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Mechanical search, the finding and extracting of a known target object from a cluttered environment, is a key challenge in automating warehouse, home, retail, and industrial tasks. In this paper, we consider contexts in which occluding objects are to remain untouched, thus minimizing disruptions and avoiding toppling. We assume a 6-DOF robot with an RGBD camera and unicontact suction gripper mounted on its wrist. With this setup, the robot can move both camera and gripper in order to identify a suitable approach vector, reach in to achieve a suction grasp of the target object, and extract it. We present AVPLUG: Approach Vector PLanning for Unicontact Grasping, an algorithm that uses an octree occupancy model and Minkowski sum computation to find a collision-free grasp approach vector. Experiments in simulation and with a physical Fetch robot suggest that AVPLUG finds an approach vector up to 20× faster than a baseline search policy.