CN114611244B - Double-planet-carrier non-circular gear train transplanting mechanism design method based on variable rod length - Google Patents
Double-planet-carrier non-circular gear train transplanting mechanism design method based on variable rod length Download PDFInfo
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- A01—AGRICULTURE; FORESTRY; ANIMAL HUSBANDRY; HUNTING; TRAPPING; FISHING
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- A01C11/00—Transplanting machines
- A01C11/003—Transplanting machines for aquatic plants; for planting underwater, e.g. rice
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- A01—AGRICULTURE; FORESTRY; ANIMAL HUSBANDRY; HUNTING; TRAPPING; FISHING
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- A01C11/00—Transplanting machines
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
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- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
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- F16H55/02—Toothed members; Worms
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
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Abstract
The invention discloses a double-planet-carrier non-circular gear system transplanting mechanism design method based on variable rod length. The existing method for designing the double-planet-carrier wheel train transplanting mechanism is high in solving difficulty, and the solved mechanism is generally large in vibration and not large in attitude angle. The invention develops the reverse design of the plane chain-opening mechanism based on the track, obtains the length of each rod and the corresponding angular displacement, and ensures the realization of an ideal track; the virtual rod of the plane open-chain mechanism is expanded into a second rod and a third rod by combining posture information of key positions on the track, namely the third rod is obtained by taking key position points on the track as end points and taking a posture angle as an inclination angle, the third rod is an executive component, the length is known, the length of the second rod is variable, and the posture requirements of different positions are met; and finally, fitting the angular displacement corresponding to different rods and distributing the transmission ratio to complete the design of the non-circular gear. The invention adopts the variable center distance non-circular gear pair to realize the requirement of variable rod length, the change of the center distance enables the obtained seedling taking angle, seedling pushing angle and track of the transplanting mechanism to be more ideal, and the solution is easy.
Description
Technical Field
The invention relates to a planetary gear train transplanting mechanism design method, in particular to a double-planet-carrier non-circular gear train transplanting mechanism design method based on variable rod length.
Background
Compared with the traditional mechanical transplanting of blanket seedlings, the mechanical transplanting of the rice pot seedlings has the advantages of no root damage, no seedling revival period, capability of shortening the growing period and the like, and has important significance for promoting the increase of the rice yield and expanding the applicable planting area of a high-latitude planting area. The existing transplanting mechanism mainly takes a single planet carrier structure as a main part, and due to the structure limitation, the single planet carrier gear train mechanism is difficult to give consideration to seedling taking and seedling planting actions (or track shape and operation posture) when describing a complex transplanting track. The transplanting mechanism with the double-planet-carrier wheel train configuration design can better realize ideal track attitude requirements and better roundness of the generated non-circular gear, but the existing design method has the problems that complicated constraint conditions need to be given and complicated equations need to be solved, in addition, the realization mechanisms all adopt fixed shafts, and the attitude angle needs to be improved; in the prior art, a double-planet-carrier vegetable pot seedling transplanting mechanism or a cam transmission type double-planet-carrier transplanting mechanism which adopts the combination transmission of a non-circular gear and a link mechanism is also limited by the structure and generally has the defects of large vibration, low operating efficiency and the like. In conclusion, the double-planet-carrier-train transplanting mechanism can effectively meet the requirements of complex transplanting track postures and round transmission non-circular gears, but the defects of large solving difficulty, large vibration, insufficient posture angle and the like generally existing in the conventional mechanism transmission limited by the structure limit are overcome, and the development and application research of the double-planet-carrier-train transplanting mechanism is limited.
Disclosure of Invention
The invention aims to provide a transplanting mechanism design method of a double-planet-carrier non-circular gear differential gear train based on variable rod length aiming at the defects of the prior art, the method develops reverse design of a plane chain opening mechanism based on a track, obtains each rod length and corresponding angular displacement, and can ensure that an ideal track is realized; the virtual rod of the plane open-chain mechanism is expanded into two rods (a second rod and a third rod) by combining the posture information of the key positions on the track, namely, the key position points on the track are used as end points, the posture angle is used as an inclination angle to obtain the third rod, the third rod is used as an executive component, the length is known, and the length of the second rod is variable, so that the posture requirements of different positions are met. And finally, fitting the angular displacement corresponding to different rods and distributing the transmission ratio to complete the design of the non-circular gear, wherein the length of the second rod is changed by using a movable shaft non-circular gear pair with a variable center distance.
In order to solve the technical problems, the invention adopts the technical scheme that:
the invention relates to a method for designing a transplanting mechanism of a double-planet-carrier non-circular gear system based on variable rod length, which comprises the following specific steps:
step one, constructing a double-planet-carrier non-circular gear train transplanting mechanism based on variable rod length; the double-planet-carrier non-circular gear train transplanting mechanism based on variable rod length mainly comprises an input shaft, a first sun gear, a second sun gear, a first intermediate gear, a second intermediate gear, a third intermediate gear, a fourth intermediate gear, a first planet carrier, a first planet gear, a second planet gear, a planting arm, a planet shaft, a spring, a fourth planet gear, a bearing seat, a third planet gear and a second planet carrier; the first planet carrier is fixed with the input shaft; the first sun wheel and the second sun wheel are fixed and are sleeved on the input shaft in an empty mode; the first intermediate wheel, the second intermediate wheel, the third intermediate wheel and the fourth intermediate wheel are coaxially fixed and form a revolute pair with the first planet carrier; the first planet wheel is fixed on a planet shaft; the planet shaft and the first planet carrier form a revolute pair and are fixed with the second planet carrier; the second planet wheel and the third planet wheel are fixed and are sleeved on the planet shaft in an empty way; the planet gear IV and the bearing seat form a revolute pair; the bearing seat and the second planet carrier form a moving pair, and a spring is arranged between the bearing seat and the second planet carrier; the first intermediate wheel and the second intermediate wheel are both incomplete gears, when the first sun wheel is meshed with the first intermediate wheel, the second sun wheel is not meshed with the second intermediate wheel, and when the first sun wheel is not meshed with the first intermediate wheel, the second sun wheel is meshed with the second intermediate wheel; the middle wheel III is meshed with the planet wheel I, the middle wheel IV is meshed with the planet wheel II, and the planet wheel III is meshed with the planet wheel IV; the shell of the planting arm is fixed with the planet wheel IV; the cam of the planting arm is fixed with the bearing seat, and the rotation center line of the cam of the planting arm is coaxial with the rotation center line of the planet wheel IV;
simplifying a double-planet-carrier non-circular gear train transplanting mechanism based on variable rod length into a plane open-chain mechanism consisting of a crank AB, a rod BC, a rod CP and a sliding block, wherein the first planet carrier is equivalent to the crank AB, the second planet carrier is equivalent to the rod BC, a planting arm is equivalent to the rod CP, a bearing seat is equivalent to the sliding block, one end of the crank AB is hinged with a rack, the other end of the crank is hinged with one end of the rod BC, the sliding block and the rod BC form a sliding pair, and the rod CP is hinged with the sliding block; then, the slide block is regarded as fixed with a rod BC, the motion reverse solution of the plane open chain mechanism is carried out based on a given expected track, and the included angle from the positive direction of the x axis to a crank AB is solved
And the angle from the positive direction of the x axis to the virtual bar BP
Step three, defining the accurate postures of the seedling taking and pushing position points and the postures of a plurality of auxiliary position points as theta i I =1, 2., N is the total number of seedling taking, pushing and auxiliary position points; then calculated at θ i Length L of corresponding position of bar BC 2i And bar BC angle displacement
And the angle displacement of the rod CP
Angular displacement is obtained by cubic B spline fitting interpolation
And angular displacement
Curve, setting auxiliary position and pose as variable, L 2 The variation is at a minimum the objective function,
monotone is a constraint condition, a differential evolution algorithm is utilized to carry out parameter optimization design, and the final crank AB angular displacement is obtained
Lever BC angular displacement
And the angle displacement of the rod CP
An expression;
step four, if the third intermediate wheel and the first planet wheel are both circular gears, the transmission ratio i between the third intermediate wheel and the first planet wheel 34 =1; then according to the AB angle position of the crankMoving device
Lever BC angular displacement
And the angle displacement of the rod CP
An expression formula is adopted, the transmission ratio between the first sun wheel and the first intermediate wheel and the transmission ratio between the second sun wheel and the second intermediate wheel are solved, and a correction coefficient k is introduced to the transmission ratio i between the fourth intermediate wheel and the second planet wheel 56 And a transmission ratio i between planet gear three and planet gear four 78 The distribution is carried out to obtain the transmission ratio i between the intermediate wheel four and the planet wheel two 56 And a transmission ratio i between planet gear three and planet gear four 78 (ii) a Then, for i 1 Dividing and splicing the transmission ratio curves again to reconstruct to meet the closure requirements of the first intermediate wheel section curve and the second intermediate wheel section curve; searching and obtaining the accurate value a of the center distance between the middle wheel I and the sun wheel I by adopting a forward-backward method 1 And the precise value R of the radial direction of the intermediate wheel 12 Then obtaining the accurate value R of the first radial direction of the sun wheel 11 Angular displacement of the intermediate wheel I
Searching and calculating accurate value R of two-way diameter of intermediate wheel by adopting advancing and retreating method 22 Then obtaining the accurate value R of the two-way diameter of the sun wheel 21 (ii) a Making the included angle between the connecting line of the rotation center of the first planet carrier and the rotation center of the first intermediate wheel and the connecting line of the rotation center of the first planet carrier and the rotation center of the first planet wheel be gamma, and solving the center distance a between the rotation center of the first intermediate wheel and the rotation center of the second planet wheel 2 Then, the accurate radial value R of the planet wheel II is searched and calculated by adopting a forward and backward method 42 Then obtaining the accurate value R of the four-way diameter of the intermediate wheel 41 (ii) a Four-way radial R of planet wheel is calculated by adopting forward and backward search method 52 Then obtaining the three-way diameter R of the planet wheel 51 The exact value of (d);
and step five, solving the coordinate expressions of the pitch curves x axis and y axis of the first sun wheel, the second sun wheel, the first intermediate wheel, the second intermediate wheel, the fourth intermediate wheel, the second planet wheel, the third planet wheel, the fourth planet wheel, the third intermediate wheel and the first planet wheel.
Preferably, in the second step, the included angle from the positive direction of the x axis to the crank AB is solved
Angle from positive direction of x-axis to back of imaginary bar
The specific process is as follows:
taking several data points P in a counterclockwise direction on a given desired trajectory i I =1,2, the.. N, n is more than or equal to 6, the first data point and the last data point are overlapped, and a cubic B-spline curve interpolation fitting method is adopted to obtain n +2 control vertexes d i I =1, \8230;, n +2, then with the control vertex d i Calculating to obtain a series of discrete points P (u) on the expected track curve according to a DeBoolean recursion formula; establishing a global coordinate system Oxy, and setting L 1 Is the length of the crank AB, L is the length of the imaginary bar BP, which is the imaginary connecting bar between the hinge point B of the crank AB and the bar BC and the end point P of the bar CP,
is an included angle from the positive direction of the x axis to the crank AB,
is the included angle from the positive direction of the x axis to the virtual bar BP; during the process that the crank AB rotates around the hinge point A, the endpoint P of the virtual rod BP directionally moves along the expected track, the crank AB rotates for two circles, and the virtual rod BP walks through the whole expected track; and (3) obtaining the following parameters according to the maximum and minimum distances between the end point P and the hinge point A:
wherein x is A Is the x-axis coordinate of the hinge point A, y A Y-axis coordinate, x, of hinge point A P As the x-axis coordinate of the end point P, y P The y-axis coordinate of the endpoint P is shown, max represents the maximum value, and min represents the minimum value; end point P is at
At position, a = pi,
alpha is a value of & lt BAP, and beta is a value of included angle between a connecting line of a hinge point A and an end point P and an x axis; end point P is at
At position, a =0,
end point P is at
Is positioned to
In the time between the positions, the position of the movable part,
end point P is at
Is positioned to
In the time between the positions of the first and second gears,
wherein the content of the first and second substances,
preferably, in step three, θ i Corresponding position of the rod BC rod length L 2i BC angle displacement of the rod
And the angle displacement of the rod CP
Calculated by equations (5), (6) and (7), respectively
Wherein the hinge point C is calculated by the formula (8)
Wherein L is 3 The length of the rod CP.
Preferably, step four is as follows:
setting the transmission ratio of the second planet carrier to the first planet carrier as I 1 The transmission ratio of the rotation angle of the planting arm relative to the second planet carrier to the rotation angle of the first planet carrier is I 2 Then there is
Wherein when the first sun gear is engaged with the first intermediate gear, i 1 ＝i 11 When the second sun wheel is engaged with the second intermediate wheel, i 1 ＝i 12 ，i 11 Is the transmission ratio between the first sun wheel and the first intermediate wheel i 12 Is the transmission ratio between the second sun gear and the second intermediate gear, i 56 Representing the transmission ratio between the fourth intermediate wheel and the second planet wheel, i 78 Representing the gear ratio between planet gear three and planet gear four. According to formula (10):
introducing a correction coefficient k to a transmission ratio i 56 And (3) distributing to obtain:
wherein i 1 In an asymmetric second-order transmission ratio, when the first planet carrier rotates for 720 degrees, the first intermediate wheel and the second intermediate wheel rotate for 360 degrees in a co-rotating way, and in order to ensure the sealing requirement of the first intermediate wheel and the second intermediate wheel on the curve, the first intermediate wheel and the second intermediate wheel are applied to the i 1 The transmission ratio curve is processed as follows:
at i 1 Searching two segmentation points P on the curve 1 And P 2 Make the division point P 1 And P 2 To satisfy a transmission ratio i 1 Equal in value and satisfies the following formula:
in the formula (I), the compound is shown in the specification,
and
are respectively a division point P 1 And P 2 Of
A value;
according to the following formula:
score cut point P 1 And P 2 Satisfy the transmission ratio i 1 When the values are equal, the division point P 1 And P 2 The radial directions of the parts are also equal;
reconstruction of a new transmission ratio i 1 Curve, dividing point P 1 And P 2 The portion of the curve in between is taken as i 11 Will divide the point P 1 The previous curve is partially spliced to the original transmission ratio i 1 Behind the curve, to be spliced at the division point P 2 The curve portion after is taken as i 12 The variation curve of (d); further solving the following steps:
Δθ 2 ＝2π-Δθ 1 (17)
in the formula,. DELTA.theta. 1 Is the central angle of the first intermediate wheel,. DELTA.theta 2 Is the central angle of the middle wheel II.
According to the structure of the transplanting mechanism, an initial value a of the center distance between the first intermediate wheel and the first sun wheel is given 10 Then, according to the section curve closing condition and meshing condition, adopting forward-backward method to search and obtain intermediate wheel I and sunAccurate value a of the center distance of the first wheel 1 The specific calculation is as follows:
one-pitch curve radial r of sun wheel 11 And a pitch curve radial r of the intermediate wheel 12 The expression is as follows:
r 12 ＝a 10 ·i 11 /(1+i 11 ) (18)
r 11 ＝a 10 -r 12 (19)
according to the meshing principle of the non-circular gear, the arc length of the first sun wheel and the first intermediate wheel is equal to obtain:
namely that
In the formula, the angular displacement of the intermediate wheel I
The first planet carrier rotates 360 degrees, and the first middle wheel rotates delta theta 1 Obtaining:
taking an initial value a of the center distance 10 Searching and calculating the accurate value a of the center distance between the middle wheel I and the sun wheel I by adopting a forward and backward method 1 And the precise value R of the radial direction of the intermediate wheel 12 Then the accurate value R of the first radial direction of the sun wheel 11 The solution is as follows:
R 11 ＝a 1 -R 12 (23)
then
Because the center distance between the second intermediate wheel and the second sun wheel is equal to the center distance between the first intermediate wheel and the first sun wheel, the two-way radial of the sun wheel and the two-way radial r of the intermediate wheel are obtained by calculation according to the pitch curve sealing condition and the meshing condition 22 The specific calculation is as follows:
the second rotation delta theta of the middle wheel is caused when the first planet carrier rotates 360 degrees 2 Obtaining:
searching and calculating accurate value R of two-way diameter of intermediate wheel by adopting advancing and retreating method 22 Then the exact value R of the two-way radial of the sun wheel 21 The solution is as follows:
R 21 ＝a 1 -R 22 (25)
in order to ensure that gears in the first planet carrier do not interfere with shafts during movement, an included angle between a connecting line of a rotation center of the first planet carrier and a rotation center of the first intermediate wheel and a connecting line of the rotation center of the first planet carrier and the rotation center of the first planet wheel is gamma, and then the center distance a between the fourth intermediate wheel and the second planet wheel 2 Is composed of
According to the central distance a between the fourth intermediate wheel and the second planet wheel 2 Then according to the joint curve closed condition and meshing condition calculating to obtain radial r of intermediate wheel four 41 And radial direction r of planet wheel II 42 The specific calculation is as follows:
according to the meshing principle of the non-circular gears, the arc length of the fourth rotation of the intermediate wheel is equal to the arc length of the second rotation of the planet wheel, and the following steps are carried out:
namely, it is
Because when the middle wheel IV rotates 360 degrees, the planet wheel II rotates 360 degrees, and the following steps are obtained:
wherein when the first sun wheel is engaged with the first intermediate wheel, the variable is
When the second sun wheel is meshed with the second intermediate wheel, the variable
Angular displacement of the second intermediate wheel
The accurate radial value R of the planet wheel II is searched and calculated by adopting a forward and backward method 42 Then the precise value R of the four-way diameter of the intermediate wheel 41 The solution is as follows:
R 41 ＝a 2 -R 42 (30)
according to the three planet gears and the four-center distance L of the planet gears 2 And (3) calculating to obtain the radial r of the planet wheel III according to the joint curve sealing condition and the meshing condition 51 And radial direction r of planet wheel IV 52 The specific calculation is as follows:
according to the meshing principle of the non-circular gears, the arc length of the fourth rotation of the intermediate wheel is equal to the arc length of the second rotation of the planet wheel:
namely, it is
When the planet wheel rotates by 360 degrees, and the following steps are obtained:
four-way radial R of planet wheel is calculated by adopting forward and backward search method 52 Then planet three-way radial R 51 The exact value of (c) is solved as follows:
R 51 ＝L 2 -R 52 (34)
wherein the content of the first and second substances,
preferably, in step five, the x-axis coordinate expression and the y-axis coordinate expression of the first-section sun wheel curve are respectively as follows:
wherein x is 0 And y 0 X-axis coordinates and y-axis coordinates of a first planet carrier rotation center respectively;
the coordinate expressions of the x axis and the y axis of the two-section curve of the sun wheel are respectively as follows:
the x-axis and y-axis coordinate expressions of the intermediate wheel one-section curve are respectively as follows:
the coordinate expressions of the x-axis and the y-axis of the intermediate wheel two-section curve are respectively as follows:
wherein λ = cos -1 ((a 1 2 +a 2 2 -L 1 2 )/(2·a 1 ·a 2 ))；
The coordinate expressions of the x axis and the y axis of the four-section curve of the middle wheel are respectively as follows:
the coordinate expressions of the x axis and the y axis of the planet wheel secondary curve are respectively as follows:
wherein the content of the first and second substances,
when the sun wheel one is engaged with the intermediate wheel one
Value of,
when the second sun wheel is engaged with the second intermediate wheel
The value of the sum of the values,
is composed of
An initial value of (1);
the coordinate expressions of the x axis and the y axis of the three-section curve of the planet wheel are respectively as follows:
wherein, the first and the second end of the pipe are connected with each other,
is composed of
The initial value of (1);
the x-axis and y-axis coordinate expressions of the four-section curve of the planet wheel are respectively as follows:
wherein, the first and the second end of the pipe are connected with each other,
when the sun wheel one is engaged with the intermediate wheel one
Value of,
when the second sun wheel is engaged with the second intermediate wheel
Value of,
is composed of
An initial value of (1);
wherein, the three-section curve x axle of middle wheel and y axle coordinate expression do respectively:
the x-axis coordinate expression and the y-axis coordinate expression of the first-section curve of the planet wheel are respectively as follows:
the invention has the following beneficial effects:
1. the invention can be applied to all double-planet-carrier non-circular-gear planetary-gear-train transmission mechanisms with track and attitude requirements, and the solution is easy;
2. according to the invention, the design is reversely made according to the track, the third rod is expanded based on the key pose, and the pose requirement of the transplanting arm is ensured by changing the center distance of the second planet carrier; the rod piece transmission is completed by using the differential gear train of the non-circular gear of the moving shaft, the flexibility of the mechanism design is increased, and the range of the available non-uniform transmission rule is expanded, so that the non-circular gear planetary system transmission mechanism can meet the requirement of more special output motion track, and the track shape reappearance and the control of the posture of clamping part of the track section are realized. In addition, the mechanism of the invention adopts differential motion shaft gear train transmission, and the transmission is more stable relative to a connecting rod or a cam. Therefore, the transplanting mechanism can better meet the requirements of tracks and postures, namely good uprightness and no return of seedlings.
3. The mechanism innovatively adopts the variable-center-distance non-circular gear pair, so that rotation can be transmitted, the requirement of variable rod length (center distance change) can be met, the change of the center distance enables the obtained seedling taking angle, seedling pushing angle and seedling track of the transplanting mechanism to be more ideal, and the transplanting verticality and success rate can be further ensured.
Drawings
FIG. 1 is a schematic diagram of a transplanting mechanism of a double-planet-carrier non-circular gear system based on variable rod length, which is constructed by the invention;
FIG. 2 is a simplified schematic diagram of a planar chain-opening mechanism and a transplanting track thereof according to the present invention;
FIG. 3 is a graph of a first sun gear and an intermediate gear in combination with a second sun gear and an intermediate gear prior to stitching in accordance with an embodiment of the present invention;
FIG. 4 is a graph of the transmission ratio of the first sun gear and the intermediate gear in combination with the second sun gear and the intermediate gear after they are spliced in accordance with an embodiment of the present invention;
FIG. 5 is a graph of the stem length of the stem BC (second stem) as a function of the angular displacement of the first carrier in an embodiment of the present invention;
FIG. 6 is a schematic view of the meshing of the profiles of the first sun gear and the first intermediate gear in accordance with an embodiment of the present invention;
FIG. 7 is a schematic view of the meshing of the profiles of the second sun gear and the second intermediate gear in accordance with an embodiment of the present invention;
FIG. 8 is a schematic view of the engagement of the tooth profiles of the fourth intermediate gear and the second planetary gear in the embodiment of the present invention;
fig. 9 is a schematic diagram of tooth profile meshing of the planet wheel three and the planet wheel four in the embodiment of the invention.
Detailed Description
The invention is further explained below with reference to the drawings and examples.
The invention relates to a double-planet-carrier non-circular gear train transplanting mechanism design method based on variable rod length, which comprises the following specific steps of:
step one, constructing a double-planet-carrier non-circular gear system transplanting mechanism based on variable rod length; as shown in fig. 1, the double-planet-carrier non-circular gear train transplanting mechanism based on variable rod length mainly comprises an input shaft 1, a first sun gear 2, a second sun gear 3, a first intermediate gear 4, a second intermediate gear 5, a third intermediate gear 6, a fourth intermediate gear 7, a first planet carrier 8, a first planet gear 9, a second planet gear 10, a planting arm 12, a planet shaft 11, a spring 13, a fourth planet gear 14, a bearing seat 15, a third planet gear 16 and a second planet carrier 17; the first planet carrier 8 is fixed with the input shaft 1; the first sun gear 2 and the second sun gear 3 are fixed and are sleeved on the input shaft 1 in an empty mode; the first intermediate wheel 4, the second intermediate wheel 5, the third intermediate wheel 6 and the fourth intermediate wheel 7 are coaxially fixed and form a revolute pair with the first planet carrier 8; the planet wheel I9 is fixed on a planet shaft 11; the planet shaft 11 and the first planet carrier form a revolute pair and are fixed with the second planet carrier 17; the second planet wheel 10 and the third planet wheel 16 are fixed and are sleeved on the planet shaft 11 in an empty way; the planet gear IV 14 and the bearing seat 15 form a revolute pair; the bearing seat 15 and the second planet carrier 17 form a moving pair, and a spring 13 is arranged between the bearing seat 15 and the second planet carrier; the first intermediate wheel 4 and the second intermediate wheel 5 are both incomplete gears, when the first sun wheel 2 is meshed with the first intermediate wheel 4, the second sun wheel 3 is not meshed with the second intermediate wheel 5, and when the first sun wheel 2 is not meshed with the first intermediate wheel 4, the second sun wheel 3 is meshed with the second intermediate wheel 5; the middle wheel III 6 is meshed with the planet wheel I9, the middle wheel IV 7 is meshed with the planet wheel II 10, and the planet wheel III 16 is meshed with the planet wheel IV 14; the shell of the planting arm 12 is fixed with the planet wheel IV 14; the cam of the planting arm 12 is fixed with the bearing seat 15, and the rotation center line of the cam of the planting arm 12 is coaxial with the rotation center line of the planet gear four 14; the planting arms 12 are made of a conventional mature technology, such as those described in the patent application No. 202010840644.7. When the transplanting mechanism with the configuration operates, the input shaft performs turnover motion relative to the rack, the first sun wheel 2 and the second sun wheel 3 are fixedly connected with the rack through flanges, gear transmission in the first planet carrier 8 is divided into two groups, the first group is that the third intermediate wheel 6 and the first planet wheel 9 transmit power to the planet shaft 11, the second planet carrier 15 is controlled to perform reverse turnover relative to the first planet carrier 8, the second group is that the fourth intermediate wheel 7 and the second planet wheel 10 transmit power to the third planet wheel 16 in the second planet carrier 17 so as to drive the fourth planet wheel 14 to move and rotate relative to the second planet carrier 17 (the springs 13 ensure that the fourth planet wheel 14 and the third planet wheel 16 are normally meshed), and the motion of the transplanting arms relative to the first planet carrier 8 is controlled through the two groups of power, so that the complex track posture of rice pot seedling transplanting is realized.
Step two, simplifying the transplanting mechanism based on the variable-rod-length double-planet-carrier non-circular gear system into a plane open-chain mechanism consisting of a crank AB, a rod BC, a rod CP and a sliding block, as shown in fig. 2, wherein the first planet carrier 8 is equivalent to the crank AB, the second planet carrier is equivalent to the rod BC, the planting arm 12 is equivalent to the rod CP, the bearing seat 15 is equivalent to the sliding block, one end of the crank AB is hinged with the frame, the other end of the crank AB is hinged with one end of the rod BC, the sliding block and the rod BC form a sliding pair, and the rod CP is hinged with the sliding block; then, firstly, the slide block is regarded as a fixed relation with the rod BC, and the motion back calculation of the plane chain opening mechanism is carried out based on a given expected track, which is specifically as follows:
in a counterclockwise direction on a given desired trajectoryTaking a number of data points P i I =1,2, the.. N, n is more than or equal to 6, the first data point and the last data point are overlapped, and a cubic B-spline curve interpolation fitting method is adopted to obtain n +2 control vertexes d i I =1, \8230;, n +2, then with the control vertex d i Calculating to obtain a series of discrete points P (u) on the expected track curve according to a Deboolean recursion formula; establishing a global coordinate system Oxy, as shown in FIG. 2, setting L 1 Is the length of the crank AB, L is the length of the imaginary bar BP, which is the imaginary connecting bar between the hinge point B of the crank AB and the bar BC and the end point P of the bar CP,
is the angle (crank angle displacement) from the positive direction of the x axis to the crank AB,
the included angle (virtual rod angular displacement) from the positive direction of the x axis to the virtual rod BP; in the process of the turnover motion of the crank AB around the hinge point A, the end point P of the virtual rod BP directionally moves along the expected track, the crank AB rotates for two circles, and the virtual rod BP just walks the whole expected track; and (3) obtaining the following parameters according to the maximum and minimum distances between the end point P and the hinge point A:
wherein x is P Is the x-axis coordinate of the end point P, y P Is the y-axis coordinate of the end point P, max represents taking the maximum value, and min represents taking the minimum value; end point P is at
At position, a = pi,
alpha is the value of & lt BAP, phi 7 Is an angle ABP value, and beta is an included angle value between a connecting line of a hinge point A and an end point P and an x axis; end point P is at
At position, a =0,
end point P is at
Is positioned to
In the time between the positions, the position of the movable part,
end point P is at
Is positioned to
In the time between the positions of the first and second gears,
according to the kinematic analysis, the absolute motion of the virtual rod BP is reciprocating swing within the range of (-pi/2, pi/2), namely
In practical application, in
And
under the action of the lever, the plane chain-opening mechanism can complete any expected track, but at different positions, expected postures can not be realized, so that the sliding block and the lever BC form a sliding pair, the virtual lever is expanded into the lever BC and the lever CP, the lever CP ensures the posture requirement, namely, the endpoint P takes a point on the expected track as an endpoint, the lever CP takes a posture angle as an inclined angle, and the length of the lever CP is given.
Thirdly, designing a pole CP based on the posture requirements of key position points of seedling taking and pushing;
defining the accurate postures of the seedling taking and pushing position points and the postures of a plurality of auxiliary position points (the angular displacement of the rod CP) as theta i I =1, 2., N is the total number of seedling taking, pushing and auxiliary position points; wherein the attitude angle of the auxiliary position point is adjustable in the design process, and the hinge point C is calculated by the formula (5)
Wherein L is 3 Is the length of the rod CP;
then at theta i Corresponding position of the rod BC rod length L 2i BC angle displacement of the rod
And the angle displacement of the rod CP
Calculated by equations (6), (7) and (8), respectively
Angular displacement is obtained by cubic B spline fitting interpolation
And angular displacement
Curve, setting pose of auxiliary position point as variable, L 2 The variation is at a minimum the objective function,
monotone is a constraint condition, a differential evolution algorithm is utilized to develop parameter optimization design, and the final crank AB angular displacement is obtained
Lever BC angular displacement
And the angle displacement of the rod CP
And (5) expressing.
Step four, calculating and distributing the transmission ratio and determining the center distance.
Setting the transmission ratio of the second planet carrier to the first planet carrier as I 1 The transmission ratio of the rotation angle of the planting arm relative to the second planet carrier to the rotation angle of the first planet carrier is I 2 Then there is
Wherein when the first sun gear is engaged with the first intermediate gear, i 1 ＝i 11 When the second sun gear is engaged with the second intermediate gear, i 1 ＝i 12 ，i 11 Is the transmission ratio between the first sun wheel and the first intermediate wheel i 12 Is the transmission ratio between the second sun gear and the second intermediate gear, i 34 Representing the transmission ratio between the third intermediate wheel and the first planet wheel, i 34 ＝1，i 56 Representing the transmission ratio between the fourth intermediate wheel and the second planet wheel, i 78 Representing the gear ratio between planet gear three and planet gear four. According to formula (10):
introducing a correction coefficient k to a transmission ratio i 56 And (3) distributing to obtain:
wherein i 1 For asymmetric second-order transmission ratio, as shown in fig. 3, when the first planet carrier rotates 720 degrees, the first intermediate wheel and the second intermediate wheel rotate 360 degrees together, and for ensuring the sealing requirement of the curves of the first intermediate wheel and the second intermediate wheel, the first intermediate wheel and the second intermediate wheel are opposite to each other 1 The transmission ratio curve is processed as follows:
at i 1 Searching two segmentation points P on the curve 1 And P 2 Make the division point P 1 And P 2 To satisfy a transmission ratio i 1 The values are equal and satisfy the following formula:
in the formula (I), the compound is shown in the specification,
and
are respectively a division point P 1 And P 2 Of
A value;
according to the following formula:
score cut point P 1 And P 2 Satisfy the transmission ratio i 1 When the values are equal, the division point P 1 And P 2 Are also equal in radial direction, wherein a 1 The accurate value of the center distance between the first intermediate wheel and the first sun wheel is obtained;
reconstruction of a new transmission ratio i 1 Curve, dividing point P 1 And P 2 The part of the curve in between is taken as i 11 Will divide the point P 1 The previous curve part is spliced to the original transmission ratio i 1 Behind the curve, the splice is located at the dividing point P 2 The curve portion after is taken as i 12 As shown in fig. 4; further solving the following steps:
Δθ 2 ＝2π-Δθ 1 (17)
in the formula,. DELTA.theta. 1 Is the central angle of the first intermediate wheel,. DELTA.theta 2 Is the central angle of the middle wheel II.
According to the structure of the transplanting mechanism, an initial value a of the center distance between the first intermediate wheel and the first sun wheel is given 10 Then according to the pitch curve closing condition and engagementThe condition is that a precise value a of the center distance between the middle wheel I and the sun wheel I is obtained by adopting a forward and backward searching method 1 The specific calculation is as follows:
radial direction r of one-pitch curve of sun gear 11 And a pitch curve radial r of the intermediate wheel 12 The expression is as follows:
r 12 ＝a 10 ·i 11 /(1+i 11 ) (18)
r 11 ＝a 10 -r 12 (19)
according to the non-circular gear meshing principle, the arc length of the first sun wheel and the first intermediate wheel is equal to obtain:
namely, it is
In the formula (I), the compound is shown in the specification,
because the first planet carrier rotates 360 degrees, the first middle wheel rotates delta theta 1 Obtaining:
taking an initial value a of the center distance 10 Searching and calculating the accurate value a of the center distance between the first intermediate wheel and the first sun wheel by adopting a forward-backward method 1 And the precise value R of the radial direction of the intermediate wheel 12 Then the accurate value R of the first radial direction of the sun wheel 11 The solution is as follows:
R 11 ＝a 1 -R 12 (23)
then
Because the center distance between the second intermediate wheel and the second sun wheel is equal to the center distance between the first intermediate wheel and the first sun wheel, the two-way radial of the sun wheel and the two-way radial r of the first intermediate wheel are obtained by calculation according to the joint curve sealing condition and the meshing condition 22 The specific calculation is as follows:
the second rotation delta theta of the middle wheel is caused when the first planet carrier rotates 360 degrees 2 Obtaining:
searching and calculating accurate value R of two-way diameter of intermediate wheel by adopting advancing and retreating method 22 Then the exact value R of the two-way radial of the sun wheel 21 The solution is as follows:
R 21 ＝a 1 -R 22 (25)
considering that each gear in the first planet carrier does not interfere with each shaft during movement, and making an included angle between a connecting line of a rotation center of the first planet carrier and a rotation center of the first intermediate wheel and a connecting line of the rotation center of the first planet carrier and the rotation center of the first planet wheel be gamma, the central distance a between the fourth intermediate wheel and the second planet wheel 2 Is composed of
According to the central distance a between the fourth intermediate wheel and the second planet wheel 2 Then according to the joint curve closed condition and meshing condition calculating to obtain radial r of intermediate wheel four 41 And radial direction r of planet wheel II 42 The specific calculation is as follows:
according to the non-circular gear meshing principle, the arc length of the four-rotation middle wheel is equal to the arc length of the two-rotation planet wheel, and the following steps are obtained:
namely that
Because when the middle wheel IV rotates 360 degrees, the planet wheel II rotates 360 degrees, and the following steps are obtained:
wherein, when the first sun wheel is meshed with the first intermediate wheel,
when the second sun wheel is meshed with the second intermediate wheel,
searching and calculating the radial accurate value R of the second planet wheel by adopting a forward and backward method 42 Then the precise value R of the four-way diameter of the intermediate wheel 41 The solution is as follows:
R 41 ＝a 2 -R 42 (30)
according to the distance L between the three planet wheels and the four centers of the planet wheels 2 Then, according to the joint curve closed condition and the meshing condition, the radial r of the planet wheel III is obtained through calculation 51 And radial direction r of planet wheel IV 52 The specific calculation is as follows:
according to the non-circular gear meshing principle, the arc length of the four-rotation middle wheel is equal to the arc length of the two-rotation planet wheel:
namely, it is
When the planet wheel rotates by 360 degrees, and the following steps are obtained:
four-way radial R of planet wheel is calculated by adopting forward and backward search method 52 Then planet gear three-way radial R 51 The exact value of (c) is solved as follows:
R 51 ＝L 2 -R 52 (34)
wherein, the first and the second end of the pipe are connected with each other,
step five, determining a curve coordinate expression of each gear pitch;
the coordinate expressions of the x axis and the y axis of the first-section curve of the sun wheel are respectively as follows:
wherein x is 0 And y 0 The x-axis coordinate and the y-axis coordinate are respectively of the rotation center of the first planet carrier;
the coordinate expressions of the x axis and the y axis of the two-section curve of the sun wheel are respectively as follows:
the coordinate expressions of the x axis and the y axis of the middle wheel section curve are respectively as follows:
the coordinate expressions of the x-axis and the y-axis of the intermediate wheel two-section curve are respectively as follows:
wherein λ = cos -1 ((a 1 2 +a 2 2 -L 1 2 )/(2·a 1 ·a 2 ))；
The coordinate expressions of the x axis and the y axis of the four-section curve of the middle wheel are respectively as follows:
the coordinate expressions of the x-axis and the y-axis of the planet wheel second-section curve are respectively as follows:
wherein, the first and the second end of the pipe are connected with each other,
is composed of
The initial value of (1);
the coordinate expressions of the x axis and the y axis of the planet wheel three-section curve are respectively as follows:
wherein the content of the first and second substances,
is composed of
The initial value of (1);
the x-axis and y-axis coordinate expressions of the four-section curve of the planet wheel are respectively as follows:
wherein the content of the first and second substances,
is composed of
An initial value of (1);
wherein, the three-section curve x-axis and y-axis coordinate expressions of the middle wheel are respectively:
the x-axis coordinate expression and the y-axis coordinate expression of the first-section curve of the planet wheel are respectively as follows:
in the following, with reference to the specific example, 19 data points P are taken counterclockwise on a given desired trajectory i Specific coordinates of i =1, 2.. 19:
P 1 ：x P1 ＝361；y P1 ＝116.9；
P 2 ：x P2 ＝345.1；y P2 ＝126.9；
P 3 ：x P3 ＝304；y P3 ＝126.4；
P 4 ：x P4 ＝303.1；y P4 ＝111.1；
P 5 ：x P5 ＝300.2；y P5 ＝80.45；
P 6 ：x P6 ＝300.9；y P6 ＝42.6；
P 7 ：x P7 ＝293.8；y P7 ＝-25.98
P 8 ：x P8 ＝263.1；y P8 ＝-32.1-63.2；
P 9 ：x P9 ＝203；y P9 ＝-95.3；
P 10 ：x P10 ＝128；y P10 ＝-165.3；
P 11 ：x P11 ＝31.34；y P11 ＝-120.8；
P 12 ：x P12 ＝2.965；y P12 ＝-55.36；
P 13 ：x P13 ＝-2.871；y P13 ＝20.23；
P 14 ：x P14 ＝36.77；y P14 ＝99.5；
P 15 ：x P15 ＝95.82；y P15 ＝148.9；
P 16 ：x P16 ＝151.6；y P16 ＝157.8；
P 17 ：x P17 ＝246.6；y P17 ＝160.1；
P 18 ：x P18 ＝313.3；y P18 ＝149.8；
P 19 ：x P19 ＝x P1 ；y P19 ＝y P1 ；
and giving the posture of the planting arm at each data point:
θ 1 ＝110；
θ 2 ＝72；
θ 3 ＝18；
θ 4 ＝111°；
θ 5 ＝70°；
θ 6 ＝16°；
θ 7 ＝-119°；
θ 8 ＝-152°；
θ 9 ＝-172°；
θ 10 ＝176°；
θ 11 ＝-157°；
θ 12 ＝-147°；
θ 13 ＝-170°；
θ 14 ＝-146°；
θ 15 ＝-161°；
θ 16 ＝-179°；
θ 17 ＝161°；
θ 18 ＝138°；
θ 19 ＝θ 1 ；
the first planet carrier rotation center coordinates (90, 0), L are given 3 ＝155mm、k＝0.9984、a 10 ＝59mm、γ＝25°、
And
solving is carried out according to the design method of the variable-rod-length-based double-planet-carrier non-circular gear system transplanting mechanism to obtain a 1 ＝60mm，a 2 ＝52.79mmm，L 1 ＝100.68mm，Δθ 1 ＝112.15°、Δθ 2 =247.85 °, front curve of the first sun gear and the intermediate gear when the first sun gear and the intermediate gear are spliced together in combination with the second sun gear and the intermediate gear is shown in fig. 3, and rear curve of the first sun gear and the intermediate gear when the first sun gear and the intermediate gear are spliced together in combination with the second sun gear and the intermediate gear is shown in fig. 4; the curve of the change of the rod length of the rod BC along with the angular displacement of the first planet carrier is shown in figure 5, the tooth profiles of the first sun gear and the first intermediate gear are meshed as shown in figure 6, the tooth profiles of the second sun gear and the second intermediate gear are meshed as shown in figure 7, the tooth profile of the fourth intermediate gear and the tooth profile of the second planet gear are meshed as shown in figure 8, and the tooth profiles of the third planet gear and the fourth planet gear are meshed as shown in figure 9, wherein the tooth profile generated according to a gear pitch curve coordinate expression is the prior art, is not the scope to be protected of the invention, and is not described repeatedly.
Claims (5)
1. A double-planet-carrier non-circular gear system transplanting mechanism design method based on variable rod length is characterized in that: the method comprises the following specific steps:
step one, constructing a double-planet-carrier non-circular gear train transplanting mechanism based on variable rod length; the double-planet-carrier non-circular gear train transplanting mechanism based on the variable rod length mainly comprises an input shaft, a first sun gear, a second sun gear, a first intermediate gear, a second intermediate gear, a third intermediate gear, a fourth intermediate gear, a first planet carrier, a first planet gear, a second planet gear, a planting arm, a planet shaft, a spring, a fourth planet gear, a bearing seat, a third planet gear and a second planet carrier; the first planet carrier is fixed with the input shaft; the first sun wheel and the second sun wheel are fixed and are sleeved on the input shaft in an empty mode; the first intermediate wheel, the second intermediate wheel, the third intermediate wheel and the fourth intermediate wheel are coaxially fixed and form a revolute pair with the first planet carrier; the first planet wheel is fixed on the planet shaft; the planet shaft and the first planet carrier form a revolute pair and are fixed with the second planet carrier; the second planet wheel and the third planet wheel are fixed and are sleeved on the planet shaft in an empty way; the planet gear IV and the bearing seat form a revolute pair; the bearing seat and the second planet carrier form a moving pair, and a spring is arranged between the bearing seat and the second planet carrier; the first intermediate wheel and the second intermediate wheel are both incomplete gears, when the first sun wheel is meshed with the first intermediate wheel, the second sun wheel is not meshed with the second intermediate wheel, and when the first sun wheel is not meshed with the first intermediate wheel, the second sun wheel is meshed with the second intermediate wheel; the middle wheel III is meshed with the planet wheel I, the middle wheel IV is meshed with the planet wheel II, and the planet wheel III is meshed with the planet wheel IV; the shell of the planting arm is fixed with the planet wheel IV; the cam of the planting arm is fixed with the bearing seat, and the rotation center line of the cam of the planting arm is coaxial with the rotation center line of the planet gear IV;
step two, simplifying the transplanting mechanism based on the variable-rod-length double-planet-carrier non-circular gear system into a plane open-chain mechanism consisting of a crank AB, a rod BC, a rod CP and a sliding block, wherein the first planet carrier is equivalent to the crank AB, the second planet carrier is equivalent to the rod BC, the planting arm is equivalent to the rod CP, the bearing seat is equivalent to a sliding block, one end of the crank AB is hinged with the frame, the other end of the crank AB is hinged with one end of the rod BC, the sliding block and the rod BC form a sliding pair, and the rod CP is hinged with the sliding block; then, the slider is first considered to be fixed to the rod BC based onThe motion of the plane open-chain mechanism is reversely solved by giving an expected track, and the included angle from the positive direction of the x axis to the crank AB is solved
Angle from positive direction of x-axis to back of imaginary bar
Step three, defining the accurate postures of the seedling taking and pushing position points and the postures of a plurality of auxiliary position points as theta i I =1, 2., N is the total number of seedling taking, pushing and auxiliary position points; then calculated at θ i Corresponding position of the rod BC rod length L 2i And bar BC angle displacement
And the angle displacement of the rod CP
Angular displacement is obtained by cubic B spline fitting interpolation
And angle displacement
Curve, setting auxiliary position and pose as variable, L 2 The variation is at a minimum the objective function,
monotone is a constraint condition, a differential evolution algorithm is utilized to carry out parameter optimization design, and the final included angle from the positive direction of the x axis to the crank AB is obtained
Lever BC angular displacement
And the angle displacement of the rod CP
An expression;
step four, if the third intermediate wheel and the first planet wheel are both circular gears, the transmission ratio i between the third intermediate wheel and the first planet wheel 34 =1; then the angle between the positive direction of the x axis and the crank AB
Lever BC angular displacement
And the angle displacement of the rod CP
An expression formula is adopted, the transmission ratio between the first sun wheel and the first intermediate wheel and the transmission ratio between the second sun wheel and the second intermediate wheel are solved, and a correction coefficient k is introduced to the transmission ratio i between the fourth intermediate wheel and the second planet wheel 56 And a transmission ratio i between planet gear three and planet gear four 78 The distribution is carried out to obtain the transmission ratio i between the intermediate wheel four and the planet wheel two 56 And a transmission ratio i between planet gear three and planet gear four 78 (ii) a Then, for i 1 Dividing and splicing the transmission ratio curves again to reconstruct to meet the sealing requirements of the first intermediate wheel section curve and the second intermediate wheel section curve; searching and obtaining the accurate value a of the center distance between the middle wheel I and the sun wheel I by adopting a forward-backward method 1 And the precise value R of the radial direction of the intermediate wheel 12 Then obtaining the accurate value R of the first radial direction of the sun wheel 11 Angular displacement of the intermediate wheel I
Searching and calculating accurate value R of two-way radial of intermediate wheel by adopting advancing and retreating method 22 Then obtaining the accurate value R of the two-way diameter of the sun wheel 21 (ii) a Making the included angle between the line connecting the first planet carrier rotation center and the middle wheel rotation center and the line connecting the first planet carrier rotation center and the planet wheel rotation center be gamma, solving the middleThe center distance a between the fourth wheel and the second planet wheel 2 Then, the accurate radial value R of the planet wheel II is searched and calculated by adopting a forward and backward method 42 Then obtaining the accurate value R of the four-way diameter of the intermediate wheel 41 (ii) a Four-way radial R of planet wheel is searched and calculated by adopting a forward and backward method 52 Then obtaining the three-way diameter R of the planet wheel 51 The exact value of (d);
and step five, solving the coordinate expressions of the pitch curves x axis and y axis of the first sun wheel, the second sun wheel, the first intermediate wheel, the second intermediate wheel, the fourth intermediate wheel, the second planet wheel, the third planet wheel, the fourth planet wheel, the third intermediate wheel and the first planet wheel.
2. The method for designing a transplanting mechanism of a double-planet-carrier non-circular gear system based on a variable rod length as claimed in claim 1, wherein the method comprises the following steps: in the second step, the included angle from the positive direction of the x axis to the crank AB is solved
Angle from positive direction of x-axis to back of imaginary bar
The specific process is as follows:
taking several data points P on a given desired trajectory in a counter-clockwise direction i I =1,2, the.. N, n is more than or equal to 6, the first data point and the last data point are overlapped, and a cubic B-spline curve interpolation fitting method is adopted to obtain n +2 control vertexes d i I =1, \ 8230;, n +2, then using the control vertex d i Calculating to obtain a series of discrete points P (u) on the expected track curve according to a Deboolean recursion formula; establishing a global coordinate system Oxy, and setting L 1 Is the length of the crank AB, L is the length of the imaginary bar BP, which is the imaginary connecting bar between the hinge point B of the crank AB and the bar BC and the end point P of the bar CP,
is an included angle from the positive direction of the x axis to the crank AB,
is positive to the x-axisThe angle from the direction to the virtual bar BP; in the process of the turnover motion of the crank AB around the hinge point A, the end point P of the virtual rod BP directionally moves along the expected track, the crank AB rotates for two circles, and the virtual rod BP moves through the whole expected track; and (3) obtaining the following parameters according to the maximum and minimum distances between the end point P and the hinge point A:
wherein x is A Is the x-axis coordinate of the hinge point A, y A Y-axis coordinate, x, of hinge point A P Is the x-axis coordinate of the end point P, y P The y-axis coordinate of the endpoint P is shown, max represents the maximum value, and min represents the minimum value; end point P is at
At position, a = pi,
alpha is a value of ≈ BAP, and beta is a value of an included angle between a connecting line of a hinge point A and an end point P and an x axis; end point P is at
At position, a =0,
end point P is at
Is positioned to
In the time between the positions of the first and second gears,
end point P is at
Is positioned to
In the time between the positions of the first and second gears,
wherein, the first and the second end of the pipe are connected with each other,
3. the method for designing a transplanting mechanism of a double-planet-carrier non-circular gear system based on a variable rod length as claimed in claim 2, wherein the method comprises the following steps: in step three, theta i Length L of corresponding position of bar BC 2i BC angle displacement of the rod
And rod CP angle displacement
Calculated by equations (5), (6) and (7), respectively
Wherein the hinge point C is calculated by equation (8)
Wherein L is 3 The length of the rod CP.
4. The method for designing a transplanting mechanism of a double-planet-carrier non-circular gear train based on variable rod length according to claim 1, wherein the method comprises the following steps: the fourth step is as follows:
setting the transmission ratio of the second planet carrier to the first planet carrier as I 1 The transmission ratio of the rotation angle of the planting arm relative to the second planet carrier to the rotation angle of the first planet carrier is I 2 Then there is
Wherein when the first sun gear is engaged with the first intermediate gear, i 1 ＝i 11 When the second sun gear is engaged with the second intermediate gear, i 1 ＝i 12 ，i 11 Is the transmission ratio between the first sun wheel and the first intermediate wheel, i 12 Is the transmission ratio between the second sun gear and the second intermediate gear, i 56 Indicating intermediate wheel four and planet wheel twoA transmission ratio of i 78 Representing the transmission ratio between planet gear three and planet gear four; according to formula (10):
introducing a correction coefficient k to a transmission ratio i 56 And (3) distributing to obtain:
wherein i 1 When the first planet carrier rotates 720 degrees, the first intermediate wheel and the second intermediate wheel rotate 360 degrees together, and the requirements on the sealing property of the curves of the first intermediate wheel and the second intermediate wheel are met for ensuring that the curves of the first intermediate wheel and the second intermediate wheel are closed 1 The transmission ratio curve is processed as follows:
at i 1 Searching two segmentation points P on the curve 1 And P 2 Make the division point P 1 And P 2 To satisfy a transmission ratio i 1 Equal in value and satisfies the following formula:
in the formula (I), the compound is shown in the specification,
and
are respectively a division point P 1 And P 2 Of
A value;
according to the following formula:
score cut point P 1 And P 2 Satisfy the transmission ratio i 1 When the values are equal, the division point P 1 And P 2 The radial directions of the parts are also equal;
reconstruction of a new transmission ratio i 1 Curve, dividing point P 1 And P 2 The portion of the curve in between is taken as i 11 Will divide the point P 1 The previous curve part is spliced to the original transmission ratio i 1 Behind the curve, the splice is located at the dividing point P 2 The curve portion after is taken as i 12 The variation curve of (d); further solving the following steps:
Δθ 2 ＝2π-Δθ 1 (17)
in the formula,. DELTA.theta. 1 Is the central angle of the first intermediate wheel, delta theta 2 Is the central angle of the middle wheel II;
according to the structure of the transplanting mechanism, an initial value a of the center distance between the first intermediate wheel and the first sun wheel is given 10 And then, according to the section curve closing condition and the meshing condition, searching and obtaining the accurate value a of the center distance between the first intermediate wheel and the first sun wheel by adopting a forward-backward method 1 The specific calculation is as follows:
one-pitch curve radial r of sun wheel 11 And a pitch curve radial r of the intermediate wheel 12 The expression is as follows:
r 12 ＝a 10 ·i 11 /(1+i 11 ) (18)
r 11 ＝a 10 -r 12 (19)
according to the meshing principle of the non-circular gear, the arc length of the first sun wheel and the first intermediate wheel is equal to obtain:
namely, it is
In the formula, the angular displacement of the intermediate wheel I
The first planet carrier rotates 360 degrees, and the first middle wheel rotates delta theta 1 Obtaining:
taking an initial value a of the center distance 10 Searching and calculating the accurate value a of the center distance between the middle wheel I and the sun wheel I by adopting a forward and backward method 1 And the precise value R of the radial direction of the intermediate wheel 12 Then the accurate value R of the first radial direction of the sun wheel 11 The solution is as follows:
R 11 ＝a 1 -R 12 (23)
then
Because the center distance between the second intermediate wheel and the second sun wheel is equal to the center distance between the first intermediate wheel and the first sun wheel, the two-way radial of the sun wheel and the two-way radial r of the intermediate wheel are obtained by calculation according to the pitch curve sealing condition and the meshing condition 22 The specific calculation is as follows:
the second rotation delta theta of the middle wheel is caused when the first planet carrier rotates 360 degrees 2 Obtaining:
searching and calculating accurate value R of two-way diameter of intermediate wheel by adopting advancing and retreating method 22 Then the exact value R of the sun gear two-way radial 21 The solution is as follows:
R 21 ＝a 1 -R 22 (25)
in order to ensure that gears in the first planet carrier do not interfere with shafts during movement, an included angle between a connecting line of a rotation center of the first planet carrier and a rotation center of the first intermediate wheel and a connecting line of the rotation center of the first planet carrier and the rotation center of the first planet wheel is gamma, and then the center distance a between the fourth intermediate wheel and the second planet wheel 2 Is composed of
According to the central distance a between the fourth intermediate wheel and the second planet wheel 2 Then according to the joint curve closed condition and meshing condition calculating to obtain radial r of intermediate wheel four 41 And radial direction r of planet wheel II 42 The specific calculation is as follows:
according to the non-circular gear meshing principle, the arc length of the four-rotation middle wheel is equal to the arc length of the two-rotation planet wheel, and the following steps are obtained:
namely, it is
Because when the middle wheel IV rotates 360 degrees, the planet wheel II rotates 360 degrees, and the following steps are obtained:
wherein when the first sun wheel is engaged with the first intermediate wheel, the variable is
When the second sun wheel is meshed with the second intermediate wheel, the variable
Angular displacement of the intermediate wheel II
The accurate radial value R of the planet wheel II is searched and calculated by adopting a forward and backward method 42 Then the precise value R of the four-way diameter of the intermediate wheel 41 The solution is as follows:
R 41 ＝a 2 -R 42 (30)
according to the distance L between the three planet wheels and the four centers of the planet wheels 2 And (3) calculating to obtain the radial r of the planet wheel III according to the joint curve sealing condition and the meshing condition 51 And radial direction r of planet wheel IV 52 The specific calculation is as follows:
according to the meshing principle of the non-circular gears, the arc length of the fourth rotation of the intermediate wheel is equal to the arc length of the second rotation of the planet wheel:
namely, it is
When the planet wheel rotates by 360 degrees, and the following steps are obtained:
four-way radial R of planet wheel is calculated by adopting forward and backward search method 52 Then planet gear three-way radial R 51 The exact value of (c) is solved as follows:
R 51 ＝L 2 -R 52 (34)
wherein the content of the first and second substances,
5. the method for designing a transplanting mechanism of a double-planet-carrier non-circular gear train based on variable rod length as claimed in claim 4, wherein: in the fifth step, the x-axis and y-axis coordinate expressions of the first-section curve of the sun wheel are respectively as follows:
wherein x is 0 And y 0 The x-axis coordinate and the y-axis coordinate are respectively of the rotation center of the first planet carrier;
the coordinate expressions of the x axis and the y axis of the two-section curve of the sun wheel are respectively as follows:
the coordinate expressions of the x axis and the y axis of the middle wheel section curve are respectively as follows:
the coordinate expressions of the x-axis and the y-axis of the intermediate wheel two-section curve are respectively as follows:
wherein λ = cos -1 ((a 1 2 +a 2 2 -L 1 2 )/(2·a 1 ·a 2 ))；
The coordinate expressions of the x axis and the y axis of the four-section curve of the middle wheel are respectively as follows:
the coordinate expressions of the x-axis and the y-axis of the planet wheel second-section curve are respectively as follows:
wherein the content of the first and second substances,
when the sun wheel one is engaged with the intermediate wheel one
Value of,
when the second sun wheel is engaged with the second intermediate wheel
Value of,
is composed of
The initial value of (1);
the coordinate expressions of the x axis and the y axis of the planet wheel three-section curve are respectively as follows:
wherein, the first and the second end of the pipe are connected with each other,
is composed of
An initial value of (1);
the x-axis and y-axis coordinate expressions of the four-section curve of the planet wheel are respectively as follows:
wherein, the first and the second end of the pipe are connected with each other,
when the sun wheel one is engaged with the intermediate wheel one
Value of,
when the second sun wheel is engaged with the second intermediate wheel
Value of a step of,
is composed of
An initial value of (1);
wherein, the three-section curve x-axis and y-axis coordinate expressions of the middle wheel are respectively:
the coordinate expressions of the x axis and the y axis of the first section of curve of the planet wheel are respectively as follows:
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