Previous research has shown automated robotic mechanism design to be both deceptive (prone to local minima) and rife with linkage problems (having highly interdependent parameters). This results in a barrier to optimization that is unable to be breached by simply applying more iterations and computational power. The research also indicates that a graph structure model of the robot in combination with an evolutionary algorithm yields useful robotic mechanisms for a limited set of simple problems. This thesis expands on this pre-existing representation by introducing an indirect model that can be used to include both controllers, motors and other new elements in the representation. Besides this extension of the mechanism model, a framework for the automated design optimization task itself is introduced. This thesis shows an equivalence between an operator based representation of the mechanisms and the graph based representation. These operators represent modifications on the mechanism structure and/or parameters. By recognizing the operators as paths in this model a graph of the search space itself can be constructed. In this graph the vertices are mechanisms and the edges are operators. Using the the operator-mechanism equivalence it is shown that designing an optimization algorithm is equivalent to (1) choosing how vertices in the space are grouped together. (2) choosing how the vertices of this search space are connected beforehand by either implicitly or explicitly picking operators and projecting onto their corresponding domain. (3) picking which of the connected paths to traverse based on accumulated information at runtime. This represents a framework that allows the accumulation of knowledge about optimization algorithms acting within it by defining a set of meta-heuristics. With these it is possible to make informed choices to build better optimization algorithms. To show the effectiveness of the framework a novel quality diversity algorithm is developed, Reduced Operator-Space Evolution (ROSE), which uses the insights mentioned above to generate a large diversity of well performing mechanisms simultaneously on a representative pick-and-place task. This confirms the theoretical results about the effect of the operator-mechanism equivalence and locality properties. A new step forward to breaching the barrier to optimization. Alongside this thesis a performant simulation and analysis Python library for mechanisms was developed called PyMechs. The library visualizes the framework and handles mechanism simulation and evaluation, as well as implements ROSE. It is available at https://github.com/kooswestra/pymechs.