Grammars for engineering design

Just as grammars for natural languages use rules to form grammatical sentences from a dictionary of words, grammars for engineering design use rules to make structures from a dictionary of shapes, properties, labels, and other elements. Engineering grammars may be used to help the designer generate and evaluate ideas and concepts during the conceptual phase of the design process. A formal definition of a grammar is given and some properties of grammars are discussed. Natural language grammars, shape grammars, and engineering grammars are defined. Some group-theoretic properties of shapes and operations are derived. It is shown that some sets of shapes form Boolean algebras under the standard regularized set operations. Polygonal tracings, which are extensions of the outlines of two-dimensional polygons, form a ring under the shape union and convolution (or generalized Minkowski sum) operations. A subset of polygonal tracings which includes all convex tracings, along with the convolution and shape scaling operations, form a vector space over the real numbers. The implications for grammar rules which use these types of shapes and operations are discussed. Grammars and expert systems are compared and contrasted. While the formalisms have similar definitions, some explicit differences exist. Furthermore, when the customary uses of the two systems are compared, large differences are evident. It is concluded that grammars are more well-suited to generating many alternative designs and searching large, unexplored design spaces, while expert systems function best in well-known domains when only one design is required. The formation and modification of grammatical rules is discussed, focusing on the relationships between form and function in design. Several strategies which could be used for the search for optimal designs in a grammar's language are considered. The significance of transformations used to apply rules is discussed. An extended example of grammars used to generate configurations of modular reconfigurable robot arms is presented. The grammars generate all non-isomorphic assembly configurations, while simultaneously calculating kinematic properties of the arms. Several methods of quickly searching for arms to satisfy various requirements are discussed.