A vision-based motion sensor for undergraduate labs

Abstract

In the undergraduate physics laboratory classes, experiments on mechanics play an important role. Famous examples like the pendulum, the freely falling body, the gyroscope and coupled pendulum are few of the first experiences with experiments for most physicists. An essential part in these experiments is to convert the motion of a three-dimensional object into a position-time diagram. Usually this conversion is made before the actual measuring process. This means that the number of data points is strongly reduced by the design of the experiment. In the investigation of the pendulum for instance, a theoretical analysis shows that the period is the quantity of interest, while in a free fall experiment three sets of y-t coordinates completely determine the motion of the falling object. This knowledge determines the way the experiment is performed. For the pendulum experiment, a simple stopwatch can be used to measure the period of oscillation. In the free fall experiment, several light sensors turned out to be sufficient to determine the gravitational acceleration. These different methods illustrate that the method is usually adapted to the system under investigation.
Recently a new, more general approach has been developed in order to investigate the mechanics of moving objects. In this method, the motion is recorded with a video camera. Hence the process of data reduction can be done after the measurement. In commercial software like Videopoint, the motion ofthe object can be determined by indicating the center of mass in each frame of the recorded video. An object of well-known size is required in the image for calibration purposes. With present capability of personal computers, this technique is now affordable for undergraduate laboratories. The drawback of this method is that estimating the center of mass at every single frame is not only boring, it also introduces significant errors in determining the position. A closer investigation of the program has revealed a second problem. The time between the consecutive frames is not constant; introducing random errors in the timing, a problem that seems to be hard to circumvent using a video camera.
In this paper we present an alternative for this, which we call the vision-based motion sensor. To avoid the timing problem, inherent on the use of the video camera, we chose a CCD camera for the recording. After retrieving a set of consecutive frames, the images were analyzed by our processing program. This program automatically finds the center of mass of the moving object. In combination with a user-friendly calibration interface, our method has the promise to become an accurate motion sensor that can be applied in many different experiments.