A kinematic model of a 6-DOF precision levitation stage is developed by equivalent chains consisting of universal joints

extensible legs and planar joints instead of non-contact actuators and bearings.The moving platform in-plane motion is independent of its out-of-plane motion while rotation displacements are small

and this kinematic characteristic does not change if extensible legs are not perpendicular with the base surface

so the accuracy of this stage mainly depends on the measurement system accuracy.Based on Euler's rotation theorem

a 3-D measurement alignment error model for in-plane motion of the precision levitation stage is derived by calculating the distance of two intersection points of the L-shape mirror and the laser beam

and the influence of alignment errors on measurement error is analyzed by calculating error distributions and their sensitivity to error sources.The results show that the sensitivity of out-of-plane alignment errors

and which is ignored in the previous 2-D analysis

may reach to 25% of the sensitivity of in-plane alignment error

and the most important error sources include L-shape mirror alignment error caused by rotation around z-axis and its orthogonal error.