Rapid Deployable Mechanisms in Flowers

1
Rapid Deployable Mechanisms in Flowers

• Authors
• Diogo Ezequiel
• Kayin Dawoodi
• Supervisor
• Dr Lin Tze Tan

2
Introduction

• Deployable Structures are structures that change
  shape by mechanical movement.
• Different types of deployable structures.

3
Deployable Structures

• Structures used to meet some restrictions, such
  as volume and weight...
• Examples of these structures are
• - satellites,
• - masts,
• - inflatable antennas,
• - natural structures such as flowers...

4
Deployable Structures in Nature

• If you were the answer to the problems of
  living, what were the original questions? -
  Julian F. V. Vincent.
• Defined by Julian F. V. Vincent (biologist) as
  perfect structures.
• Naturally occurring deployable structures.

5
Work and Results to Date

• To find interesting plants worth analysing, we
  looked at plants
• - at the Royal Botanical Gardens at Kew.
• - in the laboratory.
• Examples on following slides.

6
Deployable Flowers
Lily
Dionae Muscipula (Venus Fly trap)
Mimosa Pudica
7
Elatostema Repens var. Repens

• Very small pink-white flowers (5mm).
• The flowers explode sending spores into the
  air.
• They are heat triggered. They grow in South East
  Asia.

8
Physical Analysis

• Flower deployment mechanism
• Slow initial opening of lower filaments.
• Very fast catapult opening of upper filaments.

9
Flower elements
Hinge 2
Hinge 1
10
Analytical Analysis

• We assume our structure to be a line diagram as
  shown previously
• We have two different approaches
• One using normal spring formulas Attempt
• The other using dynamics Dynamic analysis

11
Analysis Attempt

• Looking at the last stage of deployment about
  Hinge 2. Modelling it as a torsion spring with
  circular motion.
• The bars at Hinge 2 are shown in the picture.
• Ratio

12
Attempt

• Opening Process in two stages.
• First stage is a rotation.
• Second stage is a damped rotation.

13
Attempt

• Using the equation
• k Spring constant
• P Force applied
• x Radial distance to P
• Change in angle

14
Attempt

• Using the equations of normal and circular
  motion, the force applied can be found
• Angular velocity
• Radial acceleration
• t Time
• r Radius

15
Dynamic Analysis

• We believe that this produces a more realistic
  model of the behaviour.
• The four terms are
• Force from Fma
• Damping force
• Spring force
• External forces ( 0 as assumed no external
  forces as the system stabilises by itself)

16
Dynamic Analysis

• The force balancing equation solves to give
• Assuming the system is critically damped no
  vibration, the radical term turns to 0, so the
  damping coefficient can be found

17
Dynamic Analysis

• Natural circular frequency
• The solution to our equilibrium equation becomes

18
Dynamic Analysis

• Damping Factor Vs. Angle Deployed Graph
• Equation of the Graph that best suits our model

19
Dynamic Analysis

• The last equation is non-linear, we assumed c as
  linear, so instead of an exponential we thought a
  step function should be used.
• Use boundary conditions to solve.

20

• Due to the seasonal nature of the flowers, we
  could not follow with the analysis because some
  parameters were missing
• Accurate timing
• Mass of filaments and anthers
• Mass of all flower
• More accurate measures
• We assumed some of these values and follow the
  calculations on the attempt in order to obtain
  some results.

21

• Assuming a mass of 1µg for an anther with r2
  1mm
• We can now obtain a force and so a spring
  constant

22
Bulbophyllum Vinaceum
(a type of orchid)

• This rare type of orchid is found in Borneo.
• The flowers survive a day or two at most.
• The interior has a see-saw mechanism utilised
  for propagation.

23
Physical Analysis

• The plant has evolved symbiotically with a
  specific species of insect to create a subtle and
  delicate deployment mechanism.

Reference Prof Tan
24
(1)
(2)
(3)
(4)
25
Experimental Observations

• Preserved in 70 ethanol, 30 water.
• Modelled as a beam with hinge.
• Centre of Gravity so positioned that the hinge
  must exert a restoring moment so as to permit the
  lip to return to its vertical neutral
  position.

26
Bulbophyllum Vinaceum Analytical Analysis

• Schematic diagram of flower lip
• Calculate M1 and M2 using different approaches,
  assuming
• weight acts at ends of beams (Method 1)
• weight acts as a Uniformly Distributed Load
  (Method 2)
• weight acts at Centre of Gravity (Method 3)

27

• Summary
• Method 1 244 x 10-9 Nm
• Method 2 122 x 10-9 Nm
• Method 3 176 x 10-9 Nm
• (clock wise- M2 direction)
• Means cannot only be a see-saw movement
• Some element must be acting as a spring (we
  assumed there was some torsion spring)

28

• After assuming a the mechanism can be associate
  with a torsion spring we can use equations
  previously used for the other analysis so,

29
Discussion
Angular velocity,
Acceleration,
Force,
30
Future Work

• High speed camera for accurate measurements and
  therefore analysis.
• New analysis.
• New thesis for the joint.
• Confirm and get more values so we can scale the
  values to model the mechanisms to structural
  sizes.
• Develop uses for the mechanisms.

31
Future Work Example

• Rapidly deployable compact roof for extreme
  conditions, can be used
• to collect rain water,
• to protect from wind and rain,
• to gather solar energy,
• as a shelter for refugees