Type synthesis of 90 degrees/180 degrees dual-function upenders for large shell units of nuclear reactor

In this paper, unit vectors collinear with the axes of large shell units of nuclear reactors were used to represent the poses of the workpieces. Based on the motion operator interpretation of the rotation matrix, 60 kinds of rotation matrix permutations with 90 degrees turns as the step length to achieve 180 degrees flipping of the workpiece were obtained. After eliminating invalid permutations and merging homogenous permutations, class I, II, and III flipping motion models were obtained. By calculating the Lie algebra of each step of rigid body motion in the flipping motion model, the twist and the motion pair property for each step were obtained. By means of the permutation and combination theory, the sequence of the motion pairs for different configurations was determined, and the rules between sequential transformations and axis changes of the motion pairs under the initial configuration were stipulated. Three classes of 19 initial configurations of 90 degrees/180 degrees dual-function upenders were constructed. For three of them, taking into account the characteristics of the axial dimension variation of workpieces, prismatic pairs were added along the workpiece's axis (vector), and 15 overall configurations of 90 degrees/180 degrees dual-function upenders were synthesized. This provides the basic theoretical support for the innovative design of upenders with independent intellectual property rights.