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A Science-Based Approach to Product Design Theory Part II: Formulation of Design Requirements and Products Y

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A Science-Based Approach to Product Design Theory Part II: Formulation of Design Requirements and Products Y Robotics and Computer Integrated Manufacturing 15 (1999) 341}352 A science-based approach to product design theory Part II: formulation of design requirements and products Y. Zeng, P. Gu* Department of Mechanical and Manufacturing Engineering, The University of Calgary, 2500 University Drive, Calgary, Canada, AB T2N 2N4 Abstract The Design Process begins with design requirements and ends with product descriptions. The design requirements include both structural and performance aspects. The product descriptions deal with the structural aspect of the design requirements while the product performances describe the performance aspect of design requirements. In this part of the paper, a set theory-based representation scheme is proposed to represent design objects in the design process, including design requirements, product descriptions, and product performances. This representation scheme can represent the design objects that evolve in dynamic design processes. The entire mathematical scheme is de"ned based on structural and behavioral properties. Within one uniform scheme, the design objects are represented at di!erent levels of complexity and abstraction. Several examples are included to explain the scheme and its mathematical formulations. The proposed scheme can be used for science-based studies of product design. ( 1999 Elsevier Science Ltd. All rights reserved. Keywords: Design requirement; Design description; Product performance; Complexity; Abstraction; Set theory 1. Introduction motivations for this kind of research are many. One of the most important comes from the development of Design is a basic human activity. During a long period, computer-aided design systems. Better design support design had been considered as an &art' which was taught systems can only come after better design theories are through a &master}student' model. Only after 1960s, in- developed. The success of AutoCAD, Pro-Engineer, and tensive studies into the design activity began as many other CAD systems have been largely dependent on the researchers attempted to propose better design methods development of fundamental geometric modeling the- to improve design and design education. Consequently, ories [3]. The development of more advanced computer- the research has spanned a broad range of "elds from aided systems calls for better product and design process philosophy, psychology, and engineering to computer models. But design studies have been in#uenced by applications. The &art' of design has been gradually re- engineering, computer science (in particular, software placed by the &art and science' of design [1]. The science engineering and arti"cial intelligence), information pro- aspect allows people to better understand design pro- cessing theory, cognitive science, psychology, and philos- cesses while the art aspect allows designers to keep their ophy among others. The representation schemes of creativity in rationalized design processes resulting from designs and design processes bear the characteristics of the science aspect. However, only a few systematic design di!erent "elds. There are some confusions and vagueness theories have been established and the research in this in the representation and communication of ideas. "eld is still in pre-theory stage [2], although there have The science-based design theories will certainly improve been a rich and varied body of knowledge including the development. theories, methodologies and applications. The design dis- The main aim of scienti"c design theory is to discover cipline has reached the point in its evolution where and disclose the underlying order of design processes. a science-based design theory should be established. The Like other scienti"c disciplines, design theory also needs to be completed with the formulation of laws by means of an adequate and accurate language. The laws would set the limits for the theoretical level of * Corresponding author. design and de"ne the science of design. The examples 0736-5845/99/$- see front matter ( 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 7 3 6 - 5 8 4 5 ( 9 9 ) 0 0 0 2 9 - 0 342 Y. Zeng, P. Gu / Robotics and Computer Integrated Manufacturing 15 (1999) 341}352 of law are the two axioms proposed by Suh [4]. Gomez- engineering design is design requirement formulation, Senent et al. [5] have also listed nine principles of which translates design requirements into design speci- design. With to the language, possible forms include "cations. The design process then provides a mapping graphics, #ow charts, natural languages and mathemat- from design speci"cations to design descriptions. There- ics. Theoretically, mathematics is the most accurate and fore, a comprehensive design theory should include at powerful language for scienti"c purposes. Because least three basic parts: design studies have been focused on design methodolo- gies, design philosophy, and knowledge-based design, 1. A general framework to describe and formulate design natural and graphic languages are the major representa- problem. tion tools in the research [6]. The purpose of this part of 2. A language to de"ne the two ends of a design process. the paper is to propose a mathematical framework to 3. A theory to address the processes of formulation and represent the entities involved in design processes. In the design. next section, the basic framework of the mathematical In this paper, our focus is on the second part: the representation of design problems is proposed to govern development of a language for design. This lays a founda- the following discussions. Then design speci"cations, tion for a scienti"c formulation of designs and design product descriptions, and product performance are in- processes. The other two questions are addressed in the vestigated in separate sections. Conclusions are given in Part I of this paper [7]. the "nal section. The development of a language for design should start by "nding a strict de"nition and a robust representation of the terms involved in design processes without going 2. Framework of mathematical representations to the details of concrete design tasks [8]. It can be easily seen from Fig. 1 that the terms include design require- Design is an intelligent activity that begins with design ments, design speci"cations, and product descriptions. requirements and ends with a product description as is Moreover, since design is a dynamic process from ab- shown in Fig. 1. In a typical design process, design stract, simple and conceptual to speci"c, complex and requirements are represented by design speci"cations. detailed representations, design descriptions evolve and Based on the speci"cations, candidate design descrip- change through a design process. The representation tions are generated. The product description must be schemes should be able to support the changing descrip- evaluated against the prescribed design requirements to tions along the continuously evolving design processes. determine if the designed product satis"es the require- Research has been conducted on formulating the entities ments. The process iteratively generates conceptual, involved in design process, such as Yoshikawa [9], con"guration, and detailed designs. The design require- Salustri and Venter [10], Cheng and Zeng [11], and ments can be motives or demands for a completely new Maimon and Braha [12]. product, the complaints on the performance of existing Most of the existing work focused on product data products, or the failure due to malfunctions of existing models to support the development of product informa- products. Direct evaluation against design requirements tion systems and CAD systems. According to our present is usually not possible because they are usually given by studies, the problem is that the dynamic nature of design vague customers, requirements. Thus, the "rst step in process has not been captured. Consequently, the design process cannot be reasonably modeled. The present work is fundamentally di!erent from existing design object modeling [11,12]. The mathematical framework pro- posed in this paper attempts to embody the entities in design processes at di!erent levels of abstraction and complexity. Therefore, it can be used in the entire design process. Design speci"cations manifest themselves as a set of desired product properties which represent the geometri- cal, physical, economic, and other design-related proper- ties of the product. Denoting design speci"cations and product properties as RB and E, respectively, we have B"+ B B"j G G G3 R rH: rH (e ,[e ]), e E, " " , i 1, 2,2, j 1, 2,2, nP (1) where [eG] is a constraint on product property eG. The Fig. 1. Design activity. symbol nP is the number of listed design requirements. Y. Zeng, P. Gu / Robotics and Computer Integrated Manufacturing 15 (1999) 341}352 343 According to the de"nition, a design speci"cation can be de"ning design speci"cations and product descriptions viewed as a predicate j(eG,[eG]). are then speci"ed. Product descriptions, denoted by S, are the representa- tion of design solutions. Design solutions are usually described by concepts, con"gurations, or product draw- 3. Design speci5cations ings, depending on stages of a design process. They are usually de"ned by a set of product properties 3.1. Design requirements S"+eG: i"1, 2,2, n , eG3E,, (2) Q From the product life cycle point of view, any product where nQ is the number of properties with which a prod- design must take into account a number of requirements uct can be completely de"ned. For example, a rectangle regarding functionality, safety, manufacturability, assem- can be su$ciently de"ned by its shape, length, and width bly, testing, shipping, distribution, operation, services, where nQ is three. We can also de"ne it by four vertex re-manufacturing, recycling and disposal [15]. These re- points where nQ is 4. Any more information in both cases quirements can be investigated by viewing a product as would be redundant. an object in its working environment, as is shown in A mechanical design process is generally divided into Fig. 3. A product responds to an action from its working conceptual, con"guration, and detailed design phases.
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