LINE GEAR MECHANISM HAVING VARIABLE TRANSMISSION RATIO

Abstract

The present invention is a variable-ratio line gear mechanism. The mechanism forms a transmission pair consisting of a driving line gear and a driven line gear, of which axes intersect at an arbitrary angle. Transmission is generated by point contact meshing movement of line teeth between the driving line gear and the driven line gear. A contact curve of the line tooth is designed in accordance with space conjugate curve meshing theory, and the designing equation is divided into an equal transmission ratio part and a variable transmission ratio part. The equal transmission ratio part provides a uniform transmission, and the variable transmission ratio part makes the transmission ratio smoothly transit. The line gear mechanism is able to provide periodically transmission with variable transmission ratio, to provide a plurality of transmission ratios during a movement period of the driven line gear, and to enable smooth transitions between respective transmission ratios in accordance with movement rules.

Claims

1. A variable-ratio line gear mechanism, characterized in that, the mechanism forms a transmission pair consisting of a driving line gear and a driven line gear, of which axes intersect at an arbitrary angle, the driving line gear consisting of a wheel body and line teeth, the driven line gear consisting of a wheel body and line teeth, contact curves of the line tooth of the driving line gear and the line tooth of the driven line gear meshing in accordance with a pair of space conjugate curves, the driving line gear being connected with an actuator to provide an input, there being one or more line teeth on the driving line gear, the line tooth of the driving line gear being meshed with the line tooth of the driven line gear by point contact, the driven line gear being connected with an output end to provide a movement or an output of force, the line tooth on the driven line gear being the one with property of variable transmission ratio, so that in one movement period, a plurality of transmission ratios exist, and a smooth transition among different transmission ratios can be made, resulting in a transmission with periodically variable transmission ratio.

2. The variable-ratio line gear mechanism according to claim 1, wherein the contact curve on the line tooth of the driving line gear for meshing is a circular helix, the line tooth of the driven line gear is divided into an equal transmission ratio part and a variable transmission ratio part, and there are two equations for the contact curve on the line tooth for meshing: one is an equal transmission ratio equation for realizing equal transmission ratio, and the other one is a variable transmission ratio equation for realizing variable transmission ratio.

3. The variable-ratio line gear mechanism according to claim 2, wherein during the transmission of said mechanism, the variable transmission ratio equation can make the transmission ratio of the line gear smoothly change from one value to another, i.e. a derivative value of transmission ratio function increases or decreases from 0 to a certain value, and then smoothly back to 0.

4. The variable-ratio line gear mechanism according to claim 3, wherein said variable transmission ratio equation is determined as follows: O−xyz is a Cartesian coordinate system that is arbitrarily fixed in space, O is an origin of the coordinate system O−xyz x, y, z are three coordinate axes of the coordinate system O−xyz, a Cartesian coordinate system O.sub.p−x.sub.py.sub.pz.sub.p is determined in accordance with a position of the coordinate system O−xyz, a plane x.sub.pO.sub.pz.sub.p is in a same plane as a plane xOz, a distance from a coordinate origin O.sub.p to the axis z is a, a distance from O.sub.p to the axis X is b, an angle between the axis z and an axis z.sub.p is (π−θ), θ is an angle between angular velocity vectors of the driving and driven line gears, with 0°≦θ≦180°, and coordinate systems O.sub.1−x.sub.1y.sub.1z.sub.1 and O.sub.2−x.sub.2y.sub.2z.sub.2 are respectively the coordinate systems fixed on the driving line gear and the driven line gear; during transmission, the driving line gear and driven line gear rotate around the axis z and the axis z.sub.p respectively, and an initial meshing place of the driving line gear and the driven line gear is an initial position; at the initial position, coordinate systems O.sub.1−x.sub.1y.sub.1z.sub.1 and O.sub.2−x.sub.2y.sub.2z.sub.2 coincide with the coordinate systems O−xyz and O.sub.p−x.sub.py.sub.pz.sub.p, respectively; at any time, the origin O.sub.1 coincides with O, an axis z.sub.1 coincides with the axis z, the origin O.sub.2 coincides with O.sub.p, an axis z.sub.2 coincides with the axis z.sub.p, the driving line gear rotates around the axis z at a uniform angular velocity ω.sub.1, angular velocity direction of the driving line gear is a negative direction of the axis z, and an angle that the driving line gear rotates through around the axis z is φ.sub.1; the driven line gear rotates around the axis z.sub.p at a uniform angular velocity z.sub.p, angular velocity direction of the driven line gear is a negative z.sub.p direction of the axis z.sub.p, an angle that the driven line gear rotates through around the axis z.sub.p is φ.sub.2, then an equation of the driving contact curve is as follows in the coordinate system O.sub.1−x.sub.1y.sub.1z.sub.1: $\{\begin{array}{c}{x}_M^{\left(1\right)}=m.Math..Math.\cos .Math..Math.t\\ y_M^{\left(1\right)}=m.Math..Math.\sin .Math..Math.t\\ z_M^{\left(1\right)}=n.Math..Math.\pi +\mathrm{nt}\end{array}.Math..Math.\left(-\pi \le t\le -\frac{\pi }{2}\right),$ and then an equation for variable transmission ratio contact curve is: $\hspace{1em}\{\begin{array}{c}{x}_M^{\left(2\right)}=\left[\left(m-a\right).Math..Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +\mathrm{nt}-b\right).Math..Math.\sin .Math..Math.\theta \right].Math..Math.\cos .Math..Math.{\varphi }_2\\ y_M^{\left(2\right)}=-\left[\left(m-a\right).Math..Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +\mathrm{nt}-b\right).Math..Math.\sin .Math..Math.\theta \right].Math..Math.\sin .Math..Math.{\varphi }_2\\ z_M^{\left(2\right)}=-\left(m-a\right).Math..Math.\sin .Math..Math.\theta -\left(n.Math..Math.\pi +\mathrm{nt}-b\right).Math..Math.\cos .Math..Math.\theta \\ {\varphi }_2=-\frac{{A\left({\varphi }_b-{\varphi }_a\right)}^2}{{\pi }^2}.Math.\sin .Math..Math.\frac{\pi \left({\varphi }_1-{\varphi }_a\right)}{{\varphi }_b-{\varphi }_a}+C.Math..Math.{\varphi }_1\end{array}$ wherein, A and C are determined by equations $\frac{d.Math..Math.{\varphi }_2\left({\varphi }_a\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_a}.Math..Math.\mathrm{and}.Math..Math.\frac{d.Math..Math.{\varphi }_2\left({\varphi }_b\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_b},$ m is a helical radius of the contact curve of the driving line gear, n is a parameter of the contact curve of the driving line gear related to a pitch, with $n=\frac{p}{2.Math.\pi }$ being defined if the pitch is p, and t is a parameter, with $-\pi \le t\le -\frac{\pi }{2}$ representing that the contact curve of one line tooth of the driving line gear is a helix of ¼ circumference; when t=−π, the line teeth of the driving line gear and driven line gear begin to mesh; when $t=-\frac{\pi }{2},$ the driving line gear rotates through ¼ circumference, and the line teeth of the driving line gear and driven line gear mesh to an end and begin to demesh; i.sub.a and i.sub.b are respectively the transmission ratio before and after some period of change process; φ.sub.a and φ.sub.b are respectively a start angle and an end angle of some line tooth of the driving line gear during transmission in a variable transmission ratio process, for example, when $-\pi <t<-\frac{\pi }{2},{\varphi }_b-{\varphi }_a=\frac{\pi }{2}.$

5. The variable-ratio line gear mechanism according to claim 2, wherein during the transmission of said mechanism, in order to reduce the rotation and jumpiness of the operation of said mechanism, derivative of the variable transmission ratio equation can also transit smoothly, i.e. second derivative of the variable transmission ratio equation increases or decreases from 0 to a certain value, and then smoothly back to 0.

6. The variable-ratio line gear mechanism according to claim 5, wherein said equation for variable transmission ratio contact curve can be expressed as: $\hspace{1em}\{\begin{array}{c}{x}_M^{\left(2\right)}=\left[\left(m-l_1\right).Math..Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +\mathrm{nt}-l_2\right).Math..Math.\sin .Math..Math.\theta \right].Math..Math.\cos .Math..Math.{\varphi }_2\\ y_M^{\left(2\right)}=-\left[\left(m-l_1\right).Math..Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +\mathrm{nt}-l_2\right).Math..Math.\sin .Math..Math.\theta \right].Math..Math.\sin .Math..Math.{\varphi }_2\\ z_M^{\left(2\right)}=-\left(m-l_1\right).Math..Math.\sin .Math..Math.\theta -\left(n.Math..Math.\pi +\mathrm{nt}-l_2\right).Math..Math.\cos .Math..Math.\theta \\ {\varphi }_2=\frac{{E\left({\varphi }_b-{\varphi }_a\right)}^3}{8.Math.{\pi }^3}.Math.\cos .Math..Math.\frac{\pi \left({\omega }_1.Math.t_1-{\varphi }_a\right)}{{\varphi }_b-{\varphi }_a}+\frac{F}{2}.Math.{\left({\omega }_1.Math.t_1\right)}^2+G.Math..Math.{\omega }_1.Math.t_1\\ {\varphi }_1=t+\pi \end{array}$ wherein, E, F and G are determined by equations $\frac{{d.Math.}^2.Math.{\varphi }_2\left({\varphi }_b\right)}{d.Math..Math.{\varphi }_1^2}=0,\frac{d.Math..Math.{\varphi }_2\left({\varphi }_a\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_a},.Math.\mathrm{and}.Math..Math.\frac{d.Math..Math.{\varphi }_2\left({\varphi }_b\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_b},$ m is a helical radius of the contact curve of the driving line gear, n is a parameter of the contact curve of the driving line gear related to a pitch, with $n=\frac{p}{2.Math.\pi }$ being defined if the pitch is p, and t is a parameter, with $-\pi \le t\le -\frac{\pi }{2}$ representing that the contact curve of one line tooth of the driving line gear is a helix of ¼ circumference; when t=−π, the line teeth of the driving line gear and driven line gear begin to mesh; when $t=-\frac{\pi }{2},$ the driving line gear rotates through ¼ circumference, and the line teeth of the driving line gear and driven line gear mesh to an end and begin to demesh; i.sub.a and i.sub.b are respectively the transmission ratio before and after some period of change process; φ.sub.a and φ.sub.b are respectively a start angle and an end angle of some line tooth of the driving line gear during transmission in a variable transmission ratio process, for example, when $-\pi <t<-\frac{\pi }{2},{\varphi }_b-{\varphi }_a=\frac{\pi }{2};$ and the variable transmission ratio equations created in accordance with claims 5 and 6 may be used in the variable-ratio line gear mechanism.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] FIG. 1 is the coordinate system of the mechanism according to the present invention.

[0025] FIG. 2 is two embodiments according to the present invention, including the driving line gear and driven line gear.

[0026] FIG. 3 is the embodiment of the driven line gear according to the present invention.

[0027] FIG. 4 is the establishment method of the line tooth entity.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0028] The present invention is further described below in combination with the drawings, but the implementations of the present invention are not limited hereto.

[0029] 1. A variable-ratio line gear mechanism described in the present invention comprises a driving line gear and a driven line gear. Coordinate systems of the driving line gear and driven line gear, which are shown in FIG. 1, are used for establishing a contact curve equation of a line tooth of the line gear.

[0030] As shown in FIG. 1, O−xyz and O.sub.p−x.sub.py.sub.pz.sub.p are fixed Cartesian coordinate systems, and O.sub.p−x.sub.py.sub.pz.sub.p is determined in accordance with a position of O−xyz: a plane x.sub.pO.sub.pz.sub.p is in a same plane as a plane xOz, a distance from O.sub.p to the axis z is a, a distance from O.sub.p to the axis x is b, and an angle between the axis z and an axis z.sub.p is (π−θ). θ is an angle between angular velocity vectors of the driving and driven line gears.

[0031] O.sub.1−x.sub.1y.sub.1z.sub.1 and O.sub.2−x.sub.2y.sub.2z.sub.2 are respectively the coordinate systems fixed on the driving line gear and the driven line gear. During transmission, the driving line gear and driven line gear rotate around the axis z and the axis z.sub.p, respectively.

[0032] 2. The variable-ratio line gear mechanism is shown in FIG. 2a and FIG. 2b. The left one is the driving line gear 1. On the driving line gear, a line tooth 2 of the driving line gear is provided. The right one is the driven line gear 3.

[0033] As shown in FIG. 3, line teeth 4 and 5 with equal transmission ratio and line teeth 6 and 7 with variable transmission ratio are provided on the driven line gear. When the driving line gear and driven line gear mesh to the line teeth 4 and 5 with equal transmission ratio, the transmission ratio is i.sub.a and i.sub.b. When they mesh to the line teeth 6 and 7 with variable transmission ratio, the transmission ratios smoothly transits from i.sub.a to i.sub.b, and smoothly transits from i.sub.b to i.sub.a, respectively. However, the implementations of the present invention are not limited hereto.

[0034] An equation designing the above-described line teeth with equal transmission ratio and variable transmission ratio is determined by the following equations.

[0035] The line tooth of the driving line gear is determined by its contact curve equation. The equation of the contact curve in O.sub.1−x.sub.1y.sub.1z.sub.1 is:

[00014]$\begin{array}{cc}\{\begin{array}{c}{x}_M^{\left(1\right)}=m.Math..Math.\cos .Math..Math.t\\ y_M^{\left(1\right)}=m.Math..Math.\sin .Math..Math.t\\ z_M^{\left(1\right)}=n.Math..Math.\pi +n.Math..Math.t\end{array}.Math.\left(-\pi \le t\le -\frac{\pi }{2}\right)& \left(1\right)\end{array}$

[0036] The line tooth of the driven line gear is determined by its contact curve equation. The driven contact curve is calculated by the contact curve of the line tooth of the driving line gear and a space curve meshing theory, and its equation in O.sub.2−x.sub.2y.sub.2z.sub.2 is as follows:

[0037] When the transmission ratio is i, the contact curve equation on the line tooth with equal transmission ratio is:

[00015]$\begin{array}{cc}\{\begin{array}{c}{x}_M^{\left(2\right)}=\left[\left(m-a\right).Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-b\right).Math.\sin .Math..Math.\theta \right].Math.\cos \left(\frac{t+\pi }{i}\right)\\ y_M^{\left(2\right)}=-\left[\left(m-a\right).Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-b\right).Math.\sin .Math..Math.\theta \right].Math.\sin \left(\frac{t+\pi }{i}\right)\\ z_M^{\left(2\right)}=-\left(m-a\right).Math.\sin .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-b\right).Math.\cos .Math..Math.\theta \end{array}& \left(2\right)\end{array}$

[0038] When the transmission ratio is i.sub.a to i.sub.b, there may be two forms of the contact curve equation on the variable-ratio line gear mechanism, one is:

[00016]$\begin{array}{cc}\{\begin{array}{c}{x}_M^{\left(2\right)}=\left[\left(m-a\right).Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-b\right).Math.\sin .Math..Math.\theta \right].Math.\cos .Math..Math.{\varphi }_2\\ y_M^{\left(2\right)}=-\left[\left(m-a\right).Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-b\right).Math.\sin .Math..Math.\theta \right].Math.\sin .Math..Math.{\varphi }_2\\ z_M^{\left(2\right)}=-\left(m-a\right).Math.\sin .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-b\right).Math.\cos .Math..Math.\theta \\ {\varphi }_2=\frac{{A\left({\varphi }_b-{\varphi }_a\right)}^2}{{\pi }^2}.Math.\sin .Math.\frac{\pi \left({\varphi }_1-{\varphi }_a\right)}{{\varphi }_b-{\varphi }_a}+C.Math..Math.{\varphi }_1\end{array}& \left(3\right)\end{array}$

[0039] wherein, A and C is determined by:

[00017]$\begin{array}{cc}\frac{d.Math..Math.{\varphi }_2\left({\varphi }_a\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_a}& \left(4\right)\\ \frac{d.Math..Math.{\varphi }_2\left({\varphi }_b\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_b}.& \left(5\right)\end{array}$

[0040] The other one is:

[00018]$\begin{array}{cc}\{\begin{array}{c}{x}_M^{\left(2\right)}=\left[\left(m-l_1\right).Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-l_2\right).Math.\sin .Math..Math.\theta \right].Math.\cos .Math..Math.{\varphi }_2\\ y_M^{\left(2\right)}=-\left[\left(m-l_1\right).Math.\cos .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-l_2\right).Math.\sin .Math..Math.\theta \right].Math.\sin .Math..Math.{\varphi }_2\\ z_M^{\left(2\right)}=-\left(m-l_1\right).Math.\sin .Math..Math.\theta -\left(n.Math..Math.\pi +n.Math..Math.t-l_2\right).Math.\cos .Math..Math.\theta \\ {\varphi }_2=\frac{{E\left({\varphi }_b-{\varphi }_a\right)}^3}{8.Math.{\pi }^3}.Math.\cos .Math.\frac{\pi \left({\omega }_1.Math.t_1-{\varphi }_a\right)}{{\varphi }_b-{\varphi }_a}+\frac{F}{2}.Math.{\left({\omega }_1.Math.t_1\right)}^2+G.Math..Math.{\omega }_1.Math.t_1\\ {\varphi }_1=t+\pi \end{array}& \left(6\right)\end{array}$

[0041] wherein, E, F and G are determined by:

[00019]$\begin{array}{cc}\frac{d^2.Math.{\varphi }_2\left({\varphi }_b\right)}{d.Math..Math.{\varphi }_1^2}=0& \left(7\right)\\ \frac{d.Math..Math.{\varphi }_2\left({\varphi }_a\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_a}& \left(8\right)\\ \frac{d.Math..Math.{\varphi }_2\left({\varphi }_b\right)}{d.Math..Math.{\varphi }_1}=\frac{1}{i_b}& \left(9\right)\end{array}$

[0042] The physical meaning of each parameter in the equations is as follows:

[0043] m is a helical radius of the contact curve of the driving line gear;

[0044] n is a parameter of the contact curve of the driving line gear related to a pitch, with

[00020]$n=\frac{p}{2.Math.\pi }$

[0045] being defined if the pitch is p;

[0046] t is a parameter, with

[00021]$-\pi \le t\le -\frac{\pi }{2}$

representing that the contact curve of one line tooth of the driving line gear is a helix of ¼ circumference. When t=−π, the line teeth of the driving line gear and driven line gear begin to mesh; when

[00022]$t=-\frac{\pi }{2},$

the driving line gear rotates through ¼ circumference, and the line teeth of the driving line gear and driven line gear mesh to an end and begin to demesh;

[0047] a and b are position parameters of the driving line gear and driven line gear, as shown in FIG. 1;

[0048] θ is an angle parameter of the driving line gear and driven line gear, as shown in FIG. 1;

[0049] i.sub.a and i.sub.b are two transmission ratios which are required;

[0050] φ.sub.1 is a rotation angle of the driving line gear;

[0051] φ.sub.2 is a rotation angle of the driven line gear;

[0052] φ.sub.a and φ.sub.b are respectively a start angle and an end angle of some line tooth of the driving line gear during transmission in a variable transmission ratio process, for example, when

[00023]$-\pi <t<-\frac{\pi }{2},{\varphi }_b-{\varphi }_a=\frac{\pi }{2}.$

[0053] 3. In accordance with equations (1) to (3), it is possible to establish a line tooth entity. The line tooth entity only needs to meet the strength requirement, and line tooth entity itself does not have any specific shape requirement. As shown in FIG. 4, at each meshing point, a certain bulk is inversely extended respectively at both side (−γ.sub.1 and γ.sub.1 in FIG. 4) of the contact direction of the driving and driven line teeth, that the required line teeth can be generated. A wheel body is used to fix and connect the line teeth.