CN110273979B - Three-freedom-degree ball gear transmission pair - Google Patents
Three-freedom-degree ball gear transmission pair Download PDFInfo
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- CN110273979B CN110273979B CN201910558657.2A CN201910558657A CN110273979B CN 110273979 B CN110273979 B CN 110273979B CN 201910558657 A CN201910558657 A CN 201910558657A CN 110273979 B CN110273979 B CN 110273979B
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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
- F16H1/00—Toothed gearings for conveying rotary motion
- F16H1/02—Toothed gearings for conveying rotary motion without gears having orbital motion
- F16H1/24—Toothed gearings for conveying rotary motion without gears having orbital motion involving gears essentially having intermeshing elements other than involute or cycloidal teeth
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Abstract
The invention discloses a three-freedom degree ball gear transmission pair, which relates to the technical field of mechanical transmission and bionic motion joints and comprises the following components: a discrete spherical gear and a continuous spherical gear, the discrete spherical gear and the continuous spherical gear are engaged, the discrete spherical gear and the continuous spherical gear respectively comprise a plurality of plane involute annular tooth surfaces and a plurality of spherical involute spherical conical tooth surfaces, the plane involute annular tooth surfaces and the spherical involute spherical conical tooth surfaces are vertically crossed to form a plurality of convex spherical teeth of the discrete spherical gear, the plane involute annular tooth surfaces and the spherical involute spherical conical tooth surfaces are vertically crossed to form a plurality of concave spherical teeth of the continuous spherical gear, one convex spherical tooth is inserted into one concave spherical tooth, the spherical gear has the advantages that the defects that the existing spherical gear only has two degrees of freedom, is high in processing and manufacturing difficulty and high in processing cost can be overcome, the movement of three degrees of freedom of deflection, pitching and axis rotation can be realized, the processing is easy, the meshing transmission is stable, and no transmission principle error exists.
Description
Technical Field
The invention relates to the technical field of mechanical transmission and bionic motion joints, in particular to a three-freedom-degree ball gear transmission pair.
Background
The traditional gear mechanism adopts single-degree-of-freedom transmission, can not meet the requirement of emerging fields on multiple transmission degrees of freedom, and the appearance of the spherical gear thoroughly changes the phenomenon.
The 20 th century 80 years norwegian engineer invents the first Trallfa painting robot flexible wrist with two freedom of motion based on ball gear transmission in the world, and the flexible wrist can transfer two-dimensional rotary motion.
Pan-Cin et al propose an involute ring-tooth ball gear, which is formed by a plane involute rotating around an axis, and any cross section passing through the axis is a plane involute tooth profile. The involute ring gear has no theoretical error and is easy to process and manufacture. However, the ball gear has only two degrees of freedom, and the mechanical wrist cannot be connected with the clamp based on the ball gear.
Disclosure of Invention
The invention aims to provide a spherical tooth transmission pair which is easy to process, stable in meshing transmission and free of transmission principle errors, and can realize the motions of three degrees of freedom of deflection, pitching and axis rotation.
In order to achieve the purpose, the invention provides the following scheme:
the invention provides a three-freedom-degree spherical gear transmission pair which comprises a discrete spherical gear and a continuous spherical gear, wherein the discrete spherical gear is meshed with the continuous spherical gear, the discrete spherical gear and the continuous spherical gear respectively comprise a plurality of plane involute annular tooth surfaces and a plurality of spherical involute spherical conical tooth surfaces, the plane involute annular tooth surfaces and the spherical involute spherical conical tooth surfaces on the discrete spherical gear are perpendicularly crossed to form a plurality of convex spherical teeth, the plane involute annular tooth surfaces and the spherical involute spherical conical tooth surfaces on the continuous spherical gear are perpendicularly crossed to form a plurality of concave spherical teeth, and one convex spherical tooth is used for being inserted into one concave spherical tooth.
Preferably, a plurality of that sets up on the same weft direction the convex surface ball tooth is along circumference evenly distributed, and a plurality of that same weft direction set up the convex surface ball tooth is the same along the tooth thickness and the modulus homogeneous phase of sphere involute ball awl flank of tooth.
Preferably, the number of convex spherical teeth arranged in any weft direction is equal.
Preferably, a plurality of convex spherical teeth arranged in the same warp direction are uniformly distributed in the circumferential direction, and the convex spherical teeth at different latitudes on the same warp are different in tooth thickness along the plane involute annular tooth surface.
Preferably, a plurality of that sets up on the same weft direction the concave surface ball tooth is along circumference evenly distributed, and a plurality of that same weft direction set up the concave surface ball tooth is all the same along the flute width and the modulus of sphere involute ball awl flank of tooth.
Preferably, the number of concave spherical teeth arranged in any weft direction is equal.
Preferably, a plurality of the concave spherical teeth arranged in the same warp direction are uniformly distributed in the circumferential direction, and the concave spherical teeth at different latitudes on the same warp are different in tooth socket width along the plane involute annular tooth surface.
Preferably, the convex spherical teeth are tetrahedral independent convex teeth.
Compared with the prior art, the invention has the following technical effects:
the invention provides a three-freedom-degree spherical gear transmission pair, which comprises a discrete spherical gear and a continuous spherical gear, wherein the discrete spherical gear and the continuous spherical gear respectively comprise a plurality of plane involute annular tooth surfaces and a plurality of spherical involute spherical conical tooth surfaces, the plane involute annular tooth surfaces and the spherical involute spherical conical tooth surfaces on the discrete spherical gear are vertically crossed to form a plurality of convex spherical teeth, the plane involute annular tooth surfaces and the spherical involute spherical conical tooth surfaces on the continuous spherical gear are vertically crossed to form a plurality of concave spherical teeth, the three-freedom-degree spherical gear transmission pair has the advantage of easy processing, the concave spherical teeth are four-surface grooves, one convex spherical tooth is inserted into one concave spherical tooth, so that the three-freedom-degree motions of deflection, pitching and axial rotation are realized, and in the transmission process of the discrete spherical gear and the continuous spherical gear, the spherical center distance between the discrete spherical gear and the continuous spherical gear is unchanged, the convex spherical teeth and the concave spherical teeth are in an inserted type meshing mode, so that meshing transmission stability can be guaranteed, and errors of a transmission principle do not exist.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a perspective view of a ball and socket drive countershaft provided by the present invention;
FIG. 2 is an isometric view of a discrete ball gear of the ball gear drive pair provided by the present invention;
FIG. 3 is an isometric view of a continuous ball gear of the ball gear drive set provided by the present invention;
FIG. 4 is a schematic diagram of the formation of an annular involute tooth profile for a ball gear drive pair in accordance with the present invention;
FIG. 5 is a schematic diagram of the spherical involute of the spherical gear transmission pair provided by the invention;
FIG. 6 is an isometric view of a single plane involute ring tooth flank of a spherical tooth drive pair provided in accordance with the present invention;
FIG. 7 is an isometric view of a single spherical involute spherical conical tooth surface of a spherical tooth drive pair provided by the present invention;
FIG. 8 is a schematic view of a single tetrahedron independent spur formed by the engagement of a plane involute ring tooth surface and a spherical involute spherical cone tooth surface of a spherical tooth transmission pair provided by the present invention;
fig. 9 is a schematic diagram of a single four-sided groove surrounded by a plane involute annular tooth surface and a spherical involute spherical cone tooth surface of the spherical tooth transmission pair provided by the invention.
Wherein: 1-discrete spherical gear, 2-continuous spherical gear, 3-tetrahedron independent convex tooth, 4-four-surface groove, 5-spherical involute spherical cone tooth surface and 6-plane involute annular tooth surface.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.
The invention aims to provide a spherical tooth transmission pair which is easy to process, stable in meshing transmission and free of transmission principle errors, and can realize the motions of three degrees of freedom of deflection, pitching and axis rotation.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in FIGS. 1-9: the embodiment provides a three-freedom-degree spherical gear transmission pair, which comprises a discrete spherical gear 1 and a continuous spherical gear 2, wherein the discrete spherical gear 1 is meshed with the continuous spherical gear 2, the discrete spherical gear 1 and the continuous spherical gear 2 both comprise a plurality of plane involute annular tooth surfaces 6 and a plurality of spherical involute spherical conical tooth surfaces 5, the plane involute annular tooth surfaces 6 and the spherical involute spherical conical tooth surfaces 5 on the discrete spherical gear 1 are perpendicularly crossed to form a plurality of convex spherical teeth, the plane involute annular tooth surfaces 6 and the spherical involute spherical conical tooth surfaces 5 on the continuous spherical gear 2 are perpendicularly crossed to form a plurality of concave spherical teeth, so that the motions of three degrees of freedom including deflection, pitching and rotation around an axis can be realized, the convex spherical teeth and the concave spherical teeth are easy to process, the concave spherical teeth are four-sided grooves 4, one convex spherical tooth is used for being inserted into one concave spherical tooth, in the transmission process of the discrete spherical gear 1 and the continuous spherical gear 2, the distance between the spherical centers of the discrete spherical gear 1 and the continuous spherical gear 2 is not changed, so that the meshing transmission is stable and no transmission principle error exists.
A plurality of convex surface ball teeth that set up on the same weft direction are along circumference evenly distributed, and a plurality of convex surface ball teeth that same weft direction set up are all the same along sphere involute spherical cone flank of tooth 5's tooth thickness and modulus to guarantee that the meshing transmission is stable and do not have transmission principle error.
The number of convex spherical teeth arranged in any weft direction is equal.
A plurality of convex spherical teeth that set up on the same warp direction evenly distributed on the circumferencial direction, the convex spherical teeth of different latitudes on the same warp are different along the tooth thickness of plane involute ring flank of tooth 6, are favorable to realizing beat and every single move motion.
A plurality of concave spherical teeth that set up on the same weft direction evenly distributed along the circumference, and a plurality of concave spherical teeth that set up in the same weft direction are all the same along the flute width and the modulus of sphere involute spherical cone flank of tooth 5 to guarantee that the meshing transmission is stable and do not have transmission principle error.
The number of the concave spherical teeth arranged in any weft direction is equal.
A plurality of concave surface ball teeth that set up on the same warp direction evenly distributed on the circumferencial direction, the concave surface ball tooth of different latitudes on the same warp is different along the flute width of plane involute ring flank 6, is favorable to realizing beat and every single move motion.
The convex spherical teeth are tetrahedral independent convex teeth 3.
The discrete spherical gear 1 and the continuous spherical gear 2 are based on the plane involute and spherical involute tooth surface generation theory, a mathematical model of the tooth surface of the multi-parameter spherical tooth in the warp direction and the weft direction is established, a tooth surface point cloud is obtained by a tooth profile parameter equation, and a tooth surface curved surface model and a gear tooth solid model are obtained, the method comprises the following steps,
1) in the meridian direction of the pitch spherical surface, an involute annular tooth profile curved surface parameter equation is established:
wherein r isbIs the base circle radius, u-tan αkIs roll angle, αkIs the pressure angle of the involute at point k,
is the included angle between the radial direction from the spherical center to the starting point of the involute profile on the basic sphere and the polar axis, gammaIs the angle of rotation of the involute about the y-axis.
2) In the pitch spherical surface latitude direction, a spherical involute tooth profile tooth surface parameter equation based on a continuously changed base cone angle is established:
wherein r is0Gamma is any point cone angle on the spherical involute for generating spherical radius,
in order to be the polar angle, the angle of the pole,
wherein, γbFor taper angle, β is a continuously varying taper angle parameter.
3) And obtaining tooth surface point cloud by a tooth profile parameter equation so as to obtain a tooth surface curved surface model and a gear tooth solid model.
The principle and the implementation mode of the present invention are explained by applying specific examples in the present specification, and the above descriptions of the examples are only used to help understanding the method and the core idea of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. A three-freedom-degree ball gear transmission pair is characterized in that: including a discrete spherical gear and a continuous type spherical gear, discrete spherical gear with continuous type spherical gear meshes mutually, discrete spherical gear with continuous type spherical gear all includes a plurality of planes and gradually bursts at the seams ring flank and a plurality of sphere and gradually bursts at the seams ball flank, discrete spherical gear is last the plane gradually bursts at the seams ring flank with the sphere gradually bursts at the seams ball flank vertical cross sets up in order to form a plurality of convex surface ball teeth, continuous type spherical gear is last the plane gradually bursts at the seams ring flank with sphere gradually bursts at the seams ball flank vertical cross sets up in order to form a plurality of concave surface ball teeth, one convex surface ball tooth is used for inserting one in the concave surface ball tooth.
2. The three degree of freedom ball gear drive set of claim 1 wherein: the convex spherical teeth are uniformly distributed along the circumference, and the convex spherical teeth are arranged along the same weft direction, and the tooth thickness and the modulus of the convex spherical teeth along the spherical involute spherical cone tooth surface are the same.
3. The three degree of freedom ball gear drive set of claim 1 wherein: the number of convex spherical teeth arranged in any weft direction is equal.
4. The three degree of freedom ball gear drive set of claim 1 wherein: the convex spherical teeth are uniformly distributed in the circumferential direction, and the convex spherical teeth at different latitudes on the same warp are different in tooth thickness along the plane involute annular tooth surface.
5. The three degree of freedom ball gear drive set of claim 1 wherein: the concave spherical teeth are uniformly distributed along the circumference and arranged in the same weft direction, and the concave spherical teeth are arranged in the same weft direction and have the same tooth socket width and modulus along the spherical involute spherical cone tooth surface.
6. The three degree of freedom ball gear drive set of claim 1 wherein: the number of the concave spherical teeth arranged in any weft direction is equal.
7. The three degree of freedom ball gear drive set of claim 1 wherein: the concave spherical teeth are uniformly distributed in the circumferential direction, and the concave spherical teeth at different latitudes on the same warp are different in tooth socket width along the plane involute annular tooth surface.
8. The three degree of freedom ball gear drive set of claim 1 wherein: the convex spherical teeth are tetrahedral independent convex teeth.
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| CN201910558657.2A CN110273979B (en) | 2019-06-26 | 2019-06-26 | Three-freedom-degree ball gear transmission pair |
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| CN201910558657.2A CN110273979B (en) | 2019-06-26 | 2019-06-26 | Three-freedom-degree ball gear transmission pair |
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| CN110645320A (en) * | 2019-10-16 | 2020-01-03 | 长春理工大学 | Spherical gear and toothed disc mechanism |
| JP7025801B1 (en) * | 2021-02-02 | 2022-02-25 | 国立大学法人山形大学 | Differential mechanism |
| CN113591238B (en) * | 2021-07-19 | 2024-03-22 | 北京工业大学 | Gear tangential integrated deviation calculation method based on gear point cloud data |
| CN114110129A (en) * | 2021-11-26 | 2022-03-01 | 长春理工大学 | Spherical gear and toothed disc mechanism |
| CN114060473B (en) * | 2021-11-26 | 2023-07-18 | 长春理工大学 | Three-degree-of-freedom involute ball gear pair |
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| GR1004886B (en) * | 2004-08-19 | 2005-05-23 | Spherical 3-dimensional gears. transmission of motion along any of the three dimensions at any moment | |
| CN103573921B (en) * | 2013-07-24 | 2016-02-24 | 杨兆奎 | A kind of involute spherical gear transmission pair |
| CN104565283A (en) * | 2013-10-19 | 2015-04-29 | 洪浛檩 | Involute non-annular continuous spherical-gear crown gear driving mechanism |
| CN203770578U (en) * | 2013-10-19 | 2014-08-13 | 洪浛檩 | Involute non-annular continuous-tooth spherical gear transmission mechanism |
| CN105223813A (en) * | 2015-09-24 | 2016-01-06 | 无锡职业技术学院 | Based on the spiral bevel gear 3-D geometric model modeling method of spherical involute |
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