In this paper, we present a novel grasp detection algorithm targeted towards assistive robotic manipulation systems. We consider the problem of detecting robotic grasps using only the raw point cloud depth data of a scene containing unknown objects, and apply a geometric approach that categorizes objects into geometric shape primitives based on an analysis of local surface properties. Grasps are detected without a priori models, and the approach can generalize to any number of novel objects that fall within the shape primitive categories. Our approach generates multiple candidate object grasps, which moreover are semantically meaningful and similar to what a human would generate when teleoperating the robot-and thus should be suitable manipulation goals for assistive robotic systems. An evaluation of our algorithm on 30 household objects includes a pilot user study, confirms the robustness of the detected grasps and was conducted in real-world experiments using an assistive robotic arm.