Analysis of 3D rigid-body motion using photogrammetry: A simple model based on a mechanical analogy

We present a technique based on 3D video photogrammetry for analyzing rigid body kinematics. The technique is based on a method for calculating the kinematic variables associated with rigid body motion. To illustrate the technique an analysis of the rolling motion of a truncated cone on a floor is performed. From the coordinates of a set of markers, kinematic parameters such as linear velocity, angular velocity, and the instantaneous axis of rotation can be measured. The complexity is appropriate for undergraduates using a mechanical analogy that relates linear and angular momentum to linear and angular velocities, respectively. The possibility of compounding simple rotational motions to achieve a more complex motion is also addressed.