In Ali’s original gravitational wave detection project,The gravitational wave detection telescope requires a large-size azimuth shaft coupling,while meeting the needs of a large number of cables and high torsional rigidity.Torsional stiffness needs to reach 1×10^5 N⋅m/rad.Due to its simple structure and convenient processing,the slit coupling can be widely used in the transmission of the azimuth shafting of the astronomical telescope.This paper uses finite element software to analyze and compare the key structural parameters of the slit coupling and optimize the torsional stiffness.A large-size slit coupling suitable for gravitational wave detection telescopes was designed in combination with project requirements,which meets the design requirements and has certain guiding significance for the design of other slit couplings.