Toroidal worm and arc gear / worm and arc rack transmission pair and transmission device therefor

Abstract

A toroidal worm (1, 21, 41) and arc gear / worm and arc rack (32) transmission pair and a transmission device therefor. The transmission pair comprises a toroidal worm (1, 21, 41) and an arc gear or a worm and an arc rack (32), transmitting motion and power between two spatially crossed shafts, and enabling interchangeable synchronous or intermittent transmission. A contact line (1c) is a curve enveloping an arc tooth surface (2b), allowing multi-tooth simultaneous meshing, and an adjustable backlash is adjustable. A helix curve equation is established to enable parametric modeling of the worm. A root arc of a tooth slot of the worm is large, and the tooth slot can be meshed with a rotatable arc tooth to form a composite rolling-sliding motion. The transmission device further comprises a rotation source, a base, and a bearing (60).

Description

Toroidal worm and circular arc gear, worm and circular arc rack transmission pair and transmission device Technical Field The present invention relates to the field of mechanical transmission, in particular to key basic components in the new energy vehicle and high-end equipment manufacturing industries, as well as robots, military industry, and medical equipment. It includes a toroidal worm and circular arc gear, a worm and circular arc rack transmission pair, and a transmission device thereof. Background Art Worm gear pairs, which transmit motion and power between two interlaced axes, are key components used in the new energy vehicle industry and high-end equipment manufacturing, including intelligent manufacturing, aviation, aerospace, rail transit, marine engineering, and integrated circuit equipment. They are also used in robotics, military, and medical equipment, including speed increasers, speed reducers, spindles, turntables, indexing plates, cam dividers, and robotic joints. As the demands for transmission system accuracy, lifespan, and energy efficiency in host equipment continue to increase, worm gears are developing towards high precision, high efficiency, high load capacity, high speed, low noise, low cost, miniaturization, modularization, and standardization. The disadvantages of existing worm gear transmission are: poor interchangeability of different specifications, difficulty in processing and assembling precision worm gear transmission, and high cost. Among them, the worm tooth root strength of roller bearing worm gear transmission is low, the roller bearing is supported on one side, and it occupies a large space between the two shafts, which cannot be miniaturized; the ball worm gear transmission has a small load-bearing capacity and is prone to wear. Existing patent documents: Patent document 1: US17516A; Patent document 2: GB237252A; Patent document 3: FR807908A; Patent document 4: US2883875A; Patent document 5: JPH05302649A; Patent document 6: US5381704A; Patent document 7: JP2003014056A. Solution In order to overcome the existing defects, the technical solution adopted by the present invention is: a toroidal worm and circular arc gear transmission pair, including: a toroidal worm and a circular arc gear; the circular arc gear is provided with a center line, a contour line, a pitch circle and circular arc teeth, and is formed by rotating a rotating body by rotating a straight line or a circular arc contour line without teeth around the center line, and is combined with the circular arc teeth arrayed according to the center line on the pitch circle; the toroidal worm is provided with an axis line, a main line, a trajectory line, a tooth groove and a contact line, and is a rotating body formed by rotating around the axis line with an outer contour of an arc or a straight line or a multi-segment line of a fitted arc around the pitch circle of the circular arc gear as a main line, and the tooth surface of the circular arc tooth cuts out a tooth groove with a root of an arc on the surface of the rotating body along the trajectory line, which is a single-head or multi-head worm; the toroidal worm is in contact and meshing with the single or multiple tooth lines of the circular arc gear, and the contact line is a curve that envelops the tooth surface of the circular arc tooth, transmitting motion and power between two axes intersecting in space, and the intersecting angle of the two axes is a right angle or an acute angle. The arc teeth of the above-mentioned arc gear are provided with a cross-sectional line and an axis, the axis intersects the pitch circle, the cross-sectional line is a straight line or an arc or a combination of a straight line and an arc, and is rotated along the axis to form an arc tooth, and is arrayed into multiple arc teeth along the center line, the axis is parallel to the center line or the angle between them is acute, the arc gear and the arc tooth are integrated or split, the split arc gear is a rotating body or rolling body bracket containing or not containing arc teeth, and also includes a rotating body or rolling body, the rotating body or rolling body bracket is provided with an axial hole, the rotating body or rolling body is placed in the axial hole arrayed along the center line on the pitch circle as an arc tooth, the hole axis coincides with or does not coincide with the axis, the arc gear When the cross-section line is a straight line and parallel to the axis, the position error along the axis direction does not affect the meshing accuracy with the toroidal worm. The one-piece circular arc gear has a streamlined structure and is easy to miniaturize. The rotating body or rolling body of the split circular arc gear can be disassembled to change the number of circular arc gear teeth, and the number of simultaneous meshing with the toroidal worm can be adjusted. The meshing surface can be replaced and repaired after wear. The rotating body or rolling body is easy to process and can be made of super-hard materials. The surface coating cost is low, the surface roughness can be extremely small, and the surface hardness can be extremely high. Its bracket can be made of self-lubricating and lightweight materials, the friction coefficient can be extremely small, and it is made of a simple feature array, which is easy to be gigantic, modularized and standardized. Preferably, the circular arc gear is a rolling element support, further comprising rolling elements. The rolling elements may include rollers, sleeves, or a combination thereof with bearings. The bearings may be rolling or sliding bearings, capable of withstanding unidirectional or axial forces, and may include ball bearings, roller bearings, self-lubricating bushings, oil film bearings, and air bearings. The rolling elements are placed in the axial holes of the rolling element support as circular arc teeth, rotatable about the axis, and meshing with the toroidal worm gear in a rolling-sliding composite motion. The transmission pair utilizes rolling instead of sliding for progressive engagement, reducing friction and wear, and improving efficiency and lifespan. The toroidal worm, located outside the circular arc gear, has a concave outer contour generatrix. The contour of the circular arc gear without teeth is as close to the outer contour latitude of the toroidal worm. The generatrix of the circular arc gear located inside the circular arc gear is a convex arc, and the contour is as close to the outer contour latitude. Circular arc gears with the same pitch circle diameter can be replaced with different toroidal worms to form transmission pairs with the same or different transmission ratios. This allows for a wide range of interchangeable transmission ratios. When the trajectory of the toroidal worm is a toroidal helix, the tooth groove is a toroidal spiral groove, and the center distance is the distance between the axis of the toroidal worm and the center of the pitch circle. The toroidal helix angle is the angle between the two intersection points of the toroidal helix and the pitch circle on the pitch circle. The 3D curve equation of the toroidal helix in the Cartesian coordinate system is: x=(D / 2*sin(t*α°)-C)*cos(t*360°); y=D / 2*sin(90°-t*α°); z=(D / 2*sin(t*α°)-C)*sin(t*360°); Wherein, D is the pitch circle diameter; C is the center distance; α is the angle of the toroidal helix; t is the parameter 0≤t≤180 / α (number of spiral coils). The toroidal helix also includes all equivalent transformations of the above curve equation in the coordinate system. The transmission pair has a transmission ratio of 360 / α, and features synchronous transmission. The angle between the circular arc teeth of the circular arc gears is an integer multiple of the angle between the toroidal helix of the toroidal worm. As the multiple increases, the number of teeth decreases proportionally. The same toroidal worm can mesh with circular arc gears of varying tooth counts without changing the transmission ratio. When the angle between the circular arc teeth equals the angle between the toroidal helix, the transmission pair maximizes the number of teeth engaged simultaneously and the load capacity. When the number of teeth is multiplied and the angle between the circular arc teeth is doubled, friction and heat are reduced while the transmission ratio remains unchanged, resulting in a corresponding decrease in load capacity. This reduces costs, streamlines the structure, and facilitates miniaturization, enlargement, and standardization. When the toroidal worm is an annular cam, the trajectory is a composite line of the toroidal helix and the weft arc. The arc tooth surface cuts tooth grooves on the surface of the annular cam along the composite line. When the annular cam rotates, it is synchronously driven when the tooth grooves of the annular helix segment of the annular cam mesh with the circular arc gear. When the tooth grooves of the weft arc segment of the annular cam mesh with the circular arc gear, the circular arc gear will not rotate with it, and the transmission pair is intermittent transmission. It constitutes the transmission pair of the cam intermittent divider. Furthermore, the root of the tooth groove of the toroidal worm is also provided with an air avoidance groove, which is a straight V-shaped or Gothic arch groove that abuts the arc tooth, reducing the length of the single tooth contact line, reducing friction and heat. The root of the groove can be chamfered to reduce stress concentration. The distance between the axis line of the toroidal worm and the center of the pitch circle is adjustable, which can adjust the preload, eliminate transmission clearance or compensate for wear. Furthermore, the arc tooth width of the split arc gear is reduced to make the rotating body or rolling body bracket thinner, and a clearance groove is provided on the outer ring of the rotating body or rolling body bracket shaft hole to avoid interference with the outer contour of the annular worm. Furthermore, the split circular arc gear is also provided with a retaining ring groove and a retaining ring, which is placed in the retaining ring groove to prevent the rotating body or the rolling body from moving along the axis. A worm and arc rack transmission pair comprises a worm and an arc rack. When the pitch circle diameter of the arc gear is infinite, the pitch circle becomes a pitch line, and the arc teeth are arranged in a straight line along the pitch line. The arc teeth can be integrated or split, and the split arc teeth can be non-rotating or rotatable. The annular worm is transformed into a worm, which has an outer contour with a straight line close to the pitch line as the generatrix, and rotates around the axis to form a rotating body. The worm rotates forward and reverse around the axis to contact and mesh with single or multiple tooth lines of the arc rack. The contact line is a tangent envelope curve that envelops the tooth surface of the arc tooth, causing the arc rack to reciprocate along the pitch line, transmitting motion and power. When the cross-sectional line of the arc rack is a straight line and parallel to the axis, positional errors along the axis do not affect the meshing accuracy of the worm and the worm. Doubling the distance between the two arc teeth can simplify the structure and reduce costs. When the worm is a conical worm, the angle between the axis and the index line is an acute angle, the trajectory line is a conical helix, and the tooth groove is a conical helix groove. The 3D curve equation of the conical helix Cartesian coordinate system is: x=P*cos(Θ°)*t; y=(P*sin(Θ°)*tH / cos(Θ°))*cos(t*360°); z=(H / cos(Θ°)-P*sin(Θ°)*t)*sin(t*360°); Where P is the distance between the intersection of the conical helix and the indexing line; H is the distance between the origin of the coordinate system and the indexing line; Θ is the angle between the axis and the indexing line; t is the parameter 0≤t≤the number of spiral coils. The conical helix also includes all equivalent transformations of the above curve equation in the coordinate system. When the worm is a straight worm, the axis line is parallel to the dividing line, the trajectory line is an equal-pitch spiral line, and the tooth groove is an equal-pitch spiral groove. A method for modeling the above-mentioned toroidal worm or worm comprises the steps of: S1: Set the basic parameters of the toroidal worm or worm; S2: Based on the basic parameters of step S1, the generatrix is ​​rotated around the axis to form a solid of revolution, and the cross-section line is rotated around the axis to form an arc tooth surface; S3: The tooth surface of the arc tooth cuts out the tooth groove along the trajectory line on the surface of the rotating body to generate a toroidal worm or worm solid; The basic parameters in step S1 include: the shape and position dimensions of the main line and the cross-sectional line, the axis centerline and the axis position, wherein the toroidal worm also includes the pitch circle diameter D, the center distance C, the toroidal helix angle α, the toroidal cam also includes the weft arc radius, the bevel worm also includes the spacing P between the intersection of the bevel helix and the pitch line, the spacing H from the coordinate system origin to the pitch line, the angle Θ between the axis centerline and the pitch line, the straight worm also includes the pitch, and the trajectory line in step S3 includes the toroidal helix, the composite line of the toroidal helix and the weft arc, the bevel helix or the equal-pitch helix, wherein the 3D curve equations of the toroidal helix and the bevel helix in the Cartesian coordinate system are the same as those described above. The constructed helix curve equation makes the worm modeling parameterized, without the need for tedious programming calculations, and the corresponding high-precision tooth groove model is generated by modifying the basic parameters, which can be directly used for simulation and CNC programming. A method for manufacturing the above-mentioned toroidal worm or worm comprises the steps of: S10: A toroidal worm or worm solid model is 3D printed, molded (by injection molding, casting, powder metallurgy, etc.), turned or milled, or roughly machined by turning, heat treated, and then finely machined by grinding. The solid model in step S10 is created using the aforementioned modeling method. The tooth grooves are cut along the trajectory by turning, milling, or grinding. The outer contour of the milling cutter or grinding wheel used aligns with the arc tooth cross-section. The 3D curve equations for the toroidal helix and conical helix in the Cartesian coordinate system are the same as described above. This allows for the cost-effective manufacture of hardened, high-precision worms, which can be further enhanced with surface coating. When the tooth groove is a toroidal spiral groove, the finishing steps are: S20: The rotating milling cutter or grinding wheel head feeds an angle along the centerline, and the synchronously linked rotating body feeds the corresponding angle along the axis of the axis by a transmission ratio of 360 / α times, continuously cutting a toroidal spiral groove on the surface of the rotating body; or the rotating milling cutter or grinding wheel head feeds along the toroidal spiral trajectory, cutting a toroidal spiral groove on the surface of the rotating body. The manufacturing method is consistent with the meshing method to ensure transmission accuracy. Mass production can be achieved using ordinary circular grinding wheels or end mills and general-purpose CNC grinding or milling machines. A toroidal worm and circular arc gear transmission device includes the above-mentioned toroidal worm and circular arc gear transmission pair, and also includes a rotation source, a base and bearings. The rotation source is a device that can output rotation, such as a rotor, motor, engine, pump, rotary cylinder, transmission wheel and speed increaser or reducer; the base accommodates the bearings; the bearings are rolling or sliding bearings, which can withstand unidirectional or axial forces, such as ball bearings, roller bearings, self-lubricating bushings, oil film bearings and air bearings; the rotation source is connected to any axis of the transmission pair to input motion and power, and meshes with the other axis to output motion and power, and is supported by the bearings in the base to withstand unidirectional loads or combined loads in any direction. The transmission device also includes an input shaft mount, the rotation source being the motor's rotor. The input shaft mount, stator, rotor, toroidal worm, and bearings form a drive unit, which may or may not include an encoder and a drive control board. The base is an output shaft mount, which, together with the circular arc gear and bearings, forms an output unit. The drive unit is positioned on one side of the output shaft mount, wherein the motor stator is directly fixed to the input shaft mount, and the rotor is directly connected to the toroidal worm and rotates, meshing with the circular arc gear in the output shaft mount to transmit motion and power. The output unit remains unchanged, and replacing the drive unit or the toroidal worm can change the transmission ratio or convert to intermittent transmission. A cam gap divider can be used, making modularization and standardization easy. The transmission device also includes an output shaft, which serves as a spindle or turntable. The output shaft meshes with the transmission pair. The spindle or turntable, supported by bearings in the base, connects to circular gears to output motion and power. While the base remains unchanged, the spindle and turntable can be interchanged by replacing the corresponding bearings and supporting parts. This device can be used as a speed increaser, speed reducer, spindle, turntable, indexing plate, or robot joint, facilitating modularization and standardization. The preferred transmission device has a base with a positioning surface and a positioning groove or hole, which cooperates with the input shaft fixing seat for positioning. The root of the tooth groove of the annular worm is provided with a Gothic arched avoidance groove that abuts the arc tooth. Increasing or decreasing the positioning surface can adjust the side clearance of the transmission pair, adjust the preload, eliminate the transmission clearance or compensate for wear. In the above transmission device, the toroidal worm and circular arc gear transmission pair can be replaced by other transmission pairs with two axes intersecting or staggered, such as bevel gears, hypoid gears, face gears, worm wheels and worm helical gears. A worm and arc rack transmission device includes the above-mentioned worm and arc rack transmission pair, as well as a rotation source, a slider and a bearing, and a guide rail, which is integrated with or separated from the arc rack. The rotation source is connected to the worm and supported by the bearing and placed on a slider that reciprocates linearly along the guide rail. The transmission pair engages to transmit motion and power. Furthermore, the transmission device also includes a self-lubricating unit for circular arc teeth. This unit is composed of porous resin, a high-density fiber mesh, and an elastic contact block. The porous resin in the elastic contact block stores high-viscosity lubricant, which is transported to the surface of the circular arc teeth through capillary action. The lubricant flow rate is adjusted by adjusting the elastic force between the circular arc teeth and the elastic contact block, achieving true maintenance-free operation. Furthermore, the above-mentioned rotation source is a frameless inner or outer rotor brushless motor, including a rotor and a stator. The rotor includes a permanent magnet and a yoke. The stator includes a laminated iron core, a winding, and an insulating coating layer. It includes or does not include an encoder and a drive control board. The rotor also includes a rotor cover. The rotor cover is provided with a centrifugal fan blade structure that can actively dissipate heat through convection. The drive control board includes a drive control module, a power module and a power supply, a communication interface. The drive control and power modules include resistors, capacitors, MOS tubes and drive and control chips, etc. The interface also includes a connector, and the connector can be quickly plugged in and out. The preferred transmission device comprises a toroidal worm or worm with toroidal spiral grooves or conical spiral grooves, an arc gear or rack with rolling elements, the toroidal worm or worm and rolling elements are made of hardened bearing steel, the surface is DLC coated after fine grinding, active convection heat dissipation is provided, and a self-lubricating unit is included. The drive control board drives the toroidal worm or worm directly connected to the motor rotor to rotate and correct its position based on real-time feedback from the encoder. The transmission device is meshed with a zero-backlash transmission pair to enable precise positioning, and the input speed can be above 6000 rpm. Beneficial effects The beneficial effects of the present invention are interchangeable synchronous or intermittent transmission, a wide range of interchangeable transmission ratios, a contact line that is a curve that envelops the tooth surface of an arc tooth, multiple teeth that can engage simultaneously, adjustable side clearance, and the construction of a helical curve equation enable parametric modeling of the worm and accurate and convenient manufacturing. The arc at the root of the tooth groove is large to avoid stress concentration, and its engagement with the rotatable arc tooth is a rolling-sliding compound motion. The overall structure is streamlined, with high precision, high efficiency, high load-bearing capacity, high speed, low noise, low cost, good interchangeability, and long service life, and is easy to miniaturize, giantize, modularize, and standardize. BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a three-dimensional cross-sectional schematic diagram of a toroidal worm and circular arc gear transmission pair. FIG2 is a schematic diagram of the three-dimensional structure of a toroidal worm meshing with the tooth surface of the circular arc tooth. FIG3 is a schematic three-dimensional cross-sectional view of the toroidal cam and the circular arc gear transmission pair. FIG4 is a schematic diagram of the three-dimensional structure of the toroidal cam. FIG5 is a perspective cross-sectional schematic diagram of a toroidal worm and roller wheel transmission pair. Figure 6 is a schematic example of a toroidal worm and circular arc gear transmission pair. Figure 7 is a schematic example of a circular arc tooth cross-section line. Figure 8 is a schematic diagram of the three-dimensional structure of the bevel worm and circular arc rack transmission pair. FIG9 is a schematic diagram of the three-dimensional structure of a bevel worm meshing with the tooth surface of the circular arc tooth. FIG10 is a front cross-sectional view of the toroidal worm and circular arc gear transmission device. FIG11 is a side sectional view of a toroidal worm and circular arc gear transmission device or a turntable. FIG12 is a three-dimensional view of the toroidal worm and circular arc gear transmission device with the protective cover removed. FIG13 is a front cross-sectional view of the turntable. Explanation of the accompanying drawings: 1-first toroidal worm; 1a-toroidal helix; 1b-toroidal spiral groove; 1c-contact line; 2-rotating body bracket; 2a-pitch circle; 2b-arc tooth surface; 3-first roller; 4-first retaining ring; 11-toroidal cam; 11a-helix; 11b-latitude arc; 11c-tooth groove; 21-second toroidal worm; 22-rolling body bracket; 22a-contour line; 23-second roller; 24-ball; 31-conical worm; 31a-conical helix; 31b-conical spiral groove; 31c-tangent envelope curve; 32-arc rack; 32a-pitch line; 33-third roller; 41-third toroidal worm; 41a-avoidance groove; 42-needle roller bearing; 43-first roller bracket; 43a-yield groove; 44-Fourth roller; 45-Second retaining ring; 46-Second roller bracket; 47-Output shaft fixing seat; 47a-Location surface; 47b-Location groove; 48-Nut; 49-Collet; 50-Spindle; 51-First dust seal; 52-Retaining ring; 53-Angular contact bearing; 54-Spacer; 55-Ball bearing; 56-Rotor; 57-Stator; 58-Input shaft fixing seat; 59-Locking ring; 60-Bearing; 61-Plane needle roller bearing; 62-Thrust combination needle roller bearing; 63-Bolt; 64-Retaining nut; 65-Screw; 66-Drive control board; 67-Encoder; 68-Grating; 69-Round nut; 70-Shield; 71-Turntable; 72-Second dust seal; 73-Thrust combination roller bearing; 74-Plane roller bearing. Specific embodiments Preferred embodiments of the present invention will be described below with reference to the accompanying drawings. Example 1 As shown in Figures 1 and 2, a toroidal worm and circular arc gear transmission pair of the present invention includes: a first toroidal worm 1, a rotating body bracket 2, a first roller 3 and a first retaining ring 4, the rotating body bracket 2, the first roller 3 and the first retaining ring 4 form a split circular arc gear, the rotating body bracket 2 is provided with a center line A2, a contour line, a pitch circle 2a and circular arc teeth, the rotating body is formed by rotating the straight tooth-free contour line around the center line A2, and is combined with the circular arc teeth arrayed on the pitch circle 2a according to the center line A2, and the circular arc teeth contained in the rotating body bracket 2 are provided with a cross-sectional line And axis A4, axis A4 intersects with the pitch circle 2a, the cross-section line is a straight line formed by rotating along the axis A4, and is arrayed into a plurality of arc teeth along the center line A2, the cross-section line, axis A4 and center line A2 are parallel, the rotary body bracket 2 is also provided with an axial hole and a retaining ring groove, the first roller 3 is provided with an axis A3 and a cross-section line identical to the arc teeth contained in the rotary body bracket 2, and is a rotary body formed by rotating the cross-section line along the axis A3, and is placed on the pitch circle 2a in the axial hole arrayed along the center line A2 as an arc tooth, the hole axis coincides with the axis A3, and the first retaining ring 4 is placed in the retaining ring groove to block The first roller 3 is prevented from moving along the axis. The first toroidal worm 1 is provided with an axis line A1, a generatrix, a track line, a tooth groove and a contact line 1c. The track line is a toroidal spiral line 1a, and the tooth groove is a toroidal spiral groove 1b. It is located outside the rotating body bracket 2. The outer contour is a concave arc around the pitch circle 2a as the generatrix. The rotating body is formed by rotating around the axis line A1. The arc tooth surface 2b cuts out an annular spiral groove 1b with an arc root on the surface of the rotating body along the toroidal spiral line 1a. It is a single-head worm. The first toroidal worm 1 is in contact with the multi-tooth line of the arc gear. The contact line 1c is 1c. c is the curve enveloping the circular arc tooth surface 2b, which transmits motion and power between two axes staggered in space. The staggered angle between the two axes is a right angle. The position error of the circular arc gear along the center line A2 does not affect the meshing accuracy between it and the toroidal worm. It is provided with a center distance C, which is the distance between the axis A1 of the first toroidal worm 1 and the center of the pitch circle 2a. It is provided with a toroidal helix angle α, which is the angle between the two intersection points of the toroidal helix 1a and the pitch circle 2a on the pitch circle. The transmission ratio of the transmission pair is 360 / α, and the transmission is synchronous. The 3D curve equation of the toroidal helix 1a in the Cartesian coordinate system is: x=(D / 2*sin(t*α°)-C)*cos(t*360°); y=D / 2*sin(90°-t*α°); z=(D / 2*sin(t*α°)-C)*sin(t*360°); Where D is the pitch circle diameter; C is the center distance; α is the angle between the toroidal helix and t is the parameter 0≤t≤180 / α (number of spiral coils). The angle β between the two first rollers 3 is the same as the angle between the two arc teeth contained in the rotating body bracket 2. The angle γ between the first roller 3 and the arc teeth contained in the rotating body bracket 2, β is 4 times α, and γ is 2 times α. After taking out the first retaining ring 4 in the retaining ring groove of the rotating body bracket 2, the first roller 3 can be disassembled to change the number of arc gear teeth, the number of simultaneous meshing with the first toroidal worm 1 can be adjusted, the center distance C is adjustable, and the preload can be adjusted, the transmission clearance can be eliminated or the wear can be compensated. Example 2 As shown in Figure 1, the first retaining ring 4 is taken out, the first roller 3 is completely removed, the toroidal worm and the circular arc gear are the same as the first toroidal worm 1 and the rotating body bracket 2 as in Example 1, the angle γ between the circular arc gear teeth is changed to β, the number of teeth is halved, and the transmission ratio remains unchanged. Example 3 As shown in Figures 3 and 4, a toroidal cam and circular arc gear transmission pair includes: an toroidal cam 11 and a rotating body bracket 2, the single rotating body bracket 2 containing circular arc teeth is an arc gear, and the above-mentioned toroidal worm is the toroidal cam 11, which is provided with an axis line, a main line, a trajectory line, a tooth groove and a contact line like the first toroidal worm 1 in Example 1, the trajectory line is a composite line of the toroidal helix 11a and the weft arc 11b, and is a rotating body formed by rotating around the axis line with the outer contour of the concave arc around the pitch circle of the rotating body bracket 2 as the main line, and the circular arc tooth surface cuts out tooth grooves 11c on the surface of the toroidal cam 11 along the composite line. The toroidal cam 11 rotates and is synchronously transmitted with the rotating body bracket 2 when the tooth grooves 11c of the toroidal helix 11a segment are engaged, and the rotating body bracket 2 will not rotate when the tooth grooves 11c of the weft arc 11b segment are engaged, which is an intermittent transmission, constituting a transmission pair of a cam intermittent divider. Example 4 As shown in Figure 5, a toroidal worm and roller wheel transmission pair includes: a second toroidal worm 21, a rolling element support 22, a second roller 23 and a ball 24. The above-mentioned arc gear is a roller wheel, including a rolling element support 22, a second roller 23 and a ball 24. The rolling element support 22 is provided with a center line, a contour line 22a, and a pitch circle, and does not contain arc teeth. The straight contour line 22a is rotated around the center line to form a rotating body. It is also provided with an axial hole, which serves as a bearing outer ring and a rolling bearing composed of the ball 24. The bearing supports the second roller 23 to withstand radial and axial forces. The second roller 23 is provided with a cross-sectional line and an axis, and the cross-sectional line is a straight line. The combination with the arc is rotated along the axis, and the angle between the axis and the center line is 7 degrees, which is an acute angle. The second roller 23 is placed in the axial hole of the rolling element holder 22 as an arc tooth. The hole axis and the axis do not coincide with each other and can rotate around the axis. It is a rolling element and engages with the toroidal worm in a rolling and sliding composite motion. The toroidal helix angle of the second toroidal worm 21 is 36 degrees. The second roller 23 entity cuts a toroidal spiral groove on its surface along the toroidal helix. The remaining features are the same as the first toroidal worm 1 in Example 1. The transmission pair engages in a progressive manner by rolling instead of sliding. The rolling element holder 22 is thick, and its axial hole outer ring does not interfere with the outer contour of the toroidal worm, and there is no need to cut a clearance groove. Example 5 The toroidal worm and the circular arc gear transmission pair can be meshed in any group as shown in Figure 6 a to l. The circular arc gears have the same pitch circle diameter and mesh with different toroidal worms to form transmission pairs with the same or different transmission ratios. As shown in Figure 6, the circular arc gear is a simplified structure integrated with the circular arc teeth. The toroidal worms d to g in Figure 6 are single-head worms, and a to c and h to l in Figure 6 are multi-head worms. As shown in a to c and f to l in Figure 6, the toroidal worm is located outside the circular arc gear and its outer contour generatrix is ​​a concave arc. In Figure 6 a to c, its inner generatrix of the circular arc gear is a convex arc, and the contour line of the circular arc gear without teeth is attached. The outer contour of the near-annular worm is as shown in a and i, g and h, and k and l in Figure 6. The same circular arc gear can be meshed with different annular worms to form transmission pairs with different transmission ratios, as shown in e and f in Figure 6. The angle between the teeth of the circular arc gear is equal to the angle of the annular helix, which is 24 degrees. The number of teeth is 15. The angle between the teeth of d and g in Figure 6 becomes 72 degrees, the number of teeth is reduced to 5, and the transmission ratio remains unchanged. The annular worms d and e and f and g in Figure 6 are the same. As shown in a to j in Figure 6, the arc tooth cross-section line of the circular arc gear is a straight line parallel to the axis, and the arc tooth radius is the same. The arc tooth cross-section lines from k to l in Figure 6 are arcs. Example 6 The arc teeth of the arc gear can be formed by, but are not limited to, rotating the cross-sectional lines shown by a to o in FIG. 7 along the axis. The cross-sectional lines are straight lines, circular arcs, or a combination of straight lines and circular arcs. Example 7 When the pitch circle diameter of the above-mentioned arc gear is infinite, the pitch circle becomes a pitch line, and the arc teeth are arranged in a straight line along the pitch line into an arc rack, and the toroidal worm becomes a worm, as shown in Figures 8 and 9. A worm and arc rack transmission pair includes: a bevel worm 31, an arc rack 32 and a third roller 33. The arc rack 32 is provided with a pitch line 32a, contains arc teeth with a cross-sectional line and an axis A4, and is also provided with an axial hole. It also includes a third roller 33, which is provided with the same cross-sectional line and axis A3 as the arc teeth contained in the arc rack 32. It is placed in the axial hole as an arc tooth separated from the arc rack 32. The worm is a double-headed worm, and the angle between the axis A1 and the pitch line 32a is an acute angle, which is the bevel worm 31. 1, with an axis A1, a generatrix, a conical helix 31a, a conical helical groove 31b and a tangent envelope curve 31c. The outer contour is a rotating body formed by rotating around the axis A1 with a straight line close to the index line 32a as the generatrix. The conical worm 31 rotates forward and reverse around the axis A1 and engages with the multiple tooth lines of the circular arc rack 32. The contact line is the tangent envelope curve 31c of the tooth surface of the enveloping circular arc tooth, so that the circular arc rack 32 reciprocates along the index line 32a to transmit motion and power. The cross-section line of the circular arc rack 32 is a straight line parallel to the axes A3 and A4. The position error along the axis direction does not affect the meshing accuracy between it and the conical worm. The 3D curve equation of the conical helix 31a in the Cartesian coordinate system is: x=P*cos(Θ°)*t; y=(P*sin(Θ°)*tH / cos(Θ°))*cos(t*360°); z=(H / cos(Θ°)-P*sin(Θ°)*t)*sin(t*360°); Where P is the distance between the intersection of the conical helix 31a and the dividing line 32a; H is the distance between the origin of the coordinate system and the dividing line 32a; Θ is the angle between the axis A1 and the dividing line 32a; t is the parameter 0≤t≤the number of spiral coils. The distance S2 between the two third rollers 33 is the same as the distance between the two arc teeth included in the arc rack 32. The distance S1 and S2 between the arc teeth included in the third roller 33 and the arc rack 32 are twice as large as S1. Example 8 As shown in FIG8 , the third roller 33 is completely removed, the bevel worm 31 and the arc rack 32 are the same as those in the seventh embodiment, the arc rack tooth spacing S1 is changed to S2, the number of teeth is halved, and the transmission ratio remains unchanged. Embodiment 9 When the axis line is parallel to the index line, the worm is a straight worm, the trajectory line is a constant pitch helical line with a pitch P, the tooth groove is a constant pitch helical groove, and the arc rack 32 is the same as that in the seventh embodiment. Example 10 As shown in Figures 1 and 2, a modeling method for the above-mentioned toroidal worm includes the following steps: S1: Set the basic parameters of the toroidal worm; S2: Based on the basic parameters of step S1, the generatrix is ​​rotated around the axis A1 to form a solid of revolution, and the cross-sectional line is rotated around the axes A3 and A4 to form the arc tooth surface; S3: The tooth surface of the arc tooth is cut along the trajectory line to form a tooth groove on the surface of the rotating body to generate a toroidal worm solid; The basic parameters in step S1 include: the shape, position and dimensions of the main line and the cross-sectional line, the position of the center line A1 and the axes A3 and A4, wherein the toroidal worm also includes the pitch circle diameter D, the center distance C, the toroidal helix angle α, and the toroidal cam also includes the weft arc radius. In step S3, the trajectory line is the toroidal helix 1a, and the tooth groove is the toroidal spiral groove 1b, wherein the 3D curve equation of the toroidal helix 1a in the Cartesian coordinate system is the same as that in Example 1. Example 11 As shown in Figures 3 and 4, a modeling method for the above-mentioned toroidal cam includes the same steps as Example 10. In step S1, the toroidal worm is the toroidal cam 11, and the basic parameters also include the weft arc radius. In step S3, the trajectory line is a composite line of the spiral line 11a and the weft arc 11b, and the tooth groove 11c is cut out to generate the toroidal cam 11 entity. Example 12 As shown in Figures 8 and 9, a modeling method for the above-mentioned bevel worm gear includes the same steps as in Example 10. In step S1, the annular worm gear is a bevel worm gear 31, and the basic parameters also include the spacing P between the intersection of the bevel helix and the dividing line, the spacing H from the origin of the coordinate system to the dividing line, and the angle Θ between the axis line and the dividing line. In step S3, the trajectory line is the bevel helix line 31a, and the tooth groove is the bevel helix groove 31b, generating a bevel worm gear 31 entity, wherein the 3D curve equation of the bevel helix line 31a in the Cartesian coordinate system is the same as that in Example 7. Example 13 A modeling method for the above-mentioned straight worm includes the same steps as Example 10. In step S1, the annular worm is a straight worm, and the basic parameters also include pitch. In step S3, the trajectory line is an equal-pitch helical line, and the tooth groove is an equal-pitch helical groove to generate a straight worm entity. Example 14 A method for manufacturing the above-mentioned toroidal worm or worm comprises the steps of: S10: A solid model generated by any modeling method of Examples 10 to 13, rough machining by turning and milling - heat treatment - finishing by grinding - surface coating, wherein the tooth grooves are cut out by turning, milling or grinding along the trajectory line, the outer contour of the milling cutter or grinding wheel used is consistent with the arc tooth cross-section line, and the 3D curve equations of the toroidal helix and the conical helix in the Cartesian coordinate system are the same as those described above. Example 15 The above step S10 can also be formed by 3D printing of a physical model. Example 16 The above step S10 can also be performed by injection molding according to a physical model. Embodiment 17 A method for finishing the annular spiral groove of the annular worm comprises the steps of: S20: When the grinding wheel head is rotated and fed along the center line for an angle, the synchronously linked rotating body is fed along the axis line for a corresponding angle with a transmission ratio of 360 / α times, thereby continuously cutting an annular spiral groove on the surface of the rotating body. Example 18 In the above step S20, the milling cutter can be rotated to feed along the toroidal spiral trajectory to cut the toroidal spiral groove on the surface of the rotating body. Example 19 As shown in Figures 10 to 12, a toroidal worm and circular arc gear transmission device includes a third toroidal worm 41, a needle roller bearing 42, a first roller bracket 43, a fourth roller 44, a second retaining ring 45 and a second roller bracket 46, and also includes a frameless outer rotor brushless motor, an output shaft fixing seat 47, the needle roller bearing 42, the fourth roller 44, the first roller bracket 43, the second roller bracket 46 and the second retaining ring 45 form an arc gear, the first roller bracket 43 and the second roller bracket 46 are provided with an axial hole and a retaining ring groove, the first roller bracket 43 contains circular arc teeth, the needle roller bearing 42 contains the fourth roller 44 as a rolling element, which is placed in the axial hole as a split circular arc tooth, and the second retaining ring 45 is placed in the retaining ring groove to prevent the needle roller bearing 42 from moving along the axis. The circular arc gear is thin. The first roller bracket 43 and the second roller bracket 46 are provided with a clearance groove 43a on the outer ring of the shaft hole to avoid interference with the outer contour of the third toroidal worm 41. The third toroidal worm 41 is a single-head worm, and its toroidal spiral groove is also provided with a clearance groove 41a, which is a Gothic arch abutting the arc teeth. Its root is rounded to reduce stress concentration. The frameless outer rotor brushless motor includes a rotor 56 and a stator 57. The rotor 56 includes a permanent magnet and a yoke. The stator 57 includes a laminated iron core, a winding, and an insulating coating layer. The rotor also includes a rotor cover. The rotor cover is provided with a centrifugal fan blade structure that can actively convect and dissipate heat. The output shaft fixing seat 47 serves as a base and is provided with a positioning surface 47a and a positioning groove 47b. The main shaft 50 and the angular contact bearing 53 and the ball bearing 55 are adjusted in position by a fixing ring 52 and a spacer 54. The position and clearance are set, and the tool in the collet 49 is locked by tightening the nut 48. The output unit is composed of an arc gear, and the input shaft fixing seat 58 is also included. The drive unit is composed of a frameless outer rotor brushless motor, a third annular worm 41, a bearing 60, a plane needle roller bearing 61 and a thrust combination needle roller bearing 62. The grating 68, the encoder 67 and the drive control board 66 are included. The drive control board 66 includes a drive control module, a power module and a power supply and a communication interface, which are fixed to one side of the input shaft fixing seat 58 by screws 65. The drive control and power modules include resistors, capacitors, MOS tubes and drive and control chips, etc. The interface also includes a connector, which can be quickly plugged in and out. The laminated core of the drive unit stator 57 is directly locked to one end of the input shaft fixing seat 58 by a locking ring 59, and the rotor 56 is locked directly to one end of the input shaft fixing seat 58. The cover is directly connected to one end of the third toroidal worm 41, and the other end is supported by a plane needle roller bearing 61 and a thrust combination needle roller bearing 62. The fixing nut 64 is adjusted and locked, and the grating 68 is fixed on it by a round nut 69. The drive unit is placed on one side of the output shaft fixing seat 47 and is fixed by a bolt 63. It can be rotated 180 degrees for installation and can be replaced as a modular whole. The input shaft fixing seat 58 and the output shaft fixing seat 47 are positioned by the positioning surface 47a and the positioning groove 47b. Increasing or decreasing the positioning surface 47a can adjust the side clearance of the transmission pair, adjust the preload, eliminate the transmission clearance or compensate for wear. The cross-section line of the arc gear is a straight line and parallel to the axis. The position error along the center line direction does not affect the meshing accuracy with the third toroidal worm 41. It also includes a shield 70 and a first dust ring 51 to protect the transmission device from dust.The drive control board 66 drives the third toroidal worm 41, which is directly connected to the motor rotor 56, to rotate and correct its position, with real-time feedback from the encoder 67. The circular arc gear threaded with the main shaft 50 engages with zero backlash to output motion and power. The angular contact bearing 53 and ball bearing 55 in the output shaft fixing seat 47 support and withstand all-directional loads, ensuring precise positioning of the main shaft 50. Example 20 As shown in Figures 11 and 13, a turntable includes the toroidal worm and circular arc gear transmission pair, the frameless outer rotor brushless motor and the output shaft fixing seat 47 of the nineteenth embodiment, the above-mentioned main shaft 50 is replaced by a turntable 71, the corresponding angular contact bearings 53 and ball bearings 55 are replaced by thrust combined roller bearings 73 and plane roller bearings 74, and the supporting parts nut 48, collet chuck 49, first dust ring 51, fixing ring 52, and spacer 54 are replaced by second dust ring 72. Example 21 As shown in Figures 10 to 12, a reducer is provided. In the nineteenth embodiment, the drive unit can be removed as a whole by removing the shield 70 and the bolt 63, and the needle bearing 42, the fourth roller 44 and the second retaining ring 45 can be removed. The first roller bracket 43 and the second roller bracket 46 are retained as circular arc gears, and the transmission ratio remains unchanged. The rest of the structure is the same as that of the nineteenth embodiment. Example 22 A robot joint, wherein the toroidal worm in Example 20 is replaced by a double-headed toroidal worm with a doubled toroidal helix angle, its transmission ratio is halved, and the rest of the structure is the same as that of Example 20. Example 23 A cam intermittent divider, wherein the annular worm in embodiment 20 is replaced by the above-mentioned annular cam, with intermittent transmission, and the rest of the structure is the same as that of embodiment 20. Example 24 A dividing plate, wherein the annular worm and circular arc gear transmission pair in embodiment 20 is replaced by a worm gear transmission pair, and the remaining structure is the same as that of embodiment 20. Example 25 A bevel worm and arc rack transmission device includes the above-mentioned bevel worm and arc rack transmission pair, and also includes a handwheel, a slider and a bearing, and also includes a guide rail, which is integrated with the arc rack. A dovetail groove is provided on one side of the arc rack as a guide rail groove. The handwheel is connected to the worm and supported by the bearing and placed on a slider that reciprocates along the arc rack dividing line. The transmission pair is engaged to transmit motion and power. Example 26 The above-mentioned transmission device also includes an arc tooth self-lubricating unit, which includes a porous resin, a high-density fiber mesh and an elastic contact block. The porous resin in the elastic contact block stores high-viscosity lubricant, which is transported to the surface of the arc tooth by the principle of capillary action of the resin and the high-density fiber mesh. The elastic force between the arc tooth and the elastic contact block is adjusted to adjust the lubricant flow. The present invention should not be limited to the above-mentioned preferred embodiments. Additions, changes, deletions and modifications made according to the technical essence of the present invention all fall within the scope of protection of the claims of the present invention.

Claims

1. A toroidal worm and circular arc gear transmission pair, comprising: The toroidal worm and circular arc gear are characterized in that the circular arc gear is provided with a center line, a contour line, a pitch circle and circular arc teeth. The rotating body is formed by rotating a straight line or a circular arc contour line without teeth around the center line, and is combined with the circular arc teeth arrayed according to the center line on the pitch circle; the toroidal worm is provided with an axis line, a main line, a trajectory line, a tooth groove and a contact line. The outer contour is an arc or a straight line or a multi-segment line of a fitted arc around the pitch circle of the circular arc gear as the main line, and the rotating body is formed by rotating around the axis line. The tooth surface of the circular arc tooth cuts out a tooth groove with a root of an arc on the surface of the rotating body along the trajectory line. It is a single-head or multi-head worm; the toroidal worm is in contact and meshing with the single or multiple tooth lines of the circular arc gear. The contact line is a curve that envelops the tooth surface of the circular arc tooth, which transmits motion and power between two axes that are staggered in space. The staggered angle between the two axes is a right angle or an acute angle.

2. The transmission pair according to claim 1, characterized in that: The arc teeth of the arc gear are provided with a cross-section line and an axis, the axis intersects the pitch circle, the cross-section line is a straight line or an arc or a combination of a straight line and an arc, and is rotated along the axis to form an arc tooth, and is arrayed into multiple arc teeth along the center line. The axis is parallel to the center line or the angle between them is acute. The arc gear and the arc tooth are integrated or split, and the split arc gear is a rotating body or rolling body bracket containing or not containing arc teeth, and also includes a rotating body or rolling body. The rotating body or rolling body bracket is provided with an axial hole, and the rotating body or rolling body is placed in the axial hole arrayed along the center line on the pitch circle as an arc tooth. The hole axis and the axis coincide or do not coincide. The integrated arc gear has a streamlined structure and is easy to miniaturize; the rotating body or rolling body of the split arc gear can be disassembled to change the number of arc gear teeth, and the number of teeth engaged with the toroidal worm at the same time is adjustable.

3. The transmission pair as claimed in claim 2, wherein the circular arc gear is a rolling element support and further comprises a rolling element, wherein: The rolling element includes a roller or a sleeve or a combination of them and a bearing. The bearing is a rolling or sliding bearing that can withstand unidirectional or omnidirectional forces. The rolling element is placed in the shaft hole of the rolling element bracket as an arc tooth, which can rotate around the axis and engage with the rolling and sliding composite motion of the toroidal worm.

4. The transmission pair according to claim 1 or 2, characterized in that: The toroidal worm is located outside the circular arc gear, and its outer contour generatrix is ​​a concave arc. The contour line of the circular arc gear without teeth is as large as close to the outer contour weft circle of the toroidal worm; its generatrix inside the circular arc gear is a convex arc, and its contour line is as small as close to the outer contour weft circle. Circular arc gears with the same pitch circle diameter can replace different toroidal worms to mesh and form transmission pairs with the same or different transmission ratios.

5. The transmission pair according to claim 1, characterized in that: The trajectory of the toroidal worm is a toroidal helix, and the tooth groove is a toroidal spiral groove. The center distance is the distance between the axis of the toroidal worm and the center of the pitch circle. The angle of the toroidal helix is ​​the angle between the two intersection points of the toroidal helix and the pitch circle on the pitch circle. The 3D curve equation of the toroidal helix in the Cartesian coordinate system is: x=(D / 2*sin(t*α°)-C)*cos(t*360°); y=D / 2*sin(90°-t*α°); z=(D / 2*sin(t*α°)-C)*sin(t*360°); Wherein, D is the pitch circle diameter; C is the center distance; α is the angle of the toroidal helix; t is the parameter 0≤t≤180 / α (number of spiral coils). The toroidal helix also includes all equivalent transformations of the above curve equation in the coordinate system.

6. The transmission pair according to claim 2 or 5, characterized in that: The transmission ratio is 360 / α, synchronous transmission, the angle between the circular arc teeth of the circular arc gear is an integer multiple of the toroidal helix angle of the toroidal worm. The larger the multiple, the smaller the number of teeth. The same toroidal worm can mesh with circular arc gears with different numbers of teeth, and the transmission ratio remains unchanged.

7. The transmission pair as claimed in claim 1, wherein the toroidal worm is a toroidal cam, characterized in that: The trajectory line is a composite line of the toroidal spiral line and the weft arc. The arc tooth surface cuts out tooth grooves on the surface of the toroidal cam along the composite line. The toroidal cam rotates and is synchronously transmitted when the tooth grooves of the toroidal spiral segment of the circular arc gear are engaged. The circular arc gear will not rotate when the tooth grooves of its weft arc segment are engaged. The transmission pair is an intermittent transmission.

8. The transmission pair according to claim 1, characterized in that: The root of the tooth groove of the toroidal worm is also provided with an air avoidance groove, which is a straight V-shaped or Gothic arch groove that abuts the arc tooth. The root of the groove can be chamfered to reduce stress concentration. The distance between the axis line of the toroidal worm and the center of the dividing circle is adjustable.

9. The transmission pair according to claim 2, characterized in that the split The circular arc gear is also provided with a relief groove on the outer ring of the rotating body or rolling body bracket shaft hole to avoid interference with the outer contour of the annular worm.

10. The transmission pair according to claim 2, characterized in that the split The circular arc gear is also provided with a retaining ring groove and a retaining ring, which is placed in the retaining ring groove to prevent the rotating body or the rolling body from moving along the axis.

11. A worm and arc rack transmission pair, comprising: The worm and arc rack are characterized in that, in the transmission pair as described in claim 1 or 2, when the pitch circle diameter of the arc gear is infinite, the pitch circle becomes the pitch line, and the arc teeth are arrayed in a straight line along the pitch line to form an arc rack. The arc teeth are integrated or split, and the split arc teeth do not rotate or can rotate. The annular worm becomes a worm, which is a rotating body formed by rotating around the axis with the straight line close to the pitch line as the generatrix of the outer contour. The worm rotates forward and backward around the axis to contact and mesh with the single or multiple tooth lines of the arc rack. The contact line is the tangent envelope curve of the tooth surface of the arc tooth, so that the arc rack reciprocates along the pitch line to transmit motion and power.

12. The transmission pair according to claim 11, wherein the worm is a conical worm, characterized in that: The angle between the axis and the index line is an acute angle, the trajectory line is a conical spiral line, the tooth groove is a conical spiral groove, and the 3D curve equation of the conical spiral Cartesian coordinate system is: x=P*cos(Θ°)*t; y=(P*sin(Θ°)*tH / cos(Θ°))*cos(t*360°); z=(H / cos(Θ°)-P*sin(Θ°)*t)*sin(t*360°); Where P is the distance between the intersection of the conical helix and the indexing line; H is the distance between the origin of the coordinate system and the indexing line; Θ is the angle between the axis and the indexing line; t is the parameter 0≤t≤the number of spiral coils. The conical helix also includes all equivalent transformations of the above curve equation in the coordinate system.

13. The transmission pair according to claim 11, wherein the worm is a straight worm, characterized in that: The axis line is parallel to the dividing line, the trajectory line is an equal-pitch spiral line, and the tooth groove is an equal-pitch spiral groove.

14. A method for modeling a toroidal worm or worm in a transmission pair as claimed in claim 1 or 11, comprising the steps of: S1: setting basic parameters of the toroidal worm or worm; S2: Based on the basic parameters of step S1, the generatrix is ​​rotated around the axis to form a solid of revolution, and the cross-section line is rotated around the axis to form an arc tooth surface; S3: The tooth surface of the arc tooth cuts out the tooth groove along the trajectory line on the surface of the rotating body to generate a toroidal worm or worm solid; The basic parameters in step S1 include: The shape, position and dimensions of the main line and the cross-sectional line, the axis centerline and the axis position, wherein the toroidal worm also includes the pitch circle diameter D, the center distance C, the toroidal helix angle α, the toroidal cam also includes the weft arc radius, the bevel worm also includes the spacing P between the intersection of the bevel helix and the pitch line, the spacing H from the origin of the coordinate system to the pitch line, the angle Θ between the axis centerline and the pitch line, the straight worm also includes the pitch, and the trajectory line in step S3 includes the toroidal helix, the composite line of the toroidal helix and the weft arc, the bevel helix or the equal-pitch helix, wherein the 3D curve equation of the toroidal helix in the Cartesian coordinate system is the same as described in claim 5, and the 3D curve equation of the bevel helix in the Cartesian coordinate system is the same as described in claim 12. The constructed helix curve equation makes the worm modeling parameterized, and the corresponding high-precision tooth groove model is generated by modifying the basic parameters, which can be directly used for simulation and CNC programming.

15. A method for manufacturing a toroidal worm or a worm in a transmission pair as claimed in claim 1 or 11, comprising the steps of: S10: According to the toroidal worm or worm solid model, 3D printing or cavity mold forming or turning, milling cutting forming or turning rough processing - heat treatment - grinding finishing, the solid model in step S10 is established according to the modeling method of claim 14, wherein, The tooth grooves are cut out by turning, milling or grinding along the trajectory line, the outer contour of the milling cutter or grinding wheel used is consistent with the arc tooth cross-section line, and the 3D curve equations of the toroidal helix and the conical helix in the Cartesian coordinate system are the same as described in claim 13.

16. The manufacturing method according to claim 15, wherein the tooth groove is a toroidal spiral groove, and the finishing step is: S20: When the milling cutter or the grinding wheel head is rotated along the center line for each angle, the synchronously linked rotating body is fed along the axis line by a corresponding angle of a transmission ratio of 360 / α times to continuously cut out a toroidal spiral groove on the surface of the rotating body; or the milling cutter or the grinding wheel head is rotated along the toroidal spiral trajectory to cut out a toroidal spiral groove on the surface of the rotating body.

17. A toroidal worm and circular arc gear transmission device, comprising the transmission pair according to any one of claims 1 to 10, further comprising a rotation source, a base and a bearing, wherein: The rotation source is a device that can output rotation; the base accommodates bearings; the bearings are rolling or sliding bearings, and can withstand unidirectional or omnidirectional forces; the rotation source is connected to any axis of the transmission pair to input motion and power, and engages with the other axis to output motion and power, and is supported by the bearings in the base to withstand unidirectional loads or combined loads in any directions.

18. The transmission device according to claim 17, further comprising an input shaft fixing seat, wherein: The rotation source is the rotor of the motor. The input shaft fixing seat, stator, rotor, toroidal worm and bearings constitute the drive unit, which may or may not include an encoder and a drive control board. The base is the output shaft fixing seat, which together with the circular arc gear and bearings constitute the output unit. The drive unit is placed on one side of the output shaft fixing seat, wherein the motor stator is directly fixed to the input shaft fixing seat, and the rotor is directly connected to the toroidal worm and rotates. It engages with the circular arc gear in the output shaft fixing seat to transmit motion and power. The output unit remains unchanged. By replacing the drive unit or the toroidal worm, the transmission ratio can be changed or changed to intermittent transmission.

19. The transmission device according to claim 17 or 18, further comprising an output shaft, wherein: The output shaft is the main shaft or turntable, the transmission pair is engaged for transmission, the main shaft or turntable supported by the bearing in the base is connected to the circular arc gear to output motion and power, the base remains unchanged, and the main shaft and turntable can be interchanged by replacing the corresponding bearings and supporting parts.

20. The transmission device according to claim 17 or 18, characterized in that: The base is provided with a positioning surface and a positioning groove or hole, which cooperates with the input shaft fixing seat for positioning. The root of the tooth groove of the toroidal worm is provided with a Gothic arched avoidance groove that abuts the circular arc tooth. Increasing or decreasing the positioning surface can adjust the side clearance of the transmission pair, adjust the preload, eliminate the transmission clearance or compensate for wear.

21. The transmission device according to claim 18 or 20, wherein: The toroidal worm and circular arc gear transmission pair can be replaced by other transmission pairs with two intersecting or staggered axes.

22. A worm and arc rack transmission device, comprising the transmission pair as claimed in claim 11, further comprising a rotation source, a slider and a bearing, wherein: It also includes a guide rail, which is integrated with or separated from the arc rack. The rotation source is connected to the worm, which is supported by bearings and placed on a slider that reciprocates linearly along the guide rail. The transmission pair is engaged to transmit motion and power.

23. The transmission device according to claim 17 or 22, further comprising a circular arc tooth self-lubricating unit, characterized in that: The self-lubricating unit includes porous resin, high-density fiber mesh and elastic contact blocks. The porous resin in the elastic contact block stores high-viscosity lubricant, which is transported to the surface of the arc teeth by the porous resin and the high-density fiber mesh using the principle of capillary action. The lubricant flow is adjusted by adjusting the elastic force between the arc teeth and the elastic contact block.

24. The rotation source according to claim 17 or 22, wherein the rotation source is a motor, characterized in that: The motor is a frameless inner or outer rotor brushless motor, including a rotor and a stator. The rotor includes a permanent magnet and a yoke. The stator includes a laminated iron core, a winding, and an insulating coating layer. It may or may not include an encoder and a drive control board. The rotor also includes a rotor cover. The rotor cover is provided with a centrifugal fan blade structure that can actively dissipate heat through convection. The drive control board includes a drive control module, a power module, a power supply, and a communication interface. The drive control and power modules include resistors, capacitors, MOS tubes, and drive and control chips. The interface also includes a connector, and the connector can be quickly plugged in and out.

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