Deployable Lattice_Algorithm Based Design

Computational Design

Biomimetics- Natural System Mimosa Pudica

Namraota Jain-PID20215 Sanajana Sreedhar- PID20308

CEPT University|Master of Interior Design

Abstract

This project focuses on the structure and behavior of Mimosa Pudica as a natural system and its possible application in architectural design.

Mimosa pudica belongs to family of Leguminosae.

It is commonly knows as ‘touch me not’ plant or ‘sensitive plant’. It is commonly found in tropical America, Australia and India, heavily armed with recurved thorns and having sensitive soft grey green leaflets. Once any part of surface like petiole or leaflet is stimulated, the leaves fold.1 The main aim of this project, which is based on Mimosa Pudica, is to achieve a double-curved system in which movement is transferred from one point to another when force is applied at any one point. To achieve this movement in a doubly curved surface, experiments using scissor mechanism are carried.

CEPT University|Master of Interior Design

2

Table of contents

1. Abstract 2. Introduction 2.1 The Natural System- Mimosa Pudica 2.2 The Developed System 3. Experiments 3.1. Experiment 1 Experiment 1a Experiment 1b Experiment 1c 3.2. Experiment 2 Experiment 2a Experiment 2b 3.3. Experiment 3 Experiment 3a 3.4. Experiment 4 Experiment 4a Experiment 4b 3.5. Experiment 5 Experiment 5a Experiment 5b Experiment 5c 3.6. Experiment 6 Experiment 6a Experiment 6b Experiment 6c Experiment 6d 3.7. Experiment 7 Experiment 7a Experiment 7b 3.8. Experiment 8 3.9. Experiment 9 Experiment 9a Experiment 9b Experiment 9c Experiment 9d 3.10. Experiment 10 4. Conclusion 5. References

CEPT University|Master of Interior Design

2. Introduction Natural systems are effective in producing material and energy efficient solutions in response to external stimuli and environment.

The intention of the studio is to decipher the logic embedded within these systems ­ of mathematics, geometry, hierarchical logic, material properties and jointing mechanisms to develop interior architectural systems. In order to develop a material system, concepts of material based mechanics, mathematics and science are combined By learning from the functional principles of natural forms.

Material system is a system resulting out of the properties inherent to the material or a manipulation of those, in­order to extract maximum desired performance v/s minimum materialusage. In this case, Mimosa Pudica as a natural system will be studied to develop a Material System by performing experiments. Various stages of experimenting includes developing performance active models, clear diagramming, prototyping, detailing and joineries, physical and digital fabrication processes. The results obtained will be used to explore the possibility of a material system based on the natural system.

CEPT University|Master of Interior Design

4

2.1 The Natural SystemMimosa Pudica Unlike animals, plants are often regarded as immotile organisms, as they do not normally make movements that can be easily observed by humans. However, in nature, plants can slowly displace their bodies in response to various stimuli. Such types of slow movements (minutes to hours) are widely seen in plants as they adapt to various environmental pressures. For example, in response to mechanical stimulation, the sensitive leguminous plant Mimosa Pudica quickly folds its leaves.

External stimulus Rapid movement

Reversible Slow recovery Fig 1: Factors affecting the movement in plant

When a leaf of M. pudica is mechanically stimulated (e.g., touched by hand), it drops and leaflets are folded upward. Such rapid movements are only possible due to the existence of the pulvini, found at the base of leaflet, rachilla, and petiole. Of the three types of pulvini found in M. pudica, the primary and tertiary pulvini are more sensitive to mechanical stimuli than the secondary pulvinus. When M. pudica is stimulated, it generates a stimulus-induced signal propagating toward distant organs. Early studies examining this phenomenon monitored the pulvinar movement as a visible indicator of signal transmission. Sudden turgor loss in the pulvinus caused by water redistribution is the driving force behind rapid movements in plants.2

Leaves collapse due to Loss of Turgor Pressure under Stimulus

Pulvinus

Factors affecting movement in M. pudica1. Touch 2. Sunlight 3. Temperature

Fig 2: Mimosa Pudica under stimulus

before stimulus low pressure

after stimulus high pressure

high pressure

low pressure

4. Vibration This project attempts to understand and analyze the movement in M. pudica due to touch. The findings are used to develop a material system in which movement is transferred from one point to another.

CEPT University|Master of Interior Design

Fig3: Pressure difference inside the pulvinus

5

2.2 The Developed SystemDeployable Structures Deployable scissor structures can quickly transform between different configurations, making them particularly fit for exploring the movement mechanism of M. pudica. Their ability to deploy typically comes along with a high design complexity and a limited freedom of shape.

A deployable scissor grid can be considered as a kinematic linkage of scissor units, also known as pantographs or scissor-like element. A scissor unit consists of a pair of bars crosswise interconnected by a revolute joint, allowing a relative rotation about an axis normal to the unit plane (i.e. the plane containing the scissor bars). The imaginary lines running through the upper and lower end point at both sides of the unit are called the unit lines. Depending on how these lines vary during deployment, different types of scissor units can be distinguished (Fig. 4), each offering a unique range of geometric possibilities and kinematic behaviour.

The kinematic behaviour of a scissor grid depends on the type of scissor unit used, the geometric constraints that have been applied and the configuration in which the units are assembled.3 This behaviour is described by the scissor grid’s geometric compatibility during the two outer deployment stages (e.g. the expanded, functional stage and the compact, stowed configuration) and the transition stage. A scissor grid is geometrically compatible when all its members fit together without deformations. The scissor units considered in this project consist of straight bars and curved bars that have intersecting unit lines (Fig. 4b). This is done to achieve a global double-curved deployable system.

CEPT University|Master of Interior Design

a: Parallel unit lines

b: Intersecting unit lines

Fig4: Scissor mechanism

6

3. Experiments Aim- To observe deflection from mimimum to maximum in terms of height and span of curvature by varying point to point connection The experiments use sticks of MDF joined together using hinge joint. Explorations are done using linear, curved and filleted sticks of varying lengths to achieve a double-curved geometry.

Two of the hinge joints are kept fixed and a third joint is shiftedto achieve curved deployable geometry that moves on applying force on one point. Once this is achived, the next step involves joining the modules in multiple axes to achieve similar result. Techniques such as joining alternate modules, mirroring of modules, aggregation etc are used to develop a material system.

Initially, off-centered points in one axis resulting in a single-curved system. In the next step, another axes was used to join the sticks together which gave a double-curved system. Finally, the joinery pattern obtained was replicated in the third axis by aggregating. As a result, a double-surved anticlastic deployable system was obtained.

CEPT University|Master of Interior Design

7

3.1. Experiment 1 ParametersConstant: - length of sticks: 10x - width of sticks: x - no. of sticks: 6

- distance between two points: x - Two points of connection: 1-1. 9-9

Variables: - 2nd point of connection

Module

CEPT University|Master of Interior Design

8

Experiment 1a Variables: - 2nd point of connection: 5-5

Variable Pt 5

Input Diagram

a) Close

b) Semi open

c) Open

Output: - Length (closed)= 5.5x - Length (open)= 26.5x - Geometry is linear - No curvature is formed

CEPT University|Master of Interior Design

9

Experiment 1b Variables: - 2nd point of connection: 6-6 Variable Pt 6

Input Diagram

b) Semi open

b) Semi open

height (h)

height (h)

a) Closed

c) Open

span (s)

c) Open

height (h)

a) Closed

span (s)

span (s)

Output: a) h=10x; s=9x b) h= 9.5x; s=18x c) h=14x; s=14x

CEPT University|Master of Interior Design

10

Experiment 1c Variables: - 2nd point of connection: 6-6 Variable Pt 7

Input Diagram

b) Semi open

b) Semi open

height (h)

height (h)

a) Closed

c) Open

span (s)

c) Open

height (h)

a) Closed

span (s)

span (s)

Output: a) h=9.5x; s=15.5x b) h= 10.5x; s=20x c) h=15.5x; s=10x

CEPT University|Master of Interior Design

11

3.2. Experiment 2 ParametersConstant: - length of sticks: 10x - width of sticks: x - no. of sticks: 6

- distance between two points: x - Two points of connection: 2-2. 8-8

Variables: - 2nd point of connection

Module

CEPT University|Master of Interior Design

12

Experiment 2a Variables: - 2nd point of connection: 5-5 Variable Pt 5

Input Diagram

a) Closed

b) Semi open

c) Open

Output: - Length (closed)= 6x - Length (open)= 22x - Geometry is linear - No curvature is formed

CEPT University|Master of Interior Design

13

Experiment 2b Variables: - 2nd point of connection: 6-6 Variable Pt 6

Input Diagram

a) Closed

b) Open

height (h)

b) Open

height (h)

a) Closed

span (s)

span (s)

Output: a) h=10x; s=13x b) h= 10x; s=18x

CEPT University|Master of Interior Design

14

3.3. Experiment 3

ParametersConstant: - length of sticks: 10x - width of sticks: x - no. of sticks: 8

- distance between two points: x - Two points of connection: 1-1, 9-9

Variables: - Two points of connection

Module

CEPT University|Master of Interior Design

15

Experiment 3a Variable Pt 4

Variables: - 2nd point of connection: 5-5

Variable Pt 6

Input Diagram

a) Closed

b) Semi open

c) Open

Output: - Length (closed)= 8x - Length (open)= 36x - Geometry is linear - No curvature is formed

CEPT University|Master of Interior Design

16

3.4. Experiment 4 ParametersConstant: - length of sticks: 10x - width of sticks: x - no. of sticks: 12

- distance between two points: x - Two points of connection: 1-1, 9-9

Variables: - Two points of connection

Module

CEPT University|Master of Interior Design

17

Experiment 4a Variables: - 2nd point of connection: 4-4, 6-6

Variable Pt 6 Variable Pt 4

Input Diagram

a) Closed

b) Semi open

span (s)

c) Open

height (h)

b) Semi open

height (h)

height (h)

a) Closed

c) Open

span (s)

span (s)

Output: a) h=10x; s=11x b) h= 14x; s=27.5x c) h=13.7x; s=27x CEPT University|Master of Interior Design

18

Experiment 4b Variable Pt 7

Variables: - 2nd point of connection: 3-3, 7-7 Variable Pt 3

Input Diagram

span (s)

b) Semi open

height (h)

height (h)

a) Closed

b) Semi open

span (s)

c) Open

c) Open

height (h)

a) Closed

span (s)

Output: a) h=10x; s=11x b) h= 14x; s=27.5x c) h=13.7x; s=22.5x

CEPT University|Master of Interior Design

19

3.5. Experiment 5 ParametersConstant: - length of sticks: 10x - width of sticks: x

- distance between two points: x - Points of connection

Variables: - No. of connection between Module 1 and Module 2

Module 1 in X-axis

Connector

Module 2 in Y-axis CEPT University|Master of Interior Design

20

Experiment 5a Variables: - Module in y-axis connected to the ends

Plan showing connections a) Closed

b) Open

b) Open

height (h)

height (h)

a) Closed

span (s)

span (s)

Outputa) h=8x; s=14x b) h=12.5x; s=32.5x CEPT University|Master of Interior Design

21

Experiment 5b Variables: - Module in y-axis connected intermediately

Plan showing connections

a) Closed

height (h)

b) Open

span (s)

a) close condition

Outputa) h=15x; s=28x b) h=14x; s=40x

b) open condition CEPT University|Master of Interior Design

22

Experiment 5c Variables: - Module in y-axis connected at ends as well as intermediately

Plan showing connections a) Closed

b) Open

X- axis

Y- axis

X- axis

Y- axis

Y- axis

height (h)

height (h)

X- axis

a) close condition

span (s)

span (s)

Outputa) x-axis h=10.8x; s=36x b) x- axis h=9.8x; s=35.5x

a) y-axis h=15x; s=17.5x b) y- axis h=13x; s=21.5x

CEPT University|Master of Interior Design

b) open condition

23

3.6. Experiment 6 ParametersConstant: - length of sticks: 10x - width of sticks: x

- distance between two points: x - Points of connection

Variables: - Axis of joinery - Connector

X

10

X

Module

CEPT University|Master of Interior Design

Connector-variable

24

Experiment 6a

Input Diagram

a) Closed

b) Open

Output: -Length (closed) - 15.5x -Length (open) - 10x - Geometry is linear -No curvature is formed - Geometry is linear - No curvature is formed

CEPT University|Master of Interior Design

25

Experiment 6b

Input Diagram

a) Closed

b) Open

Output: -Length (closed) - 13.5x -Length (open) - 15.5x - Geometry is linear -No curvature is formed - Geometry is linear - No curvature is formed

CEPT University|Master of Interior Design

26

Experiment 6c a) Closed

Input Diagram

b) Open

Output: -Length (closed) - 30.7x -Length (open) - 28.3x - Geometry is linear -No curvature is formed - Geometry is linear - No curvature is formed

CEPT University|Master of Interior Design

27

Experiment 6d

Variable Pt 4 Variable Pt 6

Input Diagram

a) Closed

b) Open

height (h)

height (h)

a) Closed

b) Open

span (s)

span (s)

Output: a) h=16.8x; s=53x b) h= 17x; s=69.2x

CEPT University|Master of Interior Design

28

3.7. Experiment 7 ParametersConstant: - length of sticks: 10x - width of sticks: x

- distance between two points: x - Two points of connection: 1-1, 9-9

Variables: - Third point of connection

Module

CEPT University|Master of Interior Design

29

Experiment 7a Variables: - 3rd point of connection: 5-5

Variable Pt 5

Input Diagram

b) Semi open

span (s)

span (s)

c) Open

c) Open

height (h)

a) Closed

height (h)

b) Semi open

height (h)

a) Closed

span (s)

Output: a) h=8.8x; s=8.5x b) h= 7.6x; s=19.4x c) h= 5.5x; s=21x

CEPT University|Master of Interior Design

30

Experiment 7b Variables: - Point of connection: 4-4, 6-6

Variable Pt 4 Variable Pt 6

Input Diagram

height (h)

a) Closed

span (s)

b) Semi open

span (s)

c) Open

c) Open

height (h)

b) Semi open

height (h)

a) Closed

span (s)

Output: a) h=8.7x; s=22.4x b) h= 15x; s=34.1x c) h= 24x; s=23.7x

CEPT University|Master of Interior Design

31

10

3.8. Experiment 8

10

Pt 1 Pt 2

ParametersConstant: - length of sticks: 10x - width of sticks: x

Pt 3

- distance between two points: x - no. of sticks: 6

Pt 4 Pt 5 Pt 6

Variables: - connection

Pt 7 Pt 8 Pt 9

Module

X

10

X

Connector

CEPT University|Master of Interior Design

32

Constant Pt 01

Constant Pt 1

Variable Pt

Variable Pt

Constant Pt 09

Constant Pt 9

Input Diagram b) Open

height (h)

a) Closed

Output: a) h=15.5x; s=44x b) h= 31.5x; s=76.5x span (s) a) close condition b) open condition

CEPT University|Master of Interior Design

33

3.9. Experiment 9

ParametersConstant: - length of sticks: 10x - width of sticks: x

- distance between two points: x - no. of sticks: 6

Variables: - connection of Module 2 at the centre.

Module 1- Constant

X

10

X

Module 2- Variable

CEPT University|Master of Interior Design

Connector

34

Experiment 9a

Input Diagram

height (h)

a) Closed

b) Open

Output: a) h=20.1x; s=50.2x b) h= 22x; s=63.4x span (s) a) close condition b) open condition

CEPT University|Master of Interior Design

35

Experiment 9b

Input Diagram

height (h)

a) Closed

b) Open

span (s) a) close condition b) open condition

Output: a) h=14.5x; s=47.3x b) h= 18x; s=68.3x

CEPT University|Master of Interior Design

36

Experiment 9c

Input Diagram

height (h)

a) Closed

b) Open

a) close condition

span (s)

b) open condition

Output: a) h=17.3x; s=49.3x b) h= 17.5x; s=69.3x

CEPT University|Master of Interior Design

37

Experiment 9d

Input Diagram

height (h)

a) Closed

b) Open

a) close condition

span (s)

b) open condition

Output: a) h=15x; s=47.7x b) h= 15.2x; s=68.2x

CEPT University|Master of Interior Design

38

3.10. Experiment 10

Input diagram

X- axis

Y- axis

CEPT University|Master of Interior Design

39

height (h)

Curve along x-axis

span (s)

height (h)

Curve along y-axis

span (s) a) close condition b) open condition

Outputalong x-axis open: h= 40.4x, s=100.5x close: h=33.6, s= 80.2x CEPT University|Master of Interior Design

along y-axis open: h= 28.5x, s=86.8x close: h=27.7, s= 73.5x 40

4. Conclusion The experimentations are an exploration of the stimulus movement of Mimosa Pudica plant. To achieve this, common deployable structures using scissor-hinge structural mechanisms were investigated. During this investigation, geometric and kinematic principles of these structures were examined and their shortcomings with respect to form flexibility were exposed. The proposed scissor-hinge structure has both 2D and 3D versions. 2D version of the structure can constitute various curvilinear geometries. The 3D version presents remarkable form flexibility from curvilinear to double-curved shapes. The material system developed can achieve remarkable transformations.

A deployable doubly curved system was obtained in most of the experiments. It was also observed that magnitude of movement increases as the distance between connection point and the module increases.

The explorations can contribute to the field of Architecture, Interior and Technology. Where buildings are expected to be smart and responsive, such system explorations can fulfill those expectations.

CEPT University|Master of Interior Design

41

5. Bibliography 1. Volkov, A. G., & Markin, V. S. (2014). Active and Passive Electrical Signaling in Plants.

2. Aduldejcharas, R. (2015-16). Biomimicry Mimosa Pudica. AA London.

3. Bhushan, B. (2009, April 28). Biomimetics: lessons from nature–an overview. Retrieved from https://royalsocietypublishing.org/: https://royalsocietypublishing.org/doi/10.1098/rsta.2009.0011 4. Hagihara, T., & Toyota, M. (2020). Mechanical Signaling in the Sensitive Plant.

5. Kinematic Analysis of Deployable Scissor Structures. (1999). International Journal of Space Structrures.

6. Roovers, K. (2017, August 15). Deployable scissor grids consisting of translational units. Retrieved from https://www.sciencedirect.com/: https://www.sciencedirect.com/science/article/pii/S0020768317302184 7. von, V., Akgün, Y., & Türkei, E. (2010). A NOVEL TRANSFORMATION MODEL FOR DEPLOYABLE SCISSOR-HINGE STRUCTURE. Universität Stuttgart.

CEPT University|Master of Interior Design

42