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We propose an automatic microassembly method that can be used to construct three-dimensional microelectromechanical system (MEMS) structures. A six degree-of-freedom micromanipulator, equipped with a passive microgripper, is employed to grasp, manipulate, and join the micropart using visual feedback from an optical microscope. The proposed process utilizes a two-stage alignment strategy to perform the micro-grasping and micro-joining tasks. Using a vision-based localization method, the Cartesian coordinates of the manipulated micropart in three-dimensional space are determined. Further, a vision-based contact sensor determines the contact state between two micro-components in three dimensions to facilitating the micro-joining tasks. Visual servo control is used for accurate position feedback in three Cartesian coordinates during microassembly tasks. The necessary steps towards construction of complex three-dimensional MEMS devices, i.e., grasping a micropart, manipulating it, joining it to another micropart, and finally releasing it from the microgripper, have been successfully carried out using a six degree-of-freedom micromanipulator. Experiments demonstrate both the efficiency and validity of the proposed automatic assembly approach.