Springtail
Pneumatically actuated bistable system based on biomimetic principles M. Sc. Elena Chiridnik Work based on Master Thesis 2015 ITKE, Institute of Building Structures and Structural Design Stuttgart University Supervisors: prof. Jan Knippers ITKE, Stuttgart University Axel Körner ITKE, Stuttgart University Simon Schleicher UC Berkeley Support with biological research: prof. Oliver Betz Tobias Grün University of Tübingen
Springtail is a novel bistable foldable mechanism based on the principles discovered in Collembolan (Springtail) jump. The functioning of the jump mechanism is based on the combination of pneumatic actuation and bistability. The advantage of bistability is used in the project: actuation force is needed only to switch between the equilibrium states. The pneumatic actuators need to be under pressure to fold or unfold the element, then in the folded or unfolded position the element remains still. Materialization of the concept is a fibre reinforced polymer prototype allowing varying stiffness within the element depending on the thickness and amount of fibres in the composite. Possible applications for kinetic and reversibly deployable architecture are the foldable geometries: canopies, division walls, transformable facades.
FIGURE 1: Functional mock-up of the foldable mechanism. (Source: E. Chiridnik.)
1 mm
FIGURE 2-3: Pictures of Collembola with folded and unfolded tail made with a transmitted light microscope. (Source: E. Chiridnik.)
Collembolas (Springtails) occur in the soil (different species at different depths) and they contribute to decomposition of organic matter. They are about 0.25 to 10 mm long. One of the most distinguishing features is their ability to jump with the help of forked furca at the posterior end of the animal body (Hopkin 2002). The biomimetic research was mostly conducted through the study of existing biological knowledge on the defined topic. To support the theoretical expertise, the practical experiments and observations with the specimens were conducted. The specimens were obtained and prepared in the University of T端bingen. The pictures were taken with the transmitted light microscope. Seven of the prepared Collembola specimens had folded position of the tail, and twelve of them had the tail in the unfolded position. When the tail was moved, it always returned to the clearly folded or unfolded position. This result supports the statement about the bistability of the Springtail system.
The muscles span the whole of the abdomen and their contraction causes the rise in hydraulic pressure inside the body cavity (a). This pressure provides most of the force heeded to extend the springing organ, the rest coming from stored elastic energy. Brackenbury and Hunt concluded from their experiments that “pressurizing the hemocoel via the rapid contraction of the longitudinal muscles is a way of increasing the storage of elastic energy in the enclosing sclerites.� (Brackenbury and Hunt 1993, p.222) The tergo-pleural arch (b) acts like a source of strain energy when being deformed. In mechanism the arch is a bracket, pushing the abdomen of the Springtail from the sides, so the abdoment is buckling either in or out. "Abducting the rims of the ventral groove (i) distorts tergo-pleural arch (b) from a roughly circular shape to a more elongated, ellipsoidal shape and at the same time draws the manubrium (e) out of the ventral groove via traction on the basal rods (g). If the rims are now released, recoil of the tergo-pleural arch forces the manubrium either back into the groove or out into a position of extension"(Brackenbury and Hunt 1993, p.222).
a.Fluid pressure inside the body cavity
b.The bracket (tergo-pleural arch) c.Bistable surface of the abdomen (abdominal sclerites)
d.The fold (hinge) e.The tail (manubrium) f.Muscles g.Basal rods h.Manubrial base i.Rims of the ventral groove FIGURE 4: Diagram of main parts of Collembolan jump mechanism. (Source: E. Chiridnik, based on: J. Brackenbury, H. Hunt 1993)
FUNCTIONAL ELEMENTS
a
d
The main functional elements of the Collembola jump: a) Fluid pressure. b) Bracket coiling the abdomen sclerites (making them bistable)
b
c
e
f
c) Bistable surface (abdominal sclerites). The increased pressure causes the abdomen bistable surface to flip to the other outwards stable position. d) Fold as a connection of the abdomen and the tail. e) Cross-section of the tail is a triangle. The geometry of the tail is almost not deformed during the movement.
FIGURE 5: Diagram of main principles of collembolan tail folding and unfolding. (Source: E. Chiridnik, based on: J. Brackenbury, H. Hunt 1993)
f) The group of muscles connecting the back of Collembola and the tale brings manubrium back to the folded position. This feature is not used for the technical implementation.
b
b
c
b
e e
d c
b
a
e
c c a
FIGURE 6: First step to construct the mechanism: the plate c buckles and gains bistability from the axial forces b (Source: E. Chiridnik)
FIGURE 7: Second step to construct the mechanism: the the cantilever e is attached to the buckling plate c via the compliant hinge d (Source: E. Chiridnik)
FIGURE 8: Third step to construct the mechanism: the actuation force applied to the buckling plate c causes curved folding of the system (with the condition that the cantilever e is stiff enough to sustain the initial curvature) (Source: E. Chiridnik)
Bistable element The element c deforms due to the destabilizing effect of compressive axial forces b. When this effect is a structural sideways failure and the load is symmetrical, the direction of the eccentric deformation is unpredictable. The proposed element utilizes the effect of plate buckling controlled by actuation: the force introduced by the actuators directs the buckling either in one or the other desired direction. The element is stable in both of the buckled positions. The source of the axial forces is the body sclerites in the Springtail and the polymer bracket in the prototypes. On the abstraction diagrams the pre-stress from the bracket is shown as the axial forces b. The bistable actuation mechanism consists of the buckling plates, the bracket as a source of axial load and two pneumatic actuators on both sides of the buckling place. By constructing this we have the “switch� mechanism with a small movement. To achieve folding and unfolding of the cantilever, the second part of the fold needs to be attached. Curved fold Geometrically, the movement is a result of the change of the curvature of the actuated surface c. In the stable state the curvature is maximal, then the curvature is reduced by the pressure of the actuator a. Those states between the maximum curvatures are unstable, meaning that once the pressure is released, the actuated surface will buckle in one of the curved positions. While the actuated surface is changing curvature from positive to negative, the cantilever e attached to the actuated surface via the curved fold d has always the same direction of curvature. The only transformation happening to the cantilever is flattening in the area near to the fold d when the element is at the potential energy peak.
minima of potential energy well, folded state
unstable potential energy peak
)U (x
minima of potential energy unfolded state
Functioning of the bistable system
x
activation time
activation time
relaxation time
relaxation time
FIGURE 9: Transformations of the element in relation to the potential energy. Indicative energy U vs. configuration x plot for a structure that is symmetrically-bistable. Graphic source: based on Santer , Pellegrino 2008
“Bistable structures have total potential energy functions with two distinct potential wells separated by an unstable potential hill. When an actuator is required to cause the bistable structure to switch between the stable states, it is necessary for sufficient energy to be imparted to the structure by the actuator. This energy has to bring the structure out of its current potential well and traverse the crest of the potential hill. At this point, the bistable structure will continue to change its configuration to the second stable state unassisted, as this represents the path of least resistance� (Santer, Pellegrino 2008, p.6191)
Construction of the curved fold The curved fold of the geometrical and kinematical model and the produced movement are based on the method for the design of the curved folds proposed by J. Mitani and T. Igarashi. The key consideration of the method is that a “surface created by sequential reflective folding is guaranteed to be isometrically unfolded into a plane� (Mitani and Igarashi 2011, p.1) Therefore, if we take a curved stripe and sequentially reflect it, we will have a foldable structure with a number of curved-folding hinges. The plane of reflection is the supporting geometry which helps to construct the fold correctly.
CANTILEVER
HINGE AXES Curved fold axes
PLANE OF REFLECTION
AXIAL LOAD PNEUMATIC ACTUATOR Pneumatic pressure acting as normal forces on the bistable surface from both sides sequentially
BUCKLING PLATE The bistable surface
AXES OF THE ELEMENT
z
x y
FIGURE 10: Principal element. (Source: E. Chiridnik)
Analysis. Geometric, kinematical, kinetic models
FIGURE 11: Two main parameters defined in the geometric model: geometry resulting from from the parameters of the
FIGURE 12: Kinematical model of the element: change of curvature of the actuated surface results in the cantilever movement. (Source: E.Chiridnik)
FIGURE 13: Computational kinetic model used to compare the geometric parameters to the needed pneumatic pressure and controllability. (Source: E.Chiridnik)
After the identification of functional principles in the biological rile model and abstraction of those principles to the simplified geometry, the moving mechanism was developed in three steps. To evaluate the influence of the geometrical parameters on the functioning of the element, the geometric, kinematical, and kinetic models were developed. The analysis of movement and parameters of the geometry is performed with the methodology proposed by Simon Schleicher, Julian Lienhard, Simon Poppinga, Thomas Speck, Jan Knippers in “A methodology for transferring principles of plant movements to elastic systems in architecture" (Schleicher, et al. 2014).
0 1 2 3 4
z
y
5 FIGURE 14: Parameters study. (Source: E.Chiridnik)
x
6
Three parameters mostly influence the stiffness of the structure: curvature of the actuated surface, the orientation in space and the direction of the external load. Axial lateral forces applied to the element are the less disturbance for the functioning of the element, whether they are external loads parallel to the hinge axes or they are the gravity forces applied to the element inclined in the xz plane (6.b’, 6.b’’) Higher curvature of the surfaces makes the structure stiffer, and at the same time requires higher pneumatic pressure for the actuation.
FUNCTIONING PROTOTYPE
FRP ELEMENT WITH THE HINGE
THERMOFORMED BRACKET
TWO PNEUMATIC ACTUATORS
Glass fabric
=
+
+
Diolen fabric
FIGURE 15: Assembly of the mock-up. (Source: E. Chiridnik)
The prototype was produced with a reduced area of the actuated part (as a trapezoid) to minimize the actuator area and maximize the cantilever size. In the current proposal various parts need to have different flexibility. Most of the element, except the hinge, needs to have bending stiffness. The cantilever should have the same direction of the curvature during the folding and unfolding, thus the material should have enough bending stiffness in the area around the hinge. The hinge is the part that needs to be maximally flexible with minimal bending stiffness and very strong to carry the loads and avoid flex cracking, a surface cracking induced by repeated bending or flexing, and to withstand a considerable amount of functional cycles.
4 sec.
1 sec.
FIGURE 18: Functioning of the prototype: actuation of the cushion on one side resulting in unfolding in 4 seconds and on the other side resulting in folding in 1 second. (Source: E. Chiridnik)
Hinge area
Pneumatic actuators on both sides FIGURE 16-17: Fibre-reinforced polymer mockup with the thinning in the hinge area and two pneumatic actuators on both sides of the actuated area
The material chosen for the prototype is fibre reinforced composite. This is the material which can be both strong and flexible. In the prototype the core layer going continually through the hinge is a layer of diolen fabric. In the actuated part there are three additional layers of glass fabric, and in the cantilever- four layers of glass fabric.
Design Research Proposals The following part shows a number of proposals of how the principle could be used in architecture. Two of the proposals show how independent folding elements could be arranged, the other two proposals show the possibility of extending the foldable stripe. The bistable compliant foldable system could be used to its best advantage if there is a need for the elements to be resistant to some forces in the stable positions: if there is a need to carry loads (self-weight, external weight of additional elements, wind loads) or structure is intended to remain in its equilibrium configurations for a certain time. Wind-resistant facade shutters The first proposal is the facade arrangement of the developed folding elements, which are not connected to each other in this case. The faรงade with the possibility of opening can resist wind loads due to the bistability of the components.
FIGURE 19: Wind-resistant facade shutters. (Source: E.Chiridnik) FIGURE 20: Wind Speed and Wind Load (Source:http://www.engineeringtoolbox.com/wind-load-d_1775.html)
Compliant umbrella The second proposal covers minimal area in the closed position (unfolded) and maximum area in the open (folded) position. To achieve maximum compactness, the movement was calculated with the kinematical model. To avoid the collision between the elements, the position of the elements with the rotation around their vertical axes was chosen. The foldable elements are independent from each other.
FIGURE 21: Compliant umbrella (Source: E.Chiridnik)
Flat-packed canopy If it is necessary to produce a structure several meters high, it is reasonable to design the proposal as foldable structure of several elements requiring several hinges to distribute the energy input- output amounts. The third proposal consists of the foldable stripes. Every stripe has a number of curved folds, which allows it to become volumetric in the folded state. This canopy can be stored or transported as multiple linear elements and is operational in the folded equilibrium position. Joining the elements in vertical columns, or “stripes�, requires higher capability of some elements to carry external loads, as the lower element carry all the elements above. Every foldable stripe is independent as it requires the lateral degree of freedom. FIGURE 22: Flat-packed canopy (Source: E.Chiridnik)
Foldable wall The forth proposal consists of the foldable stripes similar to the previous one. The actuated elements are connected in the longitudinal vertical direction, creating stripes that can be considerably shortened when folded. The stripe with multiple folds can help to achieve higher compactness of the folded state and reduction of the pneumatic force needed to actuate every single cushion. The overall geometry is a ruled surface, consisting of smaller foldable parts. This proposal was fabricated as a 800 mm high model from a fibre-reinforced composite (Fig.24).
FIGURE 23: Foldable wall (Source: E.Chiridnik)
FIGURE 24: Prototype of the foldable wall (Source: E. Chiridnik)
The result of the project development is the actuator mechanism able to perform the folding movement. Its main features are: it uses pneumatic force, it is a bistable compliant mechanism, uses the elastic stored energy, needs the actuation force only to fold and unfold, and it is scalable from several centimeters to several meters. If we look at the architectural environment as something assisting a human, it opens new horizons to the design development. Directing the sequence of the compact and deployed states, transformable space can be created. The compliancy can be used in a “soft architecture�- friendly interface of architecture to people.
Bibliography:
Websites:
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