For improving the quick‑return characteristics of the sley movement

an optimal mathematical model for maximum curve displacement Sm of the connectingarm pin was proposed through beating‑up principle analysis and mechanism deduction.A multivariable design space was constructed by use of the component length(lc

lh

lr

lf)and crankangleα.The parametric functional model development of the four‑bar beating‑up with short connecting rod was realized

and its kinematic posture and centroid trajectory were analyzed and verified through mechanism simulation.The results of the case study indicate that the variable lc andαhave more greater influence on the sensitivity of the objective function F(X)

and multivariable(DV_1

DV_2

DV_3)coupling can effectively enhance the design plasticity of the quick‑return characteristics of the sley.When the maximum curve displacement Sm of the connectingarm pin increases to 71.41 mm

the extreme position angleθand the travel speed ratio coefficient K are increased by 10.96°and 0.131 respectively

and the quick-return motion effect of the sley is obviously improved.The optimization results accord with the conditions of rod length and mechanism transmission requirement

which are conductive to the design innovation and performance improvement of the four‑bar beating‑up system.