A transformational approach to mechanical design synthesis

During the design process, a designer transforms an abstract functional description for a device into a physical description that satisfies the functional requirements. In this sense, design is a transformation from the functional domain to the physical domain; however, this transformation process is not well characterized nor understood for mechanical systems. The difficulty arises, at least in pan, because mechanical designs are often composed of highly-integrated, tightly-coupled components where the interactions among the components are essential to the behavior and economic execution of the design. Each component may contribute to several required behavion, and a single required system behavior may involve many components. In fact, most mechanical components perform not only the desired behavior, but also many additional, unintended behaviors. In good mechanical designs, these additional behaviors often are exploited. The long term goal of our research is to create a transformational strategy in which the design specifications for a mechanical system can be transformed into a description of a collection of mechanical components. To realize this goal requires formal representations for the behavioral and the physical specifications of mechanical systems as well as formal representations for the behaviors and the physical characteristics of mechanical components. Because the interactions of components are important in our synthesis strategy, the represenution of the behaviors of mechanical components must be linked to the representation of their physical characteristics; that is, we are concerned with modeling the relationship between form and function of components. Finally, we need a strategy that enables us to transform an abstract description of the desired behavior of a device into a description that corresponds to a collection of available physical components. We present a graph-based language to describe both the behavioral specifications of a design as well as the behavior of the available physical components. We also demonstrate how the specification graph may be transformed so as to correspond to collections of available components. Introduction During the design process, a designer transforms an abstract functional description for a device into a physical description that satisfies the functional requirements. In this sense, design is a transformation from the functional domain to the physical domain [Mostow 85, Rinderle 82); however, the basis for selecting appropriate transformations and methods for accomplishing transformations are not well understood. The implicit basis for design transformations in circuits [Steinberg 86], software (Winh 71], and some architectural applications [Fenves 87] result in a degree and type of modularity not well suited to mechanical devices rRinderle861. 'Mechanical engineer* tend ID aw Ae words nnctaoa and behavior toerchangeably. Qualitative physicists make a distinction between these worts; that is. the design's fvxtio* is what it is used for. while its fttteuor is what il does. Fbrcxjmpte.thefunctwnc/tclccktttodi^yiheum^buiiubehtvwr might be the location of hands. Similarly, a mow may be designed IO function as a prime mover, but can also function as a door flop because it has additional behaviors due to its mass. In this paper./bic&M is used io indicate the subset of behaviors which are required lor the device to perform aatistaorily. Consider the design of a simple gear box as in example of a transformational approach to design and one specific approach to selecting and applying transformations. The gear box must provide a 25:1 speed reduction, a right angle configuration between the input and output shafts, and an offset between the input and output sha/ts. These three functional requirements are shown in Figure 1. The speed reduction requirement i% further decomposed into a pair of speed reducers as shown in the figure. Each of the lowest level requirements is then transformed into a collection of physical devices. Each of the 5:1 speed reductions are transformed into spur gear pairs. The right angle requirement is transformed into a miter gear set and the offset requirement is transformed into a l l spur gear set These four sett of gears may be combined to achieve the overall device functionality. The device as a whole consists of three spur gear sets, and one miter gear set, totaling 8 separate gear* This solution is obviously large, cumbersome, and costly, particularly compared to a single worm gear set, such as that shown in Figure 2. The worm gear set accomplishes the steep speed reduction, the nght angle requirement and the offset shaft requirements ail ia a single device. UNIVERSITY LIBRARIES CARNEGIE MELLON UNIVERSITY PITTSBURGH, PA 15213-3890 does not enable the more economical