Real time kinematic solutions of a non-contacting, three dimensional metrology frame

The forward and the inverse kinematics solutions for a three dimensional, non-contacting metrology system are presented. The solutions are a continuation of earlier works involving the derivation of an error budget for the metrology system; however, the earlier work required iterative methods. The kinematic solutions presented in this paper are closed form, providing real-time feedback and making the system practical for metrology applications. The kinematics 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 requires a few assumptions. In the development of the forward and inverse kinematics solutions, singularities of the system are identified. The resulting analyses provide the kinematics necessary to enable real-time determination of position and orientation of a target in space.