The field of aerial robotics has advanced rapidly, but the design knowledge has not yet been codified into reusable design principles. Design principles have been developed for many other areas of mechanical design to both advance the field itself and help novice designers benefit from the past expert knowledge easier. We used an inductive approach and collected 90 aerial robot examples through the reviewing of recent work in aerial robotics and studying the key motivations, features, functionalities and potential design contradictions. Then, design principles are iteratively derived by identifying patterns and grouping them by the problem they solve, and the innovation made to solve it. From this, we find 35 unique design examples that can be grouped into either fourteen design principles for more sensing, battery, mission, or actuation efficient design; or six design principles to improve a desired functionality in an aerial robot such as reducing complexity or improving how the robot can interact with objects or its environment. We compared the research results with similar work in the area of mechanical design and examined the commonalities and highlighted design principles unique to aerial robots. The design principles presented in this research can support the design for future innovative aerial robots.