The theory needed to extract three-dimensional size, shape, and motion of a rigid moving body from a series of range-only measurements is explained. For a rigid body, moving with arbitrarily complex, unknown motions, the three-dimensional size and shape of a configuration of points on the body can be calculated from the range data, without any prior knowledge of the geometry of the configuration. The calculations are possible because there exist motion-invariant functions of the range data, which uniquely determine the Euclidean geometry of the points. This theory is shown to work on synthetic range data. When the synthetic data is corrupted by noise the process is shown to still produce reasonable results.