Laser Doppler Vibrometry is now a well established experimental technique and commercially available instruments are gaining in popularity. This paper sets out a comprehensive model of the velocity sensed by both a single laser beam and by a pair of parallel beams incident on a rotating shaft requiring three translational and three rotational coordinates to describe its vibratory motion fully. While the intention is to measure the six vibration components, the model reveals how it is instead only possible to measure six vibration "sets", each inseparable combinations of more than one of the vibration components. Arrangements for isolation of each "set" are detailed and an essential postprocessing technique to resolve translational and rotational vibration components is demonstrated in a measurement of crankshaft bending vibration.