In this paper, we establish the underlying foundations of mechanisms that are composed of cell structures---known as metamaterial mechanisms. Such metamaterial mechanisms were previously shown to implement complete mechanisms in the cell structure of a 3D printed material, without the need for assembly. However, their design is highly challenging. A mechanism consists of many cells that are interconnected and impose constraints on each other. This leads to unobvious and non-linear behavior of the mechanism, which impedes user design. In this work, we investigate the underlying topological constraints of such cell structures and their influence on the resulting mechanism. Based on these findings, we contribute a computational design tool that automatically creates a metamaterial mechanism from user-defined motion paths. This tool is only feasible because our novel abstract representation of the global constraints highly reduces the search space of possible cell arrangements.