TWI314504B - Internal engaging spherical gears and method of making the same - Google Patents

Description

1314504 IX. Description of the Invention: [Technical Field] The present invention relates to a spherical gear device, and more particularly to an internal meshing spherical gear device and a method of manufacturing the same. [Prior Art] Many heavy-duty industries have been slowly transformed into precision workers, and in the field of use, such as precision mating, assembly or high-precision welding technology, have been defended by robotic arms. . In the conventional manipulator arm, the toggle mechanism is a combination of a helical gear, a helical gear, and a bevel gear, so that the degree of freedom is only a single degree of freedom, and many gear components are required. Therefore, the relevant industry has developed a spherical gear and applied it to the toggle mechanism of the robot arm. The spherical window wheel has a number of conical φ on the spherical crown. The space application has one more degree of freedom than the general gear and is suitable for the joint mechanism on the robot. Therefore, the spherical gear gradually becomes one of the key components of the robot arm zero. In addition, the movement of the robot arm is nothing more than vertical movement and horizontal movement plus rotation. But whether the two axes are staggered or parallel, they can only convey • one-dimensional rotary motion along the two axes with the same relative position of degrees of freedom. However, since the spherical gear mechanism has an extra degree of freedom as compared with a general gear mechanism, it can convey a two-dimensional rotational motion. Please refer to Figure 1 for the spherical gear produced by Trallfa for the mechanical arm transmission. This mechanical arm is characterized by the application of 6 1314504 universal joint and spherical gear transmission combination, using spherical transmission two The gear teeth face each other to achieve the transmission β. Since the spherical gear is an external type, that is, the two spherical balls that are salivated are convex spherical surfaces, and therefore have a large space volume. In addition, such a spherical gear must also be combined with many single-ball gears, which also causes space waste. The main transmission element of the spherical gear H is the two cam teeth and the concave gear teeth and can allow the whole two degrees of freedom to rotate. The existing spherical gear wheel *· 胄 is a conical tooth shape, causing the spoiled teeth between the teeth. There is a phenomenon of stress concentration. Therefore, in order to make the spherical gear easy to apply, it is necessary to reduce the stress effect between the transmission element (i.e., the convex gear and the concave gear) to increase the life and efficiency of the spherical gear. Therefore, it is still necessary to solve the aforementioned problems by a spherical gear having a small volume to apply a transmission and a gear tooth design with reduced stress. SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide an internal mesh type spherical gear device for reducing the overall assembly size of the internal mesh type spherical gear device. Another object of the present invention is to provide a method of manufacturing a meshing spherical gear to provide a meshing spherical gear device having smooth rotation with two degrees of freedom and reducing stress effects. An internal meshing spherical gear device comprising at least a concave spherical gear and a convex spherical gear. The concave spherical gear has a concave spherical surface on which the teeth on the concave spherical surface are copied, and the central tooth is created by the twisting w. The convex spherical gear and the concave spherical gear are mutually opposed. Teeth, 1314504 and having a four-spherical surface corresponding to the concave spherical surface, the teeth on the convex spherical surface are copied from the central tooth, and the central tooth is created by the Confucian theory, the convex spherical surface The upper gear teeth and the gear teeth on the concave spherical surface can respectively mesh with each other, and the dynamic simulation has been completed in the computer. The method for manufacturing the internal meshing spherical gear comprises: providing a fixed coordinate system ~ (0,, ~々, Z/), and fixing the standard system 夂呔, n, y to the tool. Put two reference coordinates system coffee, ~ and

Ate, ~ know y fixed to the coordinate system of the convex spherical gear, with the convex spherical gear rotating. And the two reference coordinates are 仏, 5, Ad and

Afe, h VIII, A) is a coordinate system fixed to the concave spherical gear, which rotates with the concave spherical gear. The convex spherical gear is rotated around the U, so that the concave spherical gear rotates by 尧, and the sum is (4), where π and 乂 are the cam teeth of the convex spherical gear and the concave teeth of the concave spherical gear, respectively. Cut the coordinate system 4 on the convex spherical gear, and let the y turn the color angle around the 4 axis. The concave spherical gear rotates at an angle, and the relationship between the color and the color is ^Μ. When the convex spherical gear is wound around the Α and Ζ 3 axes, respectively, the concave spherical gears are rotated by the 戎 angle. 5 Next, using the homogeneous coordinate transformation matrix, the two-parameter surface family equations of the tool surface are generated. Finally, the two-parameter envelope convergence theory is used to generate the envelope surface of the parameter surface group of the tool surface. The effect achieved by the present invention is that, in the use of rapid prototyping and manufacturing techniques, the contours of the spherical spherical gears and the concave spherical gears 1314504 of the spherical gears can be produced in accordance with the envelope surface of the parameters. The invention provides a conical tool curved surface design with a circular arc root circle and a manufacturing method thereof, and uses the two-parameter curved surface family envelopment theory to establish the contour of the spherical gear device, and provides an internal meshing with two degrees of freedom transmission. Spherical gear transmission mechanism. In addition, the spherical gear device of the present invention can realize the smooth rotation of two degrees of freedom through the mechanism dynamic simulation and stress analysis 'internal gear type spherical gear which can be generated by the two-parameter envelope' and can improve the performance of the spherical gear device. 2 is a perspective view of a convex spherical gear according to a preferred embodiment of the present invention; and FIG. 3 is a perspective view of a concave spherical gear according to a preferred embodiment of the present invention. An inner spheroidal spherical gear device according to a preferred embodiment of the present invention comprises: a spherical spherical gear 100, a concave spherical gear 2〇〇, a convex spherical gear frame 300, and a concave spherical gear frame 4〇〇 (Fig. 9) Shown). The convex spherical gear 100 and the concave spherical gear 2 are meshed with each other in a concave-convex manner and joined to the frames 300 and 400. The convex spherical gear 1〇〇 and the concave spherical gear are distributed with a plurality of tapered teeth, including the teeth on the convex spherical surface and the teeth on the concave spherical surface. In a preferred embodiment, the teeth on the convex spherical gear 1〇〇 are set as cam teeth 110'. The teeth on the concave spherical gear 200 are set as concave teeth 2丨〇. For those of ordinary skill in the art, it should be recognized that the teeth of the convex spherical gear 100 can be set as concave teeth. In this case, the teeth of the concave spherical gear 2 13 1314504 can be set as cam teeth. Since the cam teeth 110 and the concave teeth 210 are in mesh with each other, the tooth profiles of the two will conform to the meshing principle of the gears. The tool to form the tooth shape of the cam tooth 110 and the concave tooth 210 is generally referred to as a tool design, or the face D is flushed. The cam gear 11 〇 and the concave gear teeth 21 are respectively formed on the convex spherical gear 100 and the concave spherical gear 200 by the cutter design, and these cam teeth 11 () and the concave gear teeth 210 are also referred to as created faces. Referring to Figures 4 and 5, FIG. 4 is a cross-sectional view showing a geometrical design of a tool for generating a spherical gear according to a preferred embodiment of the present invention, and FIG. 5 is a view showing a curved surface of the tool according to a preferred embodiment of the present invention. Simulation of the surface). The blade f surface (created surface) can be formed by a 3-line segment, a & line segment and a line segment, and a circle around the axis (long axis). Wherein, the & line segment is used to create the crown of the created surface (ie, the cam tooth 11 〇 and the concave tooth 21 〇), the & line segment is used to create the working area of the created surface, and the g line segment is created into the surface. The root of the tooth is used, and the line segment is used to create the bottom of the tooth. The cam teeth 110 formed by the created faces are engaged with the female teeth 21, and for the sake of simplicity of explanation, the following description will be made by forming the concave teeth 210 (created faces) by the tool curved surface (created surface). When the segments are rotated one revolution about the axis, a tool for machining the concave teeth 210 of the concave spherical gear 200 can be formed. From the above geometrical line segment of the tool, the geometric mathematical parameter of m is expressed in the coordinate system, ~ soil, d, 4, Rf superscript g is used to represent the ▲ line segment of the tool, [line segment ^ line segment and stone segment region. As shown in Fig. 4, the area defined by the section of the tool must be the area of the rounded fox 1314504 at the top of the concave tooth 21〇. If the variable number β is a parameter of the tool curve. The equation (1) of the region defined by the 3-line segment is expressed by the coordinate system & and can be expressed as: ((r + rcl)sini^ +θχ)~ rcX cos(0, + a)) cosrg + ((r + rcl) cos(6»p + &) - rd sin(6», + o〇) sin

-((r + /-cl)sin((9p +θχ)~ rcl cos(6>, + or)) sin re + ((r + rd)cos(6»p +6^)-rdsin(6> , +a))cosrs 0 〇<0t<(0c,+0c2)

Where r〇i

, , .r-rcosO

Kr=Kn +(-£ XX XO V / cost K ={rr cos θχ) tan φρρ + r sin θχ ΦΡΡ=ΦΡ+θρ+α , , Α _! .rtan^ -rsin^. Φρ =tan (-x - r-rcos&r _10π_ ~180η , _! rsin^ r + rcl -rcos^ Ο) Add (--χ-) •L·· I -t/· _ vr\r\c\ ti The parameters here, , rel, q, &, heart and 7 are given values, while other parameters are determined by mathematical geometric relations, 77 is the rotation of the tooth 11 1314504 positive coefficient, generally s, this coefficient is applicable In the backlash between the two sprockets, r is the radius of the base circle of the tool, and ~ is the radius of the root circle of the tool teeth. ' η •vf (rsinOp -(Ap ->9)sina)cos^ + (rcos^ -^)cosa)sinr0 1 -(r sin Θρ - (kp - β) sin a) sin rB + (r cos θρ + (hp - β) cos a) cos re 0 1 ^<P<hp-hxx & The area defined by the line segment produces the working area of the concave tooth 210, and A represents the design parameter of the tool. The equation for the area defined by the & line segment to produce a complete tool profile is represented by the coordinate system\, which can be expressed as:

Where hp = h-rccosa + ye _ rc (c〇s α -1 + sin a)(cos α +1 - sin α) ye---- 2 cos a in order to generate the root circle of the concave tooth 210 , use the 冱 line segment of the tool. A represents the design parameters of the tool curve. The equation for the area defined by the 冱 line segment is expressed by the coordinate system &

(rc sin 9C + w) cos r9 + (r cos + /i cos a - rc (1 - cos Qc)) sin re yld -(rcsin0c +w)sinQ +(rcos0p +Acosa-rc(l-cos0c)) Cosr0 Kd 1 0 1 O<A<0C1 (3) where w^rsin^-/isina-rccosa +

The area defined by the 忑 line segment is the tooth bottom of the tool curve for creating the bottom of the concave tooth 210. The equation for the region defined by 忑 is represented by the coordinate system fork and can be expressed as: 12 (4) 1314504 th cos τθ + (A cos or + r cos θρ ) sin re yf -^ A sin + (A cos a+ r Cos θρ ) cos re 4e 0 1 _ . 1 _ foot is the position vector of the tool. The superscript letter g symbolizes the equation (丨) to (4) defined by the line segment, & line segment, g segment, and line segment. region. The subscript symbol c indicates the equation in the coordinate system brother. When the equations (丨) to (4) are rotated around the axis, the angle is also given by 0. ~36〇. A single tooth machining tool surface is obtained, as shown in Figure 5.

Please refer to Figure 6, Figure 7, and Figure 8. The coordinate system is long, ze) indicates the coordinate system fixed on the tool. The fixed coordinate system is private, ', eight, z/) is a fixed reference coordinate. The two reference coordinate systems ～, 2l) and & 〇 (〇3% Z3) are fixed to the coordinate system of the convex spherical gear 1〇〇, and rotate with the convex spherical gear 1〇〇. The two reference coordinate systems \(〇5, 〜4) and & (〇6, 八8, 26) are fixed to the coordinate system of the concave spherical gear 2〇〇, as the concave spherical gear 200 rotates. As shown in Fig. 6, when the convex spherical gear 1 is rotated around the $, the concave spherical gear 200 is rotated by the angle, and the relationship between (4) and % is the cam tooth 110 and the concave tooth 21 分别, respectively. The number of teeth. Similarly, as shown in FIG. 7, when the coordinate system h on the convex spherical gear 100 is less than 3, 4) and the color angle is rotated around the 4 axes, the concave spherical gear 200 is rotated at an angle of 厶 and the relationship is = = 5 . The concave spherical gear 200 is a concave spherical gear supported by a concave spherical gear frame capable of two degrees of freedom, and the convex spherical gear _ is composed of a convex spherical surface wheel pivot 300 which can be used for two degrees of freedom. stand by. 13 1314504 As shown in Fig. 8, when the convex spherical gear 1 is wound around the a and & axis, respectively, when the color is rotated, the concave spherical gear 200 is rotated and also angled, so that the internal meshing spherical gear can There are two degrees of freedom to rotate. A in Figure 6 is the center distance between the coordinate origins 〇1 and 〇5.

As shown in Figure 6 and Figure 7, the coordinate system setting, in order to generate the tool surface family equation, can be used from the coordinate system, to the coordinate system \ homogeneous coordinate conversion matrix rolling! and the coordinate system S3 to the coordinate system s6 Sub-coordinate conversion matrix m63. Respectively expressed as: 0 _0 0 0 cos (木一办) sin (also a 戎) a sin (also do one) cos (color one in) 0 0 0 a cos φ5 -a sin (5) 财63 (minutes 3 )=

Cos(^6 -φ3) sin(^6 -φ3) 〇αύηφ6 -sin(^ -φ3) cos(一色色)0 -acos^6 0 0 1 〇0 〇〇1 As shown in Fig. 8, it is convex When the spherical gear 1 is wound around the * and ^ axes, respectively, when the rotation is 戎, then the concave spherical gear 200 is rotated by the angle of the yoke, so that the internal meshing spherical gear can rotate with two degrees of freedom, so when the cutter is When the coordinate system & and the 夂 rotation, the homogeneous coordinate transformation matrix from the coordinate system 5 > 3 to the coordinate system to the coordinate system & can be obtained according to the homogeneous coordinate transformation matrix method, and expressed as: (6)

°Φ6€Φι +S^6S^3C(^5 ~Ψ\) - Attack (W3 + 如(四)5 -do) ~5φ^{φ$-φι) 0 One C戎+#6C&C(木-办) +c^6c^3c(^5 -^) -〇φ^{φ5 -φ{) ο 械 S(05 D 〇Φ^{Φ$~ΦΧ) 〇(.Φί-φ\) ο as么c 5 αοφ6οφ5 (7) Through the homogeneous coordinate transformation theory, the designed tool surface equation 14 (8) (8)

The 1314504 type is set by the coordinate system of Fig. 8. From the coordinate system of & to the coordinate system, the two-parameter surface family equation of the tool is obtained, which can be recorded as R\^j, α, φν ^3)=Μ63λ| Is the design parameter, the vector 妒b α, nine do) is the tool surface family = program. Superscript? g is a 3-line segment, a [line segment, a ^ line segment, and a stone segment.垮 is the position vector of the tool in coordinate system A, as expressed by equations (1) to (4). Applying Litvin's two-parameter envelope coupling theory to obtain the envelope surface of the two-parameter tool parameter surface group. In this embodiment, the tooth profile on the convex spherical gear 100 is used as the tool, and there are two motion parameters. They are respectively necessary colors, so when seeking the envelope condition, you must first make one of the motion parameters not zero, and find the envelope condition at this time. Then let the color be zero and find the envelope condition at this time, so there will be two envelope conditions. First, let the color be zero, you can find the first envelope condition of the central tooth cutter and the concave gear on the convex gear, which is recorded as ^f * ^/ = msin^ + «cos^, + (1 + A^ 2 /Νλ){τηζλ — ny^/a = 0 where ~sin^cos+(^,cos^+ZjSin^)k ]-α^5^ 八/ = 朽+ (wcos 妁一wsin 戎)/· + ( Msin^ + ncos 戎) ft: Similarly, let 4 be zero, the second envelope condition of the central gear and the concave gear on the convex gear can be obtained, which is recorded as Ν}·ν}6 = msin(^ -£cos^ + (l +N2/-mxl)/a = 0 where ^/6 =(Φί -^6)[-(·^ιsin^3 +^,cos^3)i +(^005^3 -^sin^j)/ ] + a^6k (10) (11) (12) 15 (13) (14) 1314504 iV} =(fcos^3 -wsin^)/ + (^sin^ +mco^) j + nk From the equations (1) to (4), (8), (9), and (12), the geometric model of the concave spherical gear 200 can be obtained, and the program of the concave spherical gear 200 is obtained by writing the program in the Turb〇C++ language. Coordinate value, then turn it to

The MasterCam is presented in a line architecture. Finally, a single central tooth of the convex spherical gear 丨〇〇 and the concave spherical gear 2〇〇 is drawn by the computer aided software SolidWorks. Through the obtained central gear teeth, the central gear teeth are copied and distributed on the spherical surface to form a convex spherical gear and a concave spherical gear. The distribution angle of the gear teeth is (i=i and 2), and the subscript text i=1 The number of teeth of the convex spherical gear 100 (ie, the cam teeth 11〇) is shown. The subscript letter i=2 indicates the number of teeth of the concave spherical gear 200 (i.e., the concave teeth 21〇). The kisses are shown in Figures 2 and 3, and the first ring replicates six teeth in the shape of the center wheel $. Similarly, the second ring replicates twelve teeth with a central tooth-shaped piece, as shown in Fig. 2, which is a convex spherical gear 1〇〇 2 ... wheel 110帛3 shown as a concave spherical gear i The central tooth of the geometric model 2 of the 〇〇 is generated by a two-parameter envelope theory, with six concave teeth distributed in a white circle from a plan view and 12 concave teeth in a second circle. FIG. 9 is a schematic view of a spray-type spherical gear transmission mechanism which can be used in the fourth embodiment of the present invention. In the figure, the households are not the frame 300 and 400 are dry sound maps that are not activated. The effect of the invention is that the y-axis of the moving mechanism can be rotated and the flank of the rotator is rotated. First, the y-axis is fixed to the spherical surface. Referring to FIG. 10, FIG. 12, and FIG. 13, FIG. 13 1314504, the spherical gear of the preferred embodiment of the present invention transmits (4), and the movable coordinate is 6 The transmission mechanism rotates around the X-axis under the four angles of 9 o'clock and 11 o'clock. J January Same as the case, if the X axis is fixed, the spherical gear is rotated around the y axis. Please refer to Fig. 14, Fig. 15, Fig. 16, and Fig. 17 of Fig., and Fig. 4, Hanon 17, No., respectively, the transmission mechanism of the spherical gear of the preferred embodiment of Maoming is moving. When the coordinate is 3, the moving coordinate is 6, the moving coordinate is 9, and the moving seat is 11, the transmission mechanism rotates around the y-axis. Figure 9-17 can determine this (four) Spherical gears can indeed achieve a two-degree-of-freedom transmission.

Further, in order to explain the effect of the present invention in reducing stress between elements and to provide accurate stress and deformation data, a finite element analysis method can be used. It is assumed that there is no assembly error between the convex spherical gear 100 and the concave spherical gear 2〇〇. The stress analysis of the § hai gear transmission can be done by the finite element method and the general computer aided software program.

The material of the convex spherical gear 100 and the concave spherical gear 2〇〇 can be assumed to be isotropic and homogeneous, and has a Young's modulus of steel (Y〇ung, s modulus) five = 'Poisson ratio = 0.3. Via ANSYS

Workbench performs finite element analysis. In this analysis, the convex spherical gear 100 assumes a load with a fixed moment. The concave spherical gear 2 rotates around its axis. The counter-clockwise torque acts on the convex spherical gear 1 ,, resulting in contact between the convex spherical gear 1〇〇 and the concave spherical gear 2〇〇. The torque acting on the convex spherical gear 100 is 50 Nm. 17 1314504 As the two-toothed teeth 100,200 are engaged, the preferred embodiment of the present invention focuses on the analysis of the stress intensity of the teeth, so that the supported cross-shaped brackets are not shown. As shown in Figure 18, the β-green is a finite element mesh diagram of the inner salivary spherical gear with two degrees of freedom, meshing the surfaces of the two meshing gears to provide flexibility for numerical simulation or pilot production. Sand table derivation and plausible use 'The concave spherical gear 200 is set to be fixed, and the convex spherical gear ι is rotated around the X axis at 50 Nm. Referring to Figures 19 and 20, the three-dimensional spatial stress distribution of the v〇n_Mises stress of the convex spherical gear 1〇〇 and the concave spherical gear 200 is shown by finite element stress analysis. Although the present invention has been described above in terms of a preferred embodiment, it is not intended to limit the invention, and various modifications and refinements may be made without departing from the spirit and scope of the invention. The scope of the invention is defined by the scope of the patent application. BRIEF DESCRIPTION OF THE DRAWINGS In order to make the above and other objects, features, advantages and embodiments of the present invention more obvious, the detailed description of the drawings is as follows: Figure 1 is an externally designed spherical surface designed by Trallfa A schematic view of the gear unit. Figure 2 is a perspective view of a convex spherical gear in accordance with the preferred embodiment of the present invention. Figure 3 is a perspective view of a concave spherical gear stand 18!314504 in accordance with a preferred embodiment of the present invention. Figure 4 is a schematic illustration of a circular arc shaped tool design in accordance with a preferred embodiment of the present invention. ^ Figure 5 is a three-dimensional simulation of the circular arc-shaped tool in Figure 4. Figure 6 is a schematic diagram showing the spatial relationship of the coordinate systems &&& Figure 7 is a schematic illustration of the spatial relationship of coordinate systems &&&&> in accordance with a preferred embodiment of the present invention. Figure 8 is a schematic view showing the setting of the coordinate system of the spherical gear of the burr according to the preferred embodiment of the present invention. Figure 9 is a schematic view of a (4) combined spherical gear device in accordance with a preferred embodiment of the present invention having two degrees of freedom of rotation for illustrating the position when the movable coordinate is zero. (4) A (4) combined spherical gear according to a preferred embodiment of the present invention, when the position of the animation is 3, the y-axis of the rotating shaft is fixed and rotated along the X-axis. Fig. 11 is a view showing the (four) combined spherical gear according to the preferred embodiment of the present invention, in which the rotational axis y-axis is fixed and rotated along the X-axis when the field animation coordinate is at the 6 o'clock position. Fig. 12 is a view showing the inner shaft type spherical gear according to the preferred embodiment of the present invention. When the two-position stomach animation coordinate is at the 9 o'clock position, the rotary shaft is fixed and rotated along the X-axis. Figure 13 is a schematic view showing the inner-engaging spherical gear 19 1314504 according to a preferred embodiment of the present invention, which is fixed when the position of the animation is u, and is rotated along the X-axis. Rotating shaft and shaft The 14th drawing is a good example... Combined spherical gear When the field is at 3 o'clock, the rotating shaft is fixed and rotated along the y-axis. Figure 15 is a view of a preferred spherical spherical gear according to a preferred embodiment of the present invention.

2. When the 昼 coordinate is at the 6 o'clock position, the rotation axis is fixed and the y-axis is rotated. Figure 16 is a schematic diagram of the (4) combined spherical gear according to the invention. When the position of the animation is 9 o'clock, the rotation axis X sleeve is fixed 疋' and rotated along the y-axis. Fig. 17 is a view showing the inner spheroidal spherical gear device according to the preferred embodiment of the present invention, when the imaginary coordinate is at the position of U, the rotary shaft 固定 is fixed and rotated along the y-axis. Figure 8 is a schematic illustration of a grid cutting stress analysis of a concave spherical gear in accordance with a preferred embodiment of the present invention. Figure 19 is a schematic view showing the stress distribution of a convex spherical gear in accordance with a preferred embodiment of the present invention. Figure 20 is a schematic illustration of the stress distribution of a concave spherical gear in accordance with a preferred embodiment of the present invention. [Main component symbol description] 100 · convex spherical gear 200 : concave spherical gear 110 : cam tooth 210 : concave gear tooth 20 1314504 concave spherical gear frame 300 : convex spherical gear frame 400 :

twenty one

Claims (1)

1314504 X. Patent application garden: 1 inner-ring spherical gear device, comprising at least: a concave spherical gear, a first gear, the 4b first U) wheel having a concave spherical surface, the concave spherical surface having a plurality of The first gear teeth are duplicated by a central gear; and a convex spherical gear meshes with the concave spherical gear and has a convex spherical surface corresponding to the concave spherical surface. Two-toothed teeth, which are copied from the central teeth of the towel, the concave spherical surface and the convex Thereby, the work is performed by the convex spherical gear and the concave spherical gear to reduce the overall assembly rule of the internal meshing spherical gear device. 2. The internal meshing as described in claim 1 The spherical gear device, wherein each of the first gear teeth is a concave gear tooth, each of the second gear teeth is a cam tooth, and the concave gear teeth and the cam gear system are formed by a tool curved surface 0 3_ The internal meshing spherical gear device of the second aspect of the invention, wherein the tool surface is formed by a 3-line segment, a & line segment, a & line, and a line segment, wherein the axis is rotated one turn, wherein The 3-line segment is used to generate the crown of the concave tooth, the skill line is used to generate the working area of the concave tooth, the 3-line segment is the root arc of the concave tooth, and the 忑 line segment is used to generate the The bottom surface of the concave teeth. 22 1314504 4. The internal meshing spherical gear device according to claim 3, wherein the equation of the region defined by the 3-line segment is expressed by a coordinate system & ((r + rcl) sin% + &) — rcl cos(4) + o〇) cos + ((r + rcl) cos(^ +θχ)~ rcl sin(^ + a)) sin re —((r + rcl ) sin(0p + 0X) - rcl cos(6», + a)) sin + ((/ + rcl) cos(l + ) - rcl sin(0, + a:)) cos 0 1 〇<0t< (ec3+0c2) where, R-rcos0x c〇si/>PP hxp =(r_rcosΘχ)tanφρρ+πsinθχ , ΦΡρ=ΦΡ+θΡ+α , _! rtan^ -rsin6> ΦΡ = tan (-2 r a rcos0v , 10π 180/7 (^~θχ)/η 2n' 23 1314504 匕=taiT'(— r + rCI-rcos^ , where 'parameters r, &, %, must, ^, and 7 are given values, while other parameters are determined by mathematical geometric relations'" Is the correction factor of the tooth, r is the base circle radius of the tool 'G is the radius of the root circle of the tool tooth. 5. As defined in the 6c line segment of the internal meshing spherical window wheel device described in claim 4 The equation of the region is expressed by the coordinate system & and can be expressed as: (r sin Θρ - (hp - β) sin a) cos rg + (r cos θρ + (hp ~ β) cos a) sin re - (r sin Θρ - (hp - β) sin a) sin re + (r cos θρ + (hp - cos a) cos re 0 1 0<β<\~Ηα where hp=h-rccosa + ye _ rc(cosa-l + sina)(coso; + l —sina) e 2 cos a , Θ represents the design parameters of the tool. 6 · The inner ring type spherical gear device as described in claim 5, wherein the area defined by the 3-line segment The equation is expressed as a coordinate system & and can be expressed as: (rc sin 6C + w) cos r9 + (r cos + Λ cos a - rc (1 - cos 9C)) sin re " ~-{rc sin0c + w)sinr0 +/2cosor -rc(l-cos0c))c〇sre 0 1 24 !314504 0<<& where ^-rsm.Op —hsma — rc cos a + ^ Α represents the design parameters of the tool curve. 7. The equation for the area defined by the internal meshing spherical gear device as described in claim 6 is represented by a coordinate system fork, which can be expressed as: V, £kcosrd H-(/zcosa + rcos0p) Sinr0 Rf = yte zde - £ ksinr0 + (h cos a + r cos θρ ) cos rQ 0 _ 1 "c _ 1 〇 <L <w 〇8. — A method of manufacturing an internal meshing spherical gear, comprising: (a) provide a fixed coordinate system &(〇,,々,々,Z/); (b) provide a coordinate system fixed to the tool, v Λ, z); (4) provide two reference coordinate systems , ~ only, Ζι) and 4 (〇3, A, is, 4), fixed to a coordinate system of a convex spherical gear, with the convex spherical gear rotating; (4) provide two reference coordinate system & (05, ~> ; 5, y and Ate, ~ eight, ~), fixed to a coordinate system of a concave spherical gear, with the concave spherical gear rotating; (d) rotating the convex spherical gear around the 々 axis to make the concave spherical gear Turn 25 1314504 Μ respectively for the convex angle, the sum of the system is, · the number of teeth of the spherical gear and the concave spherical gear; ζ3) about the relationship between the color and the shaft 23 is unitary (e) the projections on the spherical coordinate system gear & (03, color rotation angle, it rotates the gear concave spherical surface angle, Νλφ3 = Ν5φ6, (g) Using the homogeneous coordinate transformation matrix to generate the double spring surface family equation of the tool surface; and the number of turns (h) using the two-parameter envelope convergence theory to generate the envelope surface of the parameter surface group of the tool surface from the two-parameter surface family equation . 9. The method for manufacturing an internal meshing spherical gear according to claim 8, wherein the tool curved surface is rotated by a 3-line segment, a clever segment, a 2-wire, and a line segment. Formed, wherein the equation of the region defined by the 3-line segment is represented by the coordinate system ', which can be expressed as: ((r + rcl) sin(^ +θχ)- rcl cos{9t + a)) cos re + ((r + rd) cos(0p + ) - sin(9) + a)) sin R C Yf -Hr + ^i) sin(^p +θχ)~ rc\ cos(e, + «)) sin re + ((r + rcl) cos(^ +θχ)~ rcl sin(^( + a)) cos Re 26 0 1314504 0<$<(H) where 〇cl =tan-1(-^L) rci , κ=ΚΗ:ζτψ^ cos^ , ^χρ ~(r~r cos θχ) tanφρρ + r sin θχ Φρρ=ΦΡ+θρ+α r — rcos0x , 0 〜10;r 180”, Θ 2n{ θχ)!η θ tan'1 ( rsin9r r + rcl -rcos0x where the parameters of 'parameters, C丨, %, &, 0 and acknowledgment are determined by mathematical geometric relations: the value of g疋, while other numbers, ?·θ 疋 疋 的 你 χ χ And the radius of the base circle of the boring tool, "the slab circle of the cutter tooth 10. The manufacturing method as described in claim 9 of the patent application, wherein [the area defined by the line segment: the combined spherical gear can be of the following formula Representation: U material is represented by coordinate system 27 1314504 (rsin6^ -(Ap -々)sma)cos4 +(rcos ～+(Ap —々)C0SQr)sin~ -(r sin θρ - (hp - β) sin a) Sin re + (r cos θρ + (hp - β) cos a) cos r9 0 1 where ~h-rc cos a + ye y ^ (c〇s -1 + sin a)(cosa +1 - sin a) 2cosa, π 1 ^ represents the design parameters of the tool. 11. The method of manufacturing a meshing spherical gear according to claim 10, wherein the equation of the region defined by the line segment is represented by a coordinate system &, and can be expressed as: , .cd , .cd (rc Sin 9C +w)cosre+{rcos9p+h cos a - ?; (1 _ c〇g ^ ^ gin ^ -(rc sin5>c + w)sinre + {r cos0p+hcosa~r〇(1 - c〇s ^^c〇g^ oc 8 Where w -?"sin0p-/jsina-^cosa + jVg , * represents the design parameters of the tool curve. ^ Please refer to the (4) combined spherical tooth method described in item U of the patent scope. The method is defined by the coordinate system I, which can be expressed as: 28 !314504 °<^<wo ih cosr0 +(Acosa + rcos0p)sinr6l -£h sinr0 +(Acosa + rcos^/,)cosr^ 0 1 The manufacturing method of the inner wheel as described in claim 12 (g) contains intermeshing spherical teeth Use the coordinate system from the coordinate system $ to the coordinate system & and the coordinate system \ to coordinate system...: under-coordinate conversion matrix ^63, where Cai 51 (she) = 〇0 0 cos (么-奂) -sin(05-戎) 0 0 sin(么-办) cos(戎-办) 0 0 a cos φ5 -a sin φ5 财63(4) = cos(么-色) -sin(^-^3) 0 0 sin(么-戎) cos(么-色) 0 0 0 asin^6 0 —a cos 么1 0 ο 1 When the knife mask rotates in the coordinate system $ and Α, according to the homogeneous coordinate transformation matrix method, the homogeneous coordinate transformation matrix from the coordinate system to the coordinate system to the coordinate system & is obtained, wherein: 163 C? 4 +伙-办) -Ξφ6〇φζ + - φλ) One s(ks(jt>5 - Φ6 0 -c outside + from c<i3C(^5 _ is) ^φ63φ3+οφ6εφ3ε(φ5 -φλ) -^ΦΑΦ5 - φχ) ο s<t>Af!>5-<k, οφ6ε(φ5 ~φχ) ε(Φβ ~Φ\) 0 ^φ6〇φ5ac<Kc<k -αεφ5 : and the theory of homogeneous coordinate transformation , get the two-parameter surface family equation of the tool surface, recorded as 29 1314504 R a, φν Φ3) = m63 where 'variable heart is the design parameter, vector 浐匕, a, l color) is the tool surface family equation, superscript text g It is a 3-line segment, a & line segment, a 9-line segment, and a line segment. H. The method for manufacturing an inner cohesive spherical gear according to claim 13 wherein step (h) comprises a first enveloping condition for the convex gear to mesh with the concave gear, For ^/ · ^/5 = m sin + n cos ^, + (1 + TV2 / iV, ){mzx - «^ ) / fl = 〇 where C=—(A-么)[-hsin色+Zlcos private )_/ . (only coffee is +qsin) k ]-α Table A: •^=^ + (wcos is -nsin in) y + (msin do +"cos is) Λ ; and the order is zero, Obtain the second envelope condition of the convex gear meshing with the concave gear, denoted as Nf *v}6 = msinφ3~£cosφ3+(\ + Ν2/N:)(i.yx -mxx)la = Q where F/36 = (Table -sin & + % cos) ί· + (X cos also -% sin color) _/· ] + α ft = (/cos-msin Lu 3)i + (£sin^j+mcos03X The manufacturing method of the internal meshing spherical gear according to claim 14, further comprising forming a single central tooth on the convex spherical gear and the concave spherical gear; 30 1314504 (4) Forming a first annular gear on the convex spherical surface and the concave spherical gear (4), the distribution angle of the teeth is The subscript text 1=1 indicates the number of teeth of the convex spherical gear' subscript text 丨=2 indicates the number of teeth of the concave spherical gear. 16. The manufacturing method of the internal meshing spherical gear according to claim 15 of the patent application, Further step _ is included in each of the first ring-shaped replicas of six tooth teeth; a second ring-shaped rim is formed on each of the convex spherical gear and the concave spherical gear; and the second ring is formed by the central tooth at each of the five Duplicate twelve teeth. 31