## 2 Passive Vibration Isolation Designs
the jumping phenomenon due to the lack of a damper. There were only simulation results and no experimental validation for the vibration isolator system. [PERSON] [62] has presented a multi-direction vibration isolator of the high-static-low-dynamic stiffness (HSLDS) struts, the schematic diagram of which is shown in Figure 9. Figure 9a shows the static equilibrium position; Figure 9b shows the base excitations x0(t), y0(t), and z0(t) applied to the isolator; Figure 9c shows the equivalent mechanical model of the isolator. The proposed multi-direction vibration isolator can possess the HSLDS characteristics in the vertical direction and quasi-zero stiffness in two horizontal directions. Besides, the low-frequency isolation bandwidth can also be extended for each of the three directions, and there is no resonance phenomenon occurring in the two horizontal directions. For the vibration in the vertical direction, only one resonance peak has been shown near 4.35 Hz, and there are no other resonance peaks that can be observed. Therefore, the suspension isolation system can be considered a good system. However, the system has a complex structure with many components and requires large packaging space. There are only simulation results and no experimental validation for the vibration isolator system. [PERSON] [64] presented a HSLDS vibration isolator system that provides excellent micro-vibration isolation performance at low frequencies. As the isolator system works under a micro-vibration environment, the maximum response amplitude is limited. The vibration displacement response amplitudes could also be limited due to the limited installation space. [PERSON] [60; 66] presented two negative-stiffness magnetic spring (NSMS) vibration isolators. The first proposed NSMS vibration isolator, as shown in Figure 10a, can effectively reduce the peak transmissibility at the resonance frequency, but the jump-down frequency would increase under the excessive base excitation. The second proposed NSMS Stewart platform vibration isolator, as shown in Figure 11, has lower resonant frequencies. Hence, it has better isolation performance in the low-frequency range. The presented compact configuration of the NSMS isolator makes it a good candidate to be applied in the Stewart platform. Figure 8: Schematic diagram of the QZS torsional vibration isolator. (**a**) Longitudinal-sectional view of the assembly, (**b**) cross-sectional view. Labels: 1-cam with radius \(r_{2}\), 2-roller with radius \(r_{1}\), 3-spring, 4-slider, 5-vulcanized rubber cam, 5-cylinder roller, 6-left shaft connector, 7-right shaft connector [58]. [PERSON] [42] presented a passive vibration isolator by combining the NSMS with a spiral flexure spring (SFS). The isolator provides good high-static-low-dynamic stiffness. The NSMS is employed to lower the resonant frequency and improve the damping property. The spiral flexure spring can provide a high load capacity under a small static deformation. According to their experimental results, the peak value of the displacement transmissibility is around 2.6 at 6 Hz. Figure 10: Schematic diagram of the first proposed negative-stiffness magnetic spring (NSMS) vibration isolator: (**a**) Geometric parameters of the first NSMS vibration isolator and (**b**) distribution of equivalent current on the first proposed NSMS vibration isolator [60]. Figure 9: Schematic diagram of the multi-direction vibration isolator (**a**) shows the static equilibrium position; (**b**) shows the base excitations x0(t), y0(t), and z0(t) applied to the isolator; (**c**) shows the equivalent mechanical model of the isolator [62].