NOVEL HOPPING MECHANISM USING PERMANENT MAGNETS FOR TINY ASTEROID EXPLORATION ROVER

Masamitsu Kurisu

Tokyo Denki University, 5, Senju-Asahi-Cho, Adachi, Tokyo, 120-8551, Japan Email:kurisu@cck.dendai.ac.jp

ABSTRACT

This paper presents the novel hopping mechanism using permanent magnets for tiny asteroid exploration rovers. The main part of the mechanism consists of one movable magnet and two stationary magnets. The mechanism uses for hopping the impact force generated when the movable magnet sticks to the stationary magnet. The features of the mechanism are that the large impact force can be generated in spite of low power consumption, and that it can be easily miniaturized and modularized. The prototype module weighs only 10g with dimension 21.5 mm in width, 28 mm in height, and 8.5 mm in depth, except for the drive circuit and power source. Preliminary experiment under 1 G environment shows the availability of the proposed mechanism. 1. INTRODUCTION

In recent years, exploration activities on asteroids attract a great deal of attention. Since an exploration rover, which is dissociated from a spacecraft and investigates on the surface of an asteroid, has restriction in size and weight, it is difficult to provide many rovers for one exploration project. For this reason, a small number of rovers with high functionalities can be thrown in an asteroid. Therefore, it is thought that the investigation range is also restricted. On the other hand, it is considered for one investigation method that many tiny rovers with simple functionality distributed on the surface collect data from wide range. In order to realize this method, development of tiny rovers with a locomotive function is required. The conventional mechanism with wheels or crawlers does not become the effective mobility, since almost no friction will act on the surface of asteroid because of low gravity. On the contrary, some hopping mechanisms to replace with conventional locomotion means have been proposed [1]-[4]. The multiple legs are not suitable to the tiny rover because of their complicated mechanism. The mechanism using torquers, which can make the rover hop in the arbitrary directions by rotating two inertial wheels, was mounted on the asteroid surface exploration rover MINEREVA [3]. Shimoda, et al. proposed the hopping method using a spring [4]. However, since the hopping mechanism using torquers requires large initial driving current in order to rotate the wheels, the mechanism is not suitable for tiny rovers which have severe restriction in available

current generated by solar cells. On the other hand, the hopping method using a spring is advantageous to tiny rover, because large force can be generated in spite of low power consumption if the conserved spring energy is released in a moment after the spring is compressed with long time by small current. However, the residual vibration of the spring may disturb the motion of rover. In this paper, the novel hopping mechanism using permanent magnets for tiny rovers is proposed. The proposed mechanism has one movable magnet and two stationary magnets, and uses for hopping the impact force generated when the movable magnet sticks to the stationary magnet. The features of the mechanism are that the large impact force can be generated in spite of low-power consumption, and that no residual vibration is generated. Also it can be easily miniaturized and modularized. The availability of the proposed mechanism is verified by a preliminary experiment under 1 G environment. The rest of this paper is organized as follows. In the next section, the basic principle of proposed mechanism is explained. The section 3 describes the structure of mechanism and details of process for hopping. Some constraints about design parameters of the mechanism for hopping will be discussed. The prototype module developed for experimental verification will be also described. In the section 4, a result of preliminary experiment shows the availability of proposed mechanism. In the section 5, conclusions and future work are addressed. 2. BASIC PRINCIPLE

Proposed hopping mechanism has three permanent magnets, and utilizes attraction force among the magnets. Fig. 1 shows the basic principles of the mechanism. The main part of one consists of two magnets fixed to the body (stationary magnets), and one magnet (movable magnet) which can be moved between the fixed magnets. Note that the magnets are arranged on a straight line so that the opposed magnets may be pulled each other. The attraction force which acts on the movable magnet from the stationary magnet of one side is equal to the force from the other when the movable magnet is located on the middle point between the stationary magnets. However, if the position of the movable magnet shifts from the middle point, the attraction forces will become out of balance. Then the movable magnet is drawn to the stationary magnet of the nearer

side. The more the moving magnet nears the stationary magnet of one side, the stronger the attraction force becomes. On the contrary, the attraction from the stationary magnet of the opposite side becomes weak. Accordingly, the movable magnet sticks to the stationary magnet of the near side in an instant. The proposed mechanism uses for hopping the impact force generated when the movable magnet sticks to the stationary magnet.

Figure 1. Basic concept

3. CONSTRUCTION OF THE MECHANISM

3.1. Structure

As shown in Fig. 2, the proposed mechanism consists of

three permanent magnets mentioned in the previous section, one DC motor with reduction gear, one pinion gear, one spur gears, one screw, one linear slide block, one slide bracket, and one housing in which they are installed. The slide bracket has a rectangle aperture, and the slide block has a rectangle jut, which is designed to go into the aperture. Fig. 3 shows the close-up view of the slide bracket. Since the aperture is designed to be longer than the jut, the bracket is slidable to the block. The distance between the upper side and lower side of bracket is designed to be longer than the length of movable magnet. Therefore, the magnet is also movable between the both sides. The DC motor rotates the screw, which is fixed to the spur gear, through the reduction gear, pinion gear and spur gear. The linear slide block is moved upward or downward according to rotation of the screw. The jut of slide block moves the bracket. Then, the bracket moves the magnet. 3.2. Hopping Process

Hopping process of the mechanism is divided into the following five states (as shown in Fig. 4).

[1st state] This is the initial state of hopping process. The movable magnet is sticking to the stationary magnet of lower side (see Fig. 4(a)).

[2nd state] In this state, the movable magnet is detached from the stationary magnet by upward movement of the bracket (see Fig. 4(b)).

[3rd state] After the movable magnet crosses the intermediate point between the stationary magnets, the attraction force from stationary magnet of upper side becomes stronger than the ones of lower side. In this state, the movable magnet leaves the upper side of bracket and is moving in the inside of the bracket (see Fig. 4(c)).

[4th state] The movable magnet and bracket moves together after the magnet arrives at the upper restraining surface of the bracket (see Fig. 4(d)) .

[5th state] This is the final state of hopping process. The whole mechanism is in motion after the movable magnet sticks to the upper stationary magnet with the bracket (see Fig. 4(e)).

Impact

Attraction forceCenter line

Stationary permanent magnets

Movable permanent magnet

N N S S

Figure 3. Close-up view of the slide bracket

Linear slide block Movable magnet

Slide bracket

Upper side

Lower side

Rectangle aperture

Rectangle jut

Linear slide block

Movable permanent magnet

Stationary permanent magnet

Planetary reduction gear head

Pinion gear

Spur gear

DC motor

Stationary permanent magnet

Screw

Slide bracket

Rectangle aperture

Figure 2. Structure of the proposed mechanism

Note that the final state is equivalent to the initial state if the mechanism is turned upside down. That is, the proposed mechanism has the symmetrical structure for the hopping process. 3.3. Design Parameters

In the aforementioned states, there are some geometric conditions which should be satisfied to the movable range of slide bracket and the distance between stationary magnets. In order to generate the impulse force by adsorption of the movable magnet, after taking the conditions into consideration, it is necessary to decide design parameters such as the length of movable magnet, the distance between the both sides of slide bracket, and so on. As shown in Fig. 5, as the design parameters, the distance between stationary magnets, the length of movable magnet, the distance between both sides of bracket, the aperture length of bracket, the thickness of each side, the jut length of slide block are denoted by lS, lM, lw, la, lb, and lh, respectively. Then, the following inequalities Eq. 1 and Eq. 2 are obtained:

whb lll , (1)

aswM llll 2 . (2)

The distance from the side of bracket to the stationary magnet is described by Eq. 3 at the time of the transition to the 3rd state from the 2nd state (see Fig.6):

aMwMs lllll )()(

2

1 . (3)

Slide stroke of the bracket to the block in the 4th state is also described by Eq. 4 (see Fig.7):

bh ll . (4)

In order to generate the impulse force, the distance denoted by Eq. 3 has to be equal to the one denoted by Eq. 4. Consequently, Eq. 5 is derived:

Figure 4. Hopping process

(a) 1st state (b) 2ndt state (c) 3rd state (d) 4th state (e) 5th state

l b l h

l al M l Sl w

Figure 5. Design parameters

l h -

l b

l a

l w -

l Ml M 2

1 2(

ls -

l M )

- (

l w -

l M )

- l a

l S 2

Figure 6. Distance from the side of bracket to the stationary magnet

Figure 7. Slide stroke of the bracket in the 4th state

ahbMsw llllll )(

2

1 . (5)

After all, the geometric condition which the design parameter of the mechanism should satisfy is given by Eqs. 1, 2, and 5. An adequate model of magnetic attraction force, and a decision method of the design parameters in consideration of the mass of movable magnet, the total mass of rover and Eqs. 1, 2, and 5 are required in order to make the impulse force by adsorption of the magnets into the maximum. Optimization of the design parameters will be built in next stage. 3.4. Circuit for Protecting End Point

If the slide block continues moving after adsorption of the magnet, the end position of the block may be broken. A limit circuit is required to protect the end position for overrunning. Fig. 8 shows the example of a circuit for stopping the slide block at the time when the adsorption of the movable magnet occurred. In the example, it is assumed that the slide bracket is made of aluminium, and all magnets conduct electricity. The DC motor is also assumed to be driven by the motor driver IC with PWM signal. The bracket is connected to GND (low voltage). While the bracket is not in contact with the stationary magnet, the logic circuit device with conjunction passes the PWM signal supplied to one input terminal from the CPU, because that the voltage of another terminal, which is connected to the power source through the resistor, is kept high level. Therefore, the DC motor is driven by the driver IC, and the slide block is moved. When the bracket touches the stationary magnet by absorption of the movable magnet, the voltage of the terminal connected to the magnet becomes low level. Therefore, the output of the logic device becomes low level. That is, the PWM signal from CPU does not reach the driver IC. The slide block stops as the result.

3.5. Prototype Module

The prototype module is developed based on the consideration described above. Fig. 9 shows the overview of the prototype module. The module is designed with 28 mm in height in consideration of small rover under present plan. The cylindrical neodymium magnet with its dimension 6 6mm and 0.28T magnetism is used as the movable magnet. Therefore, the length of magnet lM is 6mm. Also, the cylindrical neodymium magnets with 72mm and 0.452T are used as the stationary magnets. The DC motor with a planetary reduction gear, which has the mechanical details and specifications as shown in Tab. 1, is selected. Based on these components, the parameters described in previous subsection are decided as lS = 22mm, lw = 10mm, la = 0.6mm, lh = 7.4mm, and lb = 4mm. The reduction ratio from the output shaft of reduction gear to the screw is 3.2. The pitch of the screw is 0.25 mm. The width and depth of the module result in 21.5 mm and 8.5 mm respectively, except for the drive circuit, protection circuit, and power source. The weight is only 10g.

Table 1 Mechanical details and specifications of the motor

Diameter 6 mm Operating voltage 3 V

Length 21.4 mm Current 40m A

Weight 1.2g Speed 200 rpm

Gera ratio 136.02 Maximum torque 120gcm

4. PRELIMINARY EXPERIMENT

A preliminary experiment under 1 G environment using the prototype module was carried out to verify the availability of the proposed mechanism. In this experiment, the DC motor of the module was driven by 3V voltage supplied from an external regulated power supply. Since the protection circuit was not

Figure 9. Over view of the prototype module

28m

m

21.5mm

Depth: 8.5mm

VCC

VCC

AND logic device

GND

PWM signal from CPU

Motor driver IC

Figure 8. Circuit for protecting end point

implemented on the module, turning on and off of the power source was performed manually. Fig. 10 shows the snapshots of the experiment. One can see that the module jumped up at 18.7 second after the voltage was supplied. In this case, the consumed current was 50 mA at the maximum. In consideration of the result under 1 G environment, the proposed mechanism is useful as a hopping one of exploration rover which is supposed to work under low gravity. Since it takes long time to generate the impulse force from the time the mechanism is operated, total amount of power consumption is required to some extent. However, the power consumption in operation is extremely small. Consequently, the proposed mechanism is suitable as a locomotion one of tiny rovers whose production of electricity may be small. 5. CONCLUSIONS

In this paper, the novel hopping mechanism using permanent magnets was proposed as a locomotion mechanism of tiny asteroid exploration rovers. The mechanism uses for hopping the impact force generated when the movable magnet sticks to the stationary magnet. The constraints about design parameters of the mechanism in order to generate the impulse force were discussed. The example circuit for protecting the end point of slide block was also described. The prototype module, which weighs only 10g with dimension 21.5 mm in width, 28 mm in height, and 8.5 mm in depth, except for the drive circuit and power source, has been developed. The availability of the proposed mechanism was verified by the result of preliminary experiment using the prototype module under 1 G environment. The

features of the mechanism are that the large impact force can be generated in spite of low power consumption, and that it can be easily miniaturized and modularized. Although the mechanism can generate the impulse force only in two directions, if the equipment which changes the direction of the mechanism will be added or two or more mechanisms will be combined, it will be possible to generate the impulse force in arbitrary directions. In order to bring out the performance of the mechanism maximally, optimization of the design parameters is needed. This is the next stage of the research. 6. REFERENCES

1. Yoshida, K. (1999). A Robot Design for Locomotion on Micro Gravity Surface. In Proc. 5th Int. Sympo. on Artificial Intelligence, Robotics & Automation in Space, pp.705-707.

2. Burdick, J. & Goodwine, B. (2000). Quasi-Static Legged Locomotors as Nonhoronomic System. In Proc. the 2000 IEEE/RSJ Int. Conf. Intelligent Robots & Systems, pp.867-872.

3. Yoshimitsu, T., Kubota, T., Nakatani, I., Adachi, T. & Saito, H. (2003). Micro-hopping robot for asteroid exploration. Acta Astronautica, Vol.52, Iss.2–6, pp.441–446.

4. Shimoda, S., Kubota, T. & Nakatani, I. (2003). Proposal of New Mobility Using Spring Mechanism in Microgravity Environment. J. of Robotics Society Japan, Vol.21, No.6, pp.663-669 (in Japanese).

Figure 10. Snap shot of the preliminary experiment using the prototype module under 1 G environment

tt == 00..0000 ss

tt == 1188..7799 ss

tt == 1188..6677 ss tt == 1188..7700 ss

tt == 1188..7766 ss tt == 1188..7733 ss