Purpose <p>In vibration control, the lever component is generally applied as the amplifying mechanism, which can amplify the equivalent system parameters to enhance the vibration reduction performance. The vibration absorbers with rack and pinion structures as the amplifying mechanism are presented in this paper, and the performance of amplifying equivalent mass, equivalent stiffness and equivalent damping is analyzed in detail.</p> Methods <p>Firstly, the design principles and structural characteristics are introduced, and then vibration absorbers, which are composed of one group and multiple groups of rack and pinion structures, are designed. Based on the transmission characteristics and magnification ratio of the vibration absorber, it is found that the vibration absorber with multiple groups of rack and pinion structure is still a single-degree-of-freedom linear system, and the recursive formula for the dynamic equation is obtained.</p> Results <p>The recursive formula for the equivalent mass, equivalent stiffness and equivalent damping of the system are summarized, which is useful for the design and research on vibration absorbers. By analyzing the recursive formula of the vibration reduction system, it is shown that a reasonable setting of the amplification ratio of the vibration absorber can effectively reduce the vibration amplitude. Due to the numerous parameters of the system, the parameters of the vibration absorber that fulfill the requirements for vibration reduction can be efficiently obtained by using genetic algorithms.</p> Conclusion <p>Under different frequencies of external excitation and random excitation, as compared with the lever mass damper applied in the vibration control of inclined cables on cable-stayed bridges, the vibration absorbers designed in this paper have not only better vibration reduction performance but also practical application value.</p>