Shape-changing User Interfaces attract growing interest in Human-Computer Interaction. Modular robotics offer a great opportunity for their implementation. However, the current theoretical and technical advances of modular robotics are fragmented and little centered on the user. To unify existing work and center future research on the user, we perform a systematic literature review enabling us to build a unifying space for the design of modular shape-changing user interfaces.Our aim is to bridge the gap between HCI and robotics. We relate properties of different domains and identify inconsistencies to structure the design space. Towards this aim, we conduct a thorough cross-disciplinary survey to propose: 1) a set of design properties at the scale of the interface (macro-scale) and at the scale of the modules (micro-scale) and 2) the impact of these properties on each other. This paper can be used to describe and compare existing modular shape-changing UIs and generate new design ideas by building upon knowledge from robotics and HCI.