Minimal Actuation for a Flat Actuated Flexible Manifold

The fabrication of a multiactuator mechanism requires excessive wiring that may become the design's bottleneck. We introduce a novel actuation method for an actuated flexible manifold (AFM). The AFM is a 2-D surface embedded in ℝ² or ℝ³. The AFM shape can theoretically be manipulated into any continuous smooth function. The mechanism possesses dozens of degrees of freedom (DOF). However, an applicable AFM would require thousands or even an infinite number of DOF (for the continuous case). This paper addresses the need to aggressively reduce the number of inputs. To exemplify our optimization, we introduce an algorithm for the forward kinematics and the inverse kinematics for such mechanisms. We then present a periodic actuation method, which enables input reduction to its peripheral inputs alone. We show how a 40-DOF AFM can make the most of its capabilities, while the number of inputs substantially drops. To exemplify our results, we have fabricated an AFM as a grid using shape memory alloy artificial muscle wire. Our input method may simplify the fabrication process, reduce the mechanism's overall weight, and improve the actuation performance.