A Shape Metric for Design-for-Assembly

1 Introduction
\Design-for-Assembly"(DFA) is a process of improving product designs for easy and low cost assembly. An assembly-conscious design is desirable because it could result in signi cant savings in capital costs and assembly time. For example, the IBM Corporation has successfully applied the concept of DFA to one of its printer models, by redesigning and reducing the number of parts, which drastically lowered the printer's assembly cost, and price 3]. An assembly-conscious design is di cult, in general, because designers tend to focus only on the functionality of the product. Considering \assemblability" concurrently with the functionality of a product seems to be a major source of distraction that most traditional designers would like to avoid. This is especially
This project is supported in part by the Institute for Manufacturing and Automation Research (IMAR) Project No. 4 and by the National Science Foundation. Support for Dr. Goldberg is provided in part by a 1991 USC Faculty Research Initiation Fund (FRIF) grant.
Abstract
\Design-for-Assembly" (DFA) is a process of improving product designs for easy and low cost assembly. DFA often involves an analysis of an existing design according to qualitative criteria that are di cult to analyze. This paper introduces a quantitative shape metric for planar parts, called feedability, based on a stochastic parts feeding algorithm reported in 7] 8]. Although feedability is only one possible metric for DFA, it relates one aspect of assembly cost directly to part geometry. Therefore, based on feedability, one can produce a set of geometric redesign strategies. The application of feedability (or Design-for-Feedability) to DFA is illustrated and compared with other DFA methods.
apparent when there exist many parts exerting various constraints upon one other. Therefore, there is a desire to automate the DFA process, at least partially, through the use of computers. The purpose of this paper is to introduce a quantitative metric for part shapes, called feedability, and demonstrate its use. Although feedability is only one possible metric for DFA, it relates DFA cost directly to part geometry. Therefore, various redesign strategies are possible by manipulating the geometric parameters of the part and their constraints to improve the feedability. In a previous paper 10], we proposed a model for the DFA process that consists of iterations of three successive stages: analysis, suggestion, and veri cation. The actual implementation revealed some fundamental problems. One of the most important problems was that the current methods of DFA analysis lack a scienti c foundation that can associate DFA cost to a particular set of low level or geometrical design actions. Therefore, current DFA methods can only produce redesign strategies in terms of high level design axioms or design rules: for example, \make part A symmetric", \add a gripping feature to part B", \redesign part C to avoid tangling", etc. The geometric details for achieving above objectives have to made by the humans. One of the goal of this paper is to introduce low level redesign strategies by introducing a metric that can relate assembly cost to part geometry. Then, geometric redesign advice would be possible: for example, \change the length of part A from 3 inches to 5 inches in order to make it symmetror Design-for-Assembly
Gerard J. Kim, George A. Bekey and Kenneth Y. Goldberg Center for Manufacturing and Automation Research Computer Science Department University of Southern California, LA, CA 90089-0782, USA E-mail: gkim@, bekey@, goldberg@
2 Other Methods of DFA
Currently, there exist two main types of DFA methods. The most popular method is typi ed by the one pioneered by Boothroyd and Dewhurst 4]. In their approach, a product is analyzed according to various
\ease of assembly" criteria (such as symmetry, dimension, mating direction, number of parts, etc), organized with charts of scores, and a tabulated score is used to calculate a \design e ciency ratio". The scoring system (or the DFA metric) is empirically based on an engineering time study method 16]. Then, a redesign is proposed manually with the help of the score table which, more or less, pinpoints the source of the design problem. Many other commercial systems or in-house methods 11] 14] 15] are based on this approach partly because the table lookup and the arithmetic procedure is easily computerizable. The second type of approach is called the \axiomatic method". The axiomatic method is simply a set of design guidelines that have been empirically derived from years of experiences in design and assembly operations. If correctly applied either during the initial design phase or the redesign phase, they should result in a product that has an inherently low assembly cost 9]. Many such DFA axioms have been identi ed by a number of researchers 2] 3] 9]. In particular, in an e ort to make the axiomatic method more evaluative, Hoekstra has assigned scores to each of the design axioms in a subjective manner (for example, in a scale of 1 to 5). The rst method is suited for a comparative analysis of nished designs, but can not be applied to evolving designs. In practice, the score tables are very useful in analyzing and evaluating designs in terms of DFA. Nevertheless, such tools still have the drawback that they lack a capability of helping designers to explore new possibilities 6]. The second method allows the designer to consider assemblability from the initial design phase. However, in general, the second method lack quantitative measures for analysis and evaluation of nal or evolving designs 16]. Although Hoekstra's scoring system for the design axioms improved upon the evaluating capability of the axiomatic method, it is based on a subjective point of view, and can not relate its scores directly to part geometry. Suh has also cautioned against the handbook approach for the lack of theoretical conception and scienti c basis for the design axioms 17]. A more objective and analytic metric with a scienti c basis, which relates assembly cost directly to the design, could provide a systematic method of making geometric redesigns. Hoekstra best illustrated the need of such a metric by citing part of the following round table discussion on \Design for Assembly" reported in a recent Assembly Engineering Magazine 5] 9]. Among the panelists were G. Boothroyd, W. Morill (Manager, Design for Manufacturability, Digi-