Research on Degree of Freedom of Secondary Mirror Truss Mechanism Based on Screw Theory and Geometry Algebra Applied on Large Telescopes

Abstract A design for a truss mechanism of a secondary mirror based on robotics is proposed. This design would allow for the construction of larger vehicle-mobile telescopes. As the new truss mechanism combines the original support structure and adjustment mechanism, the problems in designing new structures needs to be overcome. In this paper, the basic form of the truss mechanism is determined by finite element method, and the number of limbs meeting the requirements of resonance frequencies and stiffness is obtained. Degrees-of-freedom of the new truss mechanism is calculated by motion space based on geometry algebra and screw theory, It can provide more accurate and specific results compared with the G-K formula. The optimal structure is calculated to meet the requirement in degrees-of-freedom with the minimum possible limbs and kinematic pairs. After the form and the value of joints are determined, the deformations are calculated by stiffness evaluation index. Wavefront aberrations simulated with Zernike polynomials are used to verify the structure.

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