Planetary gear train type speed reduction differential transmission mechanism

By using a two-stage planetary gear train with coupled design and optimized tooth number relationship, the technical bottlenecks of traditional transmission mechanisms in terms of reduction ratio, structural complexity and energy efficiency have been solved, achieving a large reduction ratio, lightweight design and functional integration, thereby improving transmission efficiency and vehicle handling.

CN223825540UActive Publication Date: 2026-01-23HARBIN DONGAN AUTOMOTIVE ENGINE MFG CO LTD +1
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Patent Information

Application Number
CN202520571351.1
Authority / Receiving Office
CN · China
Patent Type
Utility models(China)
Current Assignee / Owner
Filing Date
2025-03-28
Publication Date
2026-01-23
Estimated Expiration
2035-03-28

AI Technical Summary

Technical Problem

Traditional transmission mechanisms are difficult to achieve large reduction ratios, simplified structures, lightweight designs, and functional integration, and cannot meet the high efficiency and compact requirements of modern electric drive systems.

Method used

A two-stage planetary gear train coupling design is adopted. By optimizing the tooth number relationship and the differential characteristics of the planetary gear train, a compound reduction in transmission ratio is achieved. Furthermore, by coaxially arranging the motor rotor and the first output shaft, combined with the spatial symmetry of the planetary gear train, the axial dimension and machining complexity are reduced.

Benefits of technology

It achieves compound reduction of transmission ratio, improves torque output capability, meets the vehicle steering differential requirements, reduces energy loss, improves transmission efficiency, and has the advantages of compact structure and easy manufacturing, breaking through the technical bottleneck of traditional transmission mechanisms.

✦ Generated by Eureka AI based on patent content.

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Abstract

The utility model discloses a planetary gear train type speed reduction differential transmission mechanism, and belongs to the technical field of speed reducers. A stator of the motor is connected with the shell, a rotor of the motor is connected with a first sun gear and arranged outside the first output shaft in a sleeving mode, the first sun gear is meshed with a first planet gear, the first planet gear is meshed with a first gear ring, the first planet gear is installed on a first planet carrier, and the first planet carrier is connected with the first output shaft. The second sun gear is meshed with the second planet gear, the second planet gear is meshed with the third planet gear, the third planet gear is meshed with the second gear ring, and the second planet gear and the third planet gear are both installed on the second planet carrier. The first gear ring is connected with the second planet carrier, and the second sun gear is connected with the second output shaft. Or the gear ring I is connected with the sun gear II, and the planet carrier II is connected with the second output shaft; the first output shaft, the second output shaft, the first planetary gear train, the second planetary gear train and the motor are coaxially arranged. The differential mechanism is compact in structure, large in transmission ratio and easy to manufacture, the differential function is achieved through the planetary gear train, and the technical bottleneck of a traditional transmission mechanism is broken through.
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Description

TECHNICAL FIELD

[0001] The utility model relates to a planetary gear train type reduction differential transmission mechanism and belongs to the technical field of reducers. BACKGROUND

[0002] To optimize torque output characteristics and improve system energy efficiency, the transmission device needs to have a large reduction ratio design and needs to be separately configured with a differential to ensure that the motor output torque can be effectively transmitted to the drive wheel. At the same time, due to the restriction of the lightweight design and space layout of the whole vehicle, the structural complexity of the transmission mechanism needs to be significantly reduced, and the overall mass needs to be strictly controlled at a low level. In addition, modern electric drive systems have higher requirements for functional integration, and the traditional decentralized differential and reduction modules have been difficult to meet the integrated needs of high efficiency and compactness, and it is urgent to realize the collaborative integration of multiple functions through structural design innovation. Under this background, how to break through the technical bottlenecks of the existing transmission mechanism in terms of reduction ratio, structural simplification, lightweight and functional integration has become a key problem to be solved in this field. SUMMARY

[0003] To solve the problems in the background art, the utility model provides a planetary gear train type reduction differential transmission mechanism.

[0004] To achieve the above-mentioned purpose, the utility model adopts the following technical scheme:

[0005] Scheme one:

[0006] A planetary gear train type reduction differential transmission mechanism, comprising a first planetary gear train, a second planetary gear train, a motor, a housing, a first output shaft and a second output shaft; the first planetary gear train comprises a sun gear one, a planet carrier one, a ring gear one and a planetary gear one; the stator of the motor is rigidly connected with the housing, the rotor of the motor is rigidly connected with the sun gear one, the sun gear one is in meshing transmission with the planetary gear one, the planetary gear one is in meshing transmission with the ring gear one at the same time, the planetary gear one is installed on the planet carrier one, forming a first-stage planetary gear reduction mechanism; the planet carrier one is rigidly connected with the first output shaft, and the rotor of the motor is sleeved outside the first output shaft; the second planetary gear train comprises a sun gear two, a planet carrier two, a ring gear two, a planetary gear two and a planetary gear three; the sun gear two is in meshing transmission with the planetary gear two, the planetary gear two is in meshing transmission with the planetary gear three, the planetary gear three is in meshing transmission with the ring gear two fixed on the housing, and the planetary gear two and the planetary gear three are both installed on the planet carrier two, forming a second-stage planetary gear reduction mechanism; the ring gear one is rigidly connected with the sun gear two, constituting the coupling of the two-stage planetary gear train; the planet carrier two is rigidly connected with the second output shaft; the first output shaft, the second output shaft, the first planetary gear train, the second planetary gear train and the motor are coaxially arranged.

[0007] The number of teeth of the transmission mechanism is:

[0008] Z11 / Z13+2=Z23 / Z21 (1)

[0009] In formula (1):

[0010] Z11 is the number of teeth on the sun gear one;

[0011] Z13 is the number of teeth on gear ring one;

[0012] Z21 is the number of teeth on the second sun gear;

[0013] Z23 is the number of teeth on gear ring two.

[0014] The transmission ratio K of the transmission mechanism is:

[0015] K=2×W1 / (W2+W3)=1+(Z13 / Z11)×(Z23 / Z21) (2)

[0016] In formula (2):

[0017] W1 is the rotational speed of the motor rotor;

[0018] W2 is the rotational speed of the first output shaft;

[0019] W3 represents the rotational speed of the second output shaft.

[0020] Option 2:

[0021] A planetary gear train type differential transmission mechanism includes a first planetary gear train, a second planetary gear train, a motor, a housing, a first output shaft, and a second output shaft. The first planetary gear train includes a sun gear, a planet carrier, a ring gear, and planet gears. The stator of the motor is rigidly connected to the housing, and the rotor of the motor is rigidly connected to the sun gear. The sun gear meshes with the planet gears, and the planet gears simultaneously mesh with the ring gear. The planet gears are mounted on the planet carrier, forming a first-stage planetary gear reduction mechanism. The planet carrier is rigidly connected to the first output shaft, and the rotor of the motor is fitted onto the outside of the first output shaft. The second planetary gear train includes a second sun gear, a second planet carrier, a second ring gear, a second planet gear, and a third planet gear. The second sun gear meshes with the second planet gear, the second planet gear meshes with the third planet gear, and the third planet gear meshes with the second ring gear fixed to the housing. Both the second and third planet gears are mounted on the second planet carrier, forming a second-stage planetary gear reduction mechanism. The first ring gear is rigidly connected to the second planet carrier, forming a coupling of the two-stage planetary gear train. The second sun gear is rigidly connected to the second output shaft. The first output shaft, the second output shaft, the first planetary gear train, the second planetary gear train, and the motor are coaxially arranged.

[0022] The tooth count relationship of the transmission mechanism is as follows:

[0023] Z11 / Z13+1=Z21 / (Z23-Z21) (3)

[0024] In formula (3):

[0025] Z11 is the number of teeth on the sun gear one;

[0026] Z13 is the number of teeth on gear ring one;

[0027] Z21 is the number of teeth on the second sun gear;

[0028] Z23 is the number of teeth on gear ring two.

[0029] The transmission ratio K of the transmission mechanism is:

[0030] K=2×W1 / (W2+W3)=1+Z13 / Z11+(Z13 / Z11)×Z21 / (Z23-Z21) (4)

[0031] In equation (4):

[0032] W1 is the rotational speed of the motor rotor;

[0033] W2 is the rotational speed of the first output shaft;

[0034] W3 represents the rotational speed of the second output shaft.

[0035] Compared with the prior art, the beneficial effects of this utility model are:

[0036] This invention achieves a compound reduction effect in transmission ratio and improves torque output capability through the coupling and optimized tooth number relationship of a two-stage planetary gear system. It utilizes the differential characteristics of the planetary gear system to achieve dynamic distribution of the dual output shaft speeds, meeting the vehicle's steering differential requirements. By adopting a coaxial arrangement with the motor rotor nested within the first output shaft, combined with the spatial symmetry of the planetary gear system, it significantly reduces axial dimensions while achieving functional integration, meeting the requirements for lightweight and compact layout. Direct coupling between the gear ring and the sun gear or planet carrier reduces transmission links, and the standardized planetary gear system structure reduces processing costs and assembly complexity. Optimized tooth number matching ensures balanced load distribution, reduces energy loss, and improves transmission efficiency. It features a compact structure, large transmission ratio, and ease of manufacturing, achieving differential function through the planetary gear system and breaking through the technical bottlenecks of traditional transmission mechanisms in terms of reduction ratio, structural complexity, and energy efficiency. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the structure of Scheme 1 of this utility model;

[0038] Figure 2 This is a lever diagram showing the tooth number relationship of Scheme 1 of this utility model;

[0039] Figure 3 This is a schematic diagram of the structure of Scheme 2 of this utility model;

[0040] Figure 4 This is a lever diagram showing the tooth number relationship of Scheme 2 of this utility model. Detailed Implementation

[0041] The technical solutions of this utility model will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this utility model. Obviously, the described embodiments are only some embodiments of the utility model, not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this utility model without creative effort are within the protection scope of this utility model.

[0042] Example 1:

[0043] A planetary gear train type reduction differential transmission mechanism includes a first planetary gear train 41, a second planetary gear train 42, a motor 33, a housing 34, a first output shaft 31, and a second output shaft 32. The first planetary gear train 41 includes a sun gear 11, a planet carrier 12, a ring gear 13, and planet gears 14. The stator of the motor 33 is rigidly connected to the housing 34, and the rotor of the motor 33 is rigidly connected to the sun gear 11. The sun gear 11 meshes with at least three circumferentially distributed planet gears 14, and the planet gears 14 simultaneously mesh with the ring gear 13. The planet gears 14 are mounted on the planet carrier 12, forming a first-stage planetary gear reduction mechanism. The planet carrier 12 is rigidly connected to the first output shaft 31, and the rotor of the motor 33 is fitted onto the outside of the first output shaft 31. The second planetary gear train 42 includes a second sun gear 21, a second planetary carrier 22, a second ring gear 23, second planetary gears 24, and a third planetary gear 25. The second sun gear 21 meshes with at least four circumferentially distributed second planetary gears 24, the second planetary gears 24 mesh with the third planetary gear 25, and the third planetary gear 25 meshes with the second ring gear 23 fixed on the housing 34. The second planetary gears 24 and the third planetary gear 25 are both mounted on the second planetary carrier 22, forming a second-stage planetary gear reduction mechanism. The first ring gear 13 is rigidly connected to the second sun gear 21, forming a coupling of the two-stage planetary gear train. The second planetary carrier 22 is rigidly connected to the second output shaft 32. The first output shaft 31, the second output shaft 32, the first planetary gear train 41, the second planetary gear train 42, and the motor 33 are coaxially arranged.

[0044] The rigid connection described above can be one or a combination of bolted connection, splined connection, keyway connection, welded connection, riveted connection, or integral molding.

[0045] The tooth count relationship of the transmission mechanism is as follows:

[0046] Z11 / Z13+2=Z23 / Z21 (1)

[0047] In formula (1):

[0048] Z11 is the number of teeth on the sun gear 11;

[0049] Z13 is the number of teeth on gear ring 13;

[0050] Z21 is the number of teeth on the second sun gear (21).

[0051] Z23 is the number of teeth on gear ring 23.

[0052] The transmission ratio K of the transmission mechanism is:

[0053] K=2×W1 / (W2+W3)=1+(Z13 / Z11)×(Z23 / Z21) (2)

[0054] In formula (2):

[0055] W1 is the rotational speed of the rotor of motor 33;

[0056] W2 is the rotational speed of the first output shaft 31;

[0057] W3 represents the rotational speed of the second output shaft 32.

[0058] This embodiment provides a transmission method for a planetary gear train type reduction differential transmission mechanism, the method comprising the following steps:

[0059] S1: Power input: The rotation of the rotor of motor 33 drives the rotation of sun gear 11;

[0060] S2: First planetary gear transmission: When the sun gear 11 rotates, it meshes and drives the planet gear 14 to rotate. While the planet gear 14 is rotating, it drives the ring gear 13 and the planet carrier 12 to rotate.

[0061] S3: Second planetary gear train transmission: Ring gear 13 drives sun gear 21 to rotate, sun gear 21 meshes and drives planet gear 24 to rotate, planet gear 24 meshes and drives planet gear 3 to rotate, and planet gear 24 and planet gear 3 25, under the constraint of ring gear 23, drive planet carrier 22 to rotate.

[0062] S4: Power output: Planet carrier 12 drives the first output shaft 31 to output power, and planet carrier 22 drives the second output shaft 32 to output power, so that the first output shaft 31 and the second output shaft 32 rotate at the same speed when the vehicle is driving straight, and the first output shaft 31 and the second output shaft 32 rotate at different speeds when the vehicle is turning.

[0063] When the vehicle is traveling in a straight line, the resistance of the wheels on both sides is balanced. The sun gear 2 (21) rotates with the gear ring 1 (13). Since the gear ring 2 (23) is stationary, the planet gear 2 (24) and the planet gear 3 (25) rotate on the planet carrier 2 (22). Therefore, under the combined action of the sun gear 2 (21) and the gear ring 2 (23), the planet gear 2 (24) and the planet gear 3 (25) drive the planet carrier 2 (22) to rotate. The rotational speed of the planet carrier 2 (22) is determined by the rotational speed of the sun gear 2 (21). Under the condition of satisfying the tooth number relationship (Equation 1), the planet carrier 1 (12) and the planet carrier 2 (22) rotate at the same speed. The first output shaft (31) and the second output shaft (32) have the same rotational speed and satisfy the speed ratio relationship (Equation 2).

[0064] When the vehicle turns, the travel distances of the inner and outer wheels are different. The first output shaft (31) and the second output shaft (32) rotate at different speeds, and the planet carrier one (12) and planet carrier two (22) rotate at different speeds. Under the condition of satisfying the tooth number relationship (Equation 1), the change in the speed of planet carrier one (12) is equal to the change in the speed of planet carrier two (22), and the average speeds of planet carrier one (12) and planet carrier two (22) satisfy the speed ratio relationship (Equation 2).

[0065] Example 2:

[0066] The difference between this embodiment and Embodiment 1 is that:

[0067] The gear ring 13 is rigidly connected to the planet carrier 22, forming a coupling of a two-stage planetary gear system; the sun gear 21 is rigidly connected to the second output shaft 32.

[0068] The tooth count relationship of the transmission mechanism is as follows:

[0069] Z11 / Z13+1=Z21 / (Z23-Z21) (3)

[0070] In formula (3):

[0071] Z11 is the number of teeth on the sun gear 11;

[0072] Z13 is the number of teeth on gear ring 13;

[0073] Z21 is the number of teeth on the second sun gear (21).

[0074] Z23 is the number of teeth on gear ring 23.

[0075] The transmission ratio K of the transmission mechanism is:

[0076] K=2×W1 / (W2+W3)=1+Z13 / Z11+(Z13 / Z11)×Z21 / (Z23-Z21) (4)

[0077] In equation (4):

[0078] W1 is the rotational speed of the rotor of motor 33;

[0079] W2 is the rotational speed of the first output shaft 31;

[0080] W3 represents the rotational speed of the second output shaft 32.

[0081] This embodiment provides a transmission method for a planetary gear train type reduction differential transmission mechanism, the method comprising the following steps:

[0082] S1: Power input: The rotation of the rotor of motor 33 drives the rotation of sun gear 11;

[0083] S2: First planetary gear transmission: When the sun gear 11 rotates, it meshes and drives the planet gear 14 to rotate. While the planet gear 14 rotates, it drives the ring gear 13 and the planet carrier 12 to rotate. The planet carrier 12 then drives the first output shaft 31 to output power.

[0084] S3: Second planetary gear transmission: Ring gear 13 drives planet carrier 22 to rotate, and the rotation of planet carrier 22 drives the meshing planet gear 24 and planet gear 3 25 on it to move. Under the constraint of ring gear 23, planet gear 24 drives sun gear 21 to rotate.

[0085] S4: Power output: Planet carrier 12 drives the first output shaft 31 to output power, and sun gear 21 drives the second output shaft 32 to output power, so that the first output shaft 31 and the second output shaft 32 rotate at the same speed when the vehicle is driving straight, and the first output shaft 31 and the second output shaft 32 rotate at different speeds when the vehicle is turning.

[0086] When the vehicle is traveling in a straight line, the resistance of the wheels on both sides is balanced. The second planetary carrier (22) rotates with the first gear ring (13), while the second gear ring (23) remains stationary. The second planetary gear (24) and the third planetary gear (25) rotate on the second planetary carrier (22). Under the combined action of the second planetary carrier (22) and the second gear ring (23), the second planetary gear (24) and the third planetary gear (25) drive the second sun gear (21) to rotate. The rotational speed of the second sun gear (21) is determined by the rotational speed of the second planetary carrier (22). Under the condition that the number of teeth relationship (Equation 3) is satisfied, the first planetary carrier (12) and the second sun gear (21) rotate at the same speed. The first output shaft (31) and the second output shaft (32) have the same rotational speed and satisfy the speed ratio relationship (Equation 4).

[0087] When the vehicle turns, the travel distances of the inner and outer wheels are different. The first output shaft (31) and the second output shaft (32) rotate at different speeds, and the planet carrier one (12) and the sun gear two (21) rotate at different speeds. Under the condition of satisfying the tooth number relationship (Equation 3), the change in the speed of the planet carrier one (12) is equal to the change in the speed of the sun gear two (21), and the average speeds of the planet carrier one (12) and the sun gear two (21) satisfy the speed ratio relationship (Equation 4).

[0088] This invention achieves the following by utilizing the coordinated operation of a two-stage planetary gear system and the rotation-revolution characteristics of planetary gears:

[0089] Straight-line driving: Both output shafts rotate at the same speed to ensure vehicle stability.

[0090] Turning: The two output shafts rotate at different speeds to adapt to the different speed requirements of the inner and outer wheels.

[0091] This design not only improves transmission efficiency but also significantly enhances vehicle handling and passability.

[0092] It will be apparent to those skilled in the art that this invention is not limited to the details of the exemplary embodiments described above, and that it can be implemented in other forms without departing from the spirit or essential characteristics of this invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of this invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of the equivalents of the claims be included within this invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0093] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A planetary gear train type reduction differential transmission mechanism, characterized in that: The system includes a first planetary gear train (41), a second planetary gear train (42), a motor (33), a housing (34), a first output shaft (31), and a second output shaft (32); the first planetary gear train (41) includes a sun gear (11), a planet carrier (12), a ring gear (13), and planet gears (14); the stator of the motor (33) is rigidly connected to the housing (34), and the rotor of the motor (33) is rigidly connected to the sun gear (11). The sun gear (11) meshes with the planet gears (14), and the planet gears (14) mesh with the ring gears (13). The planet gears (14) are mounted on the planet carrier (12) to form a first-stage planetary gear reduction mechanism; the planet carrier (12) is rigidly connected to the first output shaft (31), and the rotor of the motor (33) is mounted on the outside of the first output shaft (31); the second planetary gear train (42) includes a first planetary gear train (41), a second planetary gear train (42), a motor (33), a housing (34), a first output shaft (31), and a second output shaft (32); the second planetary gear train (43) includes a first planetary gear train (41), a second planetary gear train (42), a third planetary gear train (43), a fourth planetary gear train (43), a fifth planetary gear train (43), a sixth planetary gear train (43), a seventh planetary gear train (43), a seventh planetary gear train (43), a stern gear train (44), a stern gear train (43 ... 42) Includes a second sun gear (21), a second planetary carrier (22), a second ring gear (23), a second planetary gear (24), and a third planetary gear (25); the second sun gear (21) meshes with the second planetary gear (24), the second planetary gear (24) meshes with the third planetary gear (25), the third planetary gear (25) meshes with the second ring gear (23) fixed on the housing (34), the second planetary gear (24) and the third planetary gear (25) are both mounted on the second planetary carrier (22) to form a second-stage planetary gear reduction mechanism; the first ring gear (13) is rigidly connected to the second sun gear (21) to form a series coupling of two-stage planetary gear systems; the second planetary carrier (22) is rigidly connected to the second output shaft (32); the first output shaft (31), the second output shaft (32), the first planetary gear system (41), the second planetary gear system (42), and the motor (33) are coaxially arranged.

2. The planetary gear train type reduction differential transmission mechanism according to claim 1, characterized in that: The tooth count relationship of the transmission mechanism is as follows: Z11 / Z13+2=Z23 / Z21 (1) In formula (1): Z11 is the number of teeth of the sun gear (11); Z13 is the number of teeth of gear ring one (13); Z21 is the number of teeth of the second sun gear (21); Z23 is the number of teeth of gear ring two (23).

3. The planetary gear train type reduction differential transmission mechanism according to claim 2, characterized in that: The transmission ratio K of the transmission mechanism is: K=2×W1 / (W2+W3)=1+(Z13 / Z11)×(Z23 / Z21) (2) In formula (2): W1 is the rotational speed of the rotor of motor (33); W2 is the rotational speed of the first output shaft (31); W3 is the rotational speed of the second output shaft (32).

4. A planetary gear train type reduction differential transmission mechanism, characterized in that: The system includes a first planetary gear train (41), a second planetary gear train (42), a motor (33), a housing (34), a first output shaft (31), and a second output shaft (32); the first planetary gear train (41) includes a sun gear (11), a planet carrier (12), a ring gear (13), and planet gears (14); the stator of the motor (33) is rigidly connected to the housing (34), and the rotor of the motor (33) is rigidly connected to the sun gear (11). The sun gear (11) meshes with the planet gear (14), and the planet gear (14) meshes with the ring gear (13). The planet gear (14) is mounted on the planet carrier (12) to form a first-stage planetary gear reduction mechanism; the planet carrier (12) is rigidly connected to the first output shaft (31), and the rotor of the motor (33) is fitted onto the outside of the first output shaft (31); the second planetary gear train... (42) includes a second sun gear (21), a second planetary carrier (22), a second ring gear (23), a second planetary gear (24), and a third planetary gear (25); the second sun gear (21) meshes with the second planetary gear (24), the second planetary gear (24) meshes with the third planetary gear (25), the third planetary gear (25) meshes with the second ring gear (23) fixed on the housing (34), the second planetary gear (24) and the third planetary gear (25) are both mounted on the second planetary carrier (22) to form a second-stage planetary gear reduction mechanism; the first ring gear (13) is rigidly connected to the second planetary carrier (22) to form a series coupling of two-stage planetary gear systems; the second sun gear (21) is rigidly connected to the second output shaft (32); the first output shaft (31), the second output shaft (32), the first planetary gear system (41), the second planetary gear system (42), and the motor (33) are coaxially arranged.

5. The planetary gear train type reduction differential transmission mechanism according to claim 4, characterized in that: The tooth count relationship of the transmission mechanism is as follows: Z11 / Z13+1=Z21 / (Z23-Z21) (3) In formula (3): Z11 is the number of teeth of the sun gear (11); Z13 is the number of teeth of gear ring one (13); Z21 is the number of teeth of the second sun gear (21); Z23 is the number of teeth of gear ring two (23).

6. The planetary gear train type reduction differential transmission mechanism according to claim 5, characterized in that: The transmission ratio K of the transmission mechanism is: K=2×W1 / (W2+W3)=1+Z13 / Z11+(Z13 / Z11)×Z21 / (Z23-Z21) (4) In equation (4): W1 is the rotational speed of the rotor of motor (33); W2 is the rotational speed of the first output shaft (31); W3 is the rotational speed of the second output shaft (32).