This paper presents some theorems of the fixed point for decreasing operators in Banach spaces with lattice structure. The results are applied to nonlinear second-order elliptic equations. MSC: 47H10; 34B15

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The analytical expression of driving force is helpful to quickly plan the kinematic trajectory of parallel mechanism for automatic drilling and riveting. For parallel posture alignment mechanism, because of its closed-loop characteristics, the inverse dynamic solution is more complex, especially for parallel bracket with actuation redundancy. Considering that the telescopic rods are actually flexible parts, the dynamic analytical modeling is carried out with deformation supplementary equation. Taking the force at the spherical joint as the intermediate variable and the driving force of each active prismatic pair are analytically analyzed by vector cross-product. The modeling was verified by experiment. Compared with previous research methods, the analytical method proposed improves the solution accuracy of driving force slightly and reduces the driving force solution time by 56.28%, which is high efficiency. The maximum error percentage is 1.61%, and the experimental results show that the method of inverse dynamics modeling is practical. This paper can be used for driving force analysis of parallel posture alignment mechanism based on positioner in the field of aircraft assembly.