Design and Demonstration of a Locust-Like Jumping ... - Science Direct

Journal of Bionic Engineering 9 (2012) 271–281

Design and Demonstration of a Locust-Like Jumping Mechanism for Small-Scale Robots Quoc-Viet Nguyen, Hoon Cheol Park Department of Advanced Technology Fusion, Konkuk University, Seoul 143-701, Republic of Korea

Abstract A jumping mechanism can be an efficient mode of motion for small robots to overcome large obstacles on the ground and rough terrain. In this paper, we present a 7 g prototype of locust-inspired jumping mechanism that uses springs, wire, reduction gears, and a motor as the actuation components. The leg structure and muscles of a locust or grasshopper were mimicked using springs and wire, springs for passive extensor muscles, and a wire as a flexor muscle. A small motor was used to slowly charge the spring through a lever and gear system, and a cam with a special profile was used as a clicking mechanism for quick release of elastic energy stored in the springs to create a sudden kick for a quick jump. Performance analysis and experiments were conducted for comparison and performance estimation of the jumping mechanism prototype. Our prototype could produce standing jumps over obstacles that were about 14 times its own size (approximate to 71 cm) and a jumping distance of 20 times its own size (approximate to 100 cm). Keywords: biomimetics, locust, jumping mechanism, passive tibia extensor muscle Copyright © 2012, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(11)60121-2

1 Introduction Biomimetics is the study of biological systems in nature with the extraction of design, in terms of structure and function, for engineering applications of materials and machines in modern technology. Surprisingly, insects have the largest population and variety of creatures in nature. They are present everywhere on earth and are well known for their ability to travel over the most difficult environments: on desert, the surface of water, rocky and rough terrain, and even on vertical or upside-down surfaces. Their unsurpassed abilities have constantly attracted the interests of engineers and scientists for the development of many outstanding bio-inspired robots for many different types of motion in air[1,2], water[3,4], and on the ground[5–8]. Typically, there are four kinds of robots for locomotion on the ground: wheeled robots, snake-like robots, walking robots, and jumping robots. The first two types have been well developed and are documented in the literature[5–8]. However, at the small scale, they will encounter obstacles more often than large robots will and also face difficulties in moving over rough terrain. Corresponding author: Hoon Cheol Park E-mail: [email protected]

For example, small-wheeled robots can run fast on a flat surface, but have difficulty in overcoming obstacles on rough terrain that are larger than twice the wheel diameter. Walking robots can adjust their feet on a rough surface but they typically face difficulty to move in large steps over a crevasse or large obstacles. In addition, they have very complex motion systems both in terms of control and the mechanics of the leg structures themselves. Therefore, jumping seems to be a plausible solution and an effective means for small robots to move rough terrain. Many insects possess very powerful hind leg muscles for jumping which have constantly attracted the interests of researchers, resulting in significant progress in biological research[9–16] as well as in insect-inspired jumping robots[17–24]. Having adopted a jumping mechanism of natural jumpers, jumping robots are able to store energy in their elastic components and can quickly release all the energy in one jump, similar to a catapult mechanism. Basically, there are two types of jump: a continuous jump, such as the jump of kangaroos, and a pause-and-leap jump, such as the jumps of fleas, locusts/grasshoppers, and frogs, whereby the jumps are separated by long time

272

Journal of Bionic Engineering (2012) Vol.9 No.3

intervals. The former type of jump requires high speed and high muscle power. The latter jump type is performed at low speed, allowing time for directional control, and requires low power and energy storage. This jumping mechanism is used by several small jumping animals[9–16,25–27]. However, it requires a clicking mechanism for sudden energy release. Furthermore, it is difficult to accurately control the jumping destination, stability after takeoff, and safe landing. Our work adopts the pause-and-leap jump mechanism because of its low power requirement. We chose to mimic the jumping mechanism of locusts because they are quite well researched and documented in the literature[9–16] and because they are well known for their abilities of flying and jumping over long distances. Jumping is important both as an escape mechanism and for initiating flight. For example, the locust, Schistocerca gregaria, can jump over a distance of 1 m at a takeoff velocity of 3.2 m·s−1 while the mass of the driving muscles in the leg structure is only 4%–5% of the total body mass[14]. Compared to human muscles, the driving force in the leg muscle of the locust is surprisingly powerful[14]. This paper presents the biomimetic design and development of a prototype of locust-like jumping mechanism for small-scale robots. We have concentrated on mimicking the locust leg structure in terms of driving muscles, namely the extensor tibiae and flexor tibiae muscles. Our proposed mechanism consists of muscles represented by coiled springs for the passive extensors and a wire for the flexor, which is connected to a motor through a lever, cam, and gear system. The prototype of jumping mechanism is designed to be able to slowly charge the elastic energy to the coiled springs and then suddenly release all the energy through a kicking motion of the legs for jumping. In the following sections, we describe the leg structure of the locust and its performance. Then, we roughly estimate the jumping kinetic energy for our design and fabrication. Finally, we describe the working prototype and conduct jumping tests to characterize its jumping performance.

three pairs: front, middle, and hind legs. The hind legs are much bigger than the middle and front legs, which is advantageous for jumping. Each hind leg has five segments: coxa, trochanter, femur, tibia, and tarsus, as shown in Fig. 1. For a hind leg, the joints between segments are single degree-of-freedom joints or multiple degree-of-freedom joints. The coxa and trochanter segments are very small compared to the other segments in the hind leg but they are three-degree-of-freedom joints. To simplify the robotic mechanism, the coxa and trochanter segments can be neglected in a robotic design. Therefore, all joints are single degree-of-freedom and move in one plane. At the end of the tibia, there are tarsi and claws that prevent the locust from sliding on the ground as it jumps[14]. In the femur, there are two main muscles involved in jumping: the extensor tibiae muscle and the flexor tibiae muscle, as shown in Figs. 2 and 3. The extensor muscle occupies most of the volume of the femur; hence, it is much stronger than the flexor muscle. When the extensor tibiae muscle contracts, it causes the tibia to extend by pulling on its tendon attached to the tibia on one side, as shown in Fig. 2. When the flexor tibiae muscle contracts, it causes the tibia to flex by pulling on its tendon attached to the tibia on the other side[14]. Hindleg

Antenna Simple eye

Forewing

Compound eye

(a)

Foreleg

Spiracles

2 Analysis of jumping mechanism of locust 2.1 Locust morphology Locust morphology and jumping procedure are well documented in the literature[9,10,14]. As with other insects, locusts possess six legs that are grouped into

Fig. 1 (a) Locust anatomy and (b) hind leg.

Nguyen and Park: Design and Demonstration of a Locust-Like Jumping Mechanism for Small-Scale Robots

At the femur-tibia joint or knee joint, there is a special structure known as a semilunar process (Figs. 2 and 3), which is made from a special uniform glass-like cuticle with highly condensed elasticity, and a catapult-like mechanism, which can slowly store energy and then suddenly release all the energy for quick jump. The presence of a lump, as shown in Figs. 2 and 3, enables the weak flexor muscle to hold the tibia flexed against the strong extensor muscle during the energy build-up in the semilunar process.

Fig. 2 (a) Extensor tibiae muscle and (b) flexor tibiae muscle[14].

273

high-speed camera (Photron Fastcam Ultima APX, Japan) was used to record the jumping movement of the locust. The jumping performance was conducted in a still air environment. Sequential images of the locust during jumping were captured at 2000 frames per second. From the high-speed camera images we could analyze the jumping performance of the locust. As shown in Fig. 4, the locust can make a long standing jump over a distance of about 35 cm (about 10 times its body length), rising to a height of about 23 cm (about 6.5 times its body length) with a takeoff angle of about 60˚. In order to prevent tumbling in the air and to maintain its stability after takeoff, the locust starts to open its wings just before takeoff, and then it flaps its wings during takeoff and landing. The wing opening followed by flapping enables the locust to control its stability and allows it to make a safe landing. The locust jumping performance inspired us to develop a locust-like jumping mechanism.

Fig. 4 Sequential images of a jumping locust.

3 Design of jumping mechanism

Fig. 3 Schematics of grasshopper/locust leg structure[14].

2.2 Jumping of a locust The jumping performance varies with the species and size of locusts. In our case, a locust, Tettigoniidae, 35 mm in body length and 0.42 g in weight, was used for the jumping performance test. The locust was placed on a rough surface to prevent slipping during jumping. A small rod was used to stimulate the locust for a jump. A

3.1 Conceptual design of joint mechanism The locust jump is powered by the contractile forces generated by the extensor tibiae muscles of the hind legs. The force produced by the extensor muscle is much larger than the force pushing on the ground at the end of the tibia[14] due to the small moment arms of the muscles. In order to mimic both the extensor and flexor muscles and actively control them, we need two actuators and an electronic system, which would result in a complex design and heavy prototype. Instead, we only used one actuator (a motor) to control both muscles and provide a simple design. Different from the work of Scarfogliero et al.[19], Lambrecht et al.[20] and Kovac et al.[24] in which a four-bar linkage mechanism is used for the leg structure, our proposed design mimics the locust

274


leg structure as shown in Fig. 5. We used a spring as a passive extensor muscle and its tendon. Thus, the contraction of the muscle is not actively controlled, while a wire as an active flexor muscle and its tendon is controlled by a motor and a transmission system including gears and lever. The shape of the tibia is similar to the real locust leg[28], and it can rotate about its pivot (Fig. 5). One end of the spring is attached to the tibia on one side of the pivot while the other end of the spring is attached to the body frame. One end of the wire is attached to the tibia on the other side of the pivot while the other end of wire is attached to the lever that is connected to the cam, gear, and motor system. The presence of a lump enables the flexor muscle (the wire) to increase its moment arm that is the distance between the position of the tension force in the wire and the tibia pivot, such as in the real case of a locust leg[28]. The increase of the moment arm of the flexor muscle (the wire) reduces the working load on the motor. One end of the lever, at which a bearing is installed to reduce friction, is in contact with the cam profile (outer contour of the cam). Therefore, when the cam driven by the motor rotates, the lever rotates in the opposite direction and pulls the wire to flex the tibia about its pivot while the spring is extended for elastic energy storage, as shown in Fig. 5a. The cam profile was inspired from a work of Leonardo da Vinci (hammer driven by an eccentric cam), and it can be seen in Fig. 6[29]. This cam was also used in some studies as a clicking mechanism[19,20,24]. The cam profile was designed to yield a constant torque on the motor[19,20,24]. The sharp change in cam profile plays the role of a clicking mechanism that enables the system to suddenly release all stored energy for jumping when the lever passes the critical point on the cam. 3.2 Mechanical design and fabrication of jumping mechanism The design objective of our prototype of jumping mechanism was that it should have an estimated total weight of about 7 g and body length of about 5 cm. It should also be capable of jumping over obstacles that are 10 to 15 times higher than its own body length, approximate to 50 cm to 75 cm, with a takeoff angle of 60˚ (Fig. 7) that is similar to the takeoff angle of a real locust such as that observed several times in the previous section (Fig. 4). According to the design objective, we first estimated the required kinetic energy for jumping in

(a) Spring in tension for elastic energy storage

(b) Release of elastic energy stored in the spring

Fig. 5 Diagram of joint and clicking mechanism mimicking locust leg.

Fig. 6 Hammer driven by an eccentric cam by Leonardo da Vinci[29]. y

vtop v

60˚ x

Fig. 7 Design objective of the jumping mechanism prototype.


order to design the structural elements of the prototype of the jumping mechanism, and then we created a Computer-Aided Design (CAD) model for fabrication. Finally, we assembled a jumping prototype for performance tests. In addition, the designed prototype of the jumping mechanism should be able to jump even on slippery surfaces. 3.2.1 Jumping kinetic energy The jumping mechanism can be regarded as a projectile of mass, m, launched with an initial velocity, vo, at a shooting angle, θo, at time, t = 0; the equations of ballistic motion for the jumping mechanism can be expressed by Newton’s second law as F = ∑ ma ,

(1)

where F is the total force acting on the jumping mechanism and a is the acceleration. In this case, the forces are gravity and air resistance, R, which is an important factor of energy loss for small insects. The air exerts a resistance force on the jumping mechanism that is opposite to the direction of the velocity of the jumping mechanism, and proportional to the square of the instantaneous velocity, v, of the jumping mechanism R = βv2,

velocity of the jumping mechanism is v(t ) = x 2 (t ) + y 2 (t ),

(3)

at an angle with respect to the horizontal direction of

θ (t ) = tan −1 ( y (t ) x (t ) ) .

force is −R(t)cosθ(t). In the y-direction, the component of the resistance force is −R(t) sinθ(t). Hence, Eq. (1) is written as mx(t ) = − R(t ) cos θ (t ),

(5)

my(t ) = −mg − R(t )sin θ (t ).

(6)

and

Since x (t ) ⎧ ⎪cos θ (t ) = 2 x (t ) + y 2 (t ) (t ) ⎞ ⎪ −1 ⎛ y , (7) θ (t ) = tan ⎜ ⎟⇒⎨ y (t ) ⎝ x (t ) ⎠ ⎪sin θ (t ) = ⎪ x 2 (t ) + y 2 (t ) ⎩ equations of motion in Eqs. (5) and (6), respectively, become

x(t ) = −

1 2 x (t ) β v (t ) m x 2 (t ) + y 2 (t )

=−

1 β x (t ) x 2 (t ) + y 2 (t ), m

(4)

The jumping mechanism is subjected to two forces: the vertical downward gravity, mg, and the resistance force, R(t) = βv2(t). The x-component of the resistance

Fig. 8 Diagram of ballistic motion for the jumping mechanism with air resistance.

(8)

and y (t ) = − g −

1 2 y (t ) β v (t ) 2 m x (t ) + y 2 (t )

= −g −

1 β y (t ) x 2 (t ) + y 2 (t ). m

(2)

where β is a constant. At time t, the mass which is at the location (x(t), y(t)) in the Cartesian coordinate system, as shown in Fig. 8, originated at the point from where the jumping mechanism launched. The instantaneous velocity of the jumping mechanism in the x- and y-directions are x (t ) and y (t ), respectively. Thus, the

275

(9)

The initial conditions at time t = 0 are x(0) = 0, y(0) = 0, x (0) = vo cos θ o , y (0) = vo sin θ o . The constant β is 1 C ρ A ; in which Cd is the drag coefficient, ρ is the air 2 d density of 1.2 kg·m−3 at sea level, and A is the frontal area of the jumping mechanism. The equations of motion are a system of two second-order Ordinary Differential Equations (ODE) involving the first- and second-order derivatives: x (t ) , y (t ) , x(t ) , and y (t ) . The frontal area, A, and the drag coefficient, Cd, can be roughly estimated by assuming that the prototype of jumping mechanism is similar to the desert locusts in Refs. [10,24]. In accordance with Ref. [10], we modeled our prototype of jumping mechanism as a cylinder of 90 mm in length and 35 mm in diameter with a drag coefficient, Cd, of 1.3. We solved the ODEs numerically using the Matlab ode45 solver[30] to roughly obtain a required takeoff velocity, vo, of 4.8 m·s−1 for the case of a jumping height of 75 cm, which corresponds to an initial kinetic energy, Eko, of


276 Eko =

1 2 mvo = 80.64 mJ. 2

From this estimated kinetic energy, the acceleration time and jumping power can be estimated. Assuming that acceleration is constant during acceleration time and that the approximate acceleration distance (2.7 cm)[31] to discharge the kinetic energy, as estimated from the CAD model in Fig. 9a, we obtain a time duration of 11 ms for energy release, corresponding to a jumping power of 7.4 W.

(a) Assembly by CAD

The three-dimensional CAD model of the prototype of jumping mechanism (Fig. 9a) consists of a motor, a three-stage gearbox, a cam, two coiled springs as the elastic components for energy storage, two main legs on both sides (femurs and tibias), a lever with an L-shape used to transmit the torque of the cam to the pulling force of the wire, and two body supporting frames on both sides. On the body supporting frames, some holes are positioned for spring settings. Thus, the initial spring length or tension can be easily adjusted, i.e., the elastic energy stored in the springs can be adjusted. Fig. 9b details the components used and the connections between them. The cam is in contact with a bearing installed at the lever end. With rotation of the cam, the lever rotates in the opposite direction. The wire is pulled down to flex the tibia while the spring is pulled to store energy. When the cam reaches its critical point, the springs have maximum tension and store maximum elastic energy. If the cams rotate continuously over the critical point, the elastic energy stored in the spring is suddenly released and converted into the reaction forces of the ground acting on the tarsus. These forces are converted into kinetic energy by quickly accelerating the jumping mechanism until it leaves the ground at a certain takeoff velocity and angle. Fig. 10a shows the tibia position at its fully flexed position when the cam reaches the critical point, and Fig. 10b describes a fully extended position when the cam is just passed the critical point just before takeoff. The change in femur-tibia joint angle from the fully flexed to fully extended was designed to be 120˚, which is quite similar to that of a real locust[31].

(b) Mechanism details

Fig. 9 Three-dimensional model and details of parts and connections.

3.2.2 CAD design Since there is no lightweight actuator of a few grams capable of generating a high power of 7.4 W, as calculated in the previous section, we designed a mechanism that can use a small and low-power motor to slowly charge the elastic components in the system and store the elastic energy up to the maximum value. Then, this energy can be suddenly discharged by a clicking mechanism.

CG

Tibia

Femur-tibia joint Femur 120˚ CG

(a) Fully flexed position

(b) Fully extended position just before takeoff

Fig. 10 Tibia-femur angle or knee joint angle of the jumping mechanism.


3.2.3 Prototype fabrication and assembly We used a 1 mm-thick glass epoxy panel to fabricate the cam, legs, and supporting frames of the jumping mechanism. All the fabricated parts are illustrated in Fig. 11. The glass epoxy panel was used because it has excellent machinability, including high strength, stiffness, durable ability, and high melting temperature; thus, it can be easily cut by a milling machine. For fabrication of the small parts, we used a precision milling machine (M300S CE, 0.001 mm resolution, Woosung E&I Co. Ltd, Korea). First, we drew all the links and supporting frames in AutoCAD software, then, the coordinate data was transferred to the milling machine for cutting. The gears, bought from Didel company, are made of polyoxymethylene (POM) for its low weight and low surface friction coefficient. In order to slowly charge the two coiled springs, we used a small pager motor (1.27 g, 6 mm DC from Didel company) to actuate a cam through a gear system which has one 0.3 mm gear with 60 teeth and two 0.3 mm gears with 81 teeth. The total gear ratio was 1 to 228. Fig. 12 shows a fully assembled prototype of the jumping mechanism that weighs about 7 g ex-

277

cluding the battery and control system. We used double-face tape to cover one end of the tibia that, owing to its sticky nature, works like a tarsus to prevent slipping on the slippery surface. Fig. 13 shows the jumping mechanism at the fully flexed and extended positions. The steel wire ring attached at the front plays the role of an absorber that stores the impact energy when the mechanism crashes to the ground after jumping. The materials and weights of components of the jumping prototype are summarized in Table 1.

Fig. 13 Prototype jumping mechanism at fully extended (top) and fully flexed (bottom) positions. Table 1 Materials and weights of the prototype components

Fig. 11 Components for assembly of the jumping mechanism: lever, body frames, cam, legs, motor, gears, and springs.

Components

Material

Weight (g)

Body frame

Glass epoxy panel

1.27

Cam

Glass epoxy panel

0.50

Lever

Glass epoxy panel

0.44

Legs

Glass epoxy panel

0.51

Gears

POM

0.96

2 coil springs

Steel

0.63

Shafts

Steel

1.30

Front leg

Steel wire

0.13

Motor

-

1.27

Total weight

CG

Length = 50 mm

Fig. 12 Fully assembled prototype jumping mechanism.

7.01

4 Experiment and results 4.1 Experiment In order to analyze the performance of the jumping prototype, we captured the jumping sequence by using a high-speed camera (Photron Fastcam Ultima APX, Japan) that was placed perpendicular to the jumping plane,

278


Vertical axis

as shown in Fig. 14. The camera was operated at a recording speed of 1000 frames per second to capture the jump from the beginning to the end. The recorded images were then analyzed for jumping performance in terms of jumping height, jumping distance, and acceleration time. The jumping performance tests were conducted for four cases of spring tension, and repeated three times for each case. To clearly provide an entire picture of the jumping sequence from takeoff to landing for each case of spring tension, we overlaid multiple snapshots to construct a jumping sequence picture. The time interval between two snapshots was 30 frames, equivalent to 30 ms. The takeoff angle of about 60˚, which is similar to the takeoff angle of the real locust observed in the previous section, was set for all cases of jumping tests.

Fig. 15 shows the calculated takeoff velocity and jumping power for different elastic energies stored in the springs. The calculations were based on the assumption that the elastic energy stored in a spring is completely converted into kinetic energy at takeoff of the jumping mechanism. It is obvious that the takeoff velocity and jumping power increase when the elastic energy stored in the springs increases. Fig. 16 shows a comparison between the calculated jumping height and measured jumping height. Overall, the two results are quite similar to each other. For a small amount of elastic energy stored in the springs or low spring tension, the two results of the calculated jumping height and measured jumping height are in better agreement. The small discrepancy is due to a slightly larger takeoff angle than was the case for the 60˚ measured previously, with an angle of about 62˚ measured from the captured images. The discrepancy at high elastic energy stored in the springs or large spring tension may be due to plastic deformation of the spring at high tension, which slightly degrades the spring stiffness, resulting in the actual elastic energy stored in the springs being slightly smaller than the calculated value. 12

6

10

5

8

4

6

3

4

2

Fig. 14 Diagram of experimental set-up.

Jumping power Takeoff velocity

2 0 30

40 50 60 70 Elastic energy stored in springs (mJ)

1 0 80

Fig. 15 Takeoff velocity and jumping power with respect to elastic energy stored in springs. 0.9 0.8 Jumping height (m)

4.2 Jumping performance In order to specify the performance of the prototype of jumping mechanism, we adjusted the front leg that is made of steel wire ring to obtain a takeoff angle of about 60˚, as measured from the captured images. The maximum jumping height, measured from the recorded images, was about 71 cm, i.e., the prototype is able to jump over obstacles of more than 14 times its own body size. Since the designed jumping height was 75 cm, the measured height is about 5% less than that. The time duration for a complete jump was 0.74 s, and the jumping distance was about 100 cm (20 times its own body size). The measured initial takeoff velocity was 4.7 m·s−1, which is in good agreement with the required takeoff velocity of 4.8 m·s−1 in the previous section of the design phase. The acceleration time of about 12 ms is comparable with the predicted value of 11 ms.

0.7 0.6 0.5 0.4 0.3 0.2

Calculated jumping height Measured jumping height

0.1 0.0 30

35

40 45 50 55 60 65 70 Elastic energy stored in springs (mJ)

75

80

Fig. 16 Comparison between calculated jumping height and measured jumping height.


of jumping mechanism could not maintain stability after takeoff as the locust can; it stumbled, rotated in the air, and landed arbitrarily on the ground. This problem arose because the resultant reaction force from the ground acting on the jumping mechanism does not go through the center of gravity of the jumping mechanism. Thus, for future work we will focus on this problem to improve the jumping stability. 160 140 120 100 80 60 40 20 0

Jumping height (cm) Jumping height per mass (cm·g−1) Jumping height per size

30 25 20 15 10 5 0

Re sc u Ju e r o m pi bot ng ( ro 200 bo 0 g t( 13 ) [22] 00 Jo llb g) [2 ot 3] (4 6 5 Sc g) [2 ou M 1] in i-W t (20 0 he g) [3 gs 3] (1 90 G g) [2 0] 7g rillo (8 ju m g) [1 pi 9] ng O r ur ob ot [2 pr 4] ot ot yp e( 7g )

Fig. 17 shows the comparison in performance between our prototype jumping mechanism and other existing jumping robots taken from Refs. [19–24,32] in terms of jumping height, jumping height per mass, and jumping height per size. It can be seen that our prototype jumping mechanism is in good agreement with the others. In terms of jumping height per mass and jumping height per size, our prototype jumping mechanism outperforms the others save the 7 g jumping robot described in Ref. [24]. Fig. 18 describes the jumping performance and jumping sequence of the prototype of jumping mechanism for four cases of elastic energy stored in the springs: 31.69 mJ (Fig. 18a), 44.76 mJ (Fig. 18b), 60.08 mJ (Fig. 18c), and 77.64 mJ (Fig. 18d). The measured jumping heights were 45 cm, 52 cm, 59 cm, and 71 cm, respectively. The takeoff angle for all case was set to about 60˚. Compared to the jumping of the real locust, as observed in the previous section, our jumping prototype can jump over obstacles that are 9 to 14 times its own body size, and jump higher than the locust. However, our prototype

279

Fig. 17 Performance comparison between our prototype jumping mechanism and other robots.

Fig. 18 Jumping performance of the prototype mechanism at various elastic energy stored in the springs.

280


5 Conclusions

Fife A J, Beer R D, Yu X, Garverick S L, Laksanacharoen S,

We presented the design and performance tests of a 7 g prototype of jumping mechanism that mimics a locust or grasshopper. We successfully mimicked the locust or grasshopper leg structure by using springs and wire as the driving muscles for the artificial legs. As with the pause-and-leap jumping mechanism in many small insects, our prototype of jumping mechanism slowly charges the elastic components and then suddenly releases all the stored energy for a quick jump. The fabricated prototype of jumping mechanism could jump over obstacles of about 14 times and a jumping distance of about 20 times its own size, respectively, at the takeoff angle of about 60˚. In comparison with existing jumping robots, in terms of jumping height per weight and jumping height per size, our jumping mechanism outperforms most of them. For future work, we will focus on the jumping stability after takeoff, optimal design for further weight reduction, and integration with a wing folding/unfolding mechanism for a longer jumping distance and safe landing.

ing an autonomous hybrid microrobot propelled by legs and

Acknowledgments This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, the Science and Technology (grant number: 2011-0020438) and partly supported by the 2011 KU Brain Pool Program of Konkuk University, Korea.

References [1]

Quinn R D, Nelson G M, Bachmann R J, Kingsley D A, Offi J, Ritzmann R E. Insect designs for improved robot mobility. Proceedings of 4th International Conference on Climbing and Walking Robots, Karlsruhe, Germany, 2001, 69–76.

[7]

Ward C C, Iagnemma K. A dynamic-model-based wheel slip detector for mobile robots on outdoor terrain. IEEE Transactions on Robotics, 2008, 24, 821–831.

[8]

Hirose S, Yamada H. Snake-like robots: Machine design of biologically inspired robots. IEEE Magazine, 2009, 16, 88–98.

[9]

Heitler W J. The locust jump: Specialisations of the metathoracic femoral-tibial joint. Journal of Comparative Physiology, 1974, 89, 93–104.

[10] Bennet-Clark H C. The energetics of the jump of the locust Schistocerca gregaria. Journal of Experimental Biology, 1975, 63, 53–83. [11] Bennet-Clark H C, Lucey E C. The jump of the flea: A study of the energetics and a model of the mechanism. Journal of Experimental Biology, 1967, 47, 59–76. [12] Burrows M, Morris O. Jumping and kicking in bush crickets. Journal of Experimental Biology, 2003, 206, l035–1049. [13] Burrows M, Harald W. Jumping and kicking in the false stick insect Prosarthria teretrirostris: Kinematics and motor control. Journal of Experimental Biology, 2002, 205, 1519–1530. [14] Heitler W J. How grasshoppers jump, [2012-5-16], http://www.st-andrews.ac.uk/~wjh/jumping/index.html [15] Burrows M. Jumping strategies and performance in shore perimental Biology, 2009, 212, 106–115. [16] Burrows M, Hartung V, Hoch H. Jumping behaviour in a Gondwanan relict insect (Hemiptera: Coleorrhyncha: Pelo-

Wood R J. The first takeoff of a biologically inspired at-scale

ridiidae). Journal of Experimental Biology, 2007, 210,

robotic insect. IEEE Transactions on Robotics, 2008, 24,

3311–3318. [17] Nelson, G M, Quinn R D, Bachmann R J, Flannigan W C,

Ozcan O, Wang H, Taylor J D, Sitti M. Surface tension

Ritzmann R E, Watson J T. Design and simulation of a

driven water strider robot using circular footpads. Proceed-

cockroach-like hexapod robot. Proceedings of IEEE Inter-

ings of IEEE International Conference on Robotics and

national Conference on Robotics and Automation, Albu-

Automation, Anchorage, AK, USA, 2010, 3799–3804.

[5]

[6]

bugs (Hemiptera, Heteroptera, Saldidae). Journal of Ex-

341–347.

[4]

Magazine, 2002, 9, 20–30.

of a beetle’s free flight and a flapping-wing system that 77–86.

[3]

supported by legs and wheels. IEEE Robotics & Automation

Nguyen Q V, Park H C, Goo N S, Byun D Y. Characteristics mimics beetle flight. Journal of Bionic Engineering, 2010, 7,

[2]

Pollack A J, Ritzmann R E. Cricket-based robots: Introduc-

querque, NM, USA, 1997, 2, 1106–1111.

Zhang W, Guo S, Asaka K. Development of underwater

[18] Scarfogliero U, Stefanini C, Dario P. A bioinspired concept

microrobot with biomimetic locomotion. Journal of Applied

for high efficiency locomotion in micro robots: The jumping

Bionics and Biomechanics, 2006, 3, 245–252.

robot grillo. Proceedings of IEEE International Conference

Birch M C, Quinn R D, Hahm G, Phillips S M, Drennan B T,

on Robotics and Automation, Orlando, FL, UAS, 2006,


281

national Conference on Robotics and Automation, Pasadena,

4037–4042. [19] Scarfogliero U, Stefanini C, Dario P. Design and develop-

CA, USA, 2008, 373–378.

ment of the long-jumping “grillo” mini robot. Proceedings

[25] Roberts T J, Marsh R L. Probing the limits to mus-

of IEEE International Conference on Robotics and Auto-

cle-powered accelerations: lessons from jumping. Journal of

mation, Roma, Italia, 2007, 467–472.

Experimental Biology, 2003, 206, 2567–2580.

[20] Lambrecht B G A, Horchler A D, Quinn R D. A small, insect

[26] Brackenbury J, Hunt H. Jumping in springtails: Mechanism

inspired robot that runs and jumps. Proceedings of IEEE

and dynamics. Journal of Zoology, 1993, 229, 217–236.

International Conference on Robotics and Automation,

[27] Gronenberg W. Fast actions in small animals: Springs and click mechanisms. Journal of Comparative Physiology A:

Barcelona, Spain, 2005, 1240–1245. [21] Armour R. Paskins K, Bowyer A, Vincent J, Megill W. Jumping robots: A biomimetic solution to locomotion across rough terrain. Journal of Bioinspiration and Biomimetics,

Sensory, Neural, and Behavioral Physiology, 1996, 178, 727–734. [28] Heitler W J. The locust jump III. Structural specializations of the metathoracic tibiae. Journal of Experimental Biology,

2007, 2, S65–S82. [22] Tsukagoshi H, Sasaki M, Kitagawa A, Tanaka T. Design of a higher jumping rescue robot with the optimized pneumatic

1977, 67, 29–36. [29] Leonardo Da Vinci. Hammer Driven by Eccentric Cam,

drive. Proceedings of IEEE International Conference on

[2012-5-16],

Robotics

2005,

http://brunelleschi.imss.fi.it/genscheda.asp?appl=LIR&xsl=

[23] Burdick J, Fiorini P. Minimalist jumping robot for celestial

[30] Shampine L F, Gladwell I, Thompson S. Solving ODEs with

and

Automation,

Barcelona,

Spain,

1276–1283. exploration. The International Journal of Robotics Research, 2003, 22, 653–674. [24] Kovac M, Fuchs M, Guignard A, Zufferey J C, Floreano D. A miniature 7 g jumping robot. Proceedings of IEEE Inter-

paginamanoscritto&lingua=ENG&chiave=100914 Matlab. Cambridge University Press, Cambridge, UK, 2003. [31] Scott J. The locust jump: An integrated laboratory investigation. Advances in Physiology Education, 2005, 29, 21–26.