Design grammars enable the formal representation of a vocabulary and rules that describe how designs can be synthesized just as the grammar rules of a spoken language define how to formulate valid, i.e., grammatically correct, sentences. Design grammars have been successfully applied in numerous engineering disciplines and enable the automated synthesis of designs within a defined design language. Design grammar development, however, is challenging and lacks methodological support. In this paper, a novel method is presented that supports the development and application of design grammars using transition graphs. In these, nodes represent generated designs and edges represent grammar rules that transform one design into another. Rather than using a tree structure to represent the possible application of rules, transition graphs are automatically generated and used to help designers better understand the developed grammar. The grammar designer is given feedback on (a) the rules, and (b) rule application sequences. This feedback can be used to (a) improve the grammar, and (b) apply it more efficiently. Two case studies, a gearbox synthesis task and a sliding tile puzzle, demonstrate the method. The results show the feasibility of the method to support design grammar development and application.