A Multi degrees of freedom displacement measurement system that is applicable to milli-structure is proposed. The principle of measurement is based on Optical Beam Deflection Method(OBDM), triangulation, and diffraction grating. A laser beam incident on a diffraction grating reflects the beam on several directions. Among these, $0^{th}$ and $±1^{st}$ order diffraction rays are detected by three 2-dimensional detectors, which are quadrant photodiodes. To solve the pose information of measured object, it is required to analyze the kinematic relation. This is composed of forward kinematics that relates object displacement and detector output and inverse kinematics which solves the pose information from the detector output. A numerical iterative method that adopted a constant number of iteration is applied to solve the nonlinear inverse kinematics. Sensitivity and uncertainty analysis show that sensitivity and uncertainty of system are related to the kinematic parameter of the system which is expressed as a condition number. Optimization is performed to find the kinematic parameters to minimize the condition number of measurement system. Experimental results show that the optimized system reduces the difference of sensitivity and uncertainty of each measurement axis. Static and dynamic experiments based on optimized parameter are performed. The results show that the proposed system has an accuracy of 1.4 $\mu$m in translation and 7.3 arcsec in rotation.
