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Kinetic Feedback between Performing User and Performing Machine

Kinetic Feedback between Performing User and Performing Machine

In interactive architecture, kinetic performance and actuators play an important role. The first consideration is how to propel the kinetic structure and subsequently evaluate the movement once it is in motion. The aim of this thesis is to present how specific kinetic behaviours in a performing machine reacting to a performing user can be achieved through the selection of a suitable actuation system. The obtaining of kinetic feedback requires the actuator to control the movement. Therefore, the research included the theory of the nature of kinetics, the classification of actuators as well as related experiments in the design process. We tested three types of actuator: a servomotor, a pneumatic artificial muscle (PAM) and a pouch motor. The servomotor was compared with soft actuators, the PAM and the pouch motor. We then developed three shapes of pouch motor and demonstrated that the hexagonal pouch motor is the most efficient. We also built a geometrical, deployable structure inspired by the reconfigurable structures made at the Harvard John A. Paulson School of Engineering and Applied Science. This deployable structure provided the transformable conditions necessary for applying the actuator. The experiment described in this paper demonstrates the transformation brought about by deploying the actuator. This establishes that different types of actuator can affect the kinetic movement of the structure.

Key words: Actuator, kinetic feedback ,deployable structure


Kinetic structures have been widely used in interactive architecture. Their adaptive nature provide communication between people and space. Usually, the kinetic structure, the actuation system and the sensing system are the important components in interactive architecture. Normally, the actuation system can be divided into three types: pneumatic and hydraulic actuation systems, mechanical actuation systems and electronic actuation systems (Huber et al., 1997).

Pneumatic actuation systems have been applied in kinetic structures. For example in transformable metamaterial which uses the inflatable pocket (pneumatic actuation system) to control the foldable structure. The Transformable Metamaterial research group at Harvard has developed a set of foldable structures inspired by both the Hoberman sphere and by origami (Heather,2016). It uses  pneumatics to make the foldable structure transform into a different mode, demonstrating that a pneumatic actuation system has the potential to move the kinetic structure.In this paper, a performing machine is defined as a kind of mechanism that can interact with performing users. It can transform into different modes applying users´ biometric data that simulate their behaviour. In this case, a pneumatic actuator was used to drive the kinetic structure that had been inspired by the Transformable Metamaterial project. The actuator controls the mechanism and generates motion to achieve the simulationof human behaviour.

tr11 tr22

 transformable metamaterial,fist one is normal mode,second one is transform mode

This leads to the main question in this report: How can specific kinetic behaviours in a performing machine reacting to a performing user be achieved through the selection of a suitable actuation system?

This can be sub-categorised into a number of more specific questions:

1. What kind of kinetic feedback system is best suited to achieve specific movement behaviours?

2. What kind of soft motor is most suitable in the selected actuation system?

3. Why is a soft mo tor ideal for simulating movement behaviours?

4. What kind of deployable structure can be used to complement the actuation system?

Finding an answer to these questions can be attempted as an integral partof the design project ‘Bio-transformer’ which is the perform ing machine.

There are two aims of this report. One is to develop a pneumatic actuator (e.g. a pouch motor) and use it to improve movement in the deploy able structure. The other, is study the kinetic feedback after application of the actuator, such as the motion of the deployable structure.This report focuses on the technical aspects of the project and is divided into five chapters. The first chapter describes the concept of this project and a brief overview is included. The second chapter describes the kinetic system, the typology of the kinetic structure and explains the kinetic feedback loops by giving examples for both the sensory and kinetic feedback components. The third chapter is on the basic theory of actuation systems and explains the input and output of the actuation system in a simple manner. The fourth chapter, which is the main focus of the paper, shows a serious of experiments involving an actuator, a deployable structure and their evaluation. The last section is the conclusion to this thesis and outlines potential future research in this area.

This report focuses on the technical aspect of the project, specifically experiments on the actuator and the deployable structure. Furthermore, the actuator should potentially overcome the limitations of the pouch motor such as the weight which it can withstand.

1.Thesis project overview

Nowadays bio-sensing is everywhere, our biometric data can easily be detected and recorded in many ways with a phone or smart watch. However, what if the biodata could be used to affect the environment? The aim of this thesis project was to

create a responsive surface which humans can interact with through their biometric data. This creates a loop enabling human biometric data and kinetic feedback to affect each other.

It is comprised of two parts: the physical part and the sensing system. The sensing system in this project used a galvanic sensor, a pulse sensor and FaceOSC for facial feature extraction, as the input. FaceOSC tracks facial expression to control a pouch motor at normal speed which activates the transform mode. At the same time, a galvanic sensor detects the subject´s skin moisture levels and a pulse sensor records heart rate. Together they control the speed of inflation and deflation with the pouch motor. As a result, kinetic movement changes with the user’s facial expression and the biodata detected by the galvanic and pulse sensors. A deployable structure and actuator were also needed. We selected a geometrical structure which was inspired by a reconfigurable structure developed at Harvard. The bio-transformer used a pouch motor. The results showed the sensor could detect new biometric data continuously while the kinetic movement were changing. Motion could also be controlled using these data, thus accomplishing a cyclic loop.


2.1 Kinetic systems

Kinetic systems have had a long history, from ancient times right up to the 21st century. Early kinetic systems in architecture were building components that could pivot and slide.

Examples are windows, shutters and doors, which move in these basic pivoting and sliding modes. A drawbridge is also a rudimentary kinetic system in architecture (Youssef, 2017). Zuk W defined “kinetic architecture as a field of architecture in which building components, or whole buildings, have the capability to adapt to change through kinetics into reversible and deformable modes” . At the end of the 20th century, as comfort became more of a general demand among people, flexible, adaptable architecture, began to develop rapidly alongside artificial intelligence.(Megahed, 2016).  Computer systems were developed that can work in a similar manner to people’s brains.  Examples would be robots and remote control systems (Ramzy and Fayed, 2011). In this context, kinetic systems have been used by architects to embed computation intelligence and thus create flexible and adaptable architectural spaces that match the changing requirements of the users (Friedman, 2011; Osório, Paio, & Oliveira, 2014) In this thesis a kinetic structure was applied to simulate human behaviour using an alternate transformation mode.

2.2 Kinetic structure typologies

Fox and Kemp (2009) provide a particularly useful contemporary definition. ‘Kinetic architecture is defined generally as buildings and/or building components with variable mobility, location, and/or geometry.’ (Megahed, 2016) Kinetic performance includes expanding sliding, folding and general shape transformation. The performance of kinetic structures can generally be facilitated by pneumatic, natural or mechanical systems. (Michael A.Fox)

Generally, kinetic structures can be classified into three categories: embedded kinetic structures, deployable kinetic structures and dynamic kinetic structures. Embedded kinetic structures are systems that exist within a larger architectural whole in a fixed location (Fotiadou, 2007). The primary function of embedded kinetic structures is to respond to a changing environment by controlling the larger architectural system (Fotiadou, 2007). Due to the demands of transport, the deployable kinetic structure usually exists in a temporary location.  Such systems possess the inherent capability to be both constructed and deconstructed. Dynamic kinetic structures also exist within a larger architectural whole but can act independently within the larger context (Fotiadou, 2007). Thus they can be subcategorized as mobile, transformable and incremental kinetic systems (Fotiadou, 2007).  This thesis focuses on deployable structures. They can be described as structures that can fold for transportation or storage (Megahed, 2016). The principal conflict is between the definitions of transformable and deployable, which are often used interchangeably (Megahed, 2016). Deployable structures are autonomously capable of major configuration changes (Megahed, 2016).

2.3 Kinetic feedback loops

The integration of an actuation system and a sensing mechanism set up a cyclic, control system. This can also be called the kinetic feedback loop which refers to the kinetic feedback affecting the whole cycle (Figure 2). Fox and Yeh demonstrated a similar system which they named a responsive indirect control system (Fox and Yeh, 2000). The control device makes decisions based on the sensing system which is the input signal (Fox and Yeh, 2000). The transforming of the kinetic structure becomes the output result.


Figure 2: kinetic feedback loop

A good example of the type of input sensing system we explored in our thesis, applying people´s bio-signals to an interactive installation, is ‘Pulse Room‘, conceived by Rafael Lozano-Hemmer in 2006. “Pulse Room”  is an interactive installation which has an interface to detect the participants’ heart rate. When a subject holds the interface, the computer detects their heart rate and immediately sets off the bulbs, to flash at the same rhythm as the participants’ heart rate. This example inspired us to use the pulse sensor to detect people’s heart rate and combine this with the galvanic sensor to detect skin moisture. The reason why we chose two types of sensor was to make the results more accurate.

 pulse room (Rafael Lozano-Hemmer, 2006)


transformable metamaterial, the position of pouch motor (air pocket) of each unit (Harvard John A. Paulson School of Engineering and Applied Science,2016)

The kinetic movement is controlled by an actuation system in a similar way to the transformable metamaterial project mentioned in the introduction. How one unit of this metamaterial structure works, can serve as a good example to explain the whole. The transformable structure was controlled by a soft pouch motor which adds force to the surface of an extruded cube in each unit when the pouch motor inflates the structure.

reference transformable metamaterial, different transformation mode (air pocket) of each unit (Harvard John A. Paulson School of Engineering and Applied Science,2016)

The extruded cube changes shape into a rhombus. What we learn from this example is that we can put the pouch motor on the surface and it can cause the surface of the kinetic structure to transform to a different mode.

2.Actuation systems in a kinetic feedback loop 

2.1 Input-sensor signal to actuation system

The sensor signal is the input to the microprocessor, which transforms the data and provides information output to an external user (Hunter et al., n.d.). Hence, the bio sensing signal can be

used as an input  to the actuation system.  Sensors detect  outside changes and obtain data which is then transformed into data relevant to the system. There are various sensors in the sensing system. In this project, a galvanic skin response (GSR) sensor and a pulse sensor were selected as bio-sensing devices.  A GSR sensor which can measure skin moisture, detected signals from fingers or wrists (Strauss et al., 2005). A pulse sensor detected people’s heart rates. They were both used for detecting the subjects´ level of physiological arousal. The combination of the two sensors controlled the speed of the pouch motor as it inflated the structure.

2.2. Actuation system 

2.2.1 Classification of actuation systems

Actuation systems are the elements of a control system that are responsible for transforming the output of a microprocessor or control system into a controlling action on a machine or device. Actuation systems are defined as “….. the elements of control systems which are responsible for transforming the output of a microprocessor or control system into a controlling action on a machine or device” in Mechatronics: A Multidisciplinary (Bolton, 2008). Commonly , actuation systems can be divided into three types (Huber, Fleck and Ashby, 1997). The first are pneumatic and hydraulic systems. Usually, pneumatic signals applied to

control systems include an electrical system, as the signals can control large valves and actuate other high power control devices. (Huber, Fleck and Ashby, 1997).The second is the mechanical system. Mechanical devices can transmit movement, such as transforming linear motion into rotational motio The third is the electrical system (Huber, Fleck and Ashby, 1997). Electrically actuated systems are very widely used in control systems, because they are easy to interface wbecause this type of actuator is easy to combine with electrical control systems. In addition, in comparison to pneumatic systems which require an air compressor, electrical power is readily available (Huber, Fleck and Ashby, 1997). Solenoids, moving coil transducers and motors are typically three forms of electromagnetic actuator.  (Huber, Fleck and Ashby, 1997).

2.2.2 Pneumatic systems and evaluation


 Pneumatic solution (Parr. A. ,1998)

The principle of a pneumatic system is using compressed air to transmit power (Parr. A., 1998). Figure 6 shows the components of a pneumatic system. Air is drawn from the atmosphere via a filter and pumped into the storage reservoir by using the compressor (Parr. A., 1998). Usually the compressor is controlled by an AC motor (Parr. A, 1998). The reason why a filter is necessary, is because the air contains airborne dirt, water vapour and other contaminants. (NFPA, 2015). The storage reservoir holds a large volume of compressed air to be used as needed. Compressed air converts to the required mechanical energy by means of a pneumatic cylinder (Rabie, 2009) which is also the basic actuator (Parr. A., 1998). Lastly, the compressed air is expelled through pipes and valves. We use pneumatic systems for the following reasons: the operating pressure of most pneumatic systems is much lower than that needed in a hydraulic system. Usually this is about 100PSI (NFPA, 2015). So pneumatic components do not need to withstand such high pressures as hydraulic systems (NFPA, 2015). Components can be thinner. Moreover, the components in a pneumatic system cost less than in the other system (Satyendra, 2015). In addition, pneumatic systems can work in an inflammable environment and will not cause a fire (Satyendra, 2015). An electrical system can overheat when working which a pneumatic system does not.

2.2.3. Deployable kinetic structures in an actuation system

Physical motion is the kinetic response to the actuation system in this project. Both the kinetic structure and connecting the actuator to our kinetic structure. We tested and compared different types of actuator in order to decide which actuator was suitable for our thesis project.

muscle sensor and motor

 the servo motor changed direction and angle

Servo motor  

This type of motor belongs to the group of Electrical Actuation Systems. It is widely used in control systems because it is easy to interface with control systems which are also electric. Our reason for testing a servo motor was because electric actuators provide exact control and positioning (Robert, 2015). A servo motor can control the rotation angle and rotation direction precisely. At this stage, we changed the muscle sensor for a pulse sensor. We tested different types of actuator on kinetic structures we made of cardboard. In a continuation of the previous experiment, we not only connected a pulse sensor to the motor, but also used fish wire to connect the motor to our kinetic structure. When the pulse sensor detected a person´s heart rate, the servo motor  rotated. The fish wire then continued to move the surface on the kinetic structure. Figure 9 shows the initial mode and the transformed mode of our prototype. We used four servos in the prototype. Figure 10 shows the positions of the servo motors and the line which drove the structure. The top row shows the position of the servos in our first prototype. Obviously, when one of the servos rotated, it pulled on the diagonal line. Simultaneously, the other servo loosened it, which meant it did not add an opposing force to drag the line and vice versa. The rotation range depended on the length of the line the servo was driving. So, the size of the rotation angle also become the limitation of the servo motors.

DSC_1777 motor-2

the servo motor in our project

motor position

the position of the servo motor

Pouch motor (Air pocket) 

A pouch motor is a kind of soft motor which uses compressed air to provide inflation energy (Niiyamaet al., 2014). Pouch motors are easily made using sheet material. Gas-tight bladders (called pouches) are fabricated by exact heat bonding (Niiyamaet al., 2014). The theoretical maximum contraction ratio of a linear pouch motor is 36 %. Pouch motors tested in the lab, were made out of 0.18mm PVC sheeting and proved to have a 10% contraction ratio. In comparison, linear pouch motors made at the  Robotics Lab at MIT, were made of 0.102mm PVC sheeting,

where the measured maximum stroke and tension of the linear pouch motor were as high as 28% and 100N (Niiyamaet al., 2014). These pneumatic actuators perform better in cases where they are fabricated with custom stencils and a heat sealing head for 3-axis CNC machines, in order to achieve the necessary precision for programmable transformations. Nonetheless, for quick experimentation and prototyping, manual sealing is simple and does not require expensive hardware. This approach satisfied our aims for easy and cheap fabrication, and facilitated the successful actuation of the transformation of our lightweight kinetic structure. We positioned the pouch motor on the surface of the prototype. Figure 11 shows the process of inflation. One of the pouch motor inflates while the other needs to deflate .

air pocket-post

 the air pocket test


the position of the air pockets

Subsequently, we scaled up our prototype and pouch motors. The issue after scaling up was the larger size of the pouch motor. It was difficult to heat the boundary of the pouch motor sufficiently to form a seal, as the length of the pouch motor edge was longer than the edge of the welding machine used to fuse the boundaries.

Air muscle

An air muscle (PAM) is an extraordinary actuator that simulates natural human muscles (Minh et al., 2012). Commonly, an air muscle is made up of a rubber inner tube surrounded by a tight plastic mesh shell cover. It works on a simple principle: the inner bladder expands and pushes against the mesh cover when it is pressurised. Due to the deforming restriction of the outside scissor-hinged cover, it can transform the circumferential stress into an axial contraction force (Tondu, 2012). Hence, the muscle contracts when it is actuated and generates tensile force. This experiment shows the soft movement of the PAM compared with the servo motor. This is more related to human beings. Figure 14 shows the positioning of the air muscle. When the air muscle inflates, it drives the surface of the prototype and moves the hexagons.

air muscle-post

 the air muscle test

position of air muscle-post

 the position of air muscle

Comparison of three actuators(Evaluation) 

Servo motors move fast and rigidly with limited rotation. Commonly, the rotation range of a motor is 0º-180º. Which means, the rotation range is limited as the servo motor can only drive a limited length of fish wire.   Also, these motors are expensive. Moreover, with the increase in the size of a project, more servo motors would be needed, increasing the weight by too much. In addition, the movement of this type of motor is rigid, so not a natural simulation of human beings. In comparison, air muscles or air pockets, belong to the group of soft motors. They move in both a softer and slower manner, which is a more natural simulation of human behaviour. The weight of air is negligible, thus not weighing down the structure. These are essential merits of pneumatic actuators (Parr, 2011). Even though air muscles and air pockets are both soft actuators, the linear movement of an air muscle is not suitable for this project because the principle behind this deployable structure is rotation . As a result, the air pocket is the preferable choice for this project. We then found that the shape of the air pocket can affect its power, so in our next experiment we tested what shape of air pocket is most efficient.


linear movement and rotational movement.

shape and weight test of pouch motor.


area and withstand of different shape

Test of air pocket  shape

The shape of pouch motors can affect their power. This is due to the fact that the area of a pouch motor can vary and the point of force application can vary. We tested three different shapes of pouch motor. They were a slender rectangle, a rectangle and a hexagon. The results showed that the slender rectangle could withstand 540g, the rectangle  1.3kg and the hexagon, which was the strongest, could withstand 2.6kg. Table 1 shows the area of each shape and the corresponding weight data. It is obvious that the area of the first two shapes (slender rectangle and rectangle) listed in Table 1 can affect the power of the pouch motor. Both are rectangles with different areas. However, the last two shapes (rectangle and hexagon) in Table 1, show that the shape of the pouch motor is also very important even though their areas are similar. We concluded that the hexagon is the most efficient shape.

After test the first three kind of actuators ,we develop a new one named air spring. This video shows the test of air spring. The air spring

4.2.2   Deployable structure experiment

First prototype 

A deployable structure is a kind of kinetic structure to which an actuation sytem is usually applied. They should be easy to deploy and have the potential to move as a response to the kinetic feedback loop. We developed two deployable prototypes. The first one was inspired by origami moving cubes. There are three cube layers and two hinge layers. The hinge layer is composed of quadrangles (adaptable, negative areas) which can fold from rectangle to rhombus to affect the height of the whole structure. Adjacent cubes are hinged. The working principle again uses the quadrangle which can change from rectangle to rhombus. This deformation of the hinge layer between the cubes causes them to rotate. Figure 17 shows the motion when the cubes are moved. The red line is the initial mode and the white, dotted line demonstrates the transformation. 


 prototype 1 movement

moveing cube-post

deployable structure test

This prototype is affected by two variables. The horizontal hinges (hinges on the cube layer) and vertical hinges (hinges on the hinge layer). It has variable transformation modes. Figures above shows the different transformation modes of this prototype.

Second prototype

The second prototype is a deployable geometrical structure inspired by the reconfigurable structures developed at Harvard.  We fabricated it out of cardboard and double-sided tape. It consists of three layers. This geometrical structure has two stable modes . This figure shows geometrical structure has two stable modes. This figure shows its stable mode and its transformed mode.The initial mode and the stable mode after actuation are totally different. This gives us a good feeling about our idea that two different facial expressions could be simulated.


second deployable structure test

For example, smiling and looking sad; two totally different facial expressions corresponding to two totally different stable modes. The transformation mode can express the changing process that the sensing system detects.

Final prototype (for this stage)

We selected one unit of the geometrical structure and scaled it up. We used plywood to make the basic structure and rubber for the hinges. The working principle of this geometrical structure is that the surface of the extruded hexagon rotates around the axis between the surface A and the surface B of the adjacent hexagon . The red line in Figure below shows the axis that the extruded hexagons rotate around. We designed the pouch motor as a central hexagon with three flanking square. This figure shows the position of the pouch motor, and the grey area shows the inflation area. When the pouch motor is inflated, rotation will occur from 90º to 180º, at the same time actuating the structure to change its mode. When the rotation angle is fixed at 90º and 180º the structure is in stable mode, while during rotation between 90º and 180º it is in transformation mode . In future developments, we consider that this could be used to make a convertible pavilion which could consist of more or fewer units .

working priciple-post

position of air pocket, first is the shape of big air pocket

a scaled up unit

wings-open wings-closed

After that the scaled up unit, we developed a new kind of transformable structure.


Actuation systems provide the driving force for kinetic feedback in interactive architecture. This report focuses on how specific kinetic behaviour results as a reaction to the selected actuation system. To achieve this aim, research on kinetic structures and actuation systems was included. The selection of the actuator should be suitable for the desired kinetic movement of the kinetic structure. We selected the pouch motor to be the actuator and a geometrical structure inspired by reconfigurable structures. In this report, research on kinetic structures and actuation systems was included. This answered the question of how the pouch motor can be applied in a deployable structure and how the kinetic structure in different transformation modes responds to the driving actuator. Firstly, some background on kinetics and the actuation system were provided. In this section which demonstrated that kinetic structures are usually controlled by a computation system, which results in the sensing system being applied to the kinetic structure. We took the ‘Pulse Room’ (Hemmer, 2006) as an example of how others

applied a pulse sensor in their project. In the Pulse Room project, an interface detected people’s heart rates to cause light bulbs to flash with the rhythm of the heart. For the kinetic structure, we were subsequently inspired by the project ‘Transformable Metamaterials’ which led us to develop our deployable structure and pouch motor. These two examples demonstrated how we could apply a sensing system, a kinetic structure and an actuator. In terms of the actuation system, this thesis focuses on the pneumatic system. We then continued to show some experiments on actuators to answer the questions dealt with in this report .We tested the servo motor, pouch motor and PAM (air muscle). These experiments compared the three types of actuator and evaluated them. It showed that the pouch motor was the ideal choice for this project, because its soft movement is more related to human movement, and also because of its many merits, such as its lightness, low cost and

simple construction. In addition, the rotation movement of pouch motors was also essential to the project. Research has demonstrated the potential of pneumatic actuators such as the pouch motor. Moreover, to seek the answer to the question of what kind of structure can complement the actuator, we continued to test deployable structures. We tested two prototypes and a scaled-up unit. For future development, we thought about the design of a pavilion consisting of more and variable units. However, there are still some limitations we need to overcome. For example, when the surface area of the pouch motor was scaled up, inflation become slow and we saw how the area of the inflation pipe cross-section had an influence on inflation. It also proved difficult to weld a large pouch motor without a CNC machine and air leakage was hard to get under control. In conclusion, pouch motors can actuate kinetic structures and have potential in this area.

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Megahed, N.A. (2016) ‘Understanding kinetic architecture: Typology, classification, and design strategy’, Architectural Engineering and Design Management, pp. 1–17.

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Youssef, M.M. (2017) ‘Kinetic behaviour, the dynamic potential through architecture and design’, International Journal of Computational Methods and Experimental Measurements, 5(4), pp. 607–618.

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List of figure

Figure 1: Harvard John A. Paulson School of Engineering and Applied Science. (2016). transformable metamaterial.[online]Available at:< > [Accessed 2016].

Figure 2: kinetic feedback loop(drawn by author)

Figure 3: Rafael Lozano-Hemmer. (2006). pulse room.[online]Available at:<> [Accessed 2006].

Figure 4: Harvard John A. Paulson School of Engineering and Applied Science. (2016). transformable metamaterial.[online]Available at:< > [Accessed 2016].

Figure 5: Harvard John A. Paulson School of Engineering and Applied Science. (2016). transformable metamaterial.[online]Available at:< > [Accessed 2016].

Figure 6: Parr, A. (1998). Pneumatic solution.[online] Available at: < >. [Accessed 2010].

Figure 7:  Harvard John A. Paulson School of Engineering and Applied Science. (2016). Reconfigurable Materials.[online]Available at:<> [Accessed 2016].

Figure 8: the servo motor changed direction and angle(drawn by author)

Figure 9: the servo motor in our project(drawn by author)

Figure 10: Lee, J.C.(2017) the position of servo motor.

Figure 11: the air pocket test(drawn by author)

Figure 12: Lee, J.C.(2017) the position of air pockets.

Figure 13: air muscle test(drawn by author)

Figure 14: the position of air muscle(drawn by author)

Figure 15: Niiyama, R. et al,.(2014).linear movement and rotational movement.

Figure 16:  shape and weight test(drawn by author)

Figure 17:  prototype 1 movement(drawn by author)

Figure 18:  deployable structure test(drawn by author)

Figure 19:  second deployable structure test(drawn by author)

Figure 20:  position of air pocket(drawn by author)

Figure 21:  a scaled up unit(drawn by author)

Table 1:  area and withstand of different shape (drawn by author)

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