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Advances in Mechanical Engineering
Volume 2013 (2013), Article ID 318173, 11 pages
Research Article

Physical Realizations: Transforming into Physical Embodiments of Concepts in the Design of Mechanical Movements

1Department of Industrial Design, Chang Gung University, Taoyuan 333, Taiwan
2Centre for Product Design and Manufacturing, Indian Institute of Science, Bangalore 560012, India

Received 8 May 2013; Revised 10 October 2013; Accepted 12 October 2013

Academic Editor: Dongxing Cao

Copyright © 2013 Ying-Chieh Liu and Amaresh Chakrabarti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Conceptual design involves identification of required functions of the intended design, generation of concepts to fulfill these functions, and evaluation of these concepts to select the most promising ones for further development. The focus of this paper is the second phase—concept generation, in which a challenge has been to develop possible physical embodiments to offer designers for exploration and evaluation. This paper investigates the issue of how to transform and thus synthesise possible generic physical embodiments and reports an implemented method that could automatically generate these embodiments. In this paper, a method is proposed to transform a variety of possible initial solutions to a design problem into a set of physical solutions that are described in terms of abstraction of mechanical movements. The underlying principle of this method is to make it possible to link common attributes between a specific abstract representation and its possible physical objects. For a given input, this method can produce a set of concepts in terms of their generic physical embodiments. The method can be used to support designers to start with a given input-output function and systematically search for physical objects for design consideration in terms of simplified functional, spatial, and mechanical movement requirements.

1. Introduction

Conceptual design is the process of exploring promising concepts (e.g., sketches); this often starts with reasoning about design from a functional point of view and involves a series of transformations with increasing detail. In general, there are three phases in conceptual design [1], namely, (1) function analysis—to develop and describe the functions required, (2) concept generation—to generate possible physical concepts from required functions, and (3) concept evaluation—to evaluate these concepts so as to select the most promising ones.

In the second phase of conceptual design, generating a range of physical concepts is seen by many as a challenging task [2]. Also, developing a method that generates these concepts is widely accepted as a principal issue to be resolved for improving current engineering design synthesis [3]. From the literature, methods proposed for generation of physical concepts include the following.

(i) Morphological Charts. A morphological chart, as used in design research, is a matrix where columns present different functional requirements of a design and rows represent alternative working principles that can fulfill each function. Each combination with a working principle from each column represents a concept. After identifying the functional requirements, one or more working principles are found for every function required. These principles are then combined using a morphological chart in order to meet all the functions; principal researchers include Hundal and Langholtz [4], Roozenburg and Eekels [5], Cross [6], and Pahl et al. [7]. A limitation of this method is that there is little guidance for how to transform these working principles into physical descriptions of the device (i.e., physical concepts). Moreover, whether working principles can be combined or not is implicitly decided by designers.

(ii) Catalogue of Elements. To solve the problem of generating physical concepts from required functions, one possible way is to develop a catalogue of building blocks (i.e., elements commonly found in designs). These elements with their function are first identified and listed for use by designers, for example, see Kota and Chiou [8] and Li et al. [9], who developed two levels of building blocks—motion and physical. Physical building blocks describe a set of physical artefacts that embody the motion building blocks. The link between requirements and their physical building blocks is explicitly described in a matrix. Roth [10, 11] developed a more elaborate, multiple-level solution representation to provide guidance from abstract function structures, through physical embodiments, to detailed designs. However, as to how these elements are combined is still dependent on designers’ intuition. A similar work developed into a computational framework is reported by Han and Lee [12].

(iii) Catalogue of Solutions. This provides a list of existing solutions for a given requirement. Researchers such as Murakami and Nakajima [13] and Gu et al. [14] proposed computerized methods for retrieving mechanism concepts. Mechanism concepts and their kinematic behaviour are first analyzed and stored in a library, along with additional information such as motion type. To retrieve mechanism concepts, designers specify the required behaviour in a time history of input and output and/or motion type. However, this method is limited to retrieving complete mechanism concepts rather than generating them by combining building blocks. The usefulness of this approach heavily relies on how extensive the catalogue of mechanisms is. One problem with this approach is that the granularity of building blocks is coarse; therefore, it lacks flexibility in providing as wide a range of concepts as would be possible if the building blocks underlying the designs stored in the catalogue were considered.

This paper investigates the issue of how to transform and thus synthesise possible physical concepts and proposes an implemented method for automated physical synthesis. This research extends earlier research on a functional synthesis approach that produces a wide variety of abstract concepts to mechanical design problems, which involve transmission and conversion of mechanical forces and motions [15]. For a given design problem, this approach can produce an exhaustive set of concepts in terms of their spatial configurations. These are then offered to designers for exploration. This approach has been tested by means of case studies and hands-on experiments involving experienced designers [15]. It was found that the number and variety of solutions generated by using this approach were always larger than those of the designers. This demonstrated its potential for enhancing designers’ chances of developing promising concepts. However, these experiments also revealed a problem with the approach: the representation of solutions was too abstract to adequately visualise their potential embodiments. To tackle this problem, this paper proposes a method of transformation—to develop generic physical embodiments for abstract functional representations of solutions.

2. Method

To start off the method, spatial elements, in this research, are taken as the input to the process; these spatial elements are expressed as the directional and spatial aspects of existing embodiments at a specific time-instant. A spatial element has five parts: input kind (force or torque), input direction (restricted to , , , , , or directions), length vector, output kind, and output direction [16], as shown in Figure 1. The input or output direction is related to the directional aspect of existing embodiments, while the length vector is related to the spatial aspect. The length vector (called the pin part) is defined as a vector with a qualitative distance from the input point to the output point (each described as a dot part in Figure 1) and is assigned as a vector parallel to the , , or orientation. However, in many cases, the real vector (from the input point to the output point) of existing embodiments is not parallel to the , , or direction. The input and output points are related to the contacting areas of existing embodiments and are defined as the centre points of the areas connected to the subsequent elements, such as the centre of a circle, a square, and a line. Further details upon the definition of spatial element can be seen in previous research [16].

Figure 1: The definition of a spatial element.

Before presenting the reasoning method by which a spatial element can be linked to possible physical objects that can embody it, three terms, function, behaviour, and structure, are defined.

(i) Function. It is taken here as the intended behaviour and is viewed as an intended transformation between a set of input-output characteristics. These characteristics are (1) number, (2) kind, (3) direction, (4) magnitude, (5) position, and (6) motion. Take a door latch design as an example. The handle output is a rotation (i.e., the characteristic of motion) with direction in a skew way (i.e., the characteristic of direction), and the latch output is a translation (i.e., the characteristic of motion) to enable disengagement of the latch from the doorframe with input-output relative position. It requires a generation of design solutions taking the torque (i.e., the characteristic of kind) input of the handle and producing a (i.e., the characteristic of number) force output.

(ii) Structure. It is defined as a component or an assembly of components that describes geometric aspects of an object. Component is an individual geometric entity, such as a rod, a pin, a spring, or a shaft.

(iii) Behaviour. It is defined as what a designed system or an object actually does within the motional aspects of the I-O characteristics.

A spatial element has limited information on what the structure of its physical object can be. Therefore, it is necessary to explore the link between spatial and physical descriptions of objects. One possible way is to apply various input motions to a structure, resulting in the creation of various or similar behaviours. By analysing the structure and its behaviour, the possible functions of the structure could be decided. By considering the representation of existing structures, it should be possible to abstract them into the spatial element level. Comparing these transformed objects at the spatial element level with the database of spatial elements, it would be possible to find physical objects for each database spatial element.

Note that behaviour, in the reasoning process, provides the linkage between function and its possible structures, and these structures are then abstracted to the spatial element level. A method based on these Structure-Behaviour-Function (S-B-F) links, as well as on abstracting the level of structures, is thereby built in this work.

To summarize, in order to obtain the input and output point, the contacting area of the physical object is specified, thereby defining its input and output point. To obtain the input and output kind, the physical object is analyzed by means of its S-B-F link. To obtain the length vector, the vector pointing from the input point to the output point is first identified and thus abstracted into the closest among the length vectors parallel to the , , or direction. Figure 2 is a summary of the procedure by which possible physical objects to embody a spatial element can be derived by understanding the structure-behaviour-function relationships of many objects, and abstracting these objects into the spatial element level.

Figure 2: A method based on the Structure-Behavior-Function (S-B-F) links, between standard objects and their spatial elements.

To elaborate the proposed method of transforming a spatial element into its physical embodiments, three steps are proposed: (1) develop the relationships between each spatial element and its possible physical objects, (2) develop rules for ensuring interface compatibility between any two connecting elements, and (3) develop reasoning procedures to replace each abstract spatial configuration with all its possible generic physical embodiments to complete the task of transforming a spatial configuration into geometric configurations (physical embodiments). Using this method, alternative generic physical embodiments for a spatial configuration can be generated.

2.1. Establishing Relationships between Each Spatial Element and Its Physical Objects
2.1.1. Generic Physical Elements and Physical Objects

For transformation of a spatial element into its physical objects, there are two questions to be answered: (1) what are the possible forms representing the pin part of the spatial element, (see Figure 3)? (2) what are the possible interfaces representing the dot parts?

Figure 3: Representations of generic physical elements and physical objects.

To answer Question 1, two generic attributes are identified from the structural aspects of the spatial element.

(i) Form. This is the abstract geometric representation of an object and is the main attribute that transfers or transforms motions within itself. There are different geometric forms, such as plate, semi disk, block, and rod.

(ii) Support Interface. This provides support that interacts with the structure’s environment and sometimes contains the geometric coordinate of the object, such as the centre of a circle. Common support interfaces are revolute pairs (turning pairs), prismatic pairs, screw pairs, cylindrical pairs, spherical pairs, and planar pairs.

To answer Question 2, one generic attribute is defined.

(iii) Motion Interface. This constitutes areas through which objects contact each other in order to transfer motion. This attribute provides interactions between two connecting objects. There are at least two areas in each object: the input and output areas. The types of the motion interface considered are traction, tooth, groove, plane, or hinge. (Traction is the surface made rough. Tooth is the surface made of teeth and may be straight, helical, double helical, or others. Groove is the surface composed of a negative (such as a heart-shaped groove or slot) and a positive (such as a pin-like bar) part. Plane is the surface made of a plane or a curved surface which is perpendicular, or otherwise to , , or axis. Hinge is the surface made of a negative (such as a hole-shaped cylinder) and a positive (such as a pin) part.)

If we analyze the structural aspect of a spur gear, the form is plate, the support interface is a revolute pair, and the motion interface is the meshing of the gear teeth. The interface of any two objects is similar to what Reuleaux (1963) called a “kinematic pair.” Generic physical elements representing a spatial element have a generic representation composed of form, support interface, and motion interface. Each element represents many physical (standard) objects. For example, an element composed of a plate as the generic form, tooth as the motion interface, and a revolute pair as the support interface generically represents all sorts of gears. The relationship between generic physical elements and physical objects is shown in Figure 3. In Figure 3, the first line represents a generic physical element, which is composed of a generic form, support interface, and motion interface. Each physical object consists of its generic physical element added to its specific descriptors. Take a generic physical element with a plate as the form, a tooth as the motion interface, and a revolute pair as the support interface. If its descriptors are circle, spur tooth, and bearing, respectively, the standard object is a spur gear. If we change the form descriptor to a rectangle and the remaining parts are the same, the resulting standard object is a rectangular spur gear.

After linking each spatial element to its physical objects, these physical objects can be further classified into generic physical elements. The procedure for classifying standard objects into generic physical elements is to remove form, support interface, and motion interface specific descriptors from each standard object.

2.2. Ensuring Interface Compatibility

When transforming into its physical embodiments, it has to be ensured that any solution composed of more than one spatial element has compatibility between its connecting elements. Both structural and behavioural aspects of generic physical elements contribute to the issue of compatibility. Analysis of these two aspects reveals that compatibility contains (1) configuration compatibility and (2) motion interface compatibility.

Configuration compatibility is that the space taken by one individual element cannot be occupied by the other. However, each element in our method is qualitatively represented, and the coordinates and dimensions of the object are not quantified. Therefore, it is supposed that any two connecting elements are located and dimensioned so as to meet configuration compatibility.

As far as the motion interface compatibility between two components is concerned, three important attributes need to be considered.

(i) Contact Normal Vector. The common denominator of the contacting situations is that the normal vectors of two contacting surfaces are coincident, with the exception of a point contact where the normal vector of the contacting point can be defined with any possible direction in space. In this research, a contacting vector is restricted to be oriented along , , , , , or direction. However, in some realistic situations, the contacting vectors are not along one of these directions. For these situations, their normal vectors are approximated to be along , , , , , or direction. Examples of contact normal vectors are shown later.

(ii) Contact Motion. The connection of two connecting objects permits a certain kind of motion. The motion of two connecting objects dictates the interface. For example, if the motion of the contacting surfaces of two objects is the same, their interface can be a fixed interface. However, if the motion of the contacting surface of one object is not always the same as that of the other, the connection must allow relative motion. The contacting area of two contacting surfaces in general is therefore defined to be either fixed or changeable.

(iii) Contact Type. The type of interface of the contacting area of two objects must match. Contact type describes the form of the contacting area of two objects, such as plane, traction, tooth, hinge, or groove.

To summarise, each contacting area has three attributes: contact normal vector, contact motion, and contact type. Examples of various interfaces are shown in Figure 4. In Figure 4(a), the contact normal vector, motion, and form of a rack are specified as (even though the real contact normal vector is not in ), changeable, and tooth. In Figure 4(b), the contact normal vector, motion, and form of the bevel gear are specified as (again, even though the real contact normal vector is not in ), changeable, and tooth. The contact normal vector, motion, and form of the brush wheel are , changeable and traction, as shown in Figure 4(c). The contact normal vector, motion, and form of the shaft are , fixed, and plane, as shown in Figure 4(d). In Figure 4(e), the contact normal vector, motion, and form of a groove cam are (even though the real contact normal vector is not exactly in ). And finally, in Figure 4(f), the contact normal vector, motion, and form of a rod are , changeable, and plane.

Figure 4: Examples of various motion interfaces with their contact types, motions, and normal vectors.
2.3. Developing Reasoning Procedure

The motion interface in each generic physical element has various possible input and output areas. An example of a block element derived from a spatial element is shown in Figure 5. Five input areas with their contact types, motions, and normal vectors (shown in the top chart) and five output areas (shown in the bottom chart) enable each generic physical element to connect with different elements oriented in a three-dimensional space.

Figure 5: Motion interface of a block element derived from a spatial element.

The rules for ensuring motion interface compatibility (see Figure 6) are summarized as follows: two connecting objects must match in terms of their normal vector, motion, and type at their contacting surfaces.

Figure 6: Rules for motion interface compatibility.

The procedure for generating all possible physical embodiments is as follows: each spatial element in a spatial solution has various alternative generic physical elements with various forms, support interfaces, and motion interfaces. Considering all possible combinations of the elements’ generic physical elements, alternative physical embodiments of the solution, which meet the rule of motion interface compatibility for all connecting elements, are generated. Connections between these elements contain kinds, directions of the kinds, positions of the elements, and the motion interface with the matching normal vector, motion, and type.

The matching process between two sets of objects (each set containing alternative physical embodiments of a spatial element) is to first select an alternative from each set, followed by deciding whether the output area of the former element or the input area of the latter element obeys the rule for motion interface compatibility. This process has to be repeated for all alternative combinations.

3. Examples

3.1. Example of Spatial Element and Its Physical Realizations

Figures 710 present various generic physical elements for the four spatial elements. Each generic element is as shown in the columns of the top row with its name shown in the second row. The attributes of possible input and output areas of the physical element are shown in each column of the bottom row.

Figure 7: A torque-to-force spatial element and its generic physical elements.
Figure 8: Crank2 spatial element and its generic physical elements.
Figure 9: A Lever1 spatial element and the generic physical element.
Figure 10: A Wedge spatial elements and its possible generic physical elements.

The derivation of generic physical elements in the database is based on two concerns.

(i) Motion. Elements providing different kinematic motions, such as continuity or reciprocity, need to be distinguished. For instance, the generic element of a plate and a semidisk from the torque-to-force spatial element need to be distinguished, because one can generate a continuous output and the other cannot.

(ii) Spatial Constraint. Elements having different types need to be distinguished. For example, the distinction between Wedge1 and Wedge3 generic element derived from the Wedge spatial element is because their spatial constraints are located in different places.

Figure 7 shows the results of transforming a torque-to-force spatial element into generic physical elements. Each generic physical element consists of a generic form, support interface, and motion interface. Three generic forms—plate, semidisk, and block—are shown in this figure. The generic support interface is a revolute pair which is situated at the centre of the plane generic form and is situated at the top of the semidisk and block forms. A revolute pair provides one degree of freedom (rotation) to its generic physical form. Each generic interface has an input area and output area. The input area of a plate generic form is a plane and the output area is either a tooth or a traction. Similarly, the input area of a semidisk generic form is a plane and the output area is either a tooth or traction. The input area of a block generic form has the input area as a plane and the output area as plane, hinge, or groove. The presentation of various input and output areas for a generic element is not shown in this figure.

Figure 8 shows the results of transforming a force-to-torque spatial element to generic physical elements. Three generic forms—plate, semidisk, and block—are shown in this figure.

Figure 9 demonstrates the results of transforming a force-to-force spatial element into generic physical elements. The generic form is a lever1, the support interface is a revolute pair which provides one degree of freedom (rotation), and the motion interface has various possible input and output areas which are the hinge, groove, or plane.

Figure 10 shows the results of transforming another force-to-force spatial element into generic physical elements. Four generic forms—wedge1, wedge2, wedge3, and wedge4 are presented. The generic physical elements with wedge1 generic form and wedge4 generic form are transformed as assemblies of components rather than a single component.

Theoretically, all generic physical elements can be considered in terms of single components without assemblies. The reason for using components as well as assemblies is that there are some assemblies (such as pulley-and-belt, or screw-and-nut) that are often treated as a single building block. Therefore, if we use only components in the database, such building blocks require the use of more than one basic element. To reduce the number of elements used in a solution (which is important to contain combinatorial explosion), components and assemblies are used together.

3.2. Example of Two Consecutive Spatial Elements and Their Physical Realizations

Two examples are given below to illustrate the results of transforming spatial configurations into their generic physical embodiments. Figure 11(a) shows a spatial configuration combining a torque-to-force element taking an input torque, to produce and transfer a translational output to a force-to-torque element that produces a rotational output at the desired output point. Five generic physical embodiments are shown in Figures 11(b), 11(c), 11(d), 11(e), and 11(f). Figure 11(b) shows a pair of traction wheels or spur gears. Figure 11(c) shows an embodiment similar to that in Figure 11(b) but generates an intermittent output motion. The embodiment shown in Figure 11(d) is similar to Figure 11(c) but provides different output motion which is a repeatedly intermittent output, while that in Figure 11(e) is similar to Figure 11(c) with the same output motion. Figure 11(f) describes a rotating element driving another rotating element, through a contact surface, to transfer the rotational motion. Figure 12(a) shows a spatial configuration combining a force-to-force element taking input force, to produce and transfer a translational inverse motion to a force-to-force element that produces a perpendicular translational output at the desired output point. Four possible generic physical embodiments are shown in Figures 12(b), 12(c), 12(d), and 12(e). Figure 12(b) shows a lever connected to a wedge. Figure 12(c) shows a lever connected to a wedge assembly. The contact type in-between is a plane. Note that the wedge in the pin diagram can be more general than simply a physical wedge, as illustrated in Figures 12(d) and 12(e). Figure 12(d) shows as lever connected to a rotating rod. The contact type in-between is a groove. Figure 12(e) shows a lever connected to a double-slider crank assembly. These generic physical embodiments describe different elements with their forms, support interfaces, and motion interfaces so as to enlarge or decrease the magnitude of the input, as well as to change its direction.

Figure 11: The spatial configuration and its five possible physical embodiments.
Figure 12: The spatial configuration and its four possible physical embodiments.

4. Discussion

Developing physical embodiments from an abstract spatial configuration is more than one-to-one mapping. This is because an abstract spatial configuration of a solution provides little information as to what physical objects (i.e., components or assemblies of components) and their interfaces should be. The reasons to develop a level of generic physical object are as follows. Firstly, very little supporting theory is available, and hence the designer must rely on his/her intuition and experience for transforming spatial into physical solutions. There is no general theory that relates a spatial element to its possible physical objects, and thus developing a reasoning procedure is necessary to link the two. Secondly, each spatial element can be represented in terms of numerous physical objects, if considering these objects at the physical level with their form, dimensions, and spatial constraints. However, if all possible geometric and dimensional variants of these are considered, the number of physical objects for the spatial element could be infinite. Therefore, it is still necessary to find a way to generalize their geometry and dimensions so as to control the number of the transformed objects. Lastly, a connection between spatial elements in a spatial configuration does not explicitly consider the characteristics of that interface. However, interfaces between connecting objects in mechanical designs can have various geometric forms and dimensions. We, therefore, need to address the question of how to reason about suitable interfaces for connecting two physical objects, each of which represents a spatial element at the physical level. As reported in previous studies [17, 18], physical interface compatibility was addressed before under the framework of Function-Behavior-Structure (FBS) model. Compatibility was checked to derive types of contact (e.g., point contact or line contact). However, the major difference of this previous approach to the one proposed in this paper is as follows: while earlier work [17, 18] describes how an interface is to be connected (e.g., line contact), our proposed method proposes that, in addition to the type of contact needed, a physical interface should include information on the interface shape (e.g., groove) and the position of the contact point.

The range of physical elements of a specific spatial element would affect the variety of physical objects, while the type of spatial elements would decide the variety of the space of abstract solutions. In our method, a database of generic physical elements needs to be developed. Therefore, this raises the question: how to develop and validate generic physical embodiments from existing designs? We propose the following procedure: (a) abstract existing designs to strip irrelevant information from them in order to transform them into their generic physical embodiments, (b) from the designs identified in Step 1, distil subsolutions which are relevant to this research (because e.g., this methodology is developed based on the consideration of mechanical movements and their transformation), (c) compare these subsolutions with the ones independently generated by the proposed method. Take a corkscrew as an example. Two parts relevant to mechanical movements are considered in this case study: (1) Part I (such as the spiral-shaped metal rod) to screw the spiral into the cork so as to combine with the cork so that they can be removed together from the bottle, and (2) Part II (such as the handle) to transfer or transmit motion from hand to Part I. To develop a database, a collection of design catalogues could be used from the literature, for example, catalogues of corkscrews in Wallis [19] and Watney and Babbidge [20]. Also, machines with mechanical movements are shown in Brown [21], Jensen [22], and Sclater [23] as benchmark.

One problem of our method is that since the variety of building blocks at each solution level is wide, the number of generic physical embodiments becomes increasingly large when dealing with solutions which contain many spatial elements and may result in a combinatorial explosion. Two possible ways of resolving this are as follows.(1)To divide a design problem into subproblems. Each subproblem can then use fewer spatial elements. As a result, the number of solutions can be reduced. (2)To prune solutions at the earliest possible opportunity. A solution space can be pruned by using relevant heuristics, at the topological solution, spatial configuration, and generic physical embodiment levels (see, e.g., [1, 24]).The present method is restricted in several ways: only single input single output (aspects of) designs are currently embodied, and the databases of building blocks are all from mechanical domain. Future work involves extending and modifying the set of building blocks, integrating mechanical building blocks with building blocks from other engineering domains, and considering multiple-input multiple-output requirements.

5. Conclusion

This paper investigates a key issue in conceptual design-how to develop spatial solutions into their possible physical embodiments. The method proposed contains knowledge for transforming spatial elements into generic physical elements, as well as rules for ensuring motion interface compatibility between connecting physical elements that together form an assembly to carry out the function. The outcome of the method is generation of generic physical embodiments of spatial configurations which should lead to an improved visualisation of spatial configurations, and an increase in the number of possible concepts explored. There are three important contributions of this method. The first is that both components and assemblies are used as building blocks. The second is that motion interfaces between physical objects are explicitly considered. And finally, there are explicit rules for ensuring interface compatibility that can be used by computers rather than only implicitly handled by designers.


This research is partly funded under Grant no. CMRPD2C0021 by the Chang Gung Memorial Hospital and NSC 102-2410-H-182-014 by the National Science Council of the Republic of China.


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