Modeling of compliant-based support for large aperture rotary prisms with horizontal-axis

In the Thirty-Meter-Telescope (TMT), a pair of wedge prisms with diameters of approximately 1500 mm are proposed to mitigate atmospheric dispersion across different zenith angles. This is achieved through controlled linear and rotary movements of the prisms. However, providing stable support for such large aperture prisms, with variable cross-sections and capable of rotating 360° around a horizontal optical axis, poses a significant challenge. This paper introduces a compliant-based support method tailored for TMT's large aperture prisms. The methodology involves a mechanical analysis of the wedge prism with push-pull forces combination, followed by the development of the support principle based on degrees of freedom and constraints analysis. Subsequently, numerical modeling is conducted using compliant elements as the fundamental units. Furthermore, an integrated optomechanical analysis is performed to evaluate the performance of the support. The findings demonstrate that employing this support method results in superior optical surface accuracy under the coupled conditions of gravity and temperature, particularly for prisms with large apertures, variable cross-sections, and rotational capabilities.