. Conclusions and future work
We presented a new robot leg design for hopping locomo-
tion. A slider-crank mechanism with a linear spring was used
to generate energy-efficient hopping by conserving and releas-
ing potential energy. A clutch trigger mechanism was de-
signed to control the impact time and take advantage of con-
tinuous rotation of the motor. Dynamic analysis was per-
formed to find the optimal design parameters for the trigger.
Through experiments the proposed prototype achieved con-
stant hopping height in a series of continuous hopping motions.
Although the trigger was not able to be installed at the opti-
mum position, due to the time delay from the clutch the per-
formance of the prototype was close to that of the predicted
maximum value.
Currently, the proposed leg mechanism is designed to per-
form one degree-of-freedom hopping motion. The next plan is
to design a prototype which could perform swing motion to
propel forward as in Fig. 10. This will be achieved by rotating
the bushing that holds the slider.
Acknowledgment
This work was supported by a National Research Founda-
tion (NRF) grant (No. 2009-0087640) and partly by the Korea
Student Aid Foundation (KOSAF) grant (No. S2-2009-000-
00308-1) funded by the MEST of the Korean government.
The authors gratefully acknowledge this assistance.
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[12] I. Poulakakis and J. W. Grizzle, The spring loaded inverted
pendulum as the hybrid zero dynamics of an asymmetric
hopper, IEEE Transaction on Automatic Control, 54 (8)
(2009) 1779-1793.
[13] J.-L. Ha, R.-F. Fung, K.-Y. Chen and S.-C. Hsien, Dy-
namic modeling and identification of a Slider-Crank
mechanism, Journal of Sound and Vibration, 289 (4-5)
(2006) 1019-1044.
Doyoung Chang received his B.S.
degree in Mechanical Engineering and
Mathematics from Seoul National
University, Seoul, Korea, in 2004,
where he also received Ph.D. in Me-
chanical Engineering in 2011. He is now
a post-doctoral researcher at Urobotics
laboratory in Johns Hopkins University.
His research interests include bio-inspired robot design, indus-
trial welding carriage robots and medical robotics.
Jeongryul Kim received his B.S. degree
in mechanical and aerospace
engineering from Seoul National Uni-
versity, Seoul, in 2009. He is currently
working toward a Ph.D. degree in
Robust Design Engineering Laboratory.
His current research is focused on a bio-
inspired mobile hopping robot.

Dongkyu Choi receive his B.A. degree
in Mechanical Aerospace Engineering
from Seoul National University, Seoul,
Korea, in 2010. His dissertation was
entitled “Design an under actuated
Gecko Arm”. From 2010, he is Ph.D.
researcher at the Robust Design
Engineering Lab, in Seoul National Uni-
versity, studying hopping leg robot.
Kyu-Jin Cho received his B.S. and M.S.
degrees in mechanical engineering in
1998 and 2000, respectively, from Seoul
National University, Seoul, Korea, and
has received his Ph.D. degree in
mechanical engineering from the
Massachusetts Institute of Technology,
Cambridge. He is currently an assistant
professor of the school of mechanical and aerospace engineer-
ing at Seoul National University, Seoul, Korea. His research
interests include robotics and control, biologically inspired
robotics, artificial muscles, mechatronics, and actuator sys-
tems using smart materials.
TaeWon Seo received his Ph.D. degree in
Mechanical and Aerospace Engineering
from Seoul National University, 2008,
where he also received his B.S. degree in
2003. He was a postdoctoral researcher at
Nanorobotics Laboratory in Carnegie
Mellon University in 2009, and he is
currently an assistant professor in the
School of Mechanical Engineering of Yeungnam University,
Korea. His research interests include design, control, optimiza-
tion, and motion planning of robotic platforms.
Jongwon Kim is a professor in the
School of Mechanical and Aerospace
Engineering of Seoul National University,
Korea. He received his BS in Mechanical
Engineering from Seoul National Uni-
versity in 1978, and his MS in Mechanical
and Aerospace Engineering from Korea
Advanced Institute of Science and
Technology (KAIST), Korea, in 1980. He received his Ph.D. in
Mechanical Engineering from University of Wisconsin-
Madison, USA, in 1987. He worked with Daewoo Heavy In-
dustry & Machinery, Korea, from 1980 to 1984. From 1987 to
1989, he was Director of Central R&D Division at Daewoo
Heavy Industry & Machinery. From 1989 to 1993, he was re-
searcher at the Automation and Systems Research Institute at
Seoul National University. His research interests include paral-
lel mechanism, Taguchi methodology and field robot.

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