Optimised kinematic mount configuration for high-precision applications

Abstract

The generic kinematic mount design configuration, designated as the Maxwell-type kinematic mount, is constituted by three V-grooves on one end and three balls on the other so as to achieve an exact constraint of all six degrees of freedom. The analysis of this coupling configuration comprises force and moment balance equations, as well as expressions for stressstrain and error motion calculations. For a determined external load, the geometry of the mount will thus imply the loads at each groove-ball interface and the respective contact point reactions. The calculation comprises the necessity to deal with the non-linear Hertzian theory of point contacts. This work recalls the limits of applicability of the available analytical approaches for the calculation of ball-V groove couplings employed in ultra-high precision positioning. The analytical results are validated experimentally. In the whole range of elastic deformations the correspondence of the theoretical values with the experimental ones is within the intervals of uncertainty of the latter. The calculation procedure is then used to assess the optimal characteristics of a kinematic mount employed to support a large vacuum chamber of a particle accelerator facility. Stability conditions for different design configurations are established.