Abstract: A core issue in collaborative robotics is that of impact mitigation, especially when collisions happen with operators. Passively compliant structures can be used as the frame of the cobot, although, usually, they are implemented by means of a single DoF. However, n-DoF preloaded structures offer a number of advantages, in terms of flexibility in designing their behavior. In this work we propose a comprehensive framework for classifying n-DoF preloaded structures, including 1-, 2-, and 3-dimensional arrays. Furthermore, we investigate the implications of the peculiar behavior of these structures which present sharp stiff-to-compliant transitions at design-determined load thresholds on impact mitigation. To this regard, an analytical n-DoF dynamic model was developed and numerically implemented. A prototype of a 10-DoF structure was tested under static and impact loads, showing a very good agreement with the model. Future developments will see the application of n-DoF preloaded structures to impact mitigation on cobots and in the field of mobile robots, as well as to the field of novel architected materials.