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 1School of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Korea

2School 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: [email protected] † 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

11 0 2 1 1

2

, arcsin( sin( ))l

tl

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

12

2

2

22

1

2

2

2

1

2

12

2

1

22

1

2

2

12

2

111

−

−

−

−

−

+−=

l

ll

l

l

ll

l

l

ll

ll

dt

Sd

σ

σσω

σ

σω

σ

σωσω

(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 21 1

2 222

1l

l ll

σ− ≅ . (4)

The resulting acceleration can be simplified as follows:

2 222 1 0

1 022

cos(2( ))cos( ) .

l td Sl t

ldt

ω ω θω 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 d2S/dt

2 denotes the relative accelera-

tion of m3 with respect to M derived in Eq. (5).

212

,s

d yM F Mg

dt= − (6)

22

3 3 22( ),s s

d ym F m g k l y

dt=− + + − (7)

2 2 21 22 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

23 2 32 2

( ) ( ) 0.s

d y d SM m ky kl M m g M

dt dt+ + − + + + =

(9)

Adding the damping term to the equation, we now obtain

2 2

2 23 2 32 2

( ) ( ) 0s

d y dy d SM 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

d2S/dt

2 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)

21maximum jump height .

2outv

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.

References

[1] T. Thueer and R. Siegwart, Mobility evaluation of all-terrain

robots, Robotics and Autonomous Systems, 58 (2010) 508-

519.

[2] B.-S. Kim, Q.-H. Vu, J.-B. Song and C.-H. Yim, Novel de-

sign of a small field robot with multi-active crawlers capable

of autonomous stair climbing, Journal of Mechanical Sci-

ence and Technology, 24 (2010) 343-350.

[3] R. Reeve, B. Webb, A. Horchler, G. Indiveri and R. Quinn,

New technologies for testing a model of cricket phonotaxis

on an outdour robot, Robotics and Autonomous Systems, 51

(1) (2005) 41-54.

[4] M. H. Raibert, BigDog, the rough-terrain quadruped robot,

Proc: International Foundation on Automatic Control, Seoul,

Korea, (2008) 10822-10825.

[5] S. Lee, M. Kim, J. Kim and M.-T. Choi,. Receding horizon

viability radius for stability of humanoid robot under exter-

nal perturbation, Journal of Mechanical Science and Tech-

nology, 24 (5) (2010) 1127-1139.

[6] M. H. Raibert, M. Chepponis and H. B. Brown, JR., Run-

ning on four legs as though they were one, IEEE Transac-

tion on Robotics and Automation, 2 (2) (1986) 70-82.

[7] M. Raibert, S. Tzafestas and C. Tzafestas, Comparative

simulation study of three control techniques applied to a bi-

ped robot, Proc. of the IEEE International Conference on

Systems, Man and Cybernetics, Le Touquet, France (1993)

494-502.

[8] I. Poulakakis, J. A. Smith and M. Buehler, On the dynamics

of bounding and extensions towards the half-bound and the

gallop gaits, Adaptive Motion of Animals and Machines, Part

2 (2003) 79-88.

[9] J. A. Smith, I. Sharf and M. Trentini, PAW: a hybrid

wheeled-leg robot, Proc. of the IEEE Int’l Conference on

Robotics and Automation, Orlando, FL, USA, (2006) 4043-

4048.

[10] S. Kim, J. E. Clark and M. R. Cutkosky, ISprawl: Design

and tuning for high-speed autonomous open-loop running,

International Journal of Robotics Research, 25 (9) (2006)

903-912.

[11] U. Saranli, A. A. Rizzi and D. E. Koditschek, Model-based

dynamic self-righting maneuvers for a hexapedal robot, In-

ternational Journal of Robotics Research, 23 (9) (2004) 903-

918.

[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.

Documents

02e7e5284f777d06ed000000