## 2 The Development of Typical Rotating Motion Mechanisms
### 2.1. Gear Drive
#### 2.1.1 Traditional Metal Gears  
1. Spur gear  
Spur gears are an essential transmission component widely used in automobiles and various mechanical equipment [29]. In an ideal state, where the relative sliding between tooth surfaces during meshing is low, spur gears can effectively transmit power, achieving high transmission efficiency [30]. In the power system of machine tools and the transmission chain of simple automatic transmission systems, multi-stage spur gear transmission can effectively change speed and torque [31]. Adjusting parameters such as the gear displacement coefficient and tooth crest coefficient can increase the gear contact ratio to 2 or above. This type of spur gear is called a high coincidence ratio (HCR) spur gear [32], as shown in Figure 2. Compared with traditional spur gears with contact ratios between 1 and 2, HCR spur gears have more tooth pairs that mesh simultaneously during operation. This feature enhances their load-bearing capacity and reduces vibration and noise, making them particularly suitable for high speed and heavy-duty applications. 2. Helical gear  
The teeth of the inclined gear are spiral-shaped, and its gear profile is shown in Figure 3[33]. They form a specific angle between the inclined gear's thread and the gear shaft. Spiral gears overlap more than spur gears, meaning more load distribution teeth are in the transmission process. Therefore, helical gears have good gear performance and long fatigue life and are widely used in mechanical power transmission [34]. Face gears can be used in cross-axis transmission systems. Compared with bevel gearboxes, face gears have unique advantages in rotary transmission, with little or no axial  
Figure 3: Helical gear model [35]. Figure 2: HCR spur gear model. force [36]. The helical surface gear pair is a new pair of noncircular and helical surface gears. Figure 4[37] shows that it can achieve a variable transmission ratio between gear intersecting axes. The worm gear consists of a turbine and a worm [38]. Due to their unique characteristics, including rapid deceleration in the smallest space [39], low noise [40], high motion stability [41], and high load capacity, worm gears are widely used in various industries [42; 43]. Worm gearboxes in fields such as smart cars and smart homes can significantly reduce the weight of products [44]. [PERSON] et al. [45] designed an innovative biased worm gear transmission mechanism, as shown in Figure 5. The dual lead offset worm drive system can achieve linear contact conjugation between tooth surfaces, ensuring the accuracy of the instantaneous transmission ratio. Its transmission principle is simple and easy to implement. This transmission method not only inherits the advantages of traditional worm gear transmission (including offset worm gear transmission) but is also more flexible in adjusting the axial position. Whether it is the worm gear or worm wheel adjustment, it can effectively change the meshing clearance without interfering with the contact state of the conjugate tooth surface, simplifying the assembly process and providing adjustability of the meshing clearance. [PERSON] et al. [46] proposed a novel linear contact surface worm gear transmission mechanism consisting of a hardened cylindrical and surface worm gear, as shown in Figure 6. The worm gear is formed by grinding with a conical grinding wheel, and after hardening treatment, the surface wear resistance is significantly improved, extending its service life. The worm rotates around its axis, driving the surface worm wheel to rotate around the vertical axis, achieving non-orthogonal shaft transmission. The number of worm heads and worm teeth determines the transmission ratio. By replacing the traditional spiral-driven Archimedes worm with a conical enveloping worm, the problem of non-developable  
Figure 4: Face gear pair coordinate system (The arrow indicates the direction of rotation of the gear, E-axis offset) [36]. Figure 5: Dual guide bias worm model (Arrows indicate the direction of turbine rotation).