rapiddeployablemecha nismsinflowers 16mar 1443

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Rapid Deployable Mechanisms in Flowers: 

Rapid Deployable Mechanisms in Flowers Authors: Diogo Ezequiel Kayin Dawoodi Supervisor: Dr Lin Tze Tan

Introduction: 

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

Deployable Structures: 

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...

Deployable Structures in Nature: 

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.

Work and Results to Date: 

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.

Deployable Flowers: 

Deployable Flowers Lily Mimosa Pudica Dionae Muscipula (Venus Fly trap)

Elatostema Repens var. Repens: 

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.

Slide8: 

Flower deployment mechanism: Slow initial opening of lower filaments. Very fast “catapult” opening of upper filaments. Physical Analysis

Flower “elements”: 

Flower “elements” Hinge 1 Hinge 2

Analytical Analysis: 

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

Analysis Attempt: 

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:

Attempt: 

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

Attempt: 

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

Attempt: 

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

Dynamic Analysis: 

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

Dynamic Analysis: 

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:

Dynamic Analysis: 

Dynamic Analysis Natural circular frequency: The solution to our equilibrium equation becomes:

Dynamic Analysis: 

Dynamic Analysis Damping Factor Vs. Angle Deployed Graph Equation of the Graph that best suits our model:

Dynamic Analysis: 

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.

Slide20: 

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.

Slide21: 

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

Bulbophyllum Vinaceum: 

Bulbophyllum Vinaceum 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. (a type of orchid)

Physical Analysis: 

Physical Analysis The plant has evolved symbiotically with a specific species of insect to create a subtle and delicate deployment mechanism. Reference: Prof Tan

Slide24: 

(1) (2) (3) (4)

Experimental Observations: 

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.

Bulbophyllum Vinaceum – Analytical Analysis: 

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)

Slide27: 

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)

Slide28: 

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

Discussion: 

Discussion Angular velocity, Acceleration, Force,

Future Work: 

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.

Future Work: Example: 

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…