A concept for a three dimensional, non-contacting metrology system is presented. Both the forward and the inverse kinematics solutions for the system are developed using a line geometry, resulting in an efficient representation that may describe a general assembly of the kinematic system and error parameters determined through calibration. The inverse kinematics solution is a general solution, assuming very little about the assembly of the system. The forward kinematics solution is less general and resorts to making a few assumptions. In the development of the forward and inverse kinematics solutions singularities of the system are identified.