CN107345567B - Coplanar axis gear mechanism with conical spiral line structure driving line teeth - Google Patents

Coplanar axis gear mechanism with conical spiral line structure driving line teeth Download PDF

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CN107345567B
CN107345567B CN201710768458.5A CN201710768458A CN107345567B CN 107345567 B CN107345567 B CN 107345567B CN 201710768458 A CN201710768458 A CN 201710768458A CN 107345567 B CN107345567 B CN 107345567B
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line
driven
driving
contact line
tooth
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CN107345567A (en
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陈扬枝
李政
谢雄敦
吕月玲
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South China University of Technology SCUT
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16H—GEARING
    • F16H55/00—Elements with teeth or friction surfaces for conveying motion; Worms, pulleys or sheaves for gearing mechanisms
    • F16H55/02—Toothed members; Worms
    • F16H55/17—Toothed wheels
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation

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  • Pure & Applied Mathematics (AREA)
  • Mechanical Engineering (AREA)
  • Gears, Cams (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)

Abstract

The invention discloses a coplanar axis gear mechanism with a conical spiral line structure driving line teeth, which comprises a driving wheel and a driven wheel, wherein the driving wheel and the driven wheel meet the space curve meshing theory of a line gear, and adopt the conical spiral line which is adaptive to an inter-axis angle and a transmission ratio to carry out driving contact line structure. The invention has the advantages of small space size of the wire gear, large transmission ratio and the like; the shape of the driving wheel can adopt a conical spiral line with any vertex angle, and the driving wheel has the characteristics of high space utilization rate and small sliding rate; the bidirectional transmission of forward and reverse rotation without side gaps can be realized, and the bidirectional transmission is easy to process, and is particularly suitable for the application in the fields of microminiature machines, microminiature machines and conventional machines with limited space.

Description

Coplanar axis gear mechanism with conical spiral line structure driving line teeth
Technical Field
The invention belongs to the technical field of gear transmission, and particularly relates to a co-planar axis gear mechanism with a conical spiral line structure driving line tooth.
Background
Gear transmission is the most widely applied transmission and speed change technology, and a linear gear transmission pair can realize transmission and large transmission ratio that axes intersect or are staggered at any angle. Heretofore, line gears have also been known as space curve meshing wheels, and engaged during transmission are a pair of conjugated space curves, i.e., a pair of conjugated drive wheel contact lines and driven wheel contact lines. The existing wire gear mechanism adopts a cylindrical spiral line to construct a driving contact line consistently, such as an oblique gear mechanism disclosed in China patent application No. 2010101059023, and under the condition of intersecting shaft transmission, the constant meshing radius of the cylindrical spiral line cannot be adapted to the shaft spacing of the intersecting shaft, so that the space utilization rate is low and the sliding rate is high. Therefore, it is necessary to optimize the shape of the line gear active contact line. In many applications, the gear mechanism is required to have a function of bi-directionally transmitting power, but the wire teeth of the existing wire gear mechanism are formed by the movement of tooth profiles along a contact line, such as a concave-convex arc gear mechanism for parallel shaft transmission disclosed in China patent (patent application No. 2015105709269), and each wire tooth has only one contact line participating in meshing, so that the wire gear with the structure has a tooth side clearance and can only realize unidirectional transmission.
Disclosure of Invention
In view of the above, the invention aims to provide a co-planar axis gear mechanism with a conical spiral line structure for driving line teeth, which has the characteristics of high space utilization rate, small sliding rate, capability of realizing forward and reverse rotation bidirectional transmission, higher contact strength and bending strength, easiness in numerical control processing and the like, and is particularly suitable for microminiature machines, micromanipulators and conventional mechanical fields with limited space.
To achieve the technical purpose, the invention adopts the following technical scheme:
the co-planar axis gear mechanism with conic spiral line to constitute driving line gear includes driving wheel and driven wheel, and the driving wheel and driven wheel meet the line gear space curve meshing theory, i.e. space conjugated driving contact line and driven contact line to realize meshing transmission in the form of point contact, and the space curve meshing theory relates to the following space coordinate system, coordinate system o 0 -x 0 y 0 z 0 And coordinate system o 1 -x 1 y 1 z 1 A fixed coordinate system and a follow-up coordinate system of the driving wheel respectively, and a coordinate system o p -x p y p z p And coordinate system o 2 -x 2 y 2 z 2 The fixed coordinate system and the follow-up coordinate system of the driven wheel are respectively adopted; axis of rotation and z of the driving wheel 0 (z 1 ) The axes coincide with the z-axis of rotation of the driven wheel 2 (z p ) The axes coincide, and the included angle between the rotating axes of the driving wheel and the driven wheel is theta 0 The included angles between the axes can be crossed at any angle according to design requirements, and the any angle is any angle which is more than or equal to 0 degrees and less than 180 degrees; the driving wheel and the driven wheel respectively take angular velocityAnd->Around axis z 1 And z 2 The shaft rotates, and the driving wheel and the driven wheel rotate by an angle respectively within a certain time>And->The meshing equation of the co-planar axis gear mechanism with the conical spiral line for constructing the driving line teeth is as follows:
wherein the active contact line is in a coordinate system o 1 -x 1 y 1 z 1 The parametric equation for (2) is:
wherein t is 1 Is the parameter, t 1s 、t 1e Is the parameter t 1 The value range of (a) is the position of the engagement starting point and the engagement ending point on the active contact line;
the driven contact line is in a coordinate system o 1 -x 1 y 1 z 1 The parametric equation for (2) is:
wherein,,i is the gear ratio.
Further, the driving contact line of the mechanism is a conical spiral line, the driven contact line can adopt a cylindrical spiral line, a conical spiral line or a planar Archimedes spiral line according to the axis included angle requirement, and the parameter equations of the driving contact line and the driven contact line are as follows:
wherein t is 1 And t 2 As a parameter, θ 1 And theta 2 Semi-conical vertex angles, m, of a driving contact line and a driven contact line respectively 1 、n 1 And m 2 、n 2 The spiral parameters, k, of the driving contact line and the driven contact line respectively 1 And k 2 The spiral line is a left-handed spiral line when the spiral direction parameter is 1, and is a right-handed spiral line when the spiral direction parameter is-1.
Further, two contact lines are arranged on each line tooth of the driving wheel and the driven wheel, so that forward and reverse rotation bidirectional transmission can be realized, and the two contact lines on the driving wheel comprise a first active contact line and a second active contact line; the two contact lines comprise a first driven contact line and a second driven contact line on the driven wheel; the second active contact line is formed by the first active contact line z 1 Rotation of the shaftThe parameter equations of the first active contact line and the second active contact line are respectively:
likewise, the second driven contact line is formed by the first driven contact line z 2 Rotation of the shaftThe parameter equations of the first driven contact line and the second driven contact line are respectively:
further, the thickness of the wire teeth and the width of the tooth grooves of the co-planar axis gear mechanism are equal, and the thickness of the wire teeth and the width of the tooth grooves are defined in the axial section of the wire gear, namely, the thickness of the wire teeth and the width of the tooth grooves of the driving wheel and the driven wheel are respectively defined in the direction of the conical straight generatrix where any point on the driving contact line and the driven contact line is located.
Further, one side tooth surface of the driving line tooth of the driving wheel is formed by moving a section of circular arc tooth profile along the first driving contact line and one driving wheel tooth thickness auxiliary line, and the other side tooth surface of the driving line tooth is formed by moving a section of circular arc tooth profile along the second driving contact line and the other driving wheel tooth thickness auxiliary line; one side tooth surface of the driven line tooth of the driven wheel is formed by moving a section of circular arc tooth profile along the first driven contact line and one driven wheel tooth thickness auxiliary line, and the other side tooth surface of the driven line tooth is formed by moving a section of circular arc tooth profile along the second driven contact line and the other driven wheel tooth thickness auxiliary line; the circular arc tooth profile of the driving wheel and the circular arc tooth profile of the driven wheel are respectively positioned on the normal planes of the driving contact line and the driven contact line; the two driving wheel tooth thickness auxiliary lines comprise a first driving wheel tooth thickness auxiliary line and a second driving wheel tooth thickness auxiliary line which are equidistant curves of a first driving contact line and a second driving contact line in the normal direction respectively; the two driven wheel tooth thickness auxiliary lines comprise a first driven wheel tooth thickness auxiliary line and a second driving wheel tooth thickness auxiliary line, and are equidistant curves of a first driven contact line and a second driven contact line in the normal direction respectively. Can realize forward and reverse rotation bidirectional transmission without side gaps.
Further, the parameter equations of the first driving wheel tooth thickness auxiliary line and the second driving wheel tooth thickness auxiliary line are respectively:
wherein r is the radius of the tooth profile arc, phi is the direction parameter of the tooth thickness auxiliary line of the driving wheel and the tooth thickness auxiliary line of the driven wheel, and N 1 Is the number of teeth of the driving wheel;
the parameter equations of the first driven wheel tooth thickness auxiliary line and the second driven wheel tooth thickness auxiliary line are respectively as follows:
wherein r is the radius of the tooth profile arc, phi is the direction parameter of the tooth thickness auxiliary line of the driving wheel and the tooth thickness auxiliary line of the driven wheel, and N 2 Is the number of teeth of the driven wheel.
Further, the driving wheel body is a cone with the vertex angle equal to that of the first driving contact line; the driven wheel body is a cone with the vertex angle equal to that of the first driven contact line, and the driving line teeth and the driven line teeth are distributed on the wheel body of the driving wheel and the driven wheel.
Compared with the prior art, the invention has the following advantages:
(1) The structure is compact: the driving wheel and the driven wheel form a pair of transmission pairs, and compared with the traditional microminiature speed change mechanism, the transmission system has a very simple structure; under the condition of intersecting shaft transmission, the meshing radius of the conical spiral line is easy to adapt to the shaft distance of the intersecting shaft, the space utilization rate is high, the installation space can be greatly saved, the sliding rate is low, the vibration and noise are small, and the fatigue life is long.
(2) The transmission ratio is large: compared with the transmission of the existing transmission mechanisms such as spur gears, helical gears and the like, the single-stage transmission with large transmission ratio and high contact ratio can be realized.
(3) No tooth side gap: compared with the existing linear gear mechanism, the two sides of the tooth surfaces of the driving linear teeth and the driven linear teeth respectively comprise two contact lines, so that the forward and reverse rotation bidirectional non-side gap stable operation can be realized; the wire teeth are radially attached to the wheel body, and have good bearing capacity and running stability.
Drawings
Fig. 1 is a schematic diagram of meshing coordinates in an embodiment.
FIG. 2 is a schematic view of the thickness of a wire tooth and the width of a tooth slot defined in a cross-section of a shaft in an embodiment.
Fig. 3 is a schematic view of contact lines and tooth thickness assistance lines in an embodiment.
Fig. 4 is a schematic diagram of a driving wheel in an embodiment.
Fig. 5 is a schematic view of a driven wheel in an embodiment.
Fig. 6 is a schematic diagram of the driving wheel and the driven wheel in the embodiment.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the present invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications could be made by those skilled in the art without departing from the inventive concept. These are all within the scope of the present patent.
The co-planar axis gear mechanism with conic spiral line to constitute the driving line teeth includes driving wheel and driven wheel, and the driving wheel and the driven wheel meet the space curve meshing theory of line gear, i.e. the space conjugated driving contact line and driven contact line realize meshed transmission in the form of point contact.
The space curve meshing theory relates to a space coordinate system, a coordinate system o 0 -x 0 y 0 z 0 And coordinate system o 1 -x 1 y 1 z 1 A fixed coordinate system and a follow-up coordinate system of the driving wheel respectively, and a coordinate system o p -x p y p z p And coordinate system o 2 -x 2 y 2 z 2 The fixed coordinate system and the follow-up coordinate system of the driven wheel are respectively adopted. Axis of rotation and z of the driving wheel 0 (z 1 ) The axes coincide with the z-axis of rotation of the driven wheel 2 (z p ) The axes coincide, and the included angle between the rotating axes of the driving wheel and the driven wheel is theta 0 The included angles between the axes can be crossed at any angle according to design requirements, and the any angle is any angle larger than or equal to 0 degrees and smaller than 180 degrees, as shown in fig. 1. The driving wheel and the driven wheel respectively take angular velocityAnd->Around axis z 1 And z 2 The shaft rotates, and the driving wheel and the driven wheel rotate by an angle respectively within a certain time>And->The meshing equation of the co-planar axis gear mechanism with the conical spiral line for constructing the driving line teeth is as follows:
wherein the active contact line is in the coordinate system o 1 -x 1 y 1 z 1 The parametric equation for (2) is:
t 1 is the parameter, t 1s 、t 1e Is the parameter t 1 The value range of (a) is the position of the engagement starting point and the engagement ending point on the active contact line.
The slave contact line is in the coordinate system o 1 -x 1 y 1 z 1 The parametric equation for (2) is:
wherein,,i is the gear ratio.
The driving contact line of the mechanism is a conical spiral line, the driven contact line can adopt a cylindrical spiral line, a conical spiral line or a planar Archimedes spiral line according to the axis included angle requirement, and the parameter equations of the driving contact line and the driven contact line are as follows:
wherein t is 1 And t 2 As a parameter, θ 1 And theta 2 Semi-conical vertex angles, m, of a driving contact line and a driven contact line respectively 1 、n 1 And m 2 、n 2 The spiral parameters, k, of the driving contact line and the driven contact line respectively 1 And k 2 The spiral line is a left-handed spiral line when the spiral direction parameter is 1, and is a right-handed spiral line when the spiral direction parameter is-1.
Two contact lines are arranged on each line tooth of the driving wheel and the driven wheel, so that forward and reverse rotation bidirectional transmission can be realized. The two contact lines comprise a first active contact line and a second active contact line on the driving wheel; on the driven wheel, the two contact lines comprise a first driven contact line and a second driven contact line. The second active contact line is formed by the first active contact line z 1 Rotation of the shaftObtained. The parameter equations of the first active contact line and the second active contact line are respectively as follows:
likewise, the second driven contact line is formed by the first driven contact line z 2 Rotation of the shaftObtained. The parameter equations of the first driven contact line and the second driven contact line are respectively as follows:
the wire tooth thickness 1 and the tooth slot width 2 of the mechanism are equal. The thickness and the width of the tooth space of the wire teeth are defined in the axial section of the wire gear, namely the thickness and the width of the tooth space of the driving wheel and the driven wheel are respectively defined in the direction of the conical straight generatrix where any point on the driving contact line and the driven contact line is located, as shown in figure 2.
Specifically, the mechanism can realize forward and reverse rotation bidirectional transmission without side gaps. One side tooth surface 3 of the driving line tooth of the driving wheel is formed by a section of arc tooth profile moving along the first driving contact line 4 and the first driving wheel tooth thickness auxiliary line 5, and the other side tooth surface of the driving line tooth is formed by a section of arc tooth profile moving along the second driving contact line 6 and the second driving wheel tooth thickness auxiliary line 7, as shown in fig. 3. One side tooth surface of the driven line tooth of the driven wheel is formed by moving a section of circular arc tooth profile along the first driven contact line and the first driven wheel tooth thickness auxiliary line, and the other side tooth surface of the driven line tooth is formed by moving a section of circular arc tooth profile along the second driven contact line and the second driven wheel tooth thickness auxiliary line. The circular arc tooth profile of the driving wheel and the circular arc tooth profile of the driven wheel are respectively positioned on the normal planes of the driving contact line and the driven contact line. The first driving wheel tooth thickness auxiliary line and the second driving wheel tooth thickness auxiliary line are equidistant curves of the first driving contact line and the second driving contact line in the normal direction respectively; the first driven wheel tooth thickness auxiliary line and the second driving wheel tooth thickness auxiliary line are equidistant curves of the first driven contact line and the second driven contact line in the normal direction respectively.
The parameter equations of the first driving wheel tooth thickness auxiliary line and the second driving wheel tooth thickness auxiliary line are respectively as follows:
r is the radius of the tooth profile arc, phi is the direction parameter of the tooth thickness auxiliary line of the driving wheel and the tooth thickness auxiliary line of the driven wheel, and N 1 Is the number of teeth of the driving wheel.
The parameter equations of the first driven wheel tooth thickness auxiliary line and the second driven wheel tooth thickness auxiliary line are respectively as follows:
r is the radius of the tooth profile arc, phi is the direction parameter of the tooth thickness auxiliary line of the driving wheel and the tooth thickness auxiliary line of the driven wheel, and N 2 Is the number of teeth of the driven wheel.
The wheel body of the driving wheel is a cone with the vertex angle equal to that of the first driving contact line; the driven wheel body is a cone with the vertex angle equal to that of the first driven contact line. The driving wire teeth and the driven wire teeth are distributed on the wheel bodies of the driving wheel and the driven wheel.
Let the initial quantity be m 1 ＝2.5mm，n 1 ＝4mm，θ 1 ＝7°，m 2 ＝12mm，i＝8，θ 0 ＝90°，N 1 ＝2，N 2 ＝16。
The parameter equations for the first active contact line and the second active contact line are respectively:
the parameter equations of the first driven contact line and the second driven contact line are respectively as follows:
the parameter equations of the first driving wheel tooth thickness auxiliary line and the second driving wheel tooth thickness auxiliary line are respectively as follows:
the parameter equations of the first driven wheel tooth thickness auxiliary line and the second driven wheel tooth thickness auxiliary line are respectively as follows:
the structured driving wheel is shown in fig. 4, the structured driven wheel is shown in fig. 5, and the engagement of the driving wheel 8 and the driven wheel 9 is shown in fig. 6.
The above examples of the present invention are merely illustrative of the present invention and are not intended to limit the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.

Claims (3)

1. The utility model provides an with the coplanar axis gear mechanism of conical helix structure initiative line tooth, includes action wheel and follow driving wheel, its characterized in that: the driving wheel and the driven wheel meet the meshing theory of the space curve of the line gear, namely, the space conjugate driving contact line and the space conjugate driven contact line realize meshing transmission in a point contact mode, and the meshing theory of the space curve relates to a space coordinate system, namely, a coordinate system o 0 -x 0 y 0 z 0 And coordinate system o 1 -x 1 y 1 z 1 A fixed coordinate system and a follow-up coordinate system of the driving wheel respectively, and a coordinate system o p -x p y p z p And coordinate system o 2 -x 2 y 2 z 2 The fixed coordinate system and the follow-up coordinate system of the driven wheel are respectively adopted; axis of rotation and z of the driving wheel 0 (z 1 ) The axes coincide with the z-axis of rotation of the driven wheel 2 (z p ) The axes coincide, and the included angle between the rotating axes of the driving wheel and the driven wheel is theta 0 The included angles between the axes can be crossed at any angle according to design requirements, and the any angle is any angle which is more than or equal to 0 degrees and less than 180 degrees; the driving wheel and the driven wheelRespectively at angular velocityAnd->Around axis z 1 And z 2 The shaft rotates, and the driving wheel and the driven wheel rotate by an angle respectively within a certain time>And->The meshing equation of the co-planar axis gear mechanism with the conical spiral line for constructing the driving line teeth is as follows:
wherein the active contact line is in a coordinate system o 1 -x 1 y 1 z 1 The parametric equation for (2) is:
wherein t is 1 Is the parameter, t 1s 、t 1e Is the parameter t 1 The value range of (a) is the position of the engagement starting point and the engagement ending point on the active contact line;
the driven contact line is in a coordinate system o 1 -x 1 y 1 z 1 The parametric equation for (2) is:
wherein,,is a transmission ratio;
the driving contact line of the mechanism is a conical spiral line, the driven contact line can adopt a cylindrical spiral line, a conical spiral line or a planar Archimedes spiral line according to the axis included angle requirement, and the parameter equations of the driving contact line and the driven contact line are as follows:
wherein t is 1 And t 2 As a parameter, θ 1 And theta 2 Semi-conical vertex angles, m, of a driving contact line and a driven contact line respectively 1 、n 1 And m 2 、n 2 The spiral parameters, k, of the driving contact line and the driven contact line respectively 1 And k 2 The spiral line is a spiral direction parameter, when the spiral direction parameter is 1, the conical spiral line is a left rotation, and when the spiral direction parameter is-1, the conical spiral line is a right rotation; two contact lines are arranged on each line tooth of the driving wheel and the driven wheel, so that forward and reverse rotation bidirectional transmission can be realized, and the two contact lines on the driving wheel comprise a first active contact line and a second active contact line; the two contact lines comprise a first driven contact line and a second driven contact line on the driven wheel; the second active contact line is formed by the first active contact line z 1 Rotation of the shaftThe parameter equations of the first active contact line and the second active contact line are respectively:
likewise, the second driven contact line is formed by the first driven contact line z 2 Rotation of the shaftThe parameter equations of the first driven contact line and the second driven contact line are respectively:
one side tooth surface of the driving line tooth of the driving wheel is formed by moving a section of arc tooth profile along the first driving contact line and one driving wheel tooth thickness auxiliary line, and the other side tooth surface of the driving line tooth is formed by moving a section of arc tooth profile along the second driving contact line and the other driving wheel tooth thickness auxiliary line; one side tooth surface of the driven line tooth of the driven wheel is formed by moving a section of circular arc tooth profile along the first driven contact line and one driven wheel tooth thickness auxiliary line, and the other side tooth surface of the driven line tooth is formed by moving a section of circular arc tooth profile along the second driven contact line and the other driven wheel tooth thickness auxiliary line; the circular arc tooth profile of the driving wheel and the circular arc tooth profile of the driven wheel are respectively positioned on the normal planes of the driving contact line and the driven contact line; the two driving wheel tooth thickness auxiliary lines comprise a first driving wheel tooth thickness auxiliary line and a second driving wheel tooth thickness auxiliary line which are equidistant curves of a first driving contact line and a second driving contact line in the normal direction respectively; the two driven wheel tooth thickness auxiliary lines comprise a first driven wheel tooth thickness auxiliary line and a second driving wheel tooth thickness auxiliary line which are equidistant curves of a first driven contact line and a second driven contact line in the normal direction respectively; the parameter equations of the first driving wheel tooth thickness auxiliary line and the second driving wheel tooth thickness auxiliary line are respectively as follows:
wherein r is the radius of the tooth profile arc, phi is the direction parameter of the tooth thickness auxiliary line of the driving wheel and the tooth thickness auxiliary line of the driven wheel, and N 1 Is the number of teeth of the driving wheel;
the parameter equations of the first driven wheel tooth thickness auxiliary line and the second driven wheel tooth thickness auxiliary line are respectively as follows:
wherein r is the radius of the tooth profile arc, phi is the direction parameter of the tooth thickness auxiliary line of the driving wheel and the tooth thickness auxiliary line of the driven wheel, and N 2 Is the number of teeth of the driven wheel.
2. The in-plane axis gear mechanism of claim 1 wherein the drive line teeth are configured in a conical helix, wherein: the thickness of the wire teeth and the width of the tooth grooves of the co-planar axis gear mechanism are equal, and the thickness of the wire teeth and the width of the tooth grooves are defined in the axial section of the wire gear, namely the thickness of the wire teeth and the width of the tooth grooves of the driving wheel and the driven wheel are respectively defined in the direction of the conical straight generatrix where any point on the driving contact line and the driven contact line is located.
3. The in-plane axis gear mechanism of claim 1 wherein the drive line teeth are configured in a conical helix, wherein: the driving wheel body is a cone with the vertex angle equal to that of the first driving contact line; the driven wheel body is a cone with the vertex angle equal to that of the first driven contact line, and the driving line teeth and the driven line teeth are distributed on the wheel body of the driving wheel and the driven wheel.
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CN108533686B (en) * 2018-06-12 2020-01-17 中国地质大学（武汉） Concave-convex mesh pure rolling bevel gear mechanism for crossed shaft transmission
CN108533685B (en) * 2018-06-12 2020-01-17 中国地质大学（武汉） Convex-concave meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission
CN108533683B (en) * 2018-06-12 2020-01-17 中国地质大学（武汉） Convex-convex meshing pure rolling spiral bevel gear mechanism for crossed shaft transmission
CN108691954B (en) * 2018-06-12 2019-12-17 中国地质大学（武汉） flat-convex meshing pure rolling bevel gear mechanism for crossed shaft transmission
CN110414078B (en) * 2019-07-08 2023-06-02 三峡大学 Construction method of meshing line gear mechanism in parallel shaft convex-concave circular arc section
CN110645334A (en) * 2019-09-23 2020-01-03 天津大学 Coaxial surface contact oscillating tooth speed reducer

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CN103075493B (en) * 2012-12-29 2015-07-15 重庆大学 Bevel gear based on conjugate curves and meshing pair thereof
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