The linkage mechanism of a cotton bundle fiber strength tester will have an unstable clamping force when clamping fiber bundle samples with uneven thickness, resulting in slippage or damage to the fibers increasing the pectin residue, leading to inaccurate test results and increased maintenance costs. To address this problem, according to the structural principle of the connecting rod-clamping mechanism, through the geometric relationship between the connecting rods to establish a parametric model of the mechanism and the use of the principle of virtual work on the mechanism to solve the force, the proposed new Dynamic Alternative Static Approximate Analysis Method (DASAAM) was based on Adams 2020. The Isight integrated Adams automatic optimization design framework was built. The variance of the change curve of the end force of the mechanism when clamping samples of different thicknesses was used as the evaluation function and the assembly conditions were used as the constraints. The dimensional parameters and angles of the mechanism were optimized using the multi-island genetic algorithm. The simulation results showed that when the thickness of the clamped sample varied in the range of 0–4 mm, the clamping force of the mechanism varied in the range of 8920–8630 N. Finally, the variance of the clamping force measured by the clamping force measurement component was 0.0367. The above results show that the DASAAM provided a new method for solving the static problem of mechanism morphological and position change, and the optimized linkage mechanism had better clamping force stability, which made the strength detection of cotton fiber more accurate, thus improving the quality of textile products.