Abstract:Abstract: The vibration equations of linkage mechanism with random physical parameters and geometrical parameters under random excitation are established. In which rigid-elastic coupling and viscous friction are considered. Dynamic equations with random parameters are transformed into static governing equations by the Newmark-β step-by-step integration method. The mean value and the variance of elastic displacement responses are calculated by moment method and algebra synthesis method. The influences of the randomness of the bar length and radius , mass density and elastic modulus, rigid-elastic coupling and viscous friction on mechanism dynamic response are studied through an example.