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We describe a simple system that localizes two-dimensional curved shapes through touch sensing, offering computational and experimental studies. The idea lies in determining the placement of a manipulator on a curved object during some special motion—rolling. A geometric algorithm is introduced to locate the boundary segment traced out by their contact using tactile data. Both completeness and local convergence have been established. The algorithm is asymptotically as efficient as evaluating the object's perimeter through numerical integration. For implementation, a two-axis force/torque sensor has been designed to realize contact sensing. Functioning like a “wrist,” the sensor is calibrated over the ratio between the bending and twisting moments, eliminating the need for known weights. A simple geometry-based control strategy is devised to implement the rolling motion. Experiments have been conducted with an Adept Cobra 600 manipulator.