"Blade Runner", "Con Air", "Heavy Rain" - what do these representatives of popular culture have in common? In all, to one degree or another, there is an ancient Japanese art of folding paper - origami. In movies, games and in real life, origami is often used as a symbol of certain feelings, some memories, or a kind of message. This is more of an emotional component of origami, but from the point of view of science, many interesting aspects are hidden in paper figures from a variety of areas: geometry, mathematics, and even mechanics. Today we'll take a look at a study in which scientists from the American Institute of Physics created a data storage device by folding/unfolding origami figures. How exactly does a paper memory card work, what principles are implemented in it, and how much data can such a device store? We will find answers to these questions in the report of scientists. Go.
Research basis
It is difficult to say exactly when origami originated. But we know for sure that not earlier than 105 AD. It was during this year that Cai Lun invented paper in China. Of course, up to this point, paper had already existed, but it was not made from wood, but from bamboo or silk. The first option was not easy, and the second was extremely expensive. Cai Lun was tasked with coming up with a new recipe for paper that would be light, cheap, and easy to make. The task is not easy, but Cai Lun turned to the most popular source of inspiration - nature. For a long time he watched the wasps, whose dwellings were made of wood and plant fibers. Cai Lun conducted many experiments in which he used a variety of materials for future paper (tree bark, ash, and even fishing nets) mixed with water. The resulting mass was laid out in a special form and dried in the sun. The result of this colossal work was a prosaic object for modern man - paper.
In 2001, a park named after Cai Lun was opened in the city of Leiyang (China).
The distribution of paper to other countries did not happen instantly, only at the beginning of the XNUMXth century its recipe reached Korea and Japan, and paper reached Europe only in the XNUMXth-XNUMXth centuries.
The most obvious use of paper is, of course, both manuscripts and printing. However, the Japanese also found a more elegant application for it - origami, i.e. folding paper figures.
A short digression into the world of origami and engineering.
There are a great many options for origami, as well as techniques for making them: simple origami, kusudama (modular), wet folding, origami pattern, kirigami, etc. ()
From the point of view of science, origami is a mechanical metamaterial, the properties of which are determined by its geometry, and not by the properties of the material from which it is made. It has long been demonstrated that versatile XNUMXD deployable structures with unique properties can be created using repeating origami patterns.
Image #1
On the image 1b shows an example of such a structure - a deployable bellows, built from a single sheet of paper according to the scheme on 1a. From the available origami options, scientists have identified a variant in which a mosaic of identical triangular panels is implemented, arranged in cyclic symmetry, known as Kresling origami.
It is important to note that there are two types of origami-based structures: rigid and non-rigid.
Rigid origami is a three-dimensional structure in which only the folds between the panels undergo deformation during deployment.
A prime example of rigid origami is Miura-ori, used to create mechanical metamaterials with a negative Poisson's ratio. Such a material has a wide range of applications: space exploration, deformable electronics, artificial muscles and, of course, reprogrammable mechanical metamaterials.
Non-rigid origami are three-dimensional structures that exhibit non-rigid elastic deformation of panels between folds during deployment.
An example of such an origami variant is the previously mentioned Kresling pattern, which has been successfully used to create structures with customizable multi-stability, stiffness, deformations, softening/hardening, and/or near-zero stiffness.
Results of the study
Inspired by ancient art, the scientists decided to use Kresling's origami to develop a cluster of mechanical binary switches that can be forced to switch between two different static states using a single controlled input in the form of a harmonic excitation attached to the base of the switch.
As seen from 1b, the bellows is fixed at one end and subjected to an external load in the x direction at the other free end. Due to this, it undergoes simultaneous deflection and rotation along and around the x-axis. The energy accumulated during the deformation of the bellows is released when the external load is removed, causing the bellows to return to its original shape.
Simply put, we see a torsion torsion spring, the restoring capacity of which depends on the shape of the potential energy function of the bellows. This in turn depends on the geometric parameters (a0, b0, Ξ³0) of the composite triangle used to construct the bellows, as well as the total number (n) of these triangles (1a).
For some combination of geometric design parameters, the bellows potential energy function has a single minimum corresponding to one stable equilibrium point. For other combinations, the potential energy function has two minima, corresponding to two stable static bellows configurations, each associated with a different equilibrium height, or alternatively spring deflection (1s). This type of spring is often called bistable (video below).
On the image 1d the geometric parameters leading to the formation of a bistable spring and the parameters leading to the formation of a monostable spring for n=12 are shown.
A bistable spring can stop at one of its equilibrium positions in the absence of external loads and can be activated to switch between them when the proper amount of energy is present. It is this property that is the basis of this study, which considers the creation of mechanical Kresling switches (KIMS from Kresling-inspired mechanical switches) with two binary states.
In particular, as shown in 1c, the switch can be activated to transition between its two states by supplying enough energy to overcome the potential barrier (βE). Energy can be applied as a slow quasi-static operation or by applying a harmonic signal to the base of the switch with a drive frequency close to the local resonant frequency of the switch in its various equilibrium states. In this study, it was decided to use the second option, since the harmonic resonant response exceeds the quasi-static one in some parameters.
First, resonant actuation requires less force to switch and is generally faster. Second, resonant switching is insensitive to external disturbances that do not resonate with the switch in its local states. Third, since the potential function of the switch is usually asymmetric about the unstable equilibrium point U0, the harmonic drive characteristics required to switch from S0 to S1 are usually different from those required to switch from S1 to S0, leading to the possibility of excitation-selective binary switching. .
This KIMS configuration is great for creating a multi-bit mechanical memory board using multiple binary switches with different characteristics placed on the same harmonic driven platform. The creation of such a device is due to the sensitivity of the form of the potential energy function of the switch to changes in the geometric parameters of the main panels (1).
Therefore, several KIMS with different design characteristics can be placed on the same platform at once and excited to transition from one state to another individually or in combination using different sets of excitation parameters.
At the stage of practical testing, a switch was created from paper with a density of 180 g/m2 with geometric parameters: Ξ³0 = 26.5Β°; b0/a0 = 1.68; a0 = 40 mm and n = 12. It is these parameters, judging by the calculations (1d), and lead to the fact that the resulting spring will be bistable. The calculations were performed using a simplified model of the axial truss (rod structure) of the bellows.
Using a laser, perforated lines (1a), which are places of folding. Then folds were made at the b0 (outward-curved) and Ξ³0 (inward-curved) edges, and the edges of the far ends were tightly connected. The top and bottom surfaces of the switch have been reinforced with acrylic polygons.
The switch restoring force curve was obtained experimentally through compression and tensile tests performed on a universal testing machine with a special setup to allow rotation of the base during the tests (1f).
The ends of the switch's acrylic polygon were rigidly fixed, and a controlled displacement was applied to the upper polygon at a specified rate of 0.1 mm/s. Tensile and compression displacements were applied cyclically and were limited to 13 mm. Just prior to the actual testing of the device, the circuit breaker is set up by performing ten such load cycles before the restoring force is recorded by the 50N load cell. On 1g the curve of the restoring force of the switch obtained experimentally is shown.
Further, by integrating the average restoring force of the switch over the operating range, the potential energy function was calculated (1h). The minima in the potential energy function are static equilibria associated with two switch states (S0 and S1). For this particular configuration, S0 and S1 occur at deployment heights u = 48 mm and 58.5 mm, respectively. The potential energy function is clearly asymmetric with different energy barriers βE0 at the point S0 and βE1 at the point S1.
The switches were placed on an electrodynamic shaker that provides controlled excitation of the base in the axial direction. In response to excitation, the upper surface of the switch oscillates in the vertical direction. The position of the top surface of the switch relative to the base was measured using a laser vibrometer (2a).
Image #2
It was found that the local resonant frequency of the switch for its two states is 11.8 Hz for S0 and 9.7 Hz for S1. To initiate a transition between two states, i.e. exit from potential well*, a very slow (0.05 Hz/s) bidirectional linear frequency sweep around the identified frequencies was performed with a base acceleration of 13 ms-2. Specifically, KIMS was initially located at S0 and the upsweep was initiated at 6 Hz.
Potential well* is the region where there is a local minimum of the potential energy of the particle.
As seen on 2b, when the drive frequency reaches approximately 7.8 Hz, the switch exits the potential well S0 and enters the potential well S1. The switch continued to stay in S1 as the frequency increased further.
The switch was then set to S0 again, but this time the down sweep was initiated at 16 Hz. In this case, as the frequency approaches 8.8 Hz, the switch exits S0 and enters and remains in the potential well of S1.
The state S0 has an activation band of 1 Hz [7.8, 8.8] at an acceleration of 13 ms-2, and S1 has 6β¦7.7 Hz (2s). It follows from this that KIMS can selectively switch between two states due to harmonic excitation of the base of the same magnitude but different frequency.
The switching bandwidth of a KIMS has a complex dependence on the shape of its potential energy function, damping characteristics, and harmonic excitation parameters (frequency and magnitude). In addition, due to the damping non-linear behavior of the switch, the activation bandwidth does not necessarily include the linear resonant frequency. Thus, it is important that a switch activation map be created for each KIMS individually. This map is used to characterize the frequency and magnitude of excitation, which results in switching from one state to another and vice versa.
Such a map can be created experimentally by frequency sweeping at different levels of excitation, but this process is very laborious. Therefore, scientists decided at this stage to move on to modeling the switch using the potential energy function determined during the experiments (1h).
The model suggests that the dynamic behavior of a switch can be well approximated by the dynamics of an asymmetric HelmholtzβDuffing bistable oscillator, whose equation of motion can be expressed as:
where u - deviation of the movable face of the acrylic polygon relative to the fixed one; m is the effective mass of the switch; c is the viscous damping coefficient determined experimentally; ais are bistable restoring force coefficients; ab and Ξ© are the base value and acceleration frequency.
The main task of modeling is to use this formula to establish combinations of ab and Ξ© that allow you to switch between two different states.
The scientists note that the critical excitation frequencies at which the bistable oscillator transitions from one state to another can be approximated by two frequencies. bifurcations*: period doubling bifurcation (PD) and cyclic fold bifurcation (CF).
Bifurcation* - a qualitative change in the system by changing the parameters on which it depends.
Using the approximation, the frequency response curves of KIMS were plotted in its two states. On the chart 2 shows the frequency response curves of the switch in S0 for two different basic acceleration levels.
With a base acceleration of 5 ms-2, the amplitude-frequency curve shows a slight softening, but no instability or bifurcations. Thus, the switch remains in the S0 state, no matter how the frequency changes.
However, when the base acceleration is increased to 13 ms-2, the stability decreases due to PD bifurcation as the drive frequency decreases.
Using the same scheme, the frequency response curves of the switch in S1 were obtained (2f). At an acceleration of 5 ms-2, the observed pattern remains the same. However, as the base acceleration increases to 10 ms-2 PD and CF bifurcations appear. Exciting the switch at any frequency between these two bifurcations results in a switch from S1 to S0.
The simulation data suggests that there are large areas in the activation map where each state can be activated in a unique way. This allows you to selectively switch between the two states depending on the frequency and amount of operation. You can also see that there is an area where both states can be switched simultaneously.
Image #3
A combination of multiple KIMS can be used to create a mechanical memory of multiple bits. By changing the geometry of the switch so that the shape of the potential energy function of any two switches is sufficiently different, it is possible to design the activation bandwidth of the switches so that they do not overlap. Due to this, each switch will have unique excitation parameters.
To demonstrate this technique, a 2-bit board was created based on two switches with different potential characteristics (3a): bit 1 - Ξ³0 = 28Β°; b0/Π°0 = 1.5; a0 = 40 mm and n = 12; bit 2 - Ξ³0 = 27Β°; b0/Π°0 = 1.7; a0 = 40 mm and n = 12.
Because each bit has two states, a total of four different states S00, S01, S10, and S11 can be reached (3b). The numbers after S indicate the value of the left (bit 1) and right (bit 2) switches.
The behavior of the 2-bit switch is shown in the video below:
On the basis of this device, you can also create a cluster of switches, which can be the basis of multi-bit mechanical memory boards.
For a more detailed acquaintance with the nuances of the study, I recommend looking at ΠΈ to him.
Finale
It is unlikely that any of the creators of origami could imagine how their creation would be used in the modern world. On the one hand, this indicates a large number of complex elements hidden in ordinary paper figures; on the other hand, that modern science is able to use these elements to create something completely new.
In this work, scientists were able to use Kresling's origami geometry to create a simple mechanical switch that can, depending on the input parameters, be in two different states. This can be compared to 0 and 1, which are the classic units of information.
The resulting devices were combined into a mechanical memory system capable of storing 2 bits. Knowing that one letter takes 8 bits (1 byte), the question arises - how many such origami will be needed to write down "War and Peace", for example.
Scientists are well aware of the skepticism that their development can cause. However, according to them, this study is an exploration in the field of mechanical memory. In addition, the origami used in the experiments should not be large, their dimensions can be significantly reduced without worsening their properties.
Be that as it may, this work cannot be called ordinary, banal or boring. Science is not always used to develop something specific, and scientists do not always initially know what they are creating. After all, most inventions and discoveries were the result of a simple question - what if?
Thanks for watching, stay curious and have a great weekend everyone! π
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Source: habr.com