The novel synthesis of origami-inspired mechanisms based on graph theory

In this paper, a novel synthesis approach based on graph theory is proposed. This approach can be used to design the creases of origami mechanisms. All possible contracted graphs of the 1-DOF origami mechanism are provided based on the number and graph synthesis methods. Then, a new method named loop synthesis is presented and this method is used to obtain different loop situations of the contracted graphs considering the structural characteristics of the origami mechanism. Two theorems are proposed and proven to determine the availability of loop situations. Furthermore, a modified thick panel design method for the origami mechanism is presented, and both single units and multiple units of the origami mechanism are modelled. At the same time, a rotary actuator based on this mechanism is introduced to verify the validity of the above synthesis approach. Finally, rotation, repeatability, and static torque tests are conducted to measure the inherent stiffness constant of the actuator. This approach, which was proven to be effective for designing the origami mechanism, can be readily applied to generate the desired mechanism.