## 2 Dual-State Logic Drive  
The core technology of the dual-state logic transmission is the planetary transmission technology of the double internal meshing coplanar gear with a large coincidence tooth profile. Dual-state logic transmission technology is the unique transmission technology first developed by Ker-Train Company in Canada. It can give full play to the characteristics of engine power and has the advantages similar to CVT technology of stepless transmission; high transmission efficiency of variable speed gear and good fuel economy; fast acceleration performance; no need to reduce the vehicle speed during the steering process; high mobility; the step ratio between gears is small; the range of the transmission ratio is large; automatic gear shifting can be realized; the handling performance is good; the reliability is high. Without a hydraulic torque converter, it adopts coplanar meshing technology with large coincidence and a long contact line, an efficient conical friction disc clutch and a steering differential system with full gears, compact structure and high power density. On the basis of dual-state logic transmission technology, a prototype SG-850 has been developed abroad, with a maximum power of 850 hp, a maximum torque of 2700 Nm, a maximum input speed of 2300 rpm, a vehicle weight of 35 tons and a transmission weight of 1750 kg. It has completed 18,000 km of real vehicle tests on the Pizarro model. KTR has adopted the above patented tooth shape technology to meet the market demand for the automatic driving function of vehicles. The new transmission system Gemini III developed by the company is a dual-state logic transmission device with 900 horsepower and 32 gears, which is a better platform to replace the current 40-50-ton tracked vehicle transmission system. Both the Gemini III and the fan transmission system adopt wire control technology, achieving integration with the automatic driving vehicle. Due to the transmission efficiency of more than 90%, the Gemini III can provide more cruise power to the vehicle, save fuel, improve the range and enhance the tactical and logistical support capabilities. KTR also developed the first generation of the \"Alpha\" unit for the US Tank Vehicle Research and Development Project (TARDEC). KTR is also actively developing the second generation \"Beta\" unit, with the goal of improving reliability, optimizing the efficiency of the unit subsystem, reducing weight, reducing design and manufacturing costs, developing the software and hardware of vehicle control and realizing the fully controlled transmission system by wire. The dual-state logic transmission is composed of a series of coplanar gear planetary array modules in series. Each module achieves its two transmission ratio output modes by the control unit that controls the conical friction plate. The output transmission ratio of the two components of the planetary array is 1:1, and the other transmission ratio is achieved by formulating one component of the planetary array. A single row can form two transmission ratios, and \(n\) rows can form \(2^{n}\) gear transmission ratio in series. If the maximum transmission ratio of the gearbox is R and the gear ratio is \(X\), then \(X=R^{\frac{1}{2^{n}-1}}\). Double-State Logic Drive-Double Internal Meshing Coplanar Gear Planetary Array Characteristic Analysis  
Planetary row can be divided into a positive and negative row. The negative row is shown in Figure 2a, and the positive row is shown in Figure 2b. The negative row is a planetary row with an external meshing transmission, and the positive row is a planetary row with two planetary gears to achieve two external meshing transmissions. The characteristic equation of negative sign row is \(n_{s}+kn_{r}-(1+k)n_{c}=0\); the characteristic equation of the positive row is \(n_{s}-kn_{r}-(1-k)n_{c}=0\). Here, \(k=\frac{z_{r}}{z_{s}}\), and \(k\) is the ratio of the number of teeth between the planetary gear ring and the sun gear.