Three-degree-of-freedom spherical gear pair

Abstract

This invention relates to a three-degree-of-freedom spherical linear gear pair, comprising a first driving linear gear, a second driving linear gear, a third driving linear gear, a spherical driven linear gear, and a base. The tooth surface of the spherical driven linear gear has staggered first and second tooth groove structures. The tooth surface of the first driving linear gear is a first cylindrical helical surface, meshing with the first tooth groove structure. The tooth surfaces of the second and third driving linear gears are both second cylindrical helical surfaces, and mesh with the same second tooth groove structure on the spherical driven linear gear from different directions. The meshing form between the first, second, and third driving linear gears and the spherical driven linear gear is point contact, and a pair of conjugate instantaneous meshing lines exist on the tooth surfaces of each meshing pair. This invention, while maintaining the compact integration and three-degree-of-freedom output of the spherical gear mechanism, overcomes the transmission ratio limitations of existing technologies, simplifies the transmission chain, improves lubrication performance, and facilitates machining.

Description

Technical Field

[0001] This invention relates to the field of mechanical transmission technology, specifically to a three-degree-of-freedom spherical linear gear pair. Background Technology

[0002] Existing robotic arm joints typically employ a single-joint, single-degree-of-freedom configuration, where the number of joints equals the number of degrees of freedom, making it difficult to achieve flexible multi-degree-of-freedom motion within a limited space. To overcome this bottleneck, multi-degree-of-freedom integrated joints have emerged as a new technological solution. This solution integrates the driving and transmission structures of multiple degrees of freedom into a single unit. By reducing the number of components, it not only simplifies the overall structure, reduces weight and size, but also minimizes the transmission backlash and elastic deformation accumulated in multi-joint serial configurations, significantly improving the joint's output accuracy. Simultaneously, multi-degree-of-freedom integrated joints also possess low inertia and high dynamic response characteristics, effectively meeting the robot's dynamic performance requirements.

[0003] Spherical drive mechanisms are a form of multi-degree-of-freedom integrated joint. Early explorations of spherical drive mechanisms mainly focused on friction wheels and omnidirectional wheel drives, but these mechanisms suffer from slippage and other problems, limiting transmission reliability. Spherical gear mechanisms eliminate slippage and possess high load-bearing capacity and good transmission accuracy. As a special-configuration transmission element, it enables multi-degree-of-freedom rotational motion around a fixed point, overcoming the limitations of limited space and the constraints between multi-degree-of-freedom transmission and lightweight design. In humanoid robot applications, its compact integration characteristics are highly similar to those of biological limb joints. Therefore, spherical gear mechanisms are an important technical path for robots, especially humanoid robots, to achieve high-performance joints.

[0004] Existing technology discloses a three-degree-of-freedom spherical gear pair, the main mechanism of which consists of a driven spherical gear and two driving special cylindrical gears. The entire spherical surface of the spherical gear is machined with an interlocking involute ring tooth structure; the special cylindrical gears are formed by cutting a cylindrical tooth blank with the spherical gear as a generating tool, and can mesh with the spherical gear. A single special cylindrical gear and its drive module can provide two rotational degrees of freedom, and when two special cylindrical gear modules work together, they can drive the spherical gear in all three degrees of freedom.

[0005] It has the following technical problems:

[0006] The geometry of each involute ring tooth on the driven spherical gear is different. Special cylindrical gears and driven spherical gears must be paired tooth by tooth, resulting in a maximum transmission ratio of only 2, which is difficult to meet the torque amplification requirements. Additional multi-stage differential mechanisms and reducers are required, making the system structure complex and not truly simplifying the transmission components. In addition, the low entrainment speed in the meshing contact area is not conducive to the formation of an elastic hydrodynamic lubrication film, thus affecting transmission efficiency and wear life. Summary of the Invention

[0007] To address the problems existing in the prior art, the purpose of this invention is to provide a three-degree-of-freedom spherical linear gear pair that, while maintaining the compact integration of the spherical gear mechanism and three-degree-of-freedom output, breaks through the transmission ratio limitations of the prior art, simplifies the transmission chain, improves lubrication performance, and facilitates machining.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A three-degree-of-freedom spherical linear gear pair includes a first driving linear gear, a second driving linear gear, a third driving linear gear, a spherical driven linear gear, and a base;

[0010] The tooth surface of the spherical driven gear has an interlaced first tooth groove structure and a second tooth groove structure, both of which are rotary structures.

[0011] The first tooth groove structure is formed by rotating and scanning the first planar tooth profile around the first axis, and the second tooth groove structure is formed by rotating and scanning the second planar tooth profile around the second axis. The first axis and the second axis intersect at the center of the spherical driven gear.

[0012] The tooth surface of the first driving gear is a first cylindrical helical surface, which meshes with the first tooth groove structure;

[0013] The tooth surfaces of the second and third driving gears are both second cylindrical helical surfaces, and they mesh with the same second tooth groove structure on the spherical driven gear from different directions.

[0014] The first, second, and third driving gears are movably mounted on the base via Hooke's hinges and their meshing with the spherical driven gear is point contact. Each meshing pair has a pair of conjugate instantaneous meshing lines on its tooth surface, and each meshing pair achieves transmission through these instantaneous meshing lines.

[0015] Furthermore, the Hooke hinge includes a first axis and a second axis, and the first axes of the first driving gear, the second driving gear and the third driving gear are their respective axes of rotation; the second axis is a radial line passing through the midpoint of the first axis and pointing to the center of the spherical driven gear.

[0016] Furthermore, the first driving gear is configured to drive the spherical driven gear to rotate around a first instantaneous axis when rotating around its first axis. The first instantaneous axis passes through the center of the sphere and is perpendicular to the first axis, and is spatially intersecting with the first axis of the first driving gear.

[0017] The second driving gear is configured to drive the spherical driven gear to rotate around a second instantaneous axis when it rotates around its first axis. The second instantaneous axis passes through the center of the sphere and is perpendicular to the second axis, and is spatially intersecting with the first axis of the second driving gear.

[0018] The third driving gear is configured to drive the spherical driven gear to rotate around the third instantaneous axis when it rotates around its first axis. The third instantaneous axis passes through the center of the sphere and is perpendicular to the second axis, and is spatially intersecting with the first axis of the third driving gear.

[0019] Furthermore, the spherical driven gear is configured to rotate about a first axis, and the first driving gear has no motion interference with the direction of rotation; the spherical driven gear is configured to rotate about a second axis, and the second and third driving gears have no motion interference with the direction of rotation.

[0020] Furthermore, the base is provided with a ball socket, and a spherical driven gear is movably disposed in the ball socket to achieve three-degree-of-freedom rotational motion.

[0021] Furthermore, the first cylindrical helical surface is a tooth surface formed by the helical motion of the first tooth profile located in its axial section around its axis; the second cylindrical helical surface is a tooth surface formed by the helical motion of the second tooth profile located in its axial section around its axis.

[0022] Furthermore, the first driving gear, the second driving gear, and the third driving gear are configured such that when they rotate around their respective first axes under the drive of the driver, the spherical driven gear has a uniquely determined spatial orientation.

[0023] Furthermore, the tooth surface of the first tooth groove structure is constructed as follows: based on the first virtual tooth surface formed when the first driving gear drives the spherical driven gear to rotate around the first instantaneous rotating axis, and formed by the meshing line that rotates around the first axis and is in tangential contact with the first virtual tooth surface and satisfies the conjugate meshing condition, and is scanned around the first axis.

[0024] The tooth surface of the second tooth groove structure is constructed as follows: based on the second virtual tooth surface formed when the second driving gear drives the spherical driven gear to rotate around the second instantaneous rotating axis, and is formed by the meshing line that rotates around the second axis and is in tangential contact with the second virtual tooth surface and satisfies the conjugate meshing condition, and is scanned around the second axis.

[0025] Furthermore, the tooth surfaces of the first, second, and third driving linear gears are involute helical surfaces, and the axial offset in the parametric equation of the involute helical surface satisfies the relationship that makes the cross-sectional shape of the two tooth surfaces symmetrical about the axis to form a tooth groove.

[0026] Furthermore, the first driving linear gear includes a left tooth surface employing an involute helical surface. and the right tooth surface In the coordinate system fixed to the first driving gear middle,

[0027] Left tooth surface The parametric equation is:

[0028] ;

[0029] Right tooth surface The parametric equation is:

[0030] ;

[0031] In the formula, Let be the base circle radius of the first cylindrical helical surface; For the first cylindrical helical surface Double the lead; and For the parameters of the first cylindrical helical surface; and Left tooth surface and the right tooth surface The axial offset and the two satisfy the following relationship: Under this constraint, the two tooth surfaces at The cross section of a plane about Axial symmetry, forming a The tooth groove is symmetrical about the negative half-axis.

[0032] In summary, the present invention has the following advantages:

[0033] (1) The present invention uses a single spherical driven gear as the motion output component and three driving gears as input components to mesh with it. Each driving gear can independently drive the spherical driven gear to rotate around different axes, realizing a single joint integrated three-degree-of-freedom output. It has the characteristics of compact structure, lightweight, high transmission accuracy and fast dynamic response.

[0034] (2) This invention has no theoretical limitation on the transmission ratio and can achieve large transmission ratio configurations of tens or even hundreds. In specific applications, the transmission ratio can be flexibly selected according to the requirements without the need for additional reduction gears, which helps to shorten the transmission chain, achieve a compact structure and reduce the overall weight.

[0035] (3) The tooth surface of the active line gear of the present invention is a cylindrical helical surface generated by the movement of the tooth profile straight or curved segment along the cylindrical helical line. It can be machined by ordinary turning method or generating method. The machining process is mature, the tool is versatile, and the manufacturing cost is low. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the overall structure of the three-degree-of-freedom spherical linear gear pair of the present invention;

[0037] Figure 2 This is a schematic diagram of the overall structure of the three-degree-of-freedom spherical linear gear pair hidden in the base of the present invention;

[0038] Figure 3 This is a schematic diagram of the planar tooth profile and tooth groove structure of the spherical driven gear of the present invention (for ease of display, one-eighth of the spherical driven gear has been cut off).

[0039] Figure 4 This is a schematic diagram of the coordinate system of the spherical driven linear gear and the three-degree-of-freedom spherical linear gear pair, which only include the first tooth groove structure of the present invention.

[0040] Figure 5 This is a schematic diagram of the structure of the first virtual tooth surface of the spherical driven gear of the present invention.

[0041] In the picture:

[0042] 1-First driving gear, 2-Second driving gear, 3-Third driving gear, 4-Spherical driven gear, 5-Base;

[0043] 411-First tooth groove structure, 412-First planar tooth profile, 413-First axis, 414-First instantaneous rotation axis, 415-First virtual tooth surface;

[0044] 421 - Second tooth groove structure, 422 - Second planar tooth profile, 423 - Second axis, 424 - Second instantaneous rotating shaft;

[0045] 43 - Center of the ball;

[0046] 11-First rotating shaft a, 21-First rotating shaft b, 31-First rotating shaft c;

[0047] 12 - Second shaft a, 22 - Second shaft b, 32 - Second shaft c;

[0048] 61-Hooke hinge a, 62-Hooke hinge b, 63-Hooke hinge c. Detailed Implementation

[0049] The present invention will now be described in further detail.

[0050] like Figures 1-5 As shown, a three-degree-of-freedom spherical linear gear pair includes: a first driving linear gear 1, a second driving linear gear 2, a third driving linear gear 3, a spherical driven linear gear 4, and a base 5.

[0051] The tooth surface of the spherical driven gear 4 is provided with an interlaced first tooth groove structure 411 and a second tooth groove structure 421. The first tooth groove structure 411 is formed by rotating and scanning the first planar tooth profile 412 around the first axis 413, and the second tooth groove structure 421 is formed by rotating and scanning the second planar tooth profile 422 around the second axis 423. The first axis 413 and the second axis 423 intersect at the center 43 of the spherical driven gear 4.

[0052] The tooth surface of the first driving gear 1 is a first cylindrical helical surface, which is formed by sweeping the first tooth profile curve along the first cylindrical helical line. The first driving gear 1 meshes with the first tooth groove structure 411. The tooth surfaces of the second driving gear 2 and the third driving gear 3 are second cylindrical helical surfaces, which are formed by sweeping the second tooth profile curve along the second cylindrical helical line. The second driving gear 2 and the third driving gear 3 both mesh with the second tooth groove structure 421.

[0053] The first driving gear 1 is movably mounted on the base 5 via a Hooke hinge a 61. The Hooke hinge a 61 includes a first rotating shaft a 11 and a second rotating shaft a 12. The first rotating shaft a 11 is the center line of the tooth surface of the first driving gear 1 and is used to rotate around its own axis. The second rotating shaft a 12 is the radius of the spherical driven gear 4 passing through the midpoint of the first rotating shaft a 11 and is used to rotate around the radius of the spherical driven gear 4. The second driving gear 2 and the third driving gear 3 have the same Hooke hinge configuration and rotational relationship as the first driving gear 1. The corresponding Hooke hinges are Hooke hinge b 62 and Hooke hinge c 63, respectively. The corresponding first rotating shafts are first rotating shaft b 21 and first rotating shaft c 31, respectively. The corresponding second rotating shafts are second rotating shaft b 22 and second rotating shaft c 32, respectively.

[0054] The first driving gear 1, the second driving gear 2 and the third driving gear 3 mesh with the spherical driven gear 4 respectively. The meshing form is point contact. There is a pair of conjugate instantaneous meshing lines on the tooth surface of each meshing pair. The instantaneous meshing lines are the trajectories of the meshing points on the tooth surfaces of the driving and driven gears.

[0055] The first driving gear 1 rotates around the first axis a11 to drive the spherical driven gear 4 to rotate around the first instantaneous axis 414. The first instantaneous axis 414 passes through the center of the spherical driven gear 4 and is perpendicular to the first axis 413, spatially intersecting with the first axis a11. The second driving gear 2 rotates around the first axis b21 to drive the spherical driven gear 4 to rotate around the second instantaneous axis 424. The second instantaneous axis 424 passes through the center of the spherical driven gear 4 and is perpendicular to the second axis 423, spatially intersecting with the first axis b21. The third driving gear 3 rotates around the first axis c31 to drive the spherical driven gear 4 to rotate around the third instantaneous axis (not shown in the figure). The third instantaneous axis passes through the center of the spherical driven gear 4 and is perpendicular to the second axis 423, spatially intersecting with the first axis c31.

[0056] Under the active force provided by the driver, when the first driving gear 1, the second driving gear 2, and the third driving gear 3 rotate around their respective first axes at any first angle, second angle, and third angle, the spherical driven gear 4 has a unique spatial posture.

[0057] Both the first toothed structure 411 and the second toothed structure 421 are rotary structures; the spherical driven gear 4 is configured to rotate around the first axis 413, and the first driving gear 1 does not restrict the rotation of the spherical driven gear 4 in this direction; the spherical driven gear 4 is configured to rotate around the second axis 423, and the second driving gear 2 and the third driving gear 3 do not restrict the rotation of the spherical driven gear 4 in this direction;

[0058] The base 5 is provided with a ball socket, and the spherical driven gear 4 is movably disposed in the ball socket of the base 5, which can realize three-degree-of-freedom rotational motion.

[0059] In the design process of the first tooth groove structure 411, the first driving gear 1 drives the spherical driven gear 4 to rotate around the first instantaneous rotating shaft 414 to construct the first virtual tooth surface 415. The tooth surface of the first driving gear 1 is denoted as... ,in , All are parameters, the unit normal vector of a point on the tooth surface of the first driving gear 1. Depend on The first virtual tooth surface 415 is obtained by taking the outer product of the partial derivatives of the two parameters. ,in Let be the angle through which the first driving gear 1 rotates about the first rotating shaft a11; let be the relative velocity at the meshing point between the tooth surface of the first driving gear 1 and the first virtual tooth surface 415. The relative pose relationship between the first driving gear 1 and the first virtual tooth surface 415 is determined by the coordinate transformation matrix. Confirmed; the first virtual tooth surface 415 and the first driving gear 1 satisfy the conjugate meshing equation (denoted as meshing equation A):

[0060] (A);

[0061] From the meshing equation A, the parameter can be eliminated. , One of the two, for example, eliminating the parameter. ,get about , Analytical or numerical solutions: .

[0062] Will Substitute the tooth surface of the first driving gear 1 The contact line equation of the first driving gear 1 during the meshing process is obtained. Then through coordinate transformation matrix By transforming the coordinate system of the first driving gear 1 to the coordinate system of the spherical driven gear 4, the expression for the first virtual tooth surface 415 is obtained:

[0063]

[0064] The first virtual tooth surface 415 is the envelope surface formed by the cluster of contact lines when the spherical driven gear 4 rotates about the first instantaneous axis 414. Let the first tooth groove structure 411 rotate about the first axis 413, and let the velocity of the first tooth groove structure 411 be denoted as... Meanwhile, the first virtual tooth surface 415 remains stationary, and the first tooth groove structure 411 is in tangential contact with the first virtual tooth surface 415. The first tooth groove structure 411 and the first virtual tooth surface 415 satisfy the conjugate meshing equation (denoted as meshing equation B) at the meshing point:

[0065] (B);

[0066] in, Let be the unit normal vector of a point on the first virtual tooth surface 415. .

[0067] The remaining parameters can be eliminated from the meshing equation B. or For example, eliminating parameters Finally obtained Analytical or numerical solutions, such as .Will Substitute the first virtual tooth surface 415 The equation of the meshing line of the first tooth groove structure 411 is obtained. Connecting lines The tooth surface of the first tooth groove structure 411 is obtained by rotating and scanning around the first axis 413.

[0068] Similarly, according to the design method of the first tooth groove structure 411, the second driving gear 2 drives the spherical driven gear 4 to rotate around the second instantaneous rotating shaft 424 to construct the second virtual tooth surface; then the second tooth groove structure 421 rotates around the second axis 423 and comes into tangential contact with the second virtual tooth surface to obtain the tooth surface of the second tooth groove structure 421.

[0069] Example:

[0070] First, construct the left tooth surface of the first driving gear 1. and the right tooth surface Left tooth surface and the right tooth surface An involute helical surface is used in a coordinate system fixed to the first driving gear 1. middle,

[0071] Left tooth surface The parametric equation is:

[0072] ;

[0073] Right tooth surface The parametric equation is:

[0074]

[0075] In the formula, Let be the base circle radius of the first cylindrical helical surface; For the first cylindrical helical surface Double the lead; and For the parameters of the first cylindrical helical surface; and Left tooth surface and the right tooth surface The axial offset and the two satisfy the following relationship: Under this constraint, the two tooth surfaces at plane (i.e.) The cross section of the plane about Axial symmetry, forming a The tooth groove is symmetrical about the negative half-axis.

[0076] The following uses the left tooth surface As an example, the derivation is based on the right tooth surface. The solution process can be obtained similarly, and will not be repeated here.

[0077] The left tooth surface The unit normal vector of the previous point From parametric equations For parameters and After taking the partial derivatives, cross product, and normalization, we get:

[0078] ;

[0079] In the design process of the first toothed structure 411, the first driving gear 1 is made to rotate around its own axis (i.e., the first rotating shaft a11). (shaft), driving the spherical driven gear 4 around the first instantaneous rotating shaft 414 (i.e. The axis (415) rotates about a fixed axis to construct the first virtual tooth surface. Attitude rotation matrix. Coordinate system used for spherical driven gear 4 Vector transformation to the coordinate system of the first driving gear 1 In the middle, the first driving gear 1 rotates around the first shaft a11 (i.e., Angle of rotation of the axis And the spherical driven gear 4 rotating around the first instantaneous axis 414 (i.e. Angle of rotation of the axis A joint decision, in which The transmission ratio between the first driving gear 1 and the spherical driven gear 4 is as follows:

[0080] ;

[0081] relative position vector For coordinate system origin Pointing coordinate system origin The relative position vector. In coordinate system The representation in is:

[0082] ;

[0083] In the formula, The center distance between the first driving gear 1 and the spherical driven gear 4 is given.

[0084] coordinate transformation matrix Used to set the coordinate system of the first driving gear 1 Transform the points in the coordinate system to the coordinate system of the spherical driven gear 4. In the middle, the angle through which the first driving gear 1 rotates around the first rotating shaft a11 is... The angle through which the spherical driven gear 4 rotates. and center distance A joint decision, specifically:

[0085] ;

[0086] In the stationary coordinate system In the above, assume that the first driving gear 1 rotates around its own axis (i.e., the first rotating shaft a11), (axis) with angular velocity If the gear rotates along a fixed axis, then the angular velocity vector of the first driving line gear 1 is... ; The spherical driven gear 4 rotates around the first instantaneous axis 414 (i.e. If the axis rotates about a fixed axis with a unit angular velocity, then the spherical driven gear has 4 angular velocity vectors. The relative velocity of the tooth surface of the first driving gear 1 relative to the tooth surface of the spherical driven gear 4 at the meshing point. In coordinate system The representation in (denoted as expression C) is as follows:

[0087] (C);

[0088] The tooth surface parameter equation of the first driving gear 1 and angular velocity Angular velocity of spherical driven gear 4 Relative position vector Substituting into expression C and rearranging, we obtain the relative velocity. The final expression

[0089] ;

[0090] relative velocity With unit normal vector Substituting into the meshing equation A, and simplifying, we get:

[0091] ;

[0092] The parameters are obtained by solving the simplified meshing equation A. about , The explicit expression (denoted as expression D):

[0093] (D)

[0094] Substitute expression D into the tooth surface of the first driving gear 1. The contact line equation of the first driving gear 1 during the meshing process is obtained. Then through coordinate transformation matrix , contact wire Transforming the coordinate system of the first driving gear 1 to the coordinate system of the spherical driven gear 4, we obtain the expression for the first virtual tooth surface 415:

[0095] ;

[0096] In the formula, , ,

[0097] .

[0098] Let the spherical driven gear 4 rotate around the first axis 413 (i.e. If the shaft rotates at a unit angular velocity, then the spherical driven gear has four angular velocity vectors. The velocity of a point on the tooth surface of the first tooth groove structure 411 The expression is

[0099] ;

[0100] The unit normal vector of a point on the first virtual tooth surface 415. The expression is

[0101] ;

[0102] From the meshing equation B,

[0103] ;

[0104] Obtained from meshing equation B The numerical solution is substituted into the first virtual tooth surface 415. The equation of the meshing line of the first tooth groove structure 411 is obtained. Connecting lines Around the first axis 413 (i.e. The tooth surface of the first tooth groove structure 411 is obtained by rotating and scanning the axis.

[0105] Similarly, according to the calculation method of the first tooth groove structure 411, the second driving gear 2 drives the spherical driven gear 4 to rotate around the second instantaneous rotating shaft 424 to construct the second virtual tooth surface; then the second tooth groove structure 421 rotates around the second axis 423 and comes into tangential contact with the second virtual tooth surface to obtain the tooth surface of the second tooth groove structure 421.

[0106] This invention utilizes point-contact conjugate meshing between three driving gears and two sets of interleaved tooth groove structures on a spherical driven gear. Combined with a Hooke's hinge, this provides each driving gear with dual-degree-of-freedom rotational capabilities around its own axis and around the radius of the spherical gear. This constructs a three-drive-one-driven, spatially interleaved transmission system with an instantaneous axis passing through the center of the sphere. Within this system, each of the three driving gears independently drives the spherical driven gear to rotate around different instantaneous axes passing through the center of the sphere. The spatial orientation of the spherical driven gear is uniquely determined by the coordinated angles of the three gears, thus compactly integrating three degrees of freedom of motion output within a single joint. This achieves high-performance spatial transmission without theoretical transmission ratio limitations or the need for additional reduction gears. The high entrainment speed between the tooth surfaces of the driving gears and the spherical driven gear is more conducive to forming an elastic hydrodynamic lubrication film in the meshing area, improving lubrication conditions, reducing wear, and increasing transmission efficiency and lifespan.

[0107] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A three-degree-of-freedom spherical linear gear pair, characterized in that, It includes a first driving gear (1), a second driving gear (2), a third driving gear (3), a spherical driven gear (4), and a base (5); The tooth surface of the spherical driven gear (4) is provided with an interlaced first tooth groove structure (411) and a second tooth groove structure (421), both of which are rotary structures. The first tooth groove structure (411) is formed by rotating and scanning the first planar tooth profile (412) around the first axis (413), and the second tooth groove structure (421) is formed by rotating and scanning the second planar tooth profile (422) around the second axis (423). The first axis (413) and the second axis (423) intersect at the center (43) of the spherical driven gear (4). The tooth surface of the first driving gear (1) is a first cylindrical helical surface, which meshes with the first tooth groove structure (411); The tooth surfaces of the second driving gear (2) and the third driving gear (3) are both second cylindrical helical surfaces, and they mesh with the same second tooth groove structure (421) on the spherical driven gear (4) from different directions. Among them, the first driving gear (1), the second driving gear (2) and the third driving gear (3) are respectively movably set on the base (5) through the Hooke hinge, and the meshing form with the spherical driven gear (4) is point contact. There is a pair of conjugate instantaneous meshing lines on the tooth surface of each meshing pair, and each meshing pair realizes transmission through the instantaneous meshing lines.

2. The three-degree-of-freedom spherical linear gear pair according to claim 1, characterized in that, The Hooke hinge includes a first axis and a second axis. The first axes of the first driving gear, the second driving gear, and the third driving gear are their respective axes of rotation. The second axis is a radial line passing through the midpoint of the first axis and pointing to the center of the spherical driven gear.

3. The three-degree-of-freedom spherical linear gear pair according to claim 2, characterized in that, When the first driving gear (1) is configured to rotate about its first axis, it drives the spherical driven gear (4) to rotate about the first instantaneous axis (414), which passes through the center of the ball (43) and is perpendicular to the first axis (413), and is spatially intersecting with the first axis of the first driving gear (1). When the second driving gear (2) is configured to rotate about its first axis, it drives the spherical driven gear (4) to rotate about the second instantaneous axis (424), which passes through the center of the ball (43) and is perpendicular to the second axis (423), and is spatially intersecting with the first axis of the second driving gear (2). The third driving gear (3) is configured to drive the spherical driven gear (4) to rotate around the third instantaneous axis when rotating around its first axis. The third instantaneous axis passes through the center of the sphere (43) and is perpendicular to the second axis (423), and is spatially intersecting with the first axis of the third driving gear (3).

4. The three-degree-of-freedom spherical linear gear pair according to claim 1, characterized in that, The spherical driven gear (4) is configured to rotate about a first axis (413), and the first driving gear (1) has no motion interference with the direction of rotation; the spherical driven gear (4) is configured to rotate about a second axis (423), and the second driving gear (2) and the third driving gear (3) have no motion interference with the direction of rotation.

5. The three-degree-of-freedom spherical linear gear pair according to claim 1, characterized in that, The base (5) is provided with a ball socket, and the spherical driven gear (4) is movably set in the ball socket to realize three-degree-of-freedom rotational motion.

6. The three-degree-of-freedom spherical linear gear pair according to claim 1, characterized in that, The first cylindrical helical surface is a tooth surface formed by the helical motion of the first tooth profile located in its axial section around its axis; the second cylindrical helical surface is a tooth surface formed by the helical motion of the second tooth profile located in its axial section around its axis.

7. The three-degree-of-freedom spherical linear gear pair according to claim 2, characterized in that, The first driving gear (1), the second driving gear (2), and the third driving gear (3) are configured such that when they rotate around their respective first axes under the drive of the driver, the spherical driven gear (4) has a uniquely determined spatial orientation.

8. The three-degree-of-freedom spherical linear gear pair according to claim 3, characterized in that, The tooth surface of the first tooth groove structure (411) is constructed as follows: based on the first virtual tooth surface (415) formed when the first driving gear (1) drives the spherical driven gear (4) to rotate around the first instantaneous rotating shaft (414) to make a fixed axis rotation, and is formed by the meshing line that rotates around the first axis (413) and is in tangential contact with the first virtual tooth surface (415) and satisfies the conjugate meshing condition, and is rotated and scanned around the first axis (413); The tooth surface of the second tooth groove structure (421) is constructed as follows: the second virtual tooth surface is formed when the second driving gear (2) drives the spherical driven gear (4) to rotate around the second instantaneous rotating shaft (424) and is formed by the meshing line that rotates around the second axis (423) and is in tangential contact with the second virtual tooth surface and satisfies the conjugate meshing condition.

9. The three-degree-of-freedom spherical linear gear pair according to claim 8, characterized in that, The tooth surfaces of the first driving gear (1), the second driving gear (2) and the third driving gear (3) are involute helical surfaces. The axial offset in the parametric equation of the involute helical surface satisfies the relationship that makes the cross-sections of the two tooth surfaces symmetrical about the axis to form tooth grooves.

10. The three-degree-of-freedom spherical linear gear pair according to claim 9, characterized in that, The first driving gear (1) includes a left tooth surface with an involute helical surface. and the right tooth surface In the coordinate system fixed with the first driving gear (1) middle, Left tooth surface The parametric equation is: ； Right tooth surface The parametric equation is: ； In the formula, Let be the base circle radius of the first cylindrical helical surface; For the first cylindrical helical surface Double the lead; and For the parameters of the first cylindrical helical surface; and Left tooth surface and the right tooth surface The axial offset and the two satisfy the following relationship: Under this constraint, the two tooth surfaces at The cross section of a plane about Axial symmetry, forming a The tooth groove is symmetrical about the negative half-axis.

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