# Design Methodology and Application Dynamics of Compact Quasi-Zero Stiffness Isolators
## 3 Compact Design of QZS Isolation
### Magnetic Type
#### 3.2.1 Permanent Iron Type Magnetic Springs  
[PERSON] et al. [47; 48] proposed a novel magnetic negative stiffness damper consisting of multiple coaxially arranged permanent magnets, which is a compact and simple design that effectively integrates negative stiffness and eddy current damping. [PERSON] et al. [49] proposed a compact energy-harvesting vibration isolator consisting of a negative-stiffness magnetic spring, a helical bending spring, and a coil, as illustrated in Figure 8a, which can suppress low-frequency vibrations in the range of 3.7-6.1 Hz and can achieve a maximum  
Figure 7: QZS isolator with transverse notch special spring structure proposed by [PERSON] et al. [46]: (**a**) Prototype model; (**b**) Experimental transmissibility curves (dB) under different excitation amplitudes.  
output power of 1.51 mW under 4.5 Hz. A maximum output power of 1.51 mW can be achieved under external excitation with a load resistance of 300 ohms. [PERSON] [50; 51] et al. proposed a novel electromagnetic negative stiffness element consisting of a coaxial permanent magnet toroidal magnet and a coil with a rectangular cross-section and adjustable negative stiffness characteristics. The element is quite compact due to the nested layout and the use of mechanical springs, and its stiffness can also be varied by changing the excitation current, which has the unique advantages of generating a wide range of adjustable negative stiffness characteristics and easy integration with semi-active control algorithms.  
Using different magnetic coupling arrays to increase the magnetic density can also achieve the goal of a compact design. Figure 8b illustrates the schematic of a compact magnetic spring array with rectangular arrays proposed by [PERSON] et al. [52], which can provide the same negative stiffness with less space consumption compared to non-arrayed magnetic springs. Similarly, as Figure 8c illustrates, [PERSON] et al. [53] proposed a magnetic Halbach high-negative-stiffness vibration isolator and verified that, when the size and weight are the same, the magnetic negative stiffness of the Halbach array is higher than other magnetic arrays, which is important in some practical situations with space and weight constraints. Subsequently, [PERSON] et al. [54] proposed a toroidal Halbach torsional negative stiffness isolator, and the starting isolation frequency of the toroidal Halbach isolator can be reduced by 32.57% compared with that of a linear isolator. [PERSON] et al. [55] proposed a compact magnetic spring consisting of two sets of alternating permanent magnets with high linear negative stiffness. Figure 8d shows a schematic of the magnetic negative stiffness mechanism proposed by [PERSON] et al., and the resonance frequency of the experimental prototype was reduced from 6.93 Hz to 1.10 Hz.  
Figure 8: QZS isolator with Permanent Magnet Magnetic Spring: (**a**) Energy harvesting dynamic damper [49]; (**b**) Schematic diagram of a compact array of magnetic springs [52]; (**c**) Structure of a Halbach high negative stiffness vibration isolator [53]; (**d**) a magnetic negative stiffness mechanism with a high linear negative stiffness [55].