1. Transition gear implementation mode:
 The transition gear is deformed based on the tooth profile data of the normal gear pair as an example. Such as figure 1 , figure 2 , image 3 The dashed line is the involute tooth profile of the unused parallel shaft gear pair. The toothless part ⑤-① or ④-① is the root arc of the usual gear, and the tooth part ⑤-④ is the involute tooth profile. , But the tooth height can be raised and lowered, and the tooth width increases (such as Figure 5 的 Rack); the transitional section ③-④ is the involute tooth profile, but the tooth profile shape can be changed as required; the transitional section ②-③ the tooth profile is the tooth top of the involute gear, but it can be as figure 1 , Figure 4 Change the height and shape of part of the tooth tip in that way, and push the rack to move forward to the end of the stroke; the transition front ①-② is the transition tooth profile that accepts the force, which is the key tooth profile to prevent rigid impact, and the rack must be received by the transition tooth Tightly contact the rack before pushing. Due to the variation of the distance between the point of action of the transition gear and the axis, the linear velocity of the transition gear's force point is V 0 Change at any time. Speed of rack reciprocating motion V F It also changes at any time. In the initial stage when the rack pushes the transition gear, V F Significantly smaller than V 0 , The closer to OO', V F Closer to V 0 , In OO′V F =V 0 , And then V F Greater than V 0 , The closer to the end of the rack stroke, V F More obviously greater than V 0. Therefore, it should be V F , V 0 Make the integral tooth profile of the transition front ②-① for the variable. Available V 0 /V F With F 1 /F is inversely proportional to the tooth profile. As long as the rigid impact can be avoided, sometimes only a few tooth profiles near the end ② are precisely made.
 2, Figure 5 Implementation of transition gear train:
 Figure 5 It is a schematic diagram of two racks alternately driving two transitional gears to convert the thrust of the gas from the two cylinders into the crankshaft O. Picture 11 Yes Figure 5 Schematic diagram of the trajectory of the action point of the rack-driven transition gear. m, n, p, q are the trajectories of the action points. The top tooth profile of the rack acts on the tooth tip of the transition gear, and the tooth profile of the rack root acts on the top tooth profile of the transition gear. The top tooth profile of the rack acts on the root profile of the transition gear, and the top tooth profile of the rack acts on the four representative points of the top profile of the transition gear. Picture 12 , Figure 13 , Figure 14 , Figure 15 These are the force transformation analysis diagrams at four points m, n, p, and q. From Figure 5 , Picture 11 Know:
 a. Picture 11 , The intersection of the centerline bb′ between the two racks and the axis line OO′ of the two transition gears is a, b, b′ are the vertical feet of the transition gear starting and ending at bb′, and OO′ Is the boundary, ab is the front stroke, ab' is the back stroke, and ab=ab'. Assuming that the addendum of the transition gear is on the addendum circle, the addendum axis angle is δ, the axis angle of the transition gear's starting point and end point is 2α′, 2α′+δ=π/2, δ=π/28, Then α′=(π/2-π/28)/2=13π/56.
 Picture 12 , Transition gear radius and torque F 1 Vertical, F 1 The angle with F is equal to the angle α between the line of action point to the center of the transition gear and 00'. The top tooth profile of the rack acts on the top of the transition gear, and when it starts to push the transition gear to do work, α'=13π/56, substitute F 1 =Fcosα=0.75F. 0.75F is the initial transmission ratio of the rack and transition gear.
 b. Figure 13 , When the root tooth profile of the rack acts on the top tooth profile of the transition gear, F is first transformed into the vertical force F on the acting surface of the transition gear 2 , Then by F 2 Convert to F 1 , The other component of F points to the axis of the transition gear, so F 1 =Fcosα. As α→0, cosα=F 1 /F→1, when α=0, F 1 =F. Figure 14 , Figure 15 , In the back stroke, the tooth profile of the rack top acts on the tooth profile of the root of the transition gear, and the tooth top of the rack acts on the top tooth profile of the transition gear. Set the action point of the rack on the transition gear to the transition gear axis line p0, q0 Interaction surface A with transition gear 0 The included angle is γ, F 2 =F/cos(α+γ), F 1 = F 2 cosγ=Fcosγ/cos(α+γ). Since γ→π/4, γ+α→π/2, F 1 The magnitude of increase exceeds the magnitude of decrease of F, F 1 Getting bigger and bigger so that F 1F.
 From the above analysis, Figure 5 The characteristics of transitional gear train force transformation are:
 a. The transmission ratio of the transition gear pair is the lowest when it starts to transmit motion, F 1 /F=75%>2F/π, therefore, the mechanical efficiency of the transition gear pair is much higher than the crankshaft connecting rod.
 b. The transition gear redistributes the force transformation of the gas thrust, the gas thrust of the front stroke of the rack is large, F 1 /F=cosα, as the action point of the rack approaches OO', α→0, F 1 /F→1, stroke behind the rack, F 1 /F=Fcosγ/cos(α+γ), (α+γ)→π/2, the late transmission ratio of the back stroke increases rapidly, even F 1F, therefore, the transitional gear internal combustion engine can make full use of the gas thrust to do work, so that the efficiency is higher, and the power output is more uniform and reasonable.
 c. The final stage of the rack stroke F 1F, it is beneficial to increase the compression ratio and improve the effective efficiency of the internal combustion engine.
 d. From the transmission ratio of the gas thrust of the front, middle and rear stroke of the rack into the crankshaft torque, it is not difficult to see that the total mechanical efficiency of the transitional gear train force conversion is higher, tending to 100%.
 e. The transmission of motion is suitable for transmission from the rack to the transition gear.
 f. It is beneficial to make an internal combustion engine with a small combustion chamber and small displacement, so that the total effective thermal efficiency is higher.
 To Figure 5 , Figure 7 Take the transition gear train as an example of the force conversion implementation scheme of a four-cylinder four-stroke diesel engine:
 The starter is mounted on the gear shaft between the two piston rods. After starting, cylinders 1, 2, 3, and 4 perform work in sequence according to the four strokes of work, exhaust, intake, and compression. Each piston drives the shaft π/2 to complete the four strokes, and the combustion engine gas drives the shaft to rotate 2π. Use the powerful thrust at the end of the rack stroke to increase the compression ratio and improve power and efficiency.
 At the end of compression, the fuel exploded, and the piston-rack did not immediately move to do work, but waited for the transition gear 1 to rotate δ degrees, and the fuel burned more fully before driving the transition gear to do work with a greater initial thrust. One piston performs work, and the gear 5 between the piston rods 7 makes the two piston rods 7 move relative to each other to cancel the vibration of the inertial motion, and drive the other three pistons to complete the exhaust, intake, and compression strokes.
 3. Figure 4 The transitional gear train implementation scheme:
 Figure 4 It is a single-tooth pure transition gear train. The rack is transformed into a transitional gear shaft torque and Figure 5 Basically the same, the difference is: 1, Figure 5 Is a double-tooth transition gear train, Figure 4 It is a single-tooth transitional gear train. 2, Figure 5 The rack and pinion only have force conversion with one transition gear in one stroke, Figure 4 A stroke of the rack and two transition gears have a force conversion effect, that is, after the rack converts the gas thrust into a transition gear torque, the stroke of the rack does not end, and it is driven by the tooth top of the other transition gear to continue forward. The purpose of this is to make the piston continue to move forward and leave the cylinder after it finishes its work, so that air enters the cylinder from the side of the piston and is discharged from the valve to achieve the purpose of air exchange. Because the arc of the tooth tip of the single-tooth transition gear coincides with the tooth tip circle is very long, on the one hand, the combustion chamber has sufficient time to burn, and on the other hand, it allows the cylinder to have sufficient air exchange time. therefore, Figure 4 The transitional gear train is suitable as a force conversion mechanism for two-stroke internal combustion engines. A rack stroke drives the crankshaft about π/2, and a four-cylinder drives the crankshaft 2π, so it is more reasonable to make a force conversion mechanism for a four-cylinder two-stroke internal combustion engine.
 4. Image 6 The transitional gear train implementation scheme:
 Image 6 The transition gear train is a hybrid transition gear train, which is characterized by: the transition gear is mixed with transition gear teeth and normal gear teeth. One stroke of the rack drives the transition gear (crankshaft) to rotate 1π, and the crankshaft linkage mechanism of one stroke is also the driving machine. The shaft rotates 1π, so it is convenient to compare the two force conversion mechanisms.
 Image 6 , Picture 11 , The maximum rotation angle of the rack drive transition gear tooth is 2α', and the addendum axis angle of the transition gear tooth is δ. Usually the axis angle of the gear tooth is θ, then δ+2α'+θ=π. After the transition gear has rotated δ degrees of inertia, the rack drives the transition gear teeth to rotate α', and then drives the normal gear teeth to rotate θ degrees, and the last rack teeth drive the last normal gear teeth to rotate α', and the transition gear rotates 1π. Among them, the time for the transition gear to rotate δ is the time for the gas to burn without work in the combustion chamber, so that the gas is burned more completely, and a greater thrust F is generated to drive the transition gear to rotate α'degrees. Let transition gear index circle diameter d=mz=10×12=120mm, addendum circle diameter d a =mz+2m=10×12+2×10=140mm, tooth tip radius R=70mm, distance from rack top motion track to transition gear axis h=R-2m=70-2×10=50mm, cosα' =h/R=50/70=0.7143, according to Picture 12 , Cosα′=0.7143=F 1 /F, 0.7143 is the initial transmission ratio of the transition gear. If the cylinder diameter is 100mm, the crankshaft turning radius converted by the crankshaft connecting rod force is r≈110/2=55mm, R/r=70/55, R=1.273r, the torque is compared to the same radius, the initial rotation of the transition gear shaft Moment T R =0.714FR×1.273r/R=0.909Fr, crankshaft torque T r The maximum value of is only about 0.8 of the maximum gas thrust torque, and the initial torque has exceeded the maximum torque of the crankshaft.
 Rack stroke s 1 =Rsinα=R(1-cos 2 α) 0.5 =70×0.714=50mm. 2 teeth indexing arc length s 2 =(2π×2/12)mz=10×12π/3=40π=125.6mm, rack stroke s=2s 1 +s 2 =2×50+125.6=225.6mm. The transition gear internal combustion engine has a long stroke, the exhaust gas temperature is lower than that of a crankshaft internal combustion engine, and the thermal efficiency is higher.
 When the rack gear teeth drive last, when the usual gear teeth rotate α', the transmission ratio increases. Assumption: γ+α=85°, α=42°, F 1 /F=cosα/cos(α+γ)=0.7431/0.08522=8.5, F 1 =8.5F, the closer to 90°F 1 /F is bigger, F 1 It can be equivalent to the initial thrust F of a gas explosion, and can provide a large compression ratio for the cylinder in the compression stroke, while the crankshaft internal combustion engine is completely provided by negative work to provide the compression ratio.
 The changing law of the transmission ratio of the transition gear train: the initial transmission ratio i of the transition gear driven by the rack 0 =0.714, the front stroke of the rack i→1, the gear ratio of the gear teeth is usually F 1 =F, transmission ratio of rear stroke of rack F 1F, the final stage of transmission F 1F. In the initial stage of transmission, within the rotation range of about α/2, the tooth moment arm of the transition gear is the addendum radius, and the crankshaft torque is greatly improved. The actual initial torque in this example is increased by 0.909-0.714=19.5%. When rotating to α=35°, F 1 /F=cos35°=0.8192, T R =0.8192FR×1.273r/R=1.043Fr, when α=22°, F 1 /F=cos22°=0.9272, T R =0.9272FR×1.273r/R=1.18Fr.
 It can be seen that the transition gear internal combustion engine has at least four advantages compared with the crankshaft internal combustion engine:
 A. At the beginning of gas drive: the transmission ratio of the crankshaft internal combustion engine is 0, and the initial transmission ratio of the transition gear exceeds the average transmission ratio of the crankshaft connecting rod, resulting in a maximum torque exceeding the crankshaft, and rapidly increasing, which is beneficial to the transition gear as a low-emission, small combustion chamber. Efficient internal combustion engine.
 B. Maximum torque of crankshaft: The transition gear internal combustion engine is larger than the crankshaft internal combustion engine.
 C. At the end of gas drive: The transmission ratio of the transition gear internal combustion engine is much greater than the gas thrust, which can make full use of the exhaust gas to provide power to the compression ratio. The crankshaft internal combustion engine transmission ratio→0, and the negative power provides the compression ratio.
 D. Thermal efficiency: The temperature of the exhaust gas of the transition gear internal combustion engine is lower than that of the crankshaft internal combustion engine, and the thermal efficiency is higher.
 5. Take Figure 8 The structure of the internal combustion engine uses very few gears. Two cylinders only use two racks and one transition gear for work. Four cylinders use only one gear, one transition gear and two racks for work, but the vibration is relatively large.
 6. Take Picture 9 The structure of the internal combustion engine requires three bevel gears, four cylinders have high work vibration, and eight cylinders have low work vibration.
 7. Take Picture 10 The structure of the internal combustion engine has low vibration and less gears. The transition gear train with four to eight cylinders for work consists of two transition gears and corresponding rack and rack intermediate gears.
 8, Figure 14 , Figure 15 , Rack and pinion drive gear, transition gear, subject to reaction force F 3 Therefore, if necessary, add sliders and pulleys at corresponding positions to avoid deformation of the rack and prevent the piston from pressing on the cylinder wall.