Design of physical systems and associated control systems are coupled tasks; design methods that manage this interaction explicitly can produce system-optimal designs, whereas conventional sequential processes may not. Here we explore a new technique for combined physical system and control design (co-design) based on a simultaneous dynamic optimization approach known as direct transcription, which transforms infinitedimensional control design problems into finite dimensional nonlinear programming problems. While direct transcription problem dimension is often large, sparse problem structures and finegrained parallelism (among other advantageous properties) can be exploited to yield computationally efficient implementations. Extension of direct transcription to co-design gives rise to a new problem structures and new challenges. Here we illustrate direct transcription for co-design using a new automotive active suspension design example developed specifically for testing codesign methods. This example builds on prior active suspension problems by incorporating a more realistic physical design component that includes independent design variables and a broad set of physical design constraints, while maintaining linearity of the associated differential equations.