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This paper proposes three design concepts for developing a crawling robot inspired by an inchworm, called the Omegabot. First, for locomotion, the robot strides by bending its body into an omega shape; anisotropic friction pads enable the robot to move forward using this simple motion. Second, the robot body is made of a single part but has two four-bar mechanisms and one spherical six-bar mechanism; the mechanisms are 2-D patterned into a single piece of composite and folded to become a robot body that weighs less than 1 g and that can crawl and steer. This design does not require the assembly of various mechanisms of the body structure, thereby simplifying the fabrication process. Third, a new concept for using a shape-memory alloy (SMA) coil-spring actuator is proposed; the coil spring is designed to have a large spring index and to work over a large pitch-angle range. This large-index-and-pitch SMA spring actuator cools faster and requires less energy, without compromising the amount of force and displacement that it can produce. Therefore, the frequency and the efficiency of the actuator are improved. A prototype was used to demonstrate that the inchworm-inspired, novel, small-scale, lightweight robot manufactured on a single piece of composite can crawl and steer.