CN207005221U - A kind of relative pinion and rack slided of engagement type nothing of convex-concave - Google Patents

Abstract

The utility model relates to a convex-concave meshing gear and rack mechanism without relative sliding, which comprises a pair of transmission pairs composed of a spiral arc gear and an arc rack. The outer surface of the spiral arc gear is evenly distributed with spiral convex arcs. The upper surface of the arc rack is evenly distributed with concave arc tooth grooves, the spiral convex arc teeth and the concave arc tooth grooves are matched, the spiral arc gear is connected to the rotating shaft of the driver, and the spiral convex arc teeth of the spiral arc gear The center lines are all cylindrical helical lines with equal pitch, and the center lines of the concave arc tooth grooves of the arc racks are all inclined straight lines. When installing this mechanism, it is necessary to ensure that the spiral convex arc teeth and concave arc tooth grooves are properly meshed, so as to realize the rack and pinion transmission. The rack and pinion mechanism has no failure forms such as relative sliding of tooth surfaces, gluing of tooth surfaces, wear of tooth surfaces and plastic deformation of tooth surfaces during transmission. It has the advantages of high coincidence, simple structure, high transmission efficiency, and strong bearing capacity. , micro-mechanical and conventional machinery field promotion and application.

Description

A rack-and-pinion mechanism with convex-concave meshing without relative sliding

technical field

The utility model relates to a convex-concave meshing type rack and pinion without relative sliding, in particular to a convex-concave meshing non-relative sliding rack and pinion for rack and pinion transmission based on the principle of curve meshing mechanism.

Background technique

Gear transmission is widely used in industry, agriculture, medicine, national defense, military and aerospace and other fields. In recent years, the design theory and manufacturing technology of new high-performance gear transmission mechanisms have promoted the continuous improvement and innovation of gear meshing theory, and diversified gear meshing forms and corresponding diversified tooth structures have emerged. In particular, the development of modern industrial equipment has further increased the requirements for the quality and performance of gear transmission components.

At home and abroad, we have innovated original micro transmission mechanisms in the field of gear meshing. For example, in the Chinese patent literature, the patent number is 201510054843.4, which discloses "a spiral arc gear mechanism for external meshing transmission of parallel shafts", and the patent number is 201510051923.4, which discloses "a spiral arc gear mechanism for internal meshing transmission of parallel shafts" . The biggest limitation of the above two kinds of transmission mechanisms is that they can only realize the motion and power transmission between two parallel axes in the plane, but cannot realize the motion and power transmission between the rack and pinion pairs.

In addition, the application number is 99114349.3, which discloses "pure rolling contact rack and pinion and its cutting tool". Design calculation formulas such as rack and pinion structural parameters and coincidence degree, therefore, the specific shape and stress state of the tooth profile of this design cannot be checked, and the bending strength and contact strength cannot be guaranteed, and cannot be applied and promoted in engineering.

At present, for the motion and power transmission between rack and pinion mechanisms, the most widely used in industry is the involute rack and pinion mechanism, including spur gear-spur rack pair and helical gear-helical rack pair. However, the meshing principles of these two rack and pinion pairs strictly follow the meshing theory of curved surfaces. From the design theory, there must be relative sliding between the tooth surfaces, so traditional tooth surface wear, tooth surface gluing and tooth surface plastic deformation cannot be avoided. The common failure mode of gear transmission has seriously affected the service life and reliability of the gear pair. At the same time, because the involute tooth shape adopted is a cantilever beam structure, and the meshing method of the tooth surface is convex-plane meshing, the bending strength and contact The strength is not high, and its carrying capacity is also limited.

Contents of the invention

The purpose of the utility model is to solve the problems existing in the prior art of the rack and pinion mechanism in the field of mechanical transmission, and to provide a simple structure, a small number of parts in the transmission system, no relative sliding between the tooth surfaces, high transmission efficiency, small size, and high quality. Lightweight, high degree of overlap, strong bearing capacity, and continuous and stable transmission of the convex-concave meshing rack and pinion mechanism without relative sliding.

In order to achieve the above object, the technical solution adopted by the utility model is to provide a convex-concave meshing gear rack mechanism without relative sliding, including a pair of transmission pairs composed of a gear and a rack, and the gear is a spiral circle Arc gear, the outer surface of the spiral arc gear has spiral convex arc teeth evenly distributed, and the rack is an arc rack with concave arc tooth grooves uniformly distributed on the upper surface, and the spiral convex arc teeth and concave arc tooth grooves are matched; The spiral arc gear is connected to the rotating shaft of the driver through the central hole of the spiral arc gear, and the rotating shaft of the driver rotates clockwise or counterclockwise, driving the spiral arc gear to rotate clockwise or counterclockwise; the outer surface of the spiral arc gear There is a transition fillet between the spiral convex arc gear to reduce the stress concentration at the root; the meshing mode of the spiral arc gear and the arc rack is convex-concave meshing, and the meshing transmission is point contact without relative sliding meshing transmission.

For the meshing of the spiral arc gear and the arc rack, the contact line formed on the spiral arc gear and the center line of the spiral convex arc tooth at the meshing point are both cylindrical helical lines with equal pitch, and the meshing point is at the arc The contact line formed on the rack and the concave arc tooth groove center line are both inclined straight lines.

There is a gap between the spiral convex arc teeth and the concave arc tooth grooves.

The transmission structure of the pair of transmission pairs composed of the spiral arc gear and the arc rack is that the spiral arc gear rotates under the drive of the driver, and the continuous meshing between the spiral convex arc teeth and the concave arc tooth grooves The function is used to realize the parallel movement of the arc rack; or the arc rack is fixed, the spiral arc gear rotates under the drive of the driver, and through the continuous meshing effect between the spiral convex arc teeth and the concave arc tooth grooves, The axis of the helical arc gear moves in parallel while rotating, and is used to realize the pure rolling of the helical arc gear along the convex-concave meshing of the arc rack.

The convex-concave meshing rack and pinion mechanism without relative sliding of the utility model is a fundamentally innovative gear transmission mechanism based on the traditional mechanical transmission mechanism. The meshing method of this mechanism transmission is different from the curved surface meshing method of the traditional gear transmission. , but based on the principle of space curve meshing, the relative movement speed of all meshing points is zero, which can provide a new rack and pinion transmission method for micro, micromechanical and conventional mechanical devices. This mechanism can effectively avoid conventional gear teeth Common failure forms such as tooth surface wear, gluing, and plastic deformation in the bar transmission mechanism, and it has the advantages of strong transmission bearing capacity and high transmission efficiency.

Compared with the existing rack and pinion transmission, the convex-concave meshing rack and pinion mechanism of the present utility model has the following advantages:

(1) The meshing mode of the convex-concave meshing rack and pinion mechanism of the present invention is a point-contact non-relative sliding meshing transmission, and the meshing point is located at the instantaneous center of the spiral arc gear and the arc rack, and the relative movement of all meshing points The speed is zero, so it can effectively avoid common failure forms such as tooth surface wear, gluing and tooth surface plastic deformation in rack and pinion transmission, and the transmission efficiency is high.

(2) The convex-concave meshing rack and pinion mechanism of the present invention has no undercutting, and the minimum number of teeth of the spiral circular arc gear is 1, and a larger tooth thickness can be designed, thereby having higher strength and rigidity, and at the same time due to the compact structure , which greatly saves installation space.

(3) The design value of the coincidence degree of the convex-concave meshing rack and pinion mechanism of the present invention can be very large, which is much higher than the coincidence degree of the existing involute gear and rack, so the transmission is more stable and reliable, and the bearing capacity is stronger .

(4) The meshing of the convex-concave meshing rack and pinion mechanism of the present invention is a concave-convex tooth profile meshing method, which has greater contact strength than the traditional involute convex-flat tooth profile meshing method, and further increases It improves the carrying capacity and is suitable for popularization and application in the fields of micro, micro machinery and conventional machinery.

Description of drawings

FIG. 1 is a structural schematic diagram of a convex-concave meshing non-relative sliding rack and pinion mechanism of the present invention.

FIG. 2 is a schematic front view of the structure of the spiral arc gear and the spiral convex arc teeth in FIG. 1 .

FIG. 3 is a schematic top view of FIG. 2 .

FIG. 4 is a schematic front view of the structure of the arc rack and its concave arc grooves in FIG. 1 .

Fig. 5 is a schematic diagram of the spatial coordinate system of the convex-concave meshing rack and pinion mechanism of the present invention.

Fig. 6 is a structural diagram of the utility model in which the rack is fixed and the gear is connected to the driver to realize pure rolling of the gear on the rack.

In the above figure: 1-driver; 2-drive mounting seat; 3-center line of spiral convex arc teeth; 4-transition fillet; 5-spiral convex arc teeth; 6-spiral arc gear; 7-concave arc tooth groove; 8-arc rack; 9-concave arc tooth groove center line; 10-helical arc gear center hole.

detailed description

Below in conjunction with accompanying drawing and example the utility model is further described, but the implementation of the utility model is not limited thereto.

Embodiment 1: The utility model provides a rack-and-pinion mechanism with convex-concave meshing without relative sliding. Its structure is shown in Figures 1, 2, 3, and 4. The gear described is a spiral arc gear 6, and the outer surface of the spiral arc gear is evenly distributed with spiral convex arc teeth 5, and the rack is an arc rack 8 with concave arc tooth grooves 7 evenly distributed on the upper surface, and the spiral convex Arc teeth and concave arc tooth grooves fit together; the spiral arc gear is connected to the rotating shaft of the driver 1 through the center hole 10 of the spiral arc gear; a transition circle is provided between the outer surface of the spiral arc gear and the spiral convex arc teeth Angle 4 is used to reduce the stress concentration at the root of the helical convex arc tooth.

The meshing of described spiral arc gear 6 and arc rack 8, the contact line formed on the spiral arc gear and the centerline 3 of the spiral convex arc teeth at the meshing point are all cylindrical helical lines with equal lift distance, and the meshing point The contact line formed on the arc rack and the center line 9 of the concave arc tooth groove are both inclined straight lines.

In this embodiment, the driver is a motor, and the rotation direction is counterclockwise, which drives the helical arc gear to drive counterclockwise to realize the horizontal movement of the arc rack to the left. The driver is installed on the driver mounting base 2, and the driver mounting base is fixed.

Referring to Figures 2 and 3, spiral convex arc teeth 5 are uniformly distributed on the outer surface of the spiral arc gear 6, the diameter of the base cylinder of the spiral arc gear is d _b , and the maximum outer diameter is D ₁ .

Referring to Figures 1 and 4, set the total length of the arc rack 8 as L, the width as B, and the thickness as T, the normal arc radius of the concave arc tooth groove 7 is ρ ₂ , and the spiral convex arc tooth 5 and There is a gap between the concave arc tooth grooves 7, and the coefficient of the tooth groove gap is k.

The installation method of the spiral arc gear 6 and the arc rack 8 is as follows: the upper surface of the arc rack with the concave arc tooth groove 7 faces upward, and the rotation axis of the spiral arc gear must be parallel to the upper surface of the arc rack , and perpendicular to the long side of the arc rack, the vertical distance from the rotation axis of the spiral arc gear to the upper surface of the arc rack is a fixed value a.

The meshing of the spiral convex arc tooth 5 and the concave arc tooth groove 7 of the utility model is a space curve meshing mode, and its meshing transmission is a point-contact convex-concave meshing meshing transmission without relative sliding, and the relative movement speed of all meshing points are all zero.

The shape and parameter equation of the spiral convex arc tooth center line 3 of the spiral arc gear 6 and the concave arc tooth groove center line 9 of the arc rack 8 in the mechanism of the utility model are determined by the following method: referring to Fig. 5 of the utility model Schematic diagram of the spatial coordinate system of the convex-concave meshing rack-and-pinion mechanism.

In o--x, y, z and o _p --x _p , y _p , z _p two fixed space coordinate systems, the z axis coincides with the rotation axis of the spiral arc gear, the x and x _p axes coincide, and the y axis is parallel to _{y p} axis, z _axis is parallel to z _p axis, the distance between coordinate origin o and o _p is _{a ;} o ₂ --x ₂ , y ₂ , z ₂ are fixedly connected to the arc rack, and the y _p axis coincides with the y ₂ axis; at the initial position, the coordinate system o ₁ --x ₁ , y ₁ , z ₁ and o ₂ --x ₂ , y ₂ , z ₂ coincide with the coordinate system o--x, y, z and o _p --x _p , y _p , z _p respectively, and the spiral arc gear revolves around the z axis at a uniform angular velocity ω ₁ Rotate, the arc rack moves parallelly along the opposite direction of the y _p axis at a constant speed v ₂ , after a period of time from the initial position, the coordinate system o ₁ --x ₁ , y ₁ , z ₁ and o ₂ --x ₂ , y ₂ , z ₂ move separately, at this time the meshing point is M, and the spiral arc gear rotates around the z axis Angle, the circular arc rack moves parallelly along the opposite direction of the y _p axis for a distance of s ₂ .

Suppose the contact line formed by all the meshing points on the given helical arc gear is C ₁ , and the parameter equation of C ₁ is:

Among them: t—is the parameter variable of the cylindrical helix with equal lift distance, and t≥0, its value range is △t>0, β is the helix angle of the contact line C ₁ of the helical arc gear, d ₁ is the diameter of the helix with contact line C ₁ ;

Assuming that the contact line of the concave arc tooth groove formed on the given arc rack is C ₂ , the relative movement speed of the meshing point M of the conjugate contact line C ₁ and C ₂ of the arc gear rack mechanism must satisfy the meshing condition: ν ₁₂ =0 (2)

In the above formula, ν ₁₂ is the relative velocity of the meshing point M;

The space coordinate transformation matrix M ₂₁ is:

In the above matrix, is the angle that the spiral arc gear rotates around the z axis;

s ₂ is the parallel movement distance of the arc rack along the opposite direction of the _yp axis;

a is the distance of oo _p , that is, the installation distance between the arc gear and the arc rack;

According to the space coordinate transformation matrix and meshing conditions, the parameter equation of the contact line C2 _on the arc rack is obtained as:

It can be seen from formula (1) and formula (6) that in the circular arc gear rack mechanism satisfying the principle of space curve meshing, the condition that a pair of conjugate meshing contact lines must satisfy is: the helix angle of the contact line of the helical arc gear 6 Must be equal to the inclination angle of the contact line on the arc rack 8 and the direction of rotation is opposite. At the same time, the normal pitch of the uniform contact line on the spiral arc gear must be equal to the normal direction of the uniform contact line on the arc rack pitch. At this time, the relative speed of all meshing points is zero, and the meshing points form a straight meshing line parallel to the z-axis in the fixed coordinate system o--x, y, z.

Thus, the helical convex arc tooth centerline 3 of the helical arc gear of this mechanism is the equal pitch cylindrical helix with the same helical parameters as the contact line _C1 on the helical arc gear, and its parameter equation is:

Thus, the concave arc tooth groove center line 9 of the arc rack 8 of this mechanism is a straight line with the same inclination angle as the contact line C ₂ on the arc rack, and its parameter equation is:

Among them, _ρ2 is the normal arc radius of the concave arc tooth groove of the arc rack.

The normal modulus of the spiral arc gear and arc rack of this mechanism is m _n , and the values of m _n are 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.8, 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50, the unit is mm;

The normal pitch between the spiral arc gear and the arc rack is p _n , p _n = πm _n (9)

The normal arc radius of the concave arc tooth groove of the arc rack in this mechanism is ρ ₂ ,

The inclination angle of the center line of the concave arc tooth groove of the arc rack is equal to the helix angle β of the spiral arc gear, The unit is in radians. The thickness of the arc rack is T, and T>0.

The total length of the arc rack is L, and L>0. with width B,

The number of teeth of the spiral arc gear in this mechanism is Z ₁ , and Z ₁ is an integer greater than or equal to 1.

The helix angle of the helical arc gear is the helix angle β of the contact line of the helical arc gear, The unit is radians.

The spiral diameter of the center line of the spiral convex arc tooth of the spiral arc gear is d ₁ ,

The tooth width B of the spiral arc gear is equal to the width of the arc rack.

The normal arc radius of the spiral convex arc tooth of the spiral arc gear is ρ ₁ , ρ ₁ =kρ ₂ (14)

Among them, k is the cogging clearance coefficient, 0.8≤k≤1

The maximum outer diameter of the spiral arc gear is D ₁ , D ₁ =d ₁ +2ρ ₁ (15)

The diameter of the base cylinder of the helical arc gear is d _b : the approximate formula d _b =d ₁ -ρ ₁ (16)

d _b is calculated using an approximate formula because if d _b is set too small, the bending strength of the root of the helical convex circular arc will decrease, so d _b =d ₁ -ρ ₁ is used for calculation.

The transition fillet radius between the helical convex arc teeth of the helical arc gear and the outer surface of the base cylinder of the helical arc gear is r ₁ , and r ₁ >0.

The installation distance between the spiral arc gear and the arc rack in this mechanism is a,

The coincidence degree of the spiral arc gear and the arc rack in this mechanism is determined by the number of teeth Z ₁ of the spiral arc gear and the value range Δt of the helical parameter t, the coincidence degree is ε, and the expression is

Where: x, y, z, x ₁ , y ₁ , z ₁ , x ₂ , y ₂ , z ₂ , s ₂ , x _p , y _p , z _p , a, B, T, D ₁ , d ₁ , d _b , r ₁ The unit of length or distance is mm; and β angle units are radians;

When the basic parameter modulus m _n , helix angle β and its direction of rotation and clearance coefficient k are determined, the normal section shape of the tooth profile of the concave arc tooth groove and the helical convex arc tooth can be determined, and then the helix parameter is given When t and its value range △t, the transition fillet radius r ₁ , the number of teeth Z ₁ of the spiral arc gear, the length L of the arc rack and the thickness T of the arc rack, the distance between the spiral arc gear and the arc rack The structure and the installation distance a are also determined accordingly, so that a convex-concave meshing circular arc gear rack mechanism with no relative sliding is obtained.

The spiral convex arc teeth 5 evenly distributed on the outer surface of the spiral arc gear 6 in this mechanism is a spiral convex circle formed by a circle with _a radius of ρ and making its center move vertically along the center line 3 of the spiral convex arc teeth Arc tooth; the concave arc tooth groove ₇ uniformly distributed on the upper surface of the arc tooth bar is a circle with a radius of ρ and makes its center move vertically along the center line of the concave arc tooth groove on the arc tooth bar The concave arc tooth groove formed.

When in the above formula: the relevant parameters are respectively set as: m _n = 4 mm, Z ₁ = 4,

dextrorotation, k=0.8, _r1 = 0.5 mm

Substituting formula (7) to obtain the spiral convex arc tooth center line equation in the present embodiment is:

Substituting into formula (8) to obtain the centerline equation of the concave circular arc tooth groove in the present embodiment is:

Substitution , to obtain the coincidence degree of the arc rack and pinion mechanism

According to the values of the above-mentioned relevant parameters, the diameter d _b of the base cylinder of the spiral arc gear can be obtained as 29.5 millimeters, the maximum outer diameter D ₁ is 38.3 millimeters, and the normal arc radius ρ ₁ of the spiral convex arc tooth = _0.8π mm, the tooth width B is 40 mm, the normal arc radius ρ ₂ of the concave arc tooth groove 7 = π mm, and then the uniformly distributed The spiral convex arc gear 5 on the base cylinder can determine the structural shape of the spiral arc gear 6 .

Set the total length L of the arc rack as 300 mm, and the thickness T of the arc rack as 30 mm. According to the equation of the center line of the concave arc tooth groove and the data such as the normal pitch p _n , the arc rack 8 can be determined Structural shape. At the same time, it can be obtained that the installation distance a between the spiral arc gear 6 and the arc rack 8 is 16 mm.

According to the calculated shape parameters of the spiral arc gear 6 and the arc rack 8 and the equation of the spiral convex arc gear 5 and the center line of the concave arc tooth groove, the gear with no relative sliding of the convex-concave meshing type can be obtained The appearance of the rack mechanism and correct assembly.

When the driver 1 drives the spiral arc gear 6 to rotate, since the coincidence degree ε>2 when the spiral arc gear 6 and the arc rack 8 are installed, it indicates that there are at least two pairs of spiral convex arc teeth during the meshing transmission process. 5 is in meshing state with the concave arc tooth groove 7, so the continuous and stable meshing transmission of the convex-concave meshing rack and pinion mechanism is realized.

Embodiment 2: The utility model provides a rack-and-pinion mechanism with convex-concave meshing without relative sliding. Its structure is shown in FIG. Driven to rotate, through the continuous meshing effect between the spiral convex arc teeth 5 and the concave arc tooth grooves 7, the spiral arc gears move in parallel while rotating, that is, the spiral arc gears move purely on the arc racks. scroll. When the spiral arc gear and the arc rack are installed, the spiral convex arc tooth 5 on the spiral arc gear and a concave arc tooth groove 7 on the arc rack are in meshing state, and as the spiral arc gear rotates, the spiral The coincidence degree of convex arc tooth and concave arc tooth groove meshing is greater than 1, so as to realize the continuous and stable meshing transmission of the convex-concave meshing gear rack mechanism without relative sliding.

Relevant parameters are respectively set as: m _n =2 mm, Z ₁ =6, left-handed, k=0.8, r ₁ =0.5 mm,

The equation of the center line of the spiral convex arc tooth in the present embodiment is obtained by the transformation of formula (7):

The equation of the center line of the concave circular arc tooth groove in the present embodiment obtained by the transformation of formula (8) is:

substitute Obtain the degree of coincidence between the meshing of the spiral convex arc teeth and the concave arc grooves of the mechanism

According to the values of the above-mentioned relevant parameters, the diameter d _b of the base cylinder of the spiral arc gear can be obtained as 15.7 millimeters, the maximum outer diameter D ₁ is 19.5 millimeters, and the normal arc radius ρ ₁ of the spiral convex arc tooth = 0.4πmm, the tooth width B is 40mm, the normal arc radius ρ ₂ of the concave arc tooth groove = 0.5π mm, and then the obtained spiral convex arc tooth centerline equation and the number of teeth Z ₁ can construct a uniform The spiral convex arc teeth 5 arranged on the base cylinder can determine the structural shape of the spiral arc gear 6 . Since the designed coincidence degree ε>4, it indicates that at least four pairs of helical convex circular arc teeth 5 and concave circular arc tooth grooves 7 are in meshing state during the meshing transmission process, so the continuous convex-concave meshing rack and pinion mechanism is realized. Stable meshing transmission, at the same time, the load on each pair of teeth is greatly reduced, and the transmission is more stable and reliable.

Set the total length L of the arc rack as 500 mm, and the thickness T of the arc rack as 15 mm. According to the concave arc tooth groove center line equation and the normal tooth pitch p _n and other data, the arc rack 8 can be determined Structural shape. At the same time, the installation center distance a between the spiral arc gear 6 and the arc rack 8 can be obtained as mm.

The convex-concave meshing rack and pinion mechanism of the utility model has the advantages of no relative sliding and no undercutting, high transmission efficiency, high coincidence degree, strong bearing capacity, and can greatly simplify the structure of conventional gear mechanisms and micromechanical transmission devices , suitable for applications in the field of micro, micro machinery and conventional machinery.

Claims (1)

1. a kind of relative pinion and rack slided of engagement type nothing of male-female, including a pair of transmissions of gear and rack composition, Gear is spiral arc gear, and spiral arc gear outer surface is evenly equipped with spiral prominence circle-arc tooth, and rack is recessed to be evenly distributed in the upper surface The arc rack of circular arc teeth groove, spiral prominence circle-arc tooth and concave arc tooth socket fit；Described spiral arc gear outer surface and spiral shell Knuckle is provided between rotation dome curved tooth to concentrate to reduce Root Stress；It is characterized in that：Described spiral arc gear The rotary shaft of driver is connected by spiral arc gear center hole, the rotation of driver is axial clockwise or counterclockwise, Spiral arc gear is driven to rotate clockwise or counterclockwise；Spiral arc gear and arc rack engagement system engage for male-female Formula, its engaged transmission slidably engage transmission relatively for the nothing of point contact；

Described spiral arc gear engages with arc rack, the contact line and spiral shell that meshing point is formed on spiral arc gear Dome curved tooth center line is revolved, the lift circular helix such as is, the contact line and concave arc that meshing point is formed on arc rack Tooth space centerline is angled straight lines；

Gap is provided between described spiral prominence circle-arc tooth and concave arc teeth groove；

The drive mechanism of a pair of transmissions of described spiral arc gear and arc rack composition is driving for spiral arc gear Rotated under the drive of dynamic device, by the continuous engagement between spiral prominence circle-arc tooth and concave arc teeth groove, for realizing circular arc Rack moves in parallel；Or arc rack is fixed, spiral arc gear rotates under the drive of driver, passes through spiral prominence circular arc Continuous engagement between tooth and concave arc teeth groove so that the axis of spiral arc gear carries out parallel shifting while rotation It is dynamic, for realizing that male-female of the spiral arc gear along arc rack engages pure rolling.