Within a short run, a novel class of mechanisms and systems has been created with parametric (elastic-dissipative) elements of sign-changing stiffness controlled in a range from positive to negative or quasi-zero values. A great deal of natural and hand-made designs on different physical bases appeared that could reveal such a phenomenon. These mechanisms and systems can cut the stiffness and provide a perfect vibration protection in a frequency range required. However, only some of them either are ready for to substitute or could be used in advanced hybrids in parallel with conventional vibration protection mechanisms and systems in certain types of machines and equipment. The main reason is very small travel where the negative or quasi-zero stiffness can be realized. A small error in passive control or a soft fault in an active one is enough to move such mechanisms and systems to performance degradation. A generic model of the parametric elements with negative and quasi-zero stiffness in small and a transition model to provide these effects in large are formulated. The model analysis led to important predictions on how to obtain an optimal trade-off between the dimensions and performance of the mechanisms and systems of novel class.