A design engine systematically explores a design space associated with a design problem related to mechanical assemblies. The design engine implements a constraint programming approach to produce mechanical assembly configurations that adhere to a set of design constraints. For each feasible configuration, the design engine then optimizes various parameters to generate design options that meet a set of design objectives. With these techniques, the design space can be explored very quickly to generate significantly more feasible design options for the mechanical assembly than possible with conventional manual approaches. Accordingly, numerous design options can be generated that may otherwise never be produced using those conventional approaches.