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We present design and experimental performance results for a novel mechanism for robotic legged locomotion at the mesoscale (from hundreds of microns to tens of centimeters). The new mechanism is compact and strikes a balance between conflicting design objectives, exhibiting high foot forces and low power consumption. It enables a small robot to traverse a compliant, slippery, tubular environment, even while climbing against gravity. This mechanism is useful for many mesoscale locomotion tasks, including endoscopic capsule robot locomotion in the gastrointestinal tract. It has enabled fabrication of the first legged endoscopic capsule robot whose mechanical components match the dimensions of commercial pill cameras (11 mm diameter by 25 mm long). A novel slot-follower mechanism driven via lead screw enables the mechanical components of the capsule robot to be as small while simultaneously generating 0.63 N average propulsive force at each leg tip. In this paper, we describe kinematic and static analyses of the lead screw and slot-follower mechanisms, optimization of design parameters, and experimental design and tuning of a gait suitable for locomotion. A series of ex vivo experiments demonstrate capsule performance and ability to traverse the intestine in a manner suitable for inspection of the colon in a time period equivalent to standard colonoscopy.