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In this paper, a new desktop orthogonal-type robot, which has abilities of compliant motion and stick-slip motion, is first presented for lapping small metallic molds with curved surface. The robot consists of three single-axis devices with a high position resolution of 1 μm. A thin wood stick tool is attached to the tip of the z-axis. The tool tip has a small ball-end shape. The control system is composed of a force feedback loop, position feedback loop and position feedforward loop. The force feedback loop controls the polishing force consisting of tool contact force and kinetic friction forces. The position feedback loop controls the position in pick feed direction, e.g., z-direction. The position feedforward loop leads the tool tip along a desired trajectory called cutter location data (CL data). The CL data are generated from the main-processor of a CAM system. The proposed robot realizes a compliant motion required for the surface following control along a spiral path. In order to improve the lapping performance, a small stick-slip motion control strategy is further added to the control system. The small stick-slip motion is orthogonally generated to the direction of the tool moving direction. Generally, the stick-slip motion is an undesirable phenomenon and should be eliminated in precision machineries. However, the proposed robot employs a small stick-slip motion to improve the lapping quality. The effectiveness of the robot is examined through an actual lapping test of an LED lens mold with a diameter of 4 mm.