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Development of Improved Morphable Beam Device with Rotation Based Shaper Shintaro Mizumuna*, Nobuhiko Kisa**, Saburo Matunaga***

*Department of Mechano-Aerospace Engineering, Tokyo Institute of Technology, Japan e-mail: mizunuma@lss.mes.titech.ac.jp

** Department of Mechano-Aerospace Engineering, Tokyo Institute of Technology, Japan e-mail: nkisa@lss.mes.titech.ac.jp

*** Department of Mechano-Aerospace Engineering, Tokyo Institute of Technology, Japan e-mail: Matunaga.Saburo@mes.titech.ac.jp

Abstract

In this paper a new beam shaping mechanism is proposed for the Morphable Beam Device (MBD) which is being developed in the LSS. The previous MBD design had several problems relating to its structure. These problems are described below. 1. The shaper control was complex due to the transfer phenomenon. 2. The deployer abrades the beam rapidly. 3. The control system of the MBD is very large and cannot be attached to attach to the MBD.

In order to solve these problems a new rotation based shaper mechanism is suggested.

Testing of the rotation based shaper was carried out with the improved MBD which attaches to the rotation based shaper. The relationship between control input and curvature of the beam was measured.

The result shows that the rotation based shaper is superior to the previous shaper in size, weight and control efficiency but is inferior in terms of accuracy of beam. Curvature.

1 Introduction

When a body or solar panel of a space craft is damaged by collision with debris, it is difficult to identify the cause or problem using only internal information of a satellite such as current or voltage measurements. A large space structure such as the International Space Station (ISS) can make visual checks using the robot arm or extra vehicle activity by astronauts but many space structures in orbit cannot make such checks because such systems necessitate large mass and have high costs. Therefore, a visual check system that incurs low costs and small mass is desired. A visual check system which can be attached to a small satellite has been proposed in the LSS. This system is called the Morphable Beam Device (MBD).

The MBD concept is shown in Figure 1 and 2. The MBD consists of a flexible beam which can keep its shape but can be bent easily, storage for the beam, a deployer which pushes or pulls the beam, a shaper which

controls the beam shape via bending and a camera attached to the beam end. One application is checking the external condition of a satellite by deploying the beam and controlling the beam shape. The MBD is suitable as a visual check system of satellites due to its light weight and small size and has many degrees of freedom when compared with conventional robot arms for on-orbital servicing.

The Experimental model of the MBD has been developed and a new model equipped with the new beam shaping mechanism is recently under development.

In this paper the new model is compared with the previous model in terms of its volume, mass, and controlling accuracy. A discussion about which is better for practical use is then made.

Figure 1: MBD attached to a satellite

Figure 2: MBD concept

i-SAIRAS 2010August 29-September 1, 2010, Sapporo, Japan

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2 Previous model of MBD

2.1 The principle of shaping A side view of the shaper is shown in Fig.3. The shaper

consists of an upper and lower plate. The upper stage moves on the ball screw fixed to lower plate. The deformation volume of the beam is decided by the position relation between the hole of the upper stage which has rollers and the hole of lower stage which is the entry point of the shaper. As shown in Fig.9, by extending from extender to shaper and touching the roller, curvature is induced on the beam. The curvature of the beam is 0 when the hole of the upper stage is in the center, and the curvature of the beam increases as the displacement of the upper stage increases. This is the basic principle of beam shaping of the MBD. However, the relationship between displacement of the upper stage and the curvature of beam in not linear meaning that it is difficult to control the beam.

The appearance of the previous MBD model of is shown in Fig.4.

Figure 3: Shaper concept of previous model

Figure 4: appearance of the previous MBD

model 2.2 Transfer phenomenon The transfer phenomenon which is confirmed with

the test model was also confirmed with the prototype model. The transfer phenomenon means that the beam bends in the opposite direction to that intended. Normally,

the beam bends in the same direction as the displacement of upper stage. The curvature of beam increases as the displacement of upper stage increases. When the upper stage reaches a certain point, the beam starts to bend in the opposite direction as shown in Fig.5. This phenomenon is termed the “transfer phenomenon” and is an important issue with regards to the beam shaping.

Figure 5: Appearance of beam shaping before and after the transfer phenomenon.

2.3 The structure of the deployer

The extender draws the beam from storage to the shaper and consists of two gears. These two gears bite the beam as shown in Fig.6. To fit the tooth to the gear chase the deployer must get enough friction to extend the beam. The deployer is driven by a stepping-motor. When the deployer stores the beam the motor is reversed.

Fig.6 The structure of the deployer 2.4 Problems of the previous MBD model

The linear motion structure demonstrates a transfer phenomenon. This makes control difficult and necessitates a transfer mechanism from rotation motion of the motor to linear motion making the structure large and heavy.

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3 New model of MBD

3.1 The principle of shaping A rotational structure which rotates the roller of the

upper stage of the shaper for beam shaping is proposed. Fig.7 shows this structure which has two rollers on the upper stage of the shaper. The beam is extended and bent when the state rollers are tilted. The transfer phenomenon does not occur in the case of this structure. This structure can use rotational motion of the motor directly which minimizes the structural size.

The appearance of the new MBD model is shown in Fig.8.

Fig.7 The deployer

Figure 8:appearance of the previous MBD

model 3.2 The modification of the deployer

The modification in the structure of the deployer of the new MBD is to adopt rollers instead of gears. However, the structure of the deployer of new MBD is otherwise same as that of the previous MBD shown in Fig.6.

To investigate the effect of rollers on the new MBD, two types of rollers are tested with a dedicated fixture as shown in Fig.9. The candidates of rollers which were selected are a V-pulley and urethane-roller as shown in Fig.10. The test result should be evaluated based on following points.

1. The rollers must produce enough frictional force. 2.The roller itself must have good resistance to

abrasion. 3. The rollers should cause less abrasion of the beam

than the gears. Firstly, the V-Pulley was tested in a deployment

experiment. The reason why the V-Pulley is selected is that it has more contact points than the normal pulley. This means that the V-pulley has a high potential to produce bigger frictional forces compared to the normal pulley. An additional effect of the V-pulley is that it can restrain the extension of beam to the desired plane.

The frictional force is relatively low because V-pulleys have no gear teeth. On the other hand the risk of abrasion of the beam is lowered.

By checking after the experiment, the slippage between the V-pulley and beam was not observed. It can then be said that the produced frictional force is high.

Secondly the Urethane-roller was tested. Because Urethane is soft it can fit the outer shape of beam. For this reason it can be said that the Urethane roller has the potential to produce big frictional forces compared to the V-Pulley. Of concern is that Urethane can be the source of outgassing when it is used in space.

After the experiment it is known that the produced frictional force is bigger than that of V-Pulley. However, one problem occurred .The beam slipped out from between the rollers and further deployment became impossible. For this reason, the adoption of the Urethane-roller as a roller for the new MBD an additional mechanism is needed.

The discussion above is summarized in Table.1. As reference the evaluation of gears in the previous model is also in the table.

Finally the V-Pulley is selected for the new MBD because it is easy and an effective enough choice for developing a new MBD.

Fig.9 Dedicated fixture for roller test

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Fig.10 Candidates of roller

Table.1 Comparison among roller candidates

4 Comparison of the two MBD models

4.1 Size and mass A comparison of the appearance of the previous and

new shapers is shown in Fig.11. It is clear that the new model is compact compared to the previous model.

The new shaper is also superior in terms of mass. With reference to Table.2 it can be seen that the mass of the new model is less than half that of the previous shaper. A detailed comparison of size of the two shaper types is also shown in Table.2.

Figure.11: Appearance of previous model and new

model of MBD

Table.2 Comparison of two types of models in terms of mass and volume

Previous model New model Size 160×150×63[mm] 80×120×50[mm] Mass 773[g] 300[g] 4.2 Control accuracy

In this section control accuracy of the two shapers types is discussed. The accuracy of the expected beam

curvature is compared to one another on assumption that control input has same accuracy.

The relation between the expected curvature of the deployed beam and the control input is calculated based on a geometric analysis. The expected curvature of the beam deployed by the previous model is shown in Fig.12 and that of new model is shown in Fig.13. The transfer phenomenon appears in Fig.12 and the line style is changed in the vicinity of transfer phenomenon. There are three different lines in Fig.13 and each represent curvature variation by three options of distance between two bending rollers. It can be said from this figure that the greater distance between the two bending rollers, the less the curvature. Note that control input of the previous model is displacement of the upper plate of the shaper relative to the lower plate. On the other hand the control input of the new model is a rotational angle of the two rollers of the shaper. The detailed information about how to derive these relations can be found in reference [4].

To make it easy to compare Fig.12 and Fig.13 the y-axis of Fig.12 is converted from curvature to curvature radius and then Fig.14 can be derived by combining these two figures. Note that the distance between the two bending rollers of new model fits to that of the previous model when Fig.14 was derived.

From Fig.14, it can be said that the inclination of the tangent line of the previous model’s curve varies not as much as that of the new model, except in the vicinity of the transfer phenomenon. This result implies that the sensitivity of curvature variation is too high to a global control input. For this reason it can be said that the previous model is more controllable than the new model in terms of precise control at any curvature radius.

Fig.12 Expected curvature of the beam deployed by

the previous model

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Fig.13 Expected curvature of the beam deployed by

the new model

Fig.14 Expected curvature of the beam deployed by

the new and previous model

5 Control scheme for new MBD models

From the discussion above the features of the new model are summarized as follows.

1. There is a rapid variation in curvature radius below certain critical angles. 2. Above these critical angles the output curvature is roughly constant. This is called the flat area. 3. The deployed beam is straight if the input angle is 0. The traditional control scheme of the MBD is shown in Fig.15. Based on this scheme the deployed beam consists of one curved part. To access the whole area around the MBD a variety of curvatures are needed. It can be said that this scheme is not suited for the new model because the variation of curvature radius of the new model is sensitive to a global control input.

To compensate for this weak point of the new model an alternative scheme is proposed. 5.1 Basic scheme The concept of this basic scheme is shown in Fig.16. The features of the basic scheme are summarized as follows.

1. The control input is selected from 0 and at a representative point along the flat area. 2. The deployed beam consists of a straight and curved part. The curvature of all of the curved part is the same (=R). 3. The control accuracy of the deployed beam is high because the control input is selected from flat area.

It is possible to move the beam end to any point around the MBD because there are enough degrees of freedom in this scheme, namely the direction of the curved part and the length of the straight part. However, there is an exception. It is impossible to move the beam end to the area within R as shown in Fig.16. This is caused by the restriction of this scheme, whereby curvature of the curved part has to be the same.

Fig.15 Traditional scheme

Fig.16 Concept of basic scheme

New MBD

Previous MBD

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Fig.17 Non-accession area

5.2 Combinatorial scheme Based on the basic scheme there are no enough degrees

of freedom to designate the direction of the beam end. This can possibly restrict of its operation.

To resolve this restriction the combinatorial scheme is proposed. This scheme is simple because it is based on the basic scheme. The degrees of freedom are increased along with the number of curved parts. Enough degrees of freedom can be easily obtained. For example, the direction of the beam end can be designated if there are more than two curved parts.

Fig.18 Combinatorial scheme

6 Conclusion

The new and the previous MBD model are compared with respect to their size (mass), controllability and control accuracy. The evaluation of the two types of MBD based on these points is shown in Table.3. Each has strong and weak points. Hence, it is difficult to say which is more suitable for MBD.

To compensate for the weak point of new model an alternative and simple control method is proposed. Whether this method can be adopted or not depends on requirements of time to complete the deployment. This is because an inertial force to the beam becomes bigger if

alternative scheme is adopted. In the certain cases of practical MBD use in orbit, time for deployment is not so important. It can be said that the new model is better than the previous model in these cases.

Table.3 Evaluation of two MBD models

References [1]S. Matunaga, S. Sugita and T. Iljic, "Morphable Beam: Concept and Initial Hardware for Spacecraft Inspection," 2006 ISAS 16th Workshop on Astrodynamics and Flight Mechanics, Sagamihara, August 1-2, C-2, 2006. [2]Yohei Tanaka, “Study of Shape Control for Morphable Beam Device,” Master Thesis, Department of Mechanical and Aerospace Engineering, Tokyo Institute of Technology, 2008. [3] Saburo Matunaga, Thomas Iljic, Yohei Tanaka, Yoshiyuki Miura “Morphable Beam Device and Beam Shape Generation Algorithm” 2008-d-06 [4] Saburo Matunaga, Shintaro Mizunuma, Nobuhiro Kisa “Improved Morphable Beam Device for Equipping Camera at Beam End” ISTS 2009-c-28