<p>This paper strengthens the link between the Moving Morphable Components (MMC) framework and feature-based CAD modelling. This has been achieved by applying CAD-based geometric constraints that define coincident, tangential, and normal constraints between components in the MMC framework. Perturbations of a parent component are propagated to connected child components and perturbations of a child component must respect the limitations imposed by any applied geometric constraint. Algebraic sensitivities have been calculated and demonstrated for each geometric constraint in the MMC framework using gradient-based optimisation. The results demonstrate the link with CAD-based modelling and highlight significant advantages from a design perspective. For example, it is shown that applying geometric constraints reduced the original eighty design variables required in a cantilever beam optimisation by 52.5% with only a 1.51% reduction in the optimised performance. This example was constructed with sixteen rectangular components.</p>