In order to meet the requirements of high-precision positioning and adjustment of the secondary mirror of the telescope, the three-dimensional models of two kinds of 3-UPU parallel mechanisms are established. Firstly, the constraints and degrees of freedom(DOF) of the 3-UPU parallel mechanism platform are compared and analyzed by screw method. The analysis results show that the DOF of the mechanism is related to the spatial position relationship of the kinematic pairs. When the type and number of the kinematic pairs in the mechanism are the same, the DOF is not necessarily the same. Therefore, it is necessary to select the mechanism according to the supporting requirements of the secondary mirror and the motion characteristics of the mechanism. It is concluded that the 3-UPU parallel mechanism with non parallel upper and lower Hooke hinge planes has two rotational DOF and one translational DOF, which can meet the motion requirements of the secondary mirror rotating around and moving along the optical axis, and achieve accurate adjustment and positioning.
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