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This paper describes a novel microassembly system that can be used to construct out-of-plane three-dimensional (3-D) microstructures. The system makes use of a surface-micromachined microgripper that is solder bonded to a robotic manipulator. The microgripper is able to grasp a micropart, remove it from the chip, reorient it about two independent axes, translate it along the x, y and z axes to a secondary location, and join it to another micropart. In this way, out-of-plane 3-D microstructures can be assembled from a set of initially planar and parallel surface micromachined microparts. The microgripper is 380 × 410 μm in size. It utilizes three geometric features for operation: 1) compliant beams to allow for deflection at the grasping tips; 2) self-tightening geometry during grasping; and 3) 3-D interlocking geometry to secure a micropart after the grasp. Each micropart has three geometric features built into its body. The first is the interlock interface feature that allows it to be grasped by the microgripper. The second is a tether feature that secures the micropart to the substrate, and breaks away after the microgripper has grasped the micropart. The third is the snap-lock feature, which is used to join the micropart to other microparts.