Although multi-touch interaction in 2D has become widespread on mobile devices, intuitive ways to interact with 3D objects has not been thoroughly explored. We present a study on natural and guided multi-touch interaction with 3D objects on a 2D multi-touch display. Specifically, we focus on interactions with 3D objects that have either rotational, tightening, or switching components on mechanisms that might be found in mechanical operation or training simulations. The results of our study led to the following contributions: a classification procedure for determining the category and nature of a gesture, an initial user-defined gesture set for multi-touch gestures applied to 3D objects, and user preferences with regards to metaphorical versus physical gestures.