<p>Multi-link mechanisms are the most basic type of mechanisms used in daily industrial production institutions, with the advantages of simple structure, large bearing capacity and easy maintenance in industrial production. Inevitably, there is clearance between moving pairs in multi-link mechanisms, and that some system parameters of the mechanism are uncertain, that is, the parameter values can change within a certain interval. Joint clearances and interval parameters of the multi-link mechanisms deteriorate the dynamic characteristics and reduce the motion accuracy of mechanisms. Current research mainly focuses on dynamic modeling and analysis of multi-link mechanisms with clearances, assuming fixed parameters. However, studies on multi-link mechanisms with joint clearances considering interval parameters are limited. Furthermore, existing research on interval parameters typically focuses on only a single interval parameter, which leads to a gap in the understanding of multi-link mechanisms with clearances under multiple interval parameters. Therefore, this paper shows an investigation on dynamic modeling and analysis of multi-link mechanisms with joint clearances considering multiple interval parameters. The magnitude of the clearances values, the driving speeds, the friction coefficients and the coefficients of restitution are taken as the interval variables, considering the uncertainty of the above parameters, the rigid body dynamic model for multi-link mechanisms with joint clearances considering interval parameters is developed, the dynamic equations of the mechanisms are solved by Chebyshev polynomial function, and the affection of interval parameters on the dynamic response of the multi-link mechanisms with joint clearances is analyzed. The study provides a theoretical basis for the accurate prediction of the dynamics of multi-link mechanisms with clearances considering interval parameters.</p>