## 1 Introduction  
Despite the massive evolution in the vibration isolation systems where cars, buses, and trucks were the main focus in road and off-road efforts until the present, they still lack the ability to provide complete comfort for drivers and passengers. Mechanical vibration is still one of the trickiest challenges that face engineers when it comes to achieving optimum comfort. Many studies have shown that drivers are exposed to a decent level of body vibrations, e.g., [1; 2]. Exposure to such high-intensity and low-frequency vibration may cause fatigue, low back pain, and discomfort, especially among long-haul drivers. Additional studies went a step further, more specifically studying the body's resonant frequency under different postural conditions, hand positions, seat heights, and back support conditions for healthy adults of different gender and ages [3; 4; 5; 6; 7; 8; 9]. The conclusions that can be drawn from the previous studies are that the resonant frequencies of the human body parts are between 4 and 17 Hz, and the average of the human body's resonant frequency is approximately 7 Hz, which means they fall into the range of the vibrations that occur at low frequency. Over the past years, numerous studies have been dedicated to finding a solution to this problem. [PERSON] et al. [10] designed a hybrid system that combines passive suspension and active actuators. The passive part consists of a conventional spring and damper to support the driver's weight and seat, whereas the active part is just two electromagnetic linear actuators controlled using a fully adaptive controller to achieve a decent isolation performance. [PERSON] et al. [11] developed a vibration isolator with a flywheel device as an essential part. In this study, the authors take into account a non-ideal case that includes factors such as the mass of the structure, friction, and stiffness along with the ideal two-terminal mass. The study focused on passenger comfort, tire grip, and suspension deflection. Speaking of passive systems, a tuned mass damper for self-excited vibration control was recently introduced by [PERSON] et al. [12]. In contrast, [PERSON] [13] proposed an active vibration isolator using a relief spring to maintain the weight and air spring controlled by a linear controller with an electro-pneumatic transducer as a sensing element. Similarly, [PERSON] et al. [14] proposed an active system consisting of a hydraulic damper and an air spring controlled by directional control valves and a controller with triple feedback loops. [PERSON] et al. [15] designed an active vibration isolator by choosing two inexpensive rotary motors controlled by an \(H_{\infty}\) controller and a careful selection of the spring stiffness to reduce the resonant frequency of the seat as much as possible. The same authors of the previous study used the same controller but replaced the two rotary motors with a generator, which consisted of a regenerative shock absorber and an energy storage circuit used to store vibration energy in a battery [16]. [PERSON] et al. [17] suggested a semi-active vibration isolator using a magnetorheological fluid damper, which is positioned at a certain angle and controlled by a skyhook controller. The previous studies [13; 14; 15; 16] share a main and common part, which is so-called the scissor mechanism [18]. This type of machine is widely used in many fields, especially in isolation applications due to its capacity for heavy load-bearing and good equilibrium stability. Permanent electromagnets, and magnet systems in general, attracted many researchers' attention in the last couple of years. [PERSON] et al. [19] proposed a high-static low-dynamic stiffness (HSLDS) vibration isolator using three magnets. Two of them are fixed on the edges, whereas the third one is located in the middle, which can move only in the vertical direction by sliding on a smooth vertical bar.