Vibration isolation devices are used to attach various systems to their base structure to reduce the transmission of vibration from and/or to the base structure. Vibration isolation devices allow relative motion between the isolated system and the base platform. This relative motion is critical to the effective operation of vibration isolation devices and is used to absorb or divert vibration energy using spring and viscous damping or dry friction elements. In general, larger the allowed relative motion, more effective will be the performance of the isolation system. In certain applications, the introduced relative motion by the vibration isolation device introduces unavoidable and unwanted motion of the isolated system and can significantly degrade its performance, particularly in terms of positioning precision, or limit the range of allowable relative motion, thereby reducing the effectiveness of the isolation system. In this paper, a novel method is presented that uses appropriate linkage mechanisms to constrain relative motions that are introduced by the vibration isolation system that are not necessary for the proper operation of the vibration isolation system but their presence would degrade the performance of the entire system. As an example, a novel double-parallelogram based motion constraining mechanism is presented, which is used to constrain rotational (rocking) motion of an isolation system without hindering its relative translational motion used for vibration isolation. The design of a prototype of such a linkage mechanism used to isolate payloads from launch vehicles during the launch and the results of its successful testing are presented. Other applications of the present method are discussed.