# A Novel Coaxial Balance Mechanism for Reciprocating Piston Engines
## 2 Design of a Novel Coaxial Balance Mechanism
### Design Principles and Ideas of a Novel Coaxial Balance Mechanism  
To balance the second-order inertia force, it is necessary to design a rotating balance mass that rotates at twice the crankshaft speed, which naturally requires corresponding gear drive and lubrication mechanisms. Thus, it is necessary to design a new larger engine body for the traditional mechanism. Because the additional parts increase the cost and size of the engine, engine manufacturers are commonly unwilling to make large changes to the engine body.  
The design scheme of a coaxial mechanism of first-order and second-order balance shafts is proposed in this study to solve the above issues, as shown in Figure 2. The planetary gear transmission mechanism was used for transmission, and the appropriate speed ratio of internal and external gears could be achieved by adjusting the ratio of the number of teeth of the inner gear ring and sun gear.  
This study also proposes a design concept that uses a compact unit body, i.e., the second-order balance mass block is arranged inside the original first-order balance mass block, and the two balance mass blocks perform coaxial rotation, which saves significant space. After adding a second-order balance mechanism, the original configuration and size of the balance mechanism were not changed.  
Based on the above mechanical design principles and the idea of a compact unit body, a novel coaxial second-order balance mechanism was designed in this study, as shown in Figure 3. The novel coaxial balance mechanism is a unit-body module, including shell, first-order balance shafts, second-order balance shafts, and planetary gear transmission mechanisms. The second-order balance shafts are installed in the shaft hole of the first-order balance shafts; their rotational axes coincide. The external gear with internal teeth (i.e., the internal gear in the planetary gear mechanism) is fixed at one end of the first-order balance shaft. The internal gear with the external teeth (the sun gear in the planetary gear mechanism) is fixed at one end of the second-order balance shafts, and the middle gear (the planetary gear in the planetary gear mechanism) meshes with the internal gear and the external gear, respectively, thereby transmitting the rotation of the first-order balance shaft to the second-order balance shaft through the planetary gear mechanism.  
Additionally, the second-order balance shafts operate at twice the speed of the first-order balance shaft based on the design of a suitable ratio of internal and external gears based on mechanical design principles. When the engine is in operation, the crankshaft drives the first-order balance shaft to rotate through the gear transmission, and the speed remains the same; when the first-order balance shaft drives the second-order balance shaft to rotate through the middle gear, the speed doubles. The balance mechanism can balance the first- and second-order inertia forces of the engine crankshaft-connecting rod mechanism.  
To counteract the inertia force along the direction of piston motion and avoid generating additional inertia force perpendicular to the direction of piston motion, the balance  
Figure 3: A 3D diagram of the coaxial balance mechanism.  
Figure 2: Schematic of single-cylinder engine coaxial balance mechanism.  
shaft is generally designed with a semi-cylindrical balance mass biaxial counter-rotation, as shown in Figure 3.  
In multi-cylinder engines, such as an in-line four-cylinder engine, the first-order inertia force is inherently balanced, and the proposed design solution can expand this application. An external balance shaft can be used to balance the second-order inertia force, and an internal balance shaft can be used to balance the fourth-order inertia force. Therefore, the coaxial balance mechanism design scheme has the potential to balance high-order inertia force.