Optimal displacement amplification ratio of bridge-type compliant mechanism flexure hinge using the Taguchi method with grey relational analysis

The compliant mechanism flexure hinge has been frequently utilized in precision enginering in recent years, such as the bridge-type and rhombus-type compliant mechanisms. While previous studies used the approximation mathamatic model to estimate the displacement amplification ratio, the results of such investigations obtained a displacement amplification ratio of approximately 30, thus, it is difficult to identify and obtain the maximum precision value. Therefore, this paper designed a new model for bridge-type compliant flexure in SOLIDWORK. The displacment amplification ratio was calculated using the finite element method in ANSYS, and the simualtion results reveal that the displacement amplification obtained 64.8 and the maximum value of stress of 101.5 MPa. Moreover, S/N analysis pointed out the factors that effect output displacement; first is the thickness of the flexure hinge, second is the length of the input body, third is the incline angle between two flexure hinges, and fourth is the fillet radius. The factors first effect on stress is the input body length, second is the thickness of the flexure hinge, third is the fillet radius of the flexure hinge, and finally, the incline angle between two flexure hinges. The ANOVA results identified the contribution of factors on the output displacement and stress. The R-sq of 99.86%, R-sq(adj) of 99.83%, and R-sq(pred) of 99.80% is output displacement. The R-sq of 99.93%, R-sq(adj) of 99.90%, and R-sq(pred) of 99.85% is output stress. The R-sq of 99.75%, R-sq(adj) of 99.67%, and R-sq(pred) of 99.57% for GRG. Regression analysis obtained the optimal output displacement of 0.6326 mm, stress of 43.398 MPa, and the optimal displacement amplification ratio of 63.26.