CN107654585A - Non-circular gear planetary gear system design method based on kinematics mapping - Google Patents
Non-circular gear planetary gear system design method based on kinematics mapping Download PDFInfo
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- CN107654585A CN107654585A CN201710760318.3A CN201710760318A CN107654585A CN 107654585 A CN107654585 A CN 107654585A CN 201710760318 A CN201710760318 A CN 201710760318A CN 107654585 A CN107654585 A CN 107654585A
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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
- F16H—GEARING
- F16H1/00—Toothed gearings for conveying rotary motion
- F16H1/28—Toothed gearings for conveying rotary motion with gears having orbital motion
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- A—HUMAN NECESSITIES
- A01—AGRICULTURE; FORESTRY; ANIMAL HUSBANDRY; HUNTING; TRAPPING; FISHING
- A01C—PLANTING; SOWING; FERTILISING
- A01C11/00—Transplanting machines
- A01C11/006—Other parts or details or planting machines
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- A—HUMAN NECESSITIES
- A01—AGRICULTURE; FORESTRY; ANIMAL HUSBANDRY; HUNTING; TRAPPING; FISHING
- A01C—PLANTING; SOWING; FERTILISING
- A01C11/00—Transplanting machines
- A01C11/02—Transplanting machines for seedlings
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Abstract
The invention discloses the non-circular gear planetary gear system design method mapped based on kinematics.The method difficulty of existing reverse transplanting mechanism is big, and optimization process is complicated.The method that the present invention is mapped by kinematics, the track of two closings can be formed by trying to achieve two sets of four-bar mechanisms by five given posture points, then taken a little in the track of two closings and obtain angular displacement curve with uniform B-Spline interpolation three times, resultant gear ratio curve is obtained by angular displacement curve, carries out gearratio distribution；The pitch curve of two pairs of non-circular gears is obtained by two stage gear ratios.The present invention optimizes adjustment respectively by the point on two closing tracks, and the coupling degree of association is small, and adjustability is stronger, and the process of optimization transplanting track is easier.
Description
Technical field
The invention belongs to field of mechanical technique, is related to transplanter, and in particular to a kind of non-knuckle-tooth based on kinematics mapping
Take turns planetary gear train design method.
Background technology
Potted-seedling transplanting is the important channel for improving agricultural performance.The use of transplanter substantially increases agricultural, plantation
The labor productivity of industry especially rice shoot, alleviates labor intensity, improves agricultural machanization integral level, agricultural production is pushed to
One new era.
Slideway mechanism easily realizes special track, and flexible design is convenient, but its is complicated, and cost is high, less efficient.
Although rotating mechanism design difficulty is big, simple in construction, cost is low, efficiency high.In the market rotary mechanism produces as replacement
Product are phased out Link -- Typed Transplanting Mechanism.
The content of the invention
The purpose of the present invention is to be directed to the problem of existing rotating mechanism design difficulty is big, is proposed based on the non-of kinematics mapping
Knucle-gear planetary gear train design method, the method mapped by kinematics, two set of four bar is tried to achieve by five given posture points
Mechanism can form the track of two closings, then take a little in the track of two closings and obtained with uniform B-Spline interpolation three times
To angular displacement curve, resultant gear ratio curve is obtained by angular displacement curve, carries out gearratio distribution；Obtained by two stage gear ratios
The pitch curve of two pairs of non-circular gears.
In order to achieve the above object, the technical solution adopted by the present invention is：
The present invention's comprises the following steps that：
Step 1: structure non-circular gear planetary gear system, including planet carrier and transplanting arm, and set in planet carrier the
One-level driving wheel, first order driven pulley, second level driving wheel and second level driven pulley；First order driving wheel is fixed in frame；
One end of planet carrier is hinged with first order driving wheel, and the other end is hinged with second level driven pulley, and middle part is cut with scissors with first order driven pulley
Connect；First order driven pulley and second level driving wheel are affixed；The pin joint of first order driving wheel is defined as fixing pin joint, the second level
The pin joint of driven pulley is defined as dynamic pin joint；First order driving wheel engages with first order driven pulley；Second level driving wheel and
Two level driven pulley engages；The housing of transplanting arm and second level driven pulley are affixed；The cam of transplanting arm and planet carrier are affixed.
Step 2: the method reverse based on kinematics mapping goes out two sets of four-bar mechanisms.
Dynamic coordinate (x, y) of the hinge point in moving coordinate system xoy is transformed into coordinate expression-form in quiet coordinate system XOY such as
Under：
Wherein, moving coordinate system xoy origins are d1 to the distance of X-axis, and the distance to Y-axis is d2, and the angle of x-axis and X-axis is
Order
Willd1And d2Use Z1、Z2、Z3And Z4Expression, is obtained
Because dynamic hinge point is inevitable on the circle using fixed hinge point as the center of circle, i.e., dynamic hinge point meets equation of a circle：
2a1X+2a2Y+a3=a0(X2+Y2) (3)
Wherein, a0、a1、a2And a3It is coefficient.
Formula (2) is substituted into formula (3), obtained：
Wherein, p1=-a0, p2=a0X, p3=a0Y, p4=a1, p5=a2, p6=-a1y+a2X, p7=-(a1x+a2Y)/2, p8
=(a3-a0(x2+y2))/4；
Eight coefficient p1、p2、p3、p4、p5、p6、p7And p8It is not independent, but it must is fulfilled for following two equations
p1p6+p2p5-p3p4=0 (5)
2p1p7-p2p4-p3p5=0 (6)
Posture point is expressed as three-dimensional coordinate formTake five posture points j
=1,2,3,4,5, formula (1) is substituted into respectively obtains five groups of ZiSolution, i=1,2,3,4, five groups of ZiSolution is designated as Zji.In order to meet to move
The requirement of track is planted, wherein three posture point seedling taking points are nearby chosen, two other posture point is pushing away the selection of seedling point, and five appearances
The whole height of state point while constrained trajectory.
Five groups of ZiThe equation that solution substitutes into formula (4) respectively, and it is as follows to be write as matrix form：
Wherein, matrix coefficientAj2=Zj1Zj3-Zj2Zj4, Aj3=Zj2Zj3+Zj1Zj4, Aj4=Zj1Zj3
+Zj2Zj4, Aj5=Zj2Zj3-Zj1Zj4, Aj6=Zj3Zj4, P=[p1 p2 p3
p4 p5 p6 p7 p8]T,
Make coefficient matrix
Matrix [A]TIt is zero that [A], which has three characteristic values, corresponding three characteristic vector vα, vβAnd vγConstitute kernel
Base.
α is made, beta, gamma is three real parameters, and vectorial p is expressed as：
P=α vα+βvβ+γvγ (7)
Vectorial p meets formula (5) and (6), the p in formula (7)1、p2、p3、p4、p5、p6And p7Substitute into formula (5) and
(6) obtain
K10α2+K11β2+K12αβ+K13αγ+K14βγ+K15γ2=0 (8)
K20α2+K21β2+K22αβ+K23αγ+K24βγ+K25γ2=0 (9)
Wherein Kmn, m=1,2, n=0,1,2,3,4,5, expressed by the expression formula of three characteristic vectors compositions.Set γ
≠ 0, γ is removed in formula (8) and (9) both sides together2, obtain onWithTwo binary quadratic equations, two dihydric phenol sides
Journey has two groups of real solutions, i.e., vectorial p has two groups of solutions.Back substitution is to p after obtaining two groups of solutions of vectorial p respectively1=-a0, p2=a0X, p3=
a0Y, p4=a1, p5=a2, p6=-a1y+a2X, p7=-(a1x+a2Y)/2, p8=(a3-a0(x2+y2))/4, try to achieve two groups of a0, a1,
a2, a3, x, y.Two groups of a0、a1、a2、a3Substitute into formula (3) and equation of a circle is converted into center of circle radius formula.The center of circle of two equation of a circles
Coordinate is exactly two fixed hinge points.
A posture point is taken in three posture points near seedling taking point, and two groups of x, y values are substituted intoWithCalculate two movements corresponding to the posture point
Hinge point coordinates.Using the line of two fixed hinge points as frame, the company with two fixed hinge points with corresponding mobile hinge point
Line is crank or swing rod, using the connection of two mobile hinge points as connecting rod, forms first set four-bar mechanism.
Push away and a posture point is taken in two posture points near seedling point, and two groups of x, y values are substituted intoWithCalculate two movements corresponding to the posture point
Hinge point coordinates.Using the line of two fixed hinge points as frame, the company with two fixed hinge points with corresponding mobile hinge point
Line is crank or swing rod, using the connection of two mobile hinge points as connecting rod, forms second set of four-bar mechanism.
Step 3: angular displacement curve is fitted, so as to try to achieve resultant gear ratio curve.
36 data points are respectively taken from two closing tracks, 10 degree every turn is followed the example of as crank and takes a bit；Then at first
Seven points are taken successively according to rotary direction of the crank close to seedling taking point position, calculate planet carrier angle position corresponding to seven points on closing track
Shifting and the angular displacement difference of planet carrier and transplanting arm；It is close on Article 2 closing track to push away seedling point position according to rotary direction of the crank
Three points are taken successively, calculate the angular displacement difference of planet carrier angular displacement and planet carrier and transplanting arm corresponding to three points.
Using planet carrier angular displacement as abscissa, the angular displacement difference of planet carrier and transplanting arm is ordinate, according to first
The planet carrier angular displacement and the angular displacement difference of planet carrier and transplanting arm that seven points taken on closing track calculate describe seven
Point, the planet carrier angular displacement and the angular displacement of planet carrier and transplanting arm calculated according to three points taken on Article 2 closing track
Difference describes three points, gives seven interpolation points in addition, ensures that the first and last point ordinate of this 17 interpolation points differs 2 π.According to
17 interpolation points obtain angular displacement curve by uniform B-Spline interpolation three times, and number is inserted between two neighboring interpolation point
Match point more than 20.Angular displacement curve need to ensure dullness, i.e. non-circular gear is not in the phenomenon toward revolution.
Resultant gear ratioWherein w1It is the angular speed of planet carrier, w2It is the angular speed of transplanting arm, and angular displacement
It is resultant gear ratio corresponding to this adjacent 2 points that the inverse of the adjacent 2 points of slopes calculated of curve takes negative value again, and then, according to angle
Displacement curve tries to achieve whole piece resultant gear ratio curve.
Step 4: calculate the length of transplanting arm.
To meet that transplanting requires, take during the length for calculating transplanting arm outside the closed loop that five posture point broken line lines are formed
Fixed hinge point, in four-bar mechanism where the fixed hinge point, the shifting according to corresponding to a posture point coordinates and the posture point
Dynamic hinge point draws the length of transplanting arm.
Step 5: carrying out the distribution of resultant gear ratio, the pitch curve of two pairs of non-circular gears is calculated.
The angular displacement of planet carrier and transplanting arm is obtained according to angular displacement curve, obtained in conjunction with the length of planet carrier and transplanting arm
To the transplanting track of transplant arm cusp.Transplanting track is optimized by the ordinate of interpolation point on adjustment angle displacement curve；By root
The planet carrier angular displacement calculated according to three points taken on Article 2 closing track and the angular displacement difference of planet carrier and transplanting arm
The three points translation described, so as to change the peak of resultant gear ratio curve, paddy section curve, being finally reached improves gear pitch curve indent
Purpose.
According to resultant gear ratio curve, two stage gear ratios are distributed.First stage gear ratio isSecond stage gear ratio is
Non-circular gear pitch curve polar coordinate representation, if planet carrier angular displacement is θ, the centre-to-centre spacing of two-stage non-circular gear is
a.The polar diameter of first order driving wheel isPolar angle isThe polar diameter of first order driven pulley is r2=a-r1, pole
Angle isWillSubstitute intoWhen being turned around due to first order driving wheel, the
One-level driven pulley also turns around, i.e., nowTry to achieve xs.The polar diameter of second level driving wheel is
Polar angle isThe polar diameter of second level driven pulley is r4=a-r3, polar angle is
The invention has the advantages that：
1st, the present invention is driven based on kinematics Mapping Design non-circular gear planetary gear system, track is met that transplanting requires, excellent
Point is exactly to meet to transplant desired closing track to try to achieve one section by merging two sections of open loop tracks, by two closing tracks
Point optimize adjustment respectively, the coupling degree of association is small, and adjustability is stronger, and the process of optimization transplanting track is easier.
Brief description of the drawings
Fig. 1 is the principle schematic of mechanism of the present invention；
Fig. 2 is the kinematic sketch of mechanism of the present invention；
Fig. 3 is the two sets of four-bar mechanism schematic diagrames obtained by example calculation；
Fig. 4 is the angular displacement curve map tried to achieve by example calculation；
Fig. 5 is the resultant gear ratio curve and gearratio distribution curve figure tried to achieve by example calculation；
Fig. 6 is the two closing track schematic diagrames tried to achieve by example calculation；
Fig. 7 is the pitch curve for the first order driving wheel tried to achieve by example calculation；
Fig. 8 is the pitch curve for the first order driven pulley tried to achieve by example calculation；
Fig. 9 is the pitch curve for the second level driving wheel tried to achieve by example calculation；
Figure 10 is the pitch curve for the second level driven pulley tried to achieve by example calculation.
Embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
As illustrated in fig. 1 and 2, the non-circular gear planetary gear system design method based on kinematics mapping, mapped with kinematics
Method tries to achieve two sets of four-bar mechanisms；Two sections of closing tracks that two sets of four-bar mechanisms are formed, close on track at two sections and take a little and lead to
Cross uniform B-Spline interpolation three times and obtain one section of complete angular displacement curve；Resultant gear ratio curve is obtained by angular displacement curve,
Carry out gearratio distribution；The pitch curve of two pairs of non-circular gears is obtained by two stage gear ratios, it is specific as follows：
Step 1: structure non-circular gear planetary gear system, including planet carrier 3 and transplanting arm 6, and set in planet carrier 3
First order driving wheel 4, first order driven pulley 2, second level driving wheel 1 and second level driven pulley 5；First order driving wheel 4 is affixed
In frame；One end of planet carrier 3 is be hinged with first order driving wheel 4, and the other end is be hinged with second level driven pulley 5, middle part and the
One-level driven pulley 2 is be hinged；First order driven pulley 2 and second level driving wheel 1 are affixed；The pin joint of first order driving wheel 4 is defined as
Fixed pin joint, the pin joint of second level driven pulley 5 are defined as dynamic pin joint；First order driving wheel 4 is nibbled with first order driven pulley 2
Close；Second level driving wheel 1 engages with second level driven pulley 5；The housing of transplanting arm 6 and second level driven pulley 5 are affixed；Transplanting arm 6
Cam and planet carrier 3 it is affixed；The structure of transplanting arm 6 is transplanted using disclosed in the patent of Application No. 201110164729.9
Arm.Planet carrier 3 drives first order driven pulley 2 to rotate；First order driven pulley 2 and second level driving wheel 1 are affixed, thus the first order from
Driving wheel 2 drives second level driving wheel 1 to rotate, and second level driving wheel 1 drives second level driven pulley 5 to rotate；Transplanting arm 6 is with the second level
Driven pulley 5 rotates, and transplanting arm end forms transplanting track.
Step 2: the method reverse based on kinematics mapping goes out two sets of four-bar mechanisms.
Dynamic coordinate (x, y) of the hinge point in moving coordinate system xoy is transformed into coordinate expression-form in quiet coordinate system XOY such as
Under：
Wherein, moving coordinate system xoy origins are d1 to the distance of X-axis, and the distance to Y-axis is d2, and the angle of x-axis and X-axis is
Order
Willd1And d2Use Z1、Z2、Z3And Z4Expression, is obtained
Because dynamic hinge point is inevitable on the circle using fixed hinge point as the center of circle, i.e., dynamic hinge point meets equation of a circle：
2a1X+2a2Y+a3=a0(X2+Y2) (3)
Wherein, a0、a1、a2And a3It is coefficient.
Formula (2) is substituted into formula (3), obtained：
Wherein, p1=-a0, p2=a0X, p3=a0Y, p4=a1, p5=a2, p6=-a1y+a2X, p7=-(a1x+a2Y)/2, p8
=(a3-a0(x2+y2))/4；
Eight coefficient p1、p2、p3、p4、p5、p6、p7And p8It is not independent, but it must is fulfilled for following two equations
p1p6+p2p5-p3p4=0 (5)
2p1p7-p2p4-p3p5=0 (6)
Posture point is expressed as three-dimensional coordinate formTake five posture points j
=1,2,3,4,5, be respectively (235,120,10), (252,112,0), (237,121,12), (80, -270, -85) and (58, -
258, -75)；Five posture point coordinates substitute into formula (1) and obtain five groups of Z respectivelyiSolution, i=1,2,3,4, five groups of ZiSolution is designated as Zji。
First group：Z11=-70.0125, Z12=111.8235, Z13=-0.0872, Z14=0.9962；Second group：Z21=-56, Z22=
126, Z23=0, Z24=1.3rd group：Z31=-47.782, Z32=124.1748, Z33=0.1045, Z34=0.9945.4th
Group：Z41=72.5088, Z42=120.6958, Z43=-0.6756, Z44=0.7373.5th group：Z51=84.6885, Z52=
101.5375, Z53=-0.6088, Z54=0.7934.
Five groups of ZiThe equation that solution substitutes into formula (4) respectively, and it is as follows to be write as matrix form：
Wherein, matrix coefficientAj2=Zj1Zj3-Zj2Zj4, Aj3=Zj2Zj3+Zj1Zj4, Aj4=Zj1Zj3
+Zj2Zj4, Aj5=Zj2Zj3-Zj1Zj4, Aj6=Zj3Zj4, P=[p1 p2 p3
p4 p5 p6 p7 p8]T,
Make coefficient matrix
Matrix [A]TIt is zero that [A], which has three characteristic values, corresponding three characteristic vector vα, vβAnd vγConstitute kernel
Base.Wherein,
vα=[0.0004,0.0320,0.0101, -0.0337,0.0138,0.9988, -0.0026,0.0017]T,
vβ=[0.0008,0.0545,0.0237, -0.0655,0.0378, -0.0021,0.9954,0.0032]T,
vγ=[- 0.0005, -0.0223, -0.0091,0.0545, -0.0266,0.0013,0.0029,0.9979]T。
α is made, beta, gamma is three real parameters, and any vector can be represented by following formula, so vectorial p is expressed in kernel
For：
P=α vα+βvβ+γvγ (7)
Vectorial p meets formula (5) and (6), the p in formula (7)1、p2、p3、p4、p5、p6And p7Substitute into formula (5) and
(6) obtain
K10α2+K11β2+K12αβ+K13αγ+K14βγ+K15γ2=0 (8)
K20α2+K21β2+K22αβ+K23αγ+K24βγ+K25γ2=0 (9)
Wherein Kmn, m=1,2, n=0,1,2,3,4,5, expressed by the expression formula of three characteristic vectors compositions.Set γ
≠ 0, γ is removed in formula (8) and (9) both sides together2, obtain onWithTwo binary quadratic equations, two dihydric phenol sides
Journey has two groups of real solutions, i.e., vectorial p has two groups of solutions.First group： Back substitution is obtained after vectorial p to p1
=-a0, p2=a0X, p3=a0Y, p4=a1, p5=a2, p6=-a1y+a2X, p7=-(a1x+a2Y)/2, p8=(a3-a0(x2+
y2))/4, corresponding a0=-8.52 × 10-5, a1=0.0037, a2=-0.0013, a3=-0.6627, x=-199.9259, y
=-69.1470.Second group：Same back substitution obtains corresponding a0=2.143 × 10-4, a1=
0.0295, a2=-0.0151, a3=3.633, x=-10.0829, y=-9.4963.Two groups of a0、a1、a2、a3Substitute into formula (3)
And equation of a circle is converted into center of circle radius formula, it is respectively：(X+43.835)2+(Y-15.533)2=99.7242(X-
137.487)2+(Y+70.4616)2=202.0462。
Fixed hinge point is exactly the central coordinate of circle of required equation of a circle, then the fixed hinge point tried to achieve be respectively (- 43.835,
15.533) with (137.487, -70.4616), because the track of mobile hinge point is round, that is, hinge point and fixed hinge point are moved
Distance L1 be 99.724mm.
In order to meet transplant track requirement, wherein three posture points (235,120,10), (252,112,0), (237,
121,12) it is for constraining sharp mouth (a small latch closure for including seedling taking point) track, two other posture point near seedling taking point
(80, -270, -85), (58, -258, -75) are used for constraining the track pushed away near seedling point, and five posture points while constrained trajectory
Whole height, remaining interlude and no requirement (NR), solid black point is posture point in Fig. 3.
A posture point coordinates (235,120,10) is taken, and two groups of x, y values are substituted into
WithCalculate the coordinate of the corresponding two mobile hinge points of posture point coordinates (235,120,10)
For (26.1041,86.6203) and (223.421,112.399).With fixed hinge point (- 43.835,15.533) with
The line of (137.487, -70.4616) is frame, with two fixed hinge points (- 43.835,15.533) and (137.487, -
70.4616) line with corresponding mobile hinge point (26.1041,86.6203) and (223.421,112.399) is crank or pendulum
Bar (bar length is shorter for crank), it is to move the connection of hinge point (26.1041,86.6203) and (223.421,112.399)
Connecting rod, form first set four-bar mechanism, upside mechanism as shown in Figure 3.
A posture point coordinates (80, -270, -85) is taken, and two groups of x, y values are substituted into WithCalculate corresponding two movements of posture point coordinates (80, -270, -85)
The coordinate of hinge point is (- 6.3085, -76.8614) and (69.6611, -260.7831).With fixed hinge point (- 43.835,
15.533) be frame with the line of (137.487, -70.4616), with two fixed hinge points (- 43.835,15.533) and
(137.487, -70.4616) and the corresponding company for moving hinge point (- 6.3085, -76.8614) and (69.6611, -260.7831)
Line is swing rod, to move the connection of hinge point (- 6.3085, -76.8614) and (69.6611, -260.7831) as connecting rod, is formed
Second set of four-bar mechanism, downside mechanism as shown in Figure 3.
Step 3: angular displacement curve is fitted, so as to try to achieve resultant gear ratio curve.
First set four-bar mechanism accurately passes through three posture points (235,120,10), (252,112,0), (237,121,12)
And form first closing track, second set four-bar mechanism accurately pass through two posture points (80, -270, -85), (58, -258, -
75) and formed Article 2 closing track.36 data points are respectively taken from two closing tracks, 10 degree every turn is followed the example of as crank and takes one
Point, then closed at first on track and take 7 points successively according to rotary direction of the crank close to seedling taking point position, calculate 7 points pair
The angular displacement difference of the planet carrier angular displacement answered and planet carrier and transplanting arm；It is close on Article 2 closing track to push away Miao Dianwei
Put and take 3 points successively according to rotary direction of the crank, calculate the angle of planet carrier angular displacement and planet carrier and transplanting arm corresponding to 3 points
Shift differences.
As shown in figure 4, using planet carrier angular displacement as abscissa, the angular displacement difference of planet carrier and transplanting arm is ordinate,
The planet carrier angular displacement and the angular displacement difference of planet carrier and transplanting arm that 7 points according to being taken on first closing track calculate
Describe seven points (being point a to point b sections in Fig. 4), the planet carrier angular displacement that 3 points taken on track calculate is closed according to Article 2
And the angular displacement difference of planet carrier and transplanting arm describes three points (being point c to point d sections in Fig. 4), gives seven interpolation in addition
Point, it need to only ensure that the first and last point ordinate of this 17 interpolation points differs 2 π.Pass through Non-uniform B three times according to 17 interpolation points
Spline interpolation obtains angular displacement curve, and precision can be set to insert 30 match points between two neighboring interpolation point.Angular displacement curve
Dullness need to be ensured, i.e. non-circular gear is not in the phenomenon toward revolution.
Resultant gear ratioWherein w1It is the angular speed of planet carrier 3, w2It is the angular speed of transplanting arm 6, and angle position
It is resultant gear ratio corresponding to this adjacent 2 points that the inverse of the adjacent 2 points of slopes calculated of shifting curve takes negative value again, and then, according to
Angular displacement curve tries to achieve whole piece resultant gear ratio curve, as shown in Figure 5.
Step 4: calculate the length of transplanting arm 6.
Taken to meet that transplanting requires, during the length for calculating transplanting arm 6 outside the closed loop that five posture point broken line lines are formed
Fixed hinge point (- 43.835,15.533), then mobile hinge point coordinates is corresponding to posture point coordinates (235,120,10)
(26.1041,86.6203), and then draw the length L2=211.5459mm of transplanting arm 6.Now, the track of hinge point is moved just
It is that round dot is (- 43.835,15.533), the circle that radius is 99.724mm.
Step 5: carrying out the distribution of resultant gear ratio, the pitch curve of two pairs of non-circular gears is calculated.
The angular displacement of planet carrier 3 and transplanting arm 6 is obtained according to angular displacement curve, in conjunction with planet carrier 3 and the length of transplanting arm 6
Degree obtains the transplanting track of the end of transplanting arm 6.It need to ensure that transplanting the height of track, the length and width of sharp mouth, transplanting arm is taking
Seedling point and angular displacement (the i.e. angle for pushing away seedling point) meet that transplanting requires, the vertical seat of interpolation point on adjustment angle displacement curve can be passed through
Mark to optimize, the transplanting track after optimization is as shown in Figure 6.Three points of the point c to point d sections can also be translated, it is total so as to change
Peak, the paddy section curve of transmission ratio curve, it is finally reached the purpose for improving pitch curve indent.
According to resultant gear ratio curve, two stage gear ratios are distributed.First stage gear ratio isSecond stage gear ratio isAs shown in figure 5, after resultant gear ratio curve is assigned, sub- transmission ratio curve becomes more steady.
Non-circular gear pitch curve polar coordinate representation, if planet carrier angular displacement is θ, the centre-to-centre spacing of two-stage non-circular gear is
a.The polar diameter of first order driving wheel 4 isPolar angle isThe polar diameter of first order driven pulley 2 is r2=a-r1,
Polar angle isWillSubstitute into Because first order driving wheel 4 turns around
When, first order driven pulley 2 also turns around, i.e., nowTry to achieve xs=0.968；Second need not so be handled
Stage gear ratio ensures that second level driving wheel 1 turns around, and second level driven pulley 5 also turns around.The polar diameter of second level driving wheel 1
ForPolar angle isThe polar diameter of second level driven pulley 5 is r4=a-r3, polar angle isTake
During a=70mm, the pitch curve of first order driving wheel 4 is calculated as shown in fig. 7, pitch curve such as Fig. 8 institutes of first order driven pulley 2
Show, the pitch curve of second level driving wheel 1 is as shown in figure 9, the pitch curve of second level driven pulley 5 is as shown in Figure 10.
Claims (1)
1. the non-circular gear planetary gear system design method based on kinematics mapping, it is characterised in that：This method is specific as follows：
Step 1: structure non-circular gear planetary gear system, including planet carrier and transplanting arm, and the first order in planet carrier is set
Driving wheel, first order driven pulley, second level driving wheel and second level driven pulley；First order driving wheel is fixed in frame；Planet
One end of frame is hinged with first order driving wheel, and the other end is hinged with second level driven pulley, and middle part is hinged with first order driven pulley；The
One-level driven pulley and second level driving wheel are affixed；The pin joint of first order driving wheel is defined as fixing pin joint, and the second level is driven
The pin joint of wheel is defined as dynamic pin joint；First order driving wheel engages with first order driven pulley；Second level driving wheel and the second level
Driven pulley engages；The housing of transplanting arm and second level driven pulley are affixed；The cam of transplanting arm and planet carrier are affixed；
Step 2: the method reverse based on kinematics mapping goes out two sets of four-bar mechanisms；
The coordinate expression-form that dynamic coordinate (x, y) of the hinge point in moving coordinate system xoy is transformed into quiet coordinate system XOY is as follows：
Wherein, moving coordinate system xoy origins are d1 to the distance of X-axis, and the distance to Y-axis is d2, and the angle of x-axis and X-axis is
Order
Willd1And d2Use Z1、Z2、Z3And Z4Expression, is obtained
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Because dynamic hinge point is inevitable on the circle using fixed hinge point as the center of circle, i.e., dynamic hinge point meets equation of a circle：
2a1X+2a2Y+a3=a0(X2+Y2) (3)
Wherein, a0、a1、a2And a3It is coefficient；
Formula (2) is substituted into formula (3), obtained：
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Wherein, p1=-a0, p2=a0X, p3=a0Y, p4=a1, p5=a2, p6=-a1y+a2X, p7=-(a1x+a2Y)/2, p8=
(a3-a0(x2+y2))/4；
Eight coefficient p1、p2、p3、p4、p5、p6、p7And p8It is not independent, but it must is fulfilled for following two equations
p1p6+p2p5-p3p4=0 (5)
2p1p7-p2p4-p3p5=0 (6)
Posture point is expressed as three-dimensional coordinate form (d1, d2,), take five posture point (dj1, dj2,), j=1,2,3,4,5,
Formula (1) is substituted into respectively obtains five groups of ZiSolution, i=1,2,3,4, five groups of ZiSolution is designated as Zji；In order to meet to transplant the requirement of track,
Wherein three posture point seedling taking points are nearby chosen, and two other posture point is pushing away the selection of seedling point, and five posture points constrain simultaneously
The whole height of track；
Five groups of ZiThe equation that solution substitutes into formula (4) respectively, and it is as follows to be write as matrix form：
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<mn>41</mn>
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<mn>43</mn>
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<mn>44</mn>
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<mi>A</mi>
<mn>45</mn>
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<mn>46</mn>
</msub>
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<mi>A</mi>
<mn>47</mn>
</msub>
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<mn>48</mn>
</msub>
</mtd>
</mtr>
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<mi>A</mi>
<mn>51</mn>
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<mn>52</mn>
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<mn>53</mn>
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<mn>54</mn>
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<mtd>
<msub>
<mi>A</mi>
<mn>55</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>A</mi>
<mn>56</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>A</mi>
<mn>57</mn>
</msub>
</mtd>
<mtd>
<msub>
<mi>A</mi>
<mn>58</mn>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mi>p</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
Wherein, matrix coefficientAj2=Zj1Zj3-Zj2Zj4, Aj3=Zj2Zj3+Zj1Zj4, Aj4=Zj1Zj3+
Zj2Zj4, Aj5=Zj2Zj3-Zj1Zj4, Aj6=Zj3Zj4, P=[p1p2 p3 p4
p5 p6 p7 p8]T,
Make coefficient matrix
Matrix [A]TIt is zero that [A], which has three characteristic values, corresponding three characteristic vector vα, vβAnd vγConstitute the base of kernel；
α is made, beta, gamma is three real parameters, and vectorial p is expressed as：
P=α vα+βvβ+γvγ (7)
Vectorial p meets formula (5) and (6), the p in formula (7)1、p2、p3、p4、p5、p6And p7Formula (5) and (6) is substituted into obtain
K10α2+K11β2+K12αβ+K13αγ+K14βγ+K15γ2=0 (8)
K20α2+K21β2+K22αβ+K23αγ+K24βγ+K25γ2=0 (9)
Wherein Kmn, m=1,2, n=0,1,2,3,4,5, expressed by the expression formula of three characteristic vectors compositions；γ ≠ 0 is set,
γ is removed in formula (8) and (9) both sides together2, obtain onWithTwo binary quadratic equations, two binary quadratic equations have two
Group real solution, i.e., vectorial p have two groups of solutions；Back substitution is to p after obtaining two groups of solutions of vectorial p respectively1=-a0, p2=a0X, p3=a0Y, p4
=a1, p5=a2, p6=-a1y+a2X, p7=-(a1x+a2Y)/2, p8=(a3-a0(x2+y2))/4, try to achieve two groups of a0, a1, a2, a3,
X, y；Two groups of a0、a1、a2、a3Substitute into formula (3) and equation of a circle is converted into center of circle radius formula；The central coordinate of circle of two equation of a circles
It is exactly two fixed hinge points；
A posture point is taken in three posture points near seedling taking point, and two groups of x, y values are substituted into
WithCalculate two mobile hinge point coordinates corresponding to the posture point；With two fixed hinges
The line of point is frame, using two fixed hinge points with the line of corresponding mobile hinge point as crank or swing rod, with two movements
The connection of hinge point is connecting rod, forms first set four-bar mechanism；
Push away and a posture point is taken in two posture points near seedling point, and two groups of x, y values are substituted into
WithCalculate two mobile hinge point coordinates corresponding to the posture point；With two fixed hinges
The line of point is frame, using two fixed hinge points with the line of corresponding mobile hinge point as crank or swing rod, with two movements
The connection of hinge point is connecting rod, forms second set of four-bar mechanism；
Step 3: angular displacement curve is fitted, so as to try to achieve resultant gear ratio curve；
36 data points are respectively taken from two closing tracks, 10 degree every turn is followed the example of as crank and takes a bit；Then in first closing
Take seven points successively according to rotary direction of the crank close to seedling taking point position on track, calculate planet carrier angular displacement corresponding to seven points with
And the angular displacement difference of planet carrier and transplanting arm；Close to pushing away seedling point position according to rotary direction of the crank successively on Article 2 closing track
Three points are taken, calculate the angular displacement difference of planet carrier angular displacement and planet carrier and transplanting arm corresponding to three points；
Using planet carrier angular displacement as abscissa, the angular displacement difference of planet carrier and transplanting arm is ordinate, according to first closing
Seven points, root are described in the planet carrier angular displacement and the angular displacement difference of planet carrier and transplanting arm that seven points taken on track calculate
The planet carrier angular displacement calculated according to three points taken on Article 2 closing track and the angular displacement difference of planet carrier and transplanting arm
Describe three points, give seven interpolation points in addition, ensure that the first and last point ordinate of this 17 interpolation points differs 2 π；According to 17
Individual interpolation point obtains angular displacement curve by uniform B-Spline interpolation three times, and insertion number is more than between two neighboring interpolation point
20 match point；Angular displacement curve need to ensure dullness, i.e. non-circular gear is not in the phenomenon toward revolution；
Resultant gear ratioWherein w1It is the angular speed of planet carrier, w2It is the angular speed of transplanting arm, and angular displacement curve
It is resultant gear ratio corresponding to this adjacent 2 points that the inverse of adjacent 2 points of slopes calculated takes negative value again, and then, according to angular displacement
Curve tries to achieve whole piece resultant gear ratio curve；
Step 4: calculate the length of transplanting arm；
To meet that transplanting requires, the fixation outside the closed loop that five posture point broken line lines are formed is taken during the length for calculating transplanting arm
Hinge point, in four-bar mechanism where the fixed hinge point, the mobile hinge according to corresponding to a posture point coordinates and the posture point
Chain point draws the length of transplanting arm；
Step 5: carrying out the distribution of resultant gear ratio, the pitch curve of two pairs of non-circular gears is calculated；
The angular displacement of planet carrier and transplanting arm is obtained according to angular displacement curve, moved in conjunction with the length of planet carrier and transplanting arm
Plant the transplanting track of arm cusp；Transplanting track is optimized by the ordinate of interpolation point on adjustment angle displacement curve；Will be according to
The planet carrier angular displacement and the angular displacement difference of planet carrier and transplanting arm that three points taken on two closing tracks calculate are described
Three points translation, so as to change the peak of resultant gear ratio curve, paddy section curve, be finally reached improve gear pitch curve indent mesh
's；
According to resultant gear ratio curve, two stage gear ratios are distributed；First stage gear ratio isSecond stage gear ratio is
Non-circular gear pitch curve polar coordinate representation, if planet carrier angular displacement is θ, the centre-to-centre spacing of two-stage non-circular gear is a；The
The polar diameter of one-level driving wheel isPolar angle isThe polar diameter of first order driven pulley is r2=a-r1, polar angle isWillSubstitute intoWhen being turned around due to first order driving wheel, the first order
Driven pulley also turns around, i.e., nowTry to achieve xs；The polar diameter of second level driving wheel isPolar angle isThe polar diameter of second level driven pulley is r4=a-r3, polar angle is
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| CN109826927B (en) * | 2019-04-04 | 2020-07-14 | 浙江理工大学 | Design method of secondary unequal-amplitude non-circular gear transmission planetary gear train seedling taking mechanism |
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