While LLM agents can generate visually plausible CAD assemblies, these designs often fail to fulfill their intended physical functions. We study functional CAD design, a setting where agents interpret underspecified requests to construct and iteratively revise mechanisms that satisfy functional requirements in physical simulation. Verifying these requirements is nontrivial: different candidate mechanisms may realize the same function through entirely different components, controls, and operating sequences. To bridge this gap, we propose FunCAD-Harness, a framework that translates abstract requirements into candidate-specific physical tests and uses simulation feedback to guide design revisions. To systematically evaluate this capability, we introduce FunCADBench, a benchmark spanning 46 mechanism families with interdependent and multi-step operations. Experiments across frontier LLM agents show that FunCAD-Harness exposes subtle mechanical failures invisible to visual inspection, substantially improving functional success rates over standard simulation-augmented baselines. Ultimately, our work marks a step toward CAD agents capable of translating human intent into working mechanisms.

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