This thesis focuses on the problem of passive vibration isolation applied to a mobile robot. The aims of the project are to analyse the disturbances that afflict the mobile robot and to develop a passive vibration isolation system as solution to this problem. Once the mobile robot will be presented, experimental measurements will be executed to estimate the main frequencies of the disturbance and the mobile robot during its motion, analysing the configurations with the higher vibration level. Theoretical model will be implemented to describe the behaviour of the mobile robot and the isolation system will be designed. Special attention will be paid to the stability problems, analysing also the responses of the mobile robot to different inputs of acceleration. The displacements caused by inertia effects will be limited by the introduction of a clamping system that blocks the deflections of the mobile robot during transient motions. Then, kineto-static simulations will be run in order to determine the static forces acting on the members of the mechanism. Theoretical results ensure the good attenuation of the vibrational phenomena and the correct behaviour of the mobile robot during its motion.