Kinematics and Discretization of Curved-Fold Mechanisms

We present several new properties of curved-fold mechanisms, those with smoothly curved surfaces joined by sharp curved folds. After describing curved folds and various relationships among their geometric properties, we show that there is an important class, uniform folds, that is particularly well suited to low-degree-of-freedom mechanisms. There is a natural discretization algorithm for uniform curved folds; we present this algorithm and show discretized example mechanisms.