This research seeks to develop a synthesis formalism to aid and enhance the design of mechanical systems by harnessing the power of the computer. For computer-assisted generative design to be effective for exploring purposeful design possibilities to a given specification, many tasks that to date are performed manually or as part of designer-intensive computer-based processes must be approached in new ways. This research contributes a new type of production system, a parallel grammar for mechanical systems, developed using a Function-Behaviour-Structure representation, to generate and modify a variety of designs. Geometric and topological constraints are used to bound the design space, termed the language of the grammar, to ensure the validity of designs that can be generated with the grammar. Four case studies are considered, namely the design domain of mechanical clocks and watches, the redesign of an electromechanical camera winding mechanism, power drill design and the generation of alternative vehicle gearbox configurations. For verification purposes, the parallel grammar is used by hand to recreate existing designs. Computational generation of novel design configurations is driven by performance-based evaluation of designs using geometry-based metrics and behavioural analysis of automatically generated simulation models. Multi-objective stochastic search, in the form of a hybrid pattern search developed as part of this research, is used to generate Pareto sets of optimally directed designs. The work is validated through an investigation into the generation of novel transaxle gearbox designs in collaboration with an automotive power transmission design company.