In order to develop better touch and gesture user interfaces, it is important to be able to measure how humans move their hands while interacting with technical devices. The recent advances in high-speed imaging technology and in image-based object tracking techniques have made it possible to accurately measure the hand movement from videos without the need for data gloves or other sensors that would limit the natural hand movements. In this paper, we propose a complete framework to measure hand movements in 3D in human-computer interaction situations. The framework includes the composition of the measurement setup, selecting the object tracking methods, post-processing of the motion trajectories, 3D trajectory reconstruction, and characterizing and visualizing the movement data. We demonstrate the framework in a context where 3D touch screen usability is studied with 3D stimuli.