Kinematic Design of Miura-Ori-Based Folding Structures Using the Screw Axis of a Relative Displacement

This chapter provides a kinematic design approach for specific folding structures, consisting of vertices with four intersecting creases, such that they can achieve two given folding configurations. These configurations are defined in terms of up to two planar curves, which are approximated by a polyline that is a particular part of the folding structure. We call these structures Miura-ori-based structures or linkages because the design approach makes use of the particular motion characteristics of the 1-DOF mechanism equivalent of the Miura-ori folding pattern. To achieve the design goal we apply a two-configuration synthesis, also provided in a previous work, which is based on the screw axis of a specific relative displacement. A classification of the slide along the screw axis allows it to determine the creases connecting consecutive links of the folding structure as revolute joints.