Taxonomies of Form Based on Morphogenesis


Timothy Jachna

School of Design, the Hong Kong Polytechnic University, Kowloon, Hong Kong.



Prof. John Frazer FCSD FRSA

International Research Co-ordinator, Digital Project Ecosystem, Gehry Technologies LLC





This paper critically evaluates the appropriate role and nature of taxonomies used in generative design. While formal descriptions of geometric properties are a familiar and obvious basis for a taxonomy of form, the paper proposes that a truly useful prescriptive taxonomy for design must be based on characteristics deeper than mere surface resemblance, and capable of supporting exploration of options by criteria that are meaningful for the role that the designed object will eventually play in the real world. To this end, the paper proposes sample taxonomic strategies for made things, based on criteria of a) assembly and manufacture, b) topology of relations between its components, c) affordances of interaction with other objects and d) ergonomics and physical interaction with the user. Each of these strategies is illustrated by applying it to a specific family of designed products. As part of this demonstration, standards of notation and graphic representation are proposed for each taxonomic strategy. Based on these descriptive taxonomies, the paper hypothesizes ways in which each of these descriptive taxonomies, and the associated modes of notation and graphic representation, might be instrumentalized as a prescriptive taxonomy for the derivation of generative design algorithms with the potential of supporting the design of genuinely new products. The paper culminates by proposing a model taxonomic structure for man-made things based on a case study using the family of writing instruments.

1. Introduction

As descriptive tools, taxonomies aspire to elucidate webs of relations between things, establishing the categories and structures by which we perceive and understand the world. Any generative design algorithm has at its base an implicit or explicit taxonomy (or taxonomies), embodying a notion of the meaningful criteria by which designed things are related.  Generative design uses taxonomies as tools of synthesis in addition to tools of analysis – to give structure and meaning to our making of the world as well as our understanding of the world.


By the same token that our taxonomies of the natural world are inextricably linked to the way in which we conceive of the genesis of new forms of things through processes such as evolution, the taxonomies that form the basis upon which generative design algorithms are built determine the very parameters of the thinkable and the makeable. The adoption of one given taxonomy rather than another is in itself a fundamental design decision. In the following pages, we identify some critical issues involved in the adoption or invention of taxonomies for generative design and propose measures for formulating taxonomies that will provide optimum support for the generative design process.

Our ongoing research into taxonomies of form, to which this paper provides an introduction and partial overview, was inspired by what the authors see as a missed opportunity in the way in which standard solid modelling programs currently deal with the definition of form. The “primitives” out of which complex forms are composed in such applications, and the means by which they are combined and transformed, provide little opportunity for using inherited design knowledge to support an evolutionary design process. To incorporate such potential into design tools, one would need to propose a model of the nested hierarchical structure by which things are related and by which relevant “genetic” information can be located and appropriated for the design of new things. One would need a taxonomy of form: a cognitive structure for the world of man-made things that would achieve what biological classification systems do for our understanding of the world of living things and, beyond that, would support designers in the creation of genuinely new products. The following pages outline different strategies for taxonomies of form that would fulfil these criteria.

2. A manufacturing and assembly-based taxonomy of ballpoint pens

Figure 1 illustrates a proposed convention of coding, applied to a set of simple manufactured objects: ballpoint pens. There are two essentially different formal and technical variants of the ballpoint pen, distinguished from one another primarily in their solutions to two ancillary technical issues that have to do with the way they interface with another designed object, namely the shirt of the pen’s owner. Just as the pocket of the shirt is a feature designed to contain pens and other small objects, the design of the pen accommodates its containment in the pocket by providing features to a) prevent the leakage of ink onto the shirt and b) hold the pen upright in the pocket. In this way, the shirt and the pen exert a forming influence on one another. The two strategies for preventing ink leakage are the ‘cap’ strategy and the ‘retract’ strategy. The ‘retract’ strategy has two sub-strategies – ‘click’ and ‘twist’ – only the former of which is reflected in the diagrams. The solution for holding the pen upright is nominally the same for both variants – the ‘clip’ – although the placement and form of the clip are different in the two variants because of the different opportunities and constraints imposed by the anti-leakage strategy, to which the stand-upright strategy is subordinate, at least in the examples under consideration.



Figure 1: the ‘cap’ (top) and ‘click’ (bottom) variants of the ballpoint pen

If the ballpoint pen is equivalent to a species in the taxonomy, then these two variants are analogous to subspecies. In the diagram above, an idealised example of each of these subspecies is annotated with letters referring to the constituent subdivisions of its formal composition. Because ballpoint pens are more or less linearly composed objects, one could imagine a language in which the ‘clip’ strategy could be unambiguously described and denoted by the ‘word’ LFCGTIP while the ‘click’ strategy would be called FSGTICXYEB.


These subspecies-level variants constitute two distinct and cohesive sub-groups of ballpoint pens, but this is not yet the base level of the taxonomy. While uniquely denoting the stereotypical form of the type of pen to which they refer, the two sequences of letters used in the above example to distinguish the two alternative strategies give a minimum of information about the pen as a material assemblage or a mechanical apparatus, and thus are of little use as description of a functioning tools or manufactured products. Each of the two ballpoint pen sub-groups can be defined as an essentially invariant set of parts with fixed spatial and functional relations to one another, but there is any number of ways in which each of these types of pen may be put together out of smaller components in the actual manufacturing process. It is at this level that ‘negotiations’ between the formal strategy of the designed object and the manufacturing strategy of the producer take place.


To illustrate this point, we differentiate between four different manners of assembly within both the ‘click’ and the ‘cap’ versions. These eight alternatives, drawn from examples of common commercially available pens, exemplify but do not exhaust the range of actually existing and potential manufacturing solutions for ballpoint pens. In order to introduce a limiting criterion, the examples include only pen types in which all outer parts are made of plastic. Following the analogy of the Linnean biological taxonomy, if the ‘lid’ and ‘click’ versions are two subspecies of the ballpoint species, then these manufacturing variants would be varieties (a term used for plants but not animals) within the subspecies.


The capital letters in figures 2a and 2b, above, label the same portions of the pen as in the previous illustration (C for clip, I for ink cartridge, B for button, etc.). Rather than being shown as a finished and complete form, each pen type is shown in an ‘exploded’ view and each component piece of the pen is labelled with the letter or letters that refer to it. Here one sees different ways of dividing up the pen into subcomponents. For example, the outer hull of the pen, which consists of the subdivisions F, G, T and P is divided differently in each of the examples of the ‘lid’ variant (F-GT-P or FGT-P or FG-TP or F-G-TP depending on the manufacturing strategy). In each annotation, the capital letter refers to the part itself, the small letters flanking the capital letter refer to the other parts of the pen with which this part comes into contact and the symbols between the capital and lower case letters shows the nature of the connection between the two parts. So the label for the funnel-shaped end of the first example, l<F>g<I, means “part F friction fits into part L at one end (the ‘left’ end in this chart), friction fits into part G at the ‘right’ end and receives part I friction fit into it from the ‘right’ end”. A linear sequence of all the descriptions of all the pen’s parts, as written under each example in the diagrams, is a ‘word’ that describes the pen in much greater depth of detail than the simple sequences of capital letters noted above. Such a description of an object contains information about the final form of the assembled object while also describing the pieces out of which the product is made, the manner in which they are assembled and even the order in which they must be assembled.


Figure 2a: four manners of assembly for the ‘cap’ version of the ballpoint pen


Figure 2b: four manners of assembly for the ‘click’ version of the ballpoint pen

Ballpoint pens provided a convenient case study for the above demonstration because of the essentially linear character of their assembly, which allows for easy notation in which each pen type could be seen as a sentence composed of words. Rules of sentence syntax would apply, which correspond to the parameters of the manufacturing and assembly process and the qualities of the materials used.

3. A topology-based taxonomy of cast plastic shells

Many manufactured products are much more complex than ballpoint pens, and must be defined by information of a three-dimensional nature. There is no reason why the one-dimensional principle illustrated by the pens could not be extended to the second and third dimension and used to generate databases of spatial information. It would be necessary to develop computer applications that would allow for the construction, reading and manipulation of such databases, which would contain information that is generic to the extent that it would not describe a specific final form but rather a strategy for manufacturing and assembly of a product, the forms of the individual pieces of which would have a greater or lesser degree of indeterminacy, depending on the extent of their interdependency with other pieces in the whole ensemble.

However, the extension of the principle described above to more complex products would require more than simply adding two more axes to the one already existing in the ballpoint pen, which would in effect create a virtual Cartesian space along all axes of which linear sentences may be written. Such a mere dimensional extension and accretion of essentially one-dimensional information would not allow for description of the topological relations needed to describe the variety of ways in which parts relate spatially to one another in a three-dimensional whole.

Figure 3: generic topological relations in shell structures


Figure 4: examples of nested hierarchies of topological relations in products


Figure 3 enumerates typical ways in which components are observed to interrelate topologically within a narrowly-defined family of products whose membership is delimited both by function (communications apparatuses and their peripherals) and manufacturing process (cast plastic shell constructions). Each of the products shown in figure 4 can be described by a linear sentence that records the topological relationships in a way that also reflects their relative position in a nested hierarchy. For example, the cellular phone is made of two pieces sandwiched (Sa) together, each of these pieces is put together from a number of smaller plates (Pl) and some of these plates have buttons penetrating (Pe) through them. Thus the notation for this item is Sa(Pl(Pe)). Of course this notation could be extended until the insertion of every clip and screw is accounted for, but for the sake of this illustration the ‘depth’ of the description was taken only as far as necessary to describe the construction as visible from the outside without disassembling the object. The result would be a linear shorthand for a nested series of three-dimensional relationships. Besides the usefulness to designers, such a system of classification and description of products could be compatible with current attempts in the area of manufacturing engineering, such as “direct engineering” that strive for a closer connection between modelling and manufacture of products [1,2].


Kinship between objects would be recognised by shared ‘outermost’ assembly strategies, and closeness of relation within a family would be reckoned by the ‘depth’ to which the two objects’ description is identical. So the mouse and the cell phone are related to a ‘depth’ of two (Sa(Pl)), while the mouse and the keyboard are related only to a depth of one (Sa) and the mouse and the printer are only related by virtue of both belonging to the family of products assembled from cast plastic shells.

4. An affordance-based taxonomy of screwdrivers and screws

No product is used in isolation. Every manmade thing must accommodate other things with which it comes into contact, and many products belong to ensembles of things that are used together even though they may be designed and manufactured by completely different people with no contact with, or knowledge of, one another. For instance, at the ‘subspecies’ level of the ballpoint pen taxonomy described above, differentiation is introduced by different strategies for how the pen interacts with another product: the shirt.


Screwdrivers are simple tools whose form derives primarily from striving to provide an optimum translation between the human hand and a screw, which in turn is designed to translate the rotary motion imparted it by the screwdriver into linear penetration into a receiving material. Aside from this common characteristic, different applications of screwdrivers put priority on different performance criteria. Accordingly, some screwdrivers are designed for high precision, others for efficient transferral of torque or axial force and yet others for avoidance of slippage between screwdriver and screw or avoidance of transmission of electrical current, to give just a few examples. The handle and tip of the screwdriver are given different shapes, sizes and materials according to the specific tasks for which the tool is designed [7]. Similar criteria apply to the design of the screw; the head and shank of which will be designed differently depending on the type of screwdriver with which it must interface at one end and the material and/or receptacle it must penetrate at the other end.


The criteria of assembly and topology used in the pen taxonomy and the shell taxonomy, respectively, will not suffice to adequately describe meaningful or useful rules of variation and relatedness among screwdrivers and screws. Although they may evince a similar range of variation in their forms and manufacturing strategies as ballpoint pens, variation in the forms of the individual parts of screwdrivers and screws has a much greater effect on the function of the tool than is the case with ballpoint pens. Alterations to the form of any part can change the purpose for which the tool is suited. The screwdriver/screw pair is designed to mediate between two ‘givens’: the human hand and the material into which the screw is to be inserted. The transition between hand and material can be subdivided into three interfaces: hand to screwdriver, screwdriver to screw and screw to material. Figure 5 depicts the more common variants for each of the components – screwdriver handle, screwdriver tip, screw head and screw shank – that are the physical points of interface within the hand-screwdriver-screw-material continuum. This diagram constitutes a graphic depiction of a taxonomy of connections and affordances, based on the way things accommodate other things with which they combine to form a functional whole. There is a large number of different possible “paths” between these the top and the bottom of this diagram, and each path represents a different set of ergonomic and functional qualities. At every interface, the shape and material of the components that come into contact affect the whole causal chain. New component solutions, such as a new handle type of new screw head, can be inserted at any point in the chart, increasing the number of possible paths through the chart, and thus the number of possible tools, exponentially. Variations in the length and thickness of the screwdriver shaft and the screw, which also vary according to application, have been omitted from the chart in the interest of simplification.

Figure 5: the core set of variants of the components of screwdrivers and screws


The taxonomy distinguishes between the shapes of different screwdriver components not because shape variation is relevant in and of itself, but because different shapes afford different uses by allowing different hand positions and accommodating different screw head types. A geometrical description of these variations in shape is of secondary interest, at best. Thus each screwdriver type would be best defined not as a geometrical composition, as in shape grammars as strictly defined, but rather as a combination of a specific head (H) and tip (T) that together must satisfy demands and restrictions being put on it by the hand at one end and the screw at the other end whilst affording a precisely-defined type of transferral of force and movement between the hand and the screw.


To reflect this added criterion, each upper-case letter of the type of linear code used to describe the ballpoint pen variants would need to be supplied with a qualifier. Thus, if the generic notation for the composition of a screwdriver is HaTi, a slotted tip jewellers screwdriver could be coded as HajwlTislt. The same would apply to screws: a phillips head countersunk wood screw would be coded as Hephil,csnkShwd. Each subscript implies a set of compatibilities and incompatibilities. For example, the slotted screwdriver tip (Tslt) is compatible with the slotted (Heslt), Phillips (Hephil) and posidriv (Hepos) screw heads but incompatible with the hex (Hehex), tri-wing (Hetrw) and torque (Hetrq) heads. Similarly, though every handle should be compatible with the human hand, each handle requires certain hand positions and actions in order to operate it correctly.

5. An ergonomics-based taxonomy of finger positions

Most of the instruments developed throughout history to extend the capabilities of humans have by definition been “hand tools”, whose form was influenced by the need to accommodate the hands and to which the hands in turn learned to adapt. Both ballpoint pens and screwdrivers, to take two examples already mentioned in this paper, are essentially machines for the conversion of hand movements and positions into effects that could not be achieved by the hand alone. The proliferation of digital electronics products has further increased the number and variety of objects with which we interact through sometimes quite complex manual manipulation.


The only design parameters shared by all hand tools, handsets, handheld and hand-operated objects are those imposed by the need to afford operation with the human hand. The hands are at the same time the common baseline of many designed products and the common “bottleneck” which imposes a familiar set of possibilities and restrictions that must be acknowledged, exploited and accommodated in the design of all sorts of things. There is therefore good reason to argue that a taxonomy based on interaction between a thing and the hands of the user could serve as a fruitful basis for a broadly applicable taxonomy for man-made products.


Figure 6 illustrates a conceptual foundation for the categorisation of man-made forms based on the way in which the hands interact with them. As in the preceding examples, a convention of linear notation is proposed for this categorisation, which has a degree of isomorphism with the physical situation that it is describing. One digit-place of the code number is allocated to each finger, based on the sequence of fingers on one’s two hands, as seen when held palm upwards in front of oneself, with the thumb of the left hand in position “1” and the thumb of the right hand in position “10”. The digit that fills each place in the sequence corresponds to the mode of interaction between the object and the corresponding finger, so that the digit 1 in position number 10 (i.e. as the last digit in the ten-digit code) means that the right thumb is being used to press part of the object (possibly a button) and the digit 5 in position number 2 would mean that the index finger of the left hand is being used to steady the object.

Figure 6: examples of different modes of manual interaction, with corresponding coding


Note that the criteria of classification have to do with the position and action of the hands and not the form of the object per se. Every one of the 610 or over 60 million unique sequences of digits possible within the code described above would correspond to a range of possible positions for the fingers based on flexibility and reach of the individual digits, the amount, direction and precision of force required for each of the modes of interaction between finger and object, interference of the fingers with one another and with the line of sight and many other ergonomically and physiologically defined factors. Besides interaction with physical objects, the recognition and classification of hand gestures is also of interest to researchers in human-computer interaction [6]. This information could be used to generate a data set defining ten interacting “clouds” of possible finger positions from which possible forms and configurations of designed objects and their sub-components could be derived.

6. A unified taxonomic table for writing instruments

Each categorisation scheme presented in this paper addresses a different way in which made things could be usefully categorised: by manufacturing and assembly typologies (the pens taxonomy), by topological relations of the object’s component parts (the shells taxonomy), by chains of affordances (the screwdriver taxonomy) and by ergonomic criteria (the fingers taxonomy). While some aspects are repeated in two or more of these categorisation schemes, they do not necessarily share enough of a common foundation to be consolidated into a single set of taxonomic principles. A taxonomy that would subsume the myriad different types of information and connections that are cogent to the complex design process and present them in a structure that could be the basis of a tool for the derivation of genuinely new types of things would require more than the mere superimposition of these various schemes.


Figure 7 illustrates a form of taxonomy capable of uniting various levels and criteria in the categorisation of man-made things. The extended family of all writing instruments has been taken as a case to demonstrate this taxonomic method. The form of the taxonomy is analogous to the Linnean biological taxonomy, in which nested hierarchies of relations are formulated based on empirical observation of definable shared characteristics and the design of the chart borrows from a chart by Henry Doktorski depicting part of Hornborstel and Sachs’ 1914 taxonomy of musical instruments [3]. Three levels of categories (or ‘taxons’) are depicted in the chart. If, as already proposed in the pen example, each distinct kind of writing instrument is taken as comparable to a species, then this chart shows the taxons analogous to species, genus and family within the order of writing instruments (which in turn would be embedded consecutively in a class, a phylum and, finally, a kingdom which could for example correspond to all designed products. These levels are not reflected in the chart).


Different criteria for categorisation apply at each level of this taxonomy, and even within each of the different “genus”-level groupings. The chart is drawn from observations of the meaningful criteria of distinction that inhere at each level and for each subgroup of these man-made objects, rather than imposing a unified theoretical structure across all categories. The manufacturing-related categorisation already demonstrated on the example of ballpoint pens does not appear on this chart because it is at a level below that of the species, but we have proposed above that the categorisation of screwdrivers and screws should be done by different criteria than those applied to ballpoint pens. If this taxonomy were extended to take in other kinds of products, more variations in criteria would be introduced at any given level to address the aspects by which those things are usefully categorised.


In defining taxonomies of man-made things, we intend to go beyond description of existing things to provide mental models for the derivation of truly novel new products. A taxonomy should be seen as a search space for innovation strategies, and the graphic representation is intended as the tool for this endeavor. A new solution could be inserted at any level of the taxonomy. The further left in the chart a new category is inserted, the greater and more profound the innovation. An example of an innovation in the leftmost column would be the invention of the typewriter. Only twice in the history of writing has an innovation been made at the “phylum” level. (We distinguish writing from printing, which is a process of mechanical or optical reproduction rather than production, thus disqualifying Gutenberg’s printing press and placing the advent of this new way of writing in the early to mid 19th century). The invention of the computer didn’t add a fundamentally new paradigm of writing, seen from the phenomenological point of view. It still uses the two options of keyboard or stylus (or clumsily with the mouse, which is still held with the hand). At the next level to the right – the so-called “genus” level – an example of an innovation would be the invention of finger painting to deposit a liquid onto a surface rather than transposing the material itself.


























Method of



Body of instrument

Material of

Gritty medium encased in sheath






is the writing

writing medium

Waxy medium wrapped in paper





body of the


and casing








(if any)

Gritty medium not encased





writing medium








and receiving

Body of instrument


Writing medium is liquid,

Fountain pens




filled with writing

process of

flows onto surface

Roller ball pens






Writing medium viscous,







of writing

pressed onto surface







medium to








the receiving

Writing medium liquid,

Felt tip pens







sponged onto surface








Writing medium solid,

Draftsman’s lead holders






abraded onto surface

Mechanical pencils






Writing medium liquid,








sprayed onto surface

Spray paint cans




Body of instrument

How writing

Bristles carry medium

Calligrapher's brushes




dipped in writing

medium is


Sign painter's brushes





carried by

Reservoir carries medium

Reed pens








Quill pens







instrument surface carries medium

Finger painting




Body of instrument


Transposing material

Finger (i.e. in sand)




conducts energy

effect of the


stick (i.e. in dirt)




which alters matl.

instrument on

Impressing material

Embossing tools







Clay tablet stylus







Graphic tablet stylus






Subtracting material by impact








Subtracting material by pressure

Engraving tools







Engraving tools (electric)







Metal / bone stylus







Etching tools






Chemically altering material

Wood burners




Fingers manipulate

Method of

Selection of character by register

w/ circular index plate




apparatus to

translation of

carriage depressed by hand

w/ swinging sector



body of the

 select character

keystroke to

to imprint (Index typewriters)

w/ dial





and actuate


Individual keys and individual





writing medium

striking elements


 typebars (keyboard typewriters)





and receiving











Individual keys, all type characters

daisy wheel







on a single striking element (single

typewheel (drum)






element keyboard typewriters)

type shuttle







Individual keys, register electronically









Stenographer’s machines




1 key, single finger






Figure 7: a taxonomy of writing instruments

7. Conclusion

This paper has illustrated the range of ways in which taxonomies of form for support of the design process might be formulated and used. Although this way of thinking about the form of products has many potential applications and implications in the design field, one immediate goal of this exercise has been to identify strategies for taking the definition and composition of form beyond the “primitives and transformations” model that is still prevalent in computer aided design applications. Both Frazer et al [5] and by Sun [8] have discussed an alternative to this model in detail. They propose that one should define “rudiments” based on the basic components out of which designed products are actually made, and then to formulate “formatives” which would embody information about the different ways in which formatives can be combined to make more complex structures. For example, a rudimentary form for a cellular phone of a certain brand would contain all the characteristics common to that brand’s line of phones, a rudiment at the next level higher in the hierarchy would be able to describe all possible handsets of all makes, the next level up would be a rudiment for all handheld devices, and so forth, until one reaches a hypothetical rudiment for all product forms. Formatives would then provide rules by which these rudiments could be interpolated into designs for specific products.


The derivation of formatives and rudiments would require a model of the useful and meaningful criteria by which man-made things are related to each other, which could form the basis for a generic and evolutionary approach to design. While each of the taxonomies discussed in this paper imply different concepts of what these formatives and rudiments might be, these various strategies are not mutually exclusive. Indeed, as implied by the taxonomy of writing instruments, the most useful taxonomy of form would integrate different criteria at different levels or for different applications.


An ultimate goal of this endeavour would be to be able to distil this information into a concept seed that would contain all the genotypic information required to inform all possible manifestations (phenotypes) of specific products of a given type. This principle of form generation was proposed in a different context by Frazer and Connor for the so-called “reptile” project [4] for generation of structural systems. Whereas the taxonomies proposed in this paper are modelled primarily on the Linnean model of biological taxonomies, which sees relatedness in terms of physical structural similarities, the pursuit of the evolutionary paradigm to the “seed” level would imply that the scope of research be expanded to include cladistic taxonomies, which see relatedness in terms of genetic (i.e. informational rather than visible) similarity.



[1] Boothroyd, Geoffrey, Product Design for Manufacture and Assembly. 2002, Marcel Dekker, New York.

[2] Direct Engineering: Toward Intelligent Manufacturing. 1999, Kluwer, Boston.

[3] Doktorski, Henry, Taxonomy of Musical Instruments, from The Free-Reed Family: A Brief Description. Retrieved 3 March 2003 from

[4] Frazer, J.H. and Connor, J.M., A Conceptual Seeding Technique for Architectural Design. ParC79, proceedings of International Conference on the Application of Computers in Architectural Design, Berlin, Online Conferences with AMK 1979, pp 425-34.

[5] Frazer, J.H., Tang, M.X. and Sun, Jian, Research on Applications of Genetic Algorithms to Computer Aided Product Design – Case Studies on Three Approaches. Proceedings of the 3rd International Conference on Computer Aided Industrial Design and Conceptual Design (CAID&CD 2000). The Hong Kong Polytechnic University, 26-28 November 2000, International Academic Publishers, Beijing PRC, pp. 223-228.

[6] Mulder, Alex, Hand Gestures for HCI. 1996, Simon Fraser University, Vancouver.

[7] Salaman, R.A., Dictionary of Tools Used in the Woodworking and Allied Trades, c. 1700-1970. 1975, Allen & Unwin, London.

[8] Sun, Jian, A Framework for Supporting Generative Product Design Using Genetic Algorithms. PhD thesis, The Hong Kong Polytechnic University, September 2001.