Morphosis of Autoreaction

Persiani, Sandra G. L.

doi:10.1007/978-981-15-6178-8_2

Sandra G. L. Persiani³

Part of the book series: Design Science and Innovation ((DSI))

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Abstract

Change in autoreaction happens through the geometrical metamorphosis of one or more parts within the system. From the selection of the geometrical features of the system, it depends on multiple factors that have consequences on its dynamic and energetic efficiency. The choice of fitting morphological features and their integration with all other mechanical and energetic factors is therefore essential to achieve an optimized design. This chapter describes the frames of reference used to represent geometries and motion, the physical parameters of the morphologies and the morphological dimensions involved in common movements.

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Geometrical Elaboration of Auxetic Structures

Article Open access 18 January 2019

Life Science 4.0

Actuated Degree-of-Control: A New Approach for Mechanisms Design

The morphology or the shape of a moving system is much more complex to represent, to understand and to design than that of a static object as it changes in time, in space and sometimes also in function.

In this chapter, the aspects concerning the morphosis, or the “shaping”, of the autoreactive system are discussed, from the spatial framework (the morphospace) within which the change happens, the geometry (morphology), the process of shape change (the morphosis), to the capacity of the shape and the motion features to add a new dimension and unique identity to the artefact.

2.1 Morphospace

The morphospace is, in evolutionary biology, an imaginary multi-dimensional space where different organisms can be compared through their different morphological parameters, represented on different axes (Valentine 2004). In a technical context, the morphospace is rather seen as the special trajectories that a body’s shape follows through space and time (Steadman and Mitchell 2010). The morphospace, therefore, defines all the positions that the object will assume acting along specific planes and paths from the starting morphology to its final morphology.

Defining and describing the parameters of a body in motion within that morphospace is essential, not only to understand and shape the morphology of an autoreactive system, but also to control its movement.

2.1.1 Frame of Reference

To describe the geometrical features of an element, a frame of reference is needed as the body can have different shape and kinetic proprieties depending on how it is oriented. A shared coding system is also necessary to describe relationships of parts within the system itself, and ultimately to represent the movement in the best way.

The virtual space used to represent a movement often resembles the body’s own morphology, for an intuitive and straightforward description and understanding of the movement. In music, the staff is divided symmetrically according to the mode of the execution (a staff for the right hand and one for the left hand for the piano), while dance notation is characterized by symmetrical features which recall the structure of the body which performs the movement (Maletic 1987).

In the context of kinetic man-made artefacts, planar geometric right-angle projections are typically used, as in the case when representing static elements. Descriptive geometry allows to represent three-dimensional objects in two dimensions by creating planar geometric right-angle projections of the object within a Cartesian coordinate system, with plan, elevation and sections as outcome. This method of representation, however, presents some major flaws when aiming to fully describe a movement.

First of all, depending on the geometry of the object and the movement performed, variations in the virtual space might be more suitable: in the case of a kinetic five-pointed star element, a pentagrammic representation might be more suitable than a two-dimensional Cartesian coordinate system.

Secondly, the same movement can appear very differently depending on the point of view it is observed from. To be fully able to describe a movement within a system, and the relationship between the moving parts and the static parts within that system, it is important to use a single frame of reference to distinguish between planes of projection of the movement.

To fully describe the complexity of the movements relatively to each other, inspiration is taken from the anatomical planes—an abstract concept used to describe human and animal body anatomy in a coordinate system. The anatomical planes are four imaginary planes that pass through a body, following its geometry, that are then used to describe anatomy, location and movements (Ogele 2013). In the context of autoreactive systems, an adaptation of this same concept is made to describe the geometrical features and their movements. The virtual planes are (Fig. 2.1):

Median plane (Anat. sagittal plane), the single vertical plane that passes through the main axis of symmetry of the body, dividing it into right and left halves. In bodies with more than one axis of symmetry, the median plane is the first reference to be set, as all other planes then refer to it;
Paramedian planes (Anat. parasagittal planes) will be used to refer to all other planes that are parallel to the median plane, but do not divide the body on its main axis of symmetry;
Frontal planes (Anat. coronal planes) are all the planes at right angles to the median plane passing through the body, dividing it into front and back portions. In those bodies, where a specific axis of symmetry identifies front and back, the frontal plane passing through that axis will be referred to as mid-frontal;
Horizontal planes (Anat. transverse planes) are all the planes at right angles to the median and the frontal plane passing through the body, dividing it into top and bottom. In those bodies, where a specific axis of symmetry identifies top and bottom, the horizontal plane passing through that axis will be referred to as mid-horizontal.

Additional terms used to describe the virtual planes above more in detail are:

View, when the plane does not intersect with the body;
Section, when the plane intersects with the body.

As can be noticed looking at many examples, the frontal view is one of the most commonly used views to represent the geometry of a man-made artefact. To represent a specific movement, however, the views of the planes where the action occurs are usually represented: human running, for instance, occurs in the median and the horizontal planes, while jumping occurs in the median and frontal planes.

2.1.2 Keeping Track of Movements

Reversible moving systems, which are the object of focus in this context, can generally be described and controlled by defining at least three of its moving stages (Fig. 2.2):

The starting position (p₀), which is the position or shape taken as reference before the system is set into motion. It is generally identified as a resting position for the system, such as a closed door which perfectly fits its frame;
The limit position (p_lim), which is usually the position furthest away from the starting position, where the system needs to be returned to, such as a door fully opened to its widest point at 180 degrees;
One or more intermediate positions (p_n), helping to identify the nature of the movement in between the starting and the limit position. Many movements move from p₀ to p_lim and then reverse the same identical movement to return to p₀, while others proceed with a new movement to return to p₀. In the second case, more than one intermediate position might be necessary to define the movement.

2.1.2.1 Transition Between Morphologies

When representing moving three-dimensional elements, the projection where the change of shape is the most representative is generally chosen and the different shapes undertaken at regular time intervals are overlapped. This type of representation mostly focuses on the geometric aspects within the movement, aiming to display their evolution rather than describing the parameters of the movement itself.

2.1.2.2 Trajectories

The most common way of describing a geometry in motion is to identify in each movable part, a point of attachment to the main body (or to other body parts) and at least one free end. Theoretically, the maximum movement is performed at the free end while no movement is performed at the point of attachment. The free end is moving relatively to its point of attachment in a specific direction described by a direction symbol. Key points on the moving part can also be identified and followed by drawing the trajectory of these specific points (Fig. 2.2).

Further variables to take into account, such as folding and bending points, variating degrees of contraction and elongation, etc. can be described with appropriately defined symbols.

2.1.2.3 Centre of Gravity

Keeping track of how the centre of gravity (G) changes during the transition from one geometry to another in the body is a key issue to control the mobility of the body, as well as its balance, and kinetic potential (these aspects are further discussed in Chap. 3) (Fig. 2.3).

Generally, the possible phases that the centre of gravity can undergo are five in number:

1.
G does not move, which means that either the whole body remains static, or parts of the body move so as to neutralize each other;
2.
G is shifted, which means that its location is adjusted within the space occupied by the body so as to improve on a specific performance;
3.
G is transferred, which relates to a displacement of the body in space;
4.
G can be identified but no part of the body actually carries the weight, which happens during jumps or flight phases;
5.
G rotates.

2.1.2.4 Timeframe

The timeframe is a central aspect in the description of a motion. It is therefore surprising how few time-related parameters are found in technical representations of kinetic systems.

Ideally, the virtual space representing the movement is subdivided in sections representing a time unit. The bars that set the basic time unit use a constant amount of space or can be flexible depending on the amount of information that needs to be indicated in between two time units. This way, the movements described inside that frame are given a specific duration (Fig. 2.4).

Within the defined timeframes representing successive movements, patterns of one or more factors can be identified as repeating themselves (geometries, movements, sounds, etc.). Controlling and shaping these patterns is a powerful tool to create unity within a work, but also to make the work dynamic by providing recognizable milestones for the observer to measure the change with. This opens up to completely different parameters that characterize the movement, the perception of the scene and conveying of emotions.

The pace of a movement strongly defines a personality and character in objects by conveying sensations and emotions to the observer. Speed gives sensations of excitement, stress, effectiveness while slower movements provide feelings of control, relaxation and encourage observation. This is why some types of movements can also be a bad or a good choice in terms of user experience. For instance, the fast and aggressive movements of a car are purposefully designed to give the impression of dealing with an organism of higher intelligence such as an animal, while slower movements reminding more of a plant’s slow reactions might fit a building skin better.

Similarly, the transition between phases, movements or gaits modulates the dynamic flow, accompanying the movement into a new pattern ensuring a smooth and effective transition between states. This happens during the slow in and slow out: in technology as in nature, systems need to go through different gaits, or gears, to allow the system to efficiently slow down before reaching a complete stop or speed up reaching full speed. The design of these stages is important from an energetic point of view, but it also enhances the feeling of the observer for the movement.

2.1.2.5 Relationship Between Parts

The relationships between movements within specific timeframes are comparatively used less in design and engineering and are much more developed in other fields such as biomechanics, music or dance, where these parameters have a recognized fundamental importance. It is however through the design and control of these kinds of relationships that a great number of characteristics of a movement are controlled, in terms of function, energy efficiency and aesthetics alike.

The arrangement and frequency of repetition of movement patterns in time, whether it is referred to as rhythm (music) or gait (biomechanics), and characterizes a great number of fundamental functions that are an intrinsic part of moving patterns (Fig. 2.5).

A gait (biomechanics) is defined by the timing and frequency with which an animal performs a specific movement (footfall) pattern: such as jumping, crawling, walking, skipping or running. Changing gait, as a machine changes gear, is a way for a system to adapt to different speeds, terrain, manoeuvres, etc. and guarantee energetic efficiency. Specific gaits are used for specific speeds: as fast walking becomes strenuous for the organism we intuitively switch to running where a different oscillating system allows a more efficient energetic return at a lower energy input (Persiani 2018).

We have evolved an innate sensitivity and attraction to rhythms. Falling into a specific rhythm or beat is an exciting active experience for humans, which often closely relates to beauty, wherein a variation is also essential. One manifestation of this tendency is entrainment, a sort of magnetic effect with which one rhythm creates an attraction upon another rhythm, influencing its frequency and drawing the phases to change timing until they couple to the same frequency (Bush and Clarac 1985). This happens as people walking next to each other fall into the same walking frequency, or when music influences coordinated motion, such as during treadmill walking, running and dancing (Leman et al. 2013).

Among the many variations that can be identified within patterns of action and can also help the description of the effect(s) achieved, two examples are:

Pitch (much used in music) which is a subjective sensation of reaching a high or low peak in a succession of actions. In a physical movement, this can be reflected by the maximum or minimum expression of a movement. In all contexts, the design of the way (modus) of reaching the climax is of extreme importance for maximizing the aesthetic and energy expression of the movement;
Climax, which individuates the building up of energy in the pattern (through acceleration, succession of size change, sound, accumulation, etc.) to reach the highest or a high point in the overall movement. In energy terms, this kind of pattern will be connected to a specific kinetic design, while in aesthetic terms, it reflects in a building up of expectations from the part of the observer which is connected to the comprehension of the overall pattern and anticipation of the rising of defined parameters.

2.2 Morphology

Motion strongly depends upon the geometrical features of the elements it is made of. Factors such as inertia, weight, energy absorption and balance depend on geometry. Therefore, the choice of fitting morphological features, as well as an integrated development of morphological, mechanical and energetic factors is of fundamental importance to design systems with an optimized capacity to move.

In nature, where kinetic systems have developed and been selected over millions of generations and trials, morphology, movement type and movement control have co-evolved exploiting the morphological features in energetic and mechanical contexts to the utmost (Pfeifer 2000). If we assume that each one of these combinations of physical, mechanical and geometrical features have adapted to the specific physical conditions it operates in at a maximum output and a minimum energetic input, then the observation of the combination of these features is enormous evolutionary advantage in technical terms (Persiani et al. 2016).

In the following section, fundamental parameters defining morphological typologies and the dynamic potentials or drawbacks that are the consequence of using these features are discussed.

2.2.1 Symmetry

Engineering structures as well as most organisms in nature are often built with some degree of symmetrical or geometrically organized body plan.

Symmetrical features not only simplify design and construction processes, as a way of forming patterns and connections through the repetition of simple sets of information (Gruber 2011; Persiani 2018), but often also represent an optimum in terms of efficiency (Várkonyi and Domokos 2007).

Setting aside the graphic or aesthetic use of symmetric and asymmetric features, the design of the body shape strongly affects the kinetic characters of a system. Correlation between morphological symmetry and locomotive efficiency has been indirectly demonstrated in biology and technology, as systems with a higher degree of symmetry tend to exhibit greater locomotive efficiency than organisms with higher asymmetry (Persiani 2018; Valentine 2004).

There are mainly three types of symmetry—reflection, rotation and translation symmetry—and a number of possible combinations of these.

2.2.1.1 Reflection Symmetry

Reflection symmetry is also known as linear or bilateral symmetry. A figure has reflection symmetry if it can be divided into two identical, mirrored halves by a single line identifying the axis or the plane of symmetry.

Linear symmetry suggests an almost monodimensional mirroring along the median plane, and partially along the horizontal plane, reproducing a sequence of similar elements along the central body axis (Fig. 2.6).

In biological terms, bilateral symmetry is so important that in Linnaean taxonomy (the science naming, defining and classifying groups of biological organisms based on their shared characteristics), organisms displaying “bilateral” symmetry are classified into one same monophyletic group—which include most animal species apart from sponges, medusae, polyps, comb jellies and basal multi-cellular organisms (Maiorana and Van Valen 2020).

In this context, the axis of reflection is generally identified with the median plane (see Sect. 2.1.1. Frame of reference) (Fig. 2.7).

Typical kinetic characteristics of systems displaying reflection symmetry are:

Directionality of motion. The symmetry axis often identifies the preferred direction of motion, which can also be further subdivided into a “forwards” and a “backwards” direction, meaning that motion happens mainly in one of the two directions highlighted by the axis, the opposite direction (when enabled) being used mainly to enable manoeuvres;
Differentiation of functional body parts. As the parts allotted for locomotion can specialize on locomotion in one prevalent direction, other body parts are freed for other uses;
Fluid dynamic proprieties. As anything that moves around on our planet needs to move through at least one medium, and mostly a fluid such as air or water, the body shape is also important in terms of fluid dynamics. Fluid dynamic shapes are in fact mostly directional (with a front and a rear) and exhibit reflection symmetry at least in one dimension.

2.2.1.2 Rotation Symmetry

Rotation symmetry is developed multi-laterally and equidistantly starting from a central point. It can be further subdivided into radial and spherical symmetries.

Radially symmetrical shapes are developed bi-dimensionally, circularly or along axes (tri-, tetra-, penta-, hexa-, octa-merism) (Fig. 2.8). In some cases, radial symmetry does not present any mirroring axis, but is rather the product of the rotation of an asymmetrical shape. Asymmetrical radial shapes are very common in mechanics, and especially in gearing, where the asymmetrical proprieties of the teeth confer different proprieties to the mechanism depending on the direction of rotation of the gear (see also Chap. 3).

Spherical symmetries are, on the other hand, three-dimensional, meaning that the system can be cut into two identical halves through any cut that runs through the geometrical centre (Fig. 2.8).

Typical characteristics of systems displaying rotation symmetry are:

Multi-directionality of motion. Ideally, systems with rotation symmetry are able to move, function or operate in more than one direction in the plane where they exhibit rotation symmetry;
Multi-functional body parts. As all radial body parts resemble each other, the functional specialization of body parts is no longer possible, and several functions need to cohabit and be managed by each segment;
Dynamic stability in the planes that do not show any radial symmetry; dynamic rotational potential in the planes that show radial symmetry, with a centred centre of gravity.

Depending on how extreme the rotation symmetry in the body is, and whether it presents any reflectional symmetrical elements, the kinetic characters that can be achieved are very varied. An example is animals with more than four legs which, although properly bilateral, exhibit radial kinetic proprieties as the ability to move sideways as well as in the direction of their heads (Biewener 2007; Cruse and Graham 1985).

2.2.1.3 Translation Symmetry

In translation symmetry, a geometry is reproduced in another position while maintaining its general or exact orientation. The intervals between the geometries do not have to be equal in order to maintain the translational symmetry, but generally bind the shapes together by respecting some kind of proportion. Translational symmetry is very important in nature and artefacts alike, as it is used for multiplication principles such as segmentation and pattern-creation.

Segmentation often combines the translation symmetry with a linear symmetrical development: more or less identical subunits are used to form a structure, as in the bones of a spinal cord. A great number of mechanical systems, and in particular chain systems, are created using this technique (Fig. 2.9).

In pattern-creation, the translation happens in a bi-dimensional or three-dimensional dimension rather than in a monodimensional one. What is mostly interesting, from a dynamic perspective, in these patterns is—more than the overall geometry of the system itself, the connections that exist between the reproduced geometries and the intervals that binds each part together with its neighbour (Fig. 2.10).

Typical characteristics of systems displaying translation symmetry are:

Directionality of motion mostly happens in the planes orthogonal to the translation plane, as the latter locks the single parts together to some extent;
Single elements tend to be monofunctional, but the system has a potential for creating complexity and emergence of behaviour on a larger scale.

2.2.1.4 Symmetry Combinations

Systems combining two or three base-symmetries also exhibit a mix of the dynamic characters of these.

The bi-radial symmetry is a particular combination of a radial and a bilateral symmetry that can be found in some natural systems such as comb jellies. In this case, the system exhibits reflection symmetry on the median plane and radial symmetry on the horizontal plane, through a succession of different elements (Fig. 2.11). Bi-radial symmetry is very common in mechanical systems, where gear trains and turbines can display this type of symmetry.

Spiral symmetries can be seen as a combination of the radial and the segmentation symmetries, where the geometry is constantly reproduced along a line, around a fixed central point/axis individuated outside the physical boundaries of the organism, at a continuously increasing or decreasing distance from the point. Natural systems using the spiral of Archimedes, the logarithmic spirals and Fibonacci sequences are quite common as this type of shape formation is a way to preserve energy and proportions of an organism during growth (Wolpert et al. 2011) (Fig. 2.12).

Helix symmetries combine the radial and linear symmetries by developing, turning around the axis while moving parallel to the axis. Double-helix symmetries add a rotated translation to the normal helix (Fig. 2.12).

Screw-like symmetries combine the spiral symmetry and the linear symmetry to obtain a helix where the distance from the centre of rotation increases or decreases at a constant rate (Fig. 2.12).

2.2.1.5 Asymmetry

An asymmetric system presents no symmetric proprieties at all throughout its overall body structure, and in all three dimensions.

Total asymmetry is relatively rare, both in nature and in man-made things. Generally, systems with higher asymmetry present several handicaps among which:

Difficulty of use (for tools). A totally asymmetric tool is not only more difficult for a user to grasp (while on the other hand, a tool’s symmetrical features give clues about its possible function) and therefore also to use;
In kinetic terms, highly asymmetric bodies tend to have erratic and deviating movements, therefore, requiring a higher energy expenditure to counterbalance and stabilize motion (Wolpert et al. 2011; Arthur 1997).

Partial asymmetry, on the other hand, meaning small deviations from the perfect geometrical symmetry, is extremely common in nature—from opposable thumbs to the asymmetric placement of important organs such as the heart. Generally, these exceptions are connected to a functional propriety or specialization of that body part (Valentine 2004).

Partial asymmetry is much less common in engineering problems, where asymmetrical proprieties are often correctly interpreted as un-optimal and imperfect. The use of small localized geometrical perturbations to improve on the response of engineering structures has, however, been theorized and suggested (Várkonyi and Domokos 2007).

2.2.2 Scale

Similar geometries are often used across very different scales, however, the size of moving parts in relation to their function and to their means of operation have a determining effect on the complexity of the kinetic system in terms of interaction with the surrounding medium, structural sizing, energetic and locomotive parameters. These geometries are here called sibling geometries, meaning they exhibit the same geometry but at different scales in size.

In fact, as the design of a mechanical system (natural or artificial) is copied and reproduced at a different scale, its dimensions and proprieties cannot be uniformly sized up or down: there are structural and functional consequences to the changes made to the linear, areal and volumetric dimensions. As these are scaled at different rates, all processes from structural design to energy balance are strongly affected by these parameters.

When the same geometry is applied to dimensionally different scales, three basic design parameters must co-evolve together with the geometry to ensure a successful kinetic outcome (Schmidt-Nielsen 2004):

Dimensions, as structures grow progressively thicker and bulkier as the size grows;
Materials, which typically need to be progressively replaced, from lighter and flexible materials at small scales to more rigid alternatives at larger scales;
Design, changing the structural behaviour of the system, such as from compression to tension elements.

These three aspects need to be integrated so as to solve different issues at different scales while ensuring the system’s efficient operation, according to the end purpose. Three of the most recurrent size-related changes in conditions are here further discussed.

2.2.2.1 Medium of Motion

The medium of locomotion is defined as the type of environment that the system moves through or on: aquatic (in or on water), terrestrial (on ground or other surfaces), fossorial (underground) or aerial (in the air).

The nature and proprieties of the medium play an important role in the design of the movement, which it influences it in different ways on different scales. This, for instance, becomes very obvious on very small scales, such as in microstructures of one centimetre or smaller. Very small autoreactive systems moving in fluids (air, water or other fluids) at low Reynolds numbers, need to be designed considering that viscous forces dominate rather than turbulent ones. As turbulence is absent, the aerodynamic or fluid dynamic shape of the system becomes largely irrelevant and even counterproductive as the ability to move through the fluid is more bound to the body’s capacity to reduce friction drag (Biewener 2007). As any symmetrical movements would cancel each other out, these systems must rely on more asymmetrical kinetics to achieve propulsion.

It is, therefore, important in these contexts to distinguish between systems where a perfect kinetic performance is not vital and success can be achieved, although the system does not unfold at its best, and systems where the good kinetic performance is inseparable from the task to be performed. The first case is, for instance, a system where the reaction is mainly aimed at unlocking a specific potential—as in remotely activated biomedical devices performing drug delivery (Genchi et al. 2017). Here, the dynamics of the kinetic reaction are secondary to the timing of the reaction: what is important is that the content is delivered at the right moment. The second case is when the dynamics of the movement itself are central to the task to be performed—as in self-folding mobile microrobots where not only the folding sequence and coordination is important to achieve the intended shape but also to enable the robot to move around and carry loads (Hardesty 2015). In this latter case, the medium becomes a main parameter in the device’s design.

2.2.2.2 Weight of the System

An aspect that radically limits the design of kinetic system is the size and the weight of the system itself. As the size of the design grows, large-scale constructions typically present bulkier structural frameworks that weigh more and take up proportionally larger areas. This affects the body’s inertia (see Sect. 3.1.4. Principle of Inertia for the definition), the physical propriety of all bodies to resist changes in their state of motion, which, becoming exponentially high as the size and the weight of the system grows, affects its capacity to move and be handled.

It is, therefore, not surprising that dynamic systems are rarely achieved on very big scales at all—unless strictly necessary. The dynamic proprieties are rather integrated by introducing smaller kinetic parts that consume in proportion less energy and are easier to handle and maintain (Fig. 2.13).

As anticipated, there are some context-specific cases where the size of the moving parts becomes an advantage rather than a drawback. This is, for instance, the case of wind turbines, where the amount of energy that can be extracted at a given wind speed is proportional to the size of the rotor—more exactly, to the cube of the wind velocity and to the square of the rotor radius (Gipe 2009). This means that a small increase in rotor diameter significantly increases the power generation of turbines. In this case, the manoeuvrability of the kinetic system is secondary to the speed of rotation and hence of the power output of the turbine.

2.2.2.3 Manoeuvrability Versus Speed

The manoeuvrability of a system—or in other words how easily it allows to be moved and directed—depends on the previously mentioned inertia of a body. This biomechanical principle can also be seen in natural systems, where, for instance, a bird’s wing shape influences their patterns of flight. Long and narrow wings allow stable long-distance flights with little energy expenditure while short and stubby wings require a more energetic flight mode but allow very quick changes in direction (Biewener 2007).

The most movable systems are those that can make sharp and sudden changes of direction, while being characterized by low centres of mass, narrow and tendentially more varied shapes. As the weight is not too much of an issue in kinetic systems with a contained size, a bigger variation in shape can be achieved without significant losses in terms of energy efficiency.

The narrowness of the shape, on the other hand, although it reduces the body’s inertia, therefore, increasing manoeuvrability has important consequences on the speed of the motion. Since stride length (or the length of a lever) is a clue factor in speed, systems with small body shapes have in fact limited possibilities to achieve speed compared to larger body structures. Low speed is, therefore, the other side of the coin of manoeuvrability, and vice versa: objects travelling at fast speeds increase their inertial mass, resisting change and becoming less manoeuvrable.

2.3 Morphosis

The morphosis is a concept that describes the change of a shape in time and space—it therefore no longer describes one shape, but a whole process of transformation from one shape to another. While in biological terms, the morphosis involves a physical formation or development through an irreversible additive process, in this context only reversible changes are taken into consideration.

In morphological terms, reversible mechanisms (mechanisms that can be returned to their initial shape before the action) are most often connected to specific geometries which accommodate and embed an intrinsic potential for change (Persiani 2018).

Overlapping is a way to organize, condense and protect a set of similar or identical geometrical shapes by allowing them to slide over one another until they take up the smallest surface possible. Overlapping geometries are often accompanied by a hinge system or similar, which allows to keep the shapes moving parallelly to each other (Fig. 2.14).