CN104240263B - A kind of motion subtree system for Delta parallel manipulators - Google Patents

Abstract

The invention discloses a kind of motion subtree system for Delta parallel manipulators, including man machine interface and algorithm two large divisions；Man machine interface includes that integration motion subtree interface, cylindrical coordinatess inverse mode interface, cylindrical coordinatess are just calculating mode interface and data output interface；Algorithm includes just algorithm and inverse algorithm, and displacement, speed, accelerating curve display algorithm and its module；The system can carry out being related to the positive inverse of arm end executive component and prime mover mutual alignment relation according to positive and negative computation algorithm, end component body dynamics information is exported in the way of curve and form, Delta parallel manipulators B joint triangle correlation geometric properties information is described in the form of space equation, and TXT format system simulation calculus data lists are made, B joints are the joint of the upper arm with underarm junction of Delta parallel manipulator arms.The present invention can effectively realize the motion subtree of Delta parallel manipulators.

Description

A kind of motion subtree system for Delta parallel manipulators

Technical field

The present invention relates to the technical field of industrial automation system structure structure and Simulation Control, referring in particular to one kind is used for The motion subtree system of Delta parallel manipulators.

Background technology

Flexible robot's (mechanical hand) is for intelligent grabbing, general to coordinate visual imaging and pneumatic execution to realize that crawl is dynamic Make, be usually used in capturing the materials such as food (chocolate, confection, cookiess, moon cake etc.), electronic component.Delta mechanisms are in three dimensions Interior efficient logistics' settlement scheme has promoted company of robot of various countries with regard to the exploitation upsurge of the mechanism.So far, it is above-mentioned various High-speed parallel manipulator have been supplied in the industrial automation such as electronics, medicine, food production or the sorting of packaging line, pick-and-place, The operation such as packaging.

The content of the invention

It is an object of the invention to overcome the deficiencies in the prior art and defect, there is provided a kind of to be used for Delta parallel manipulators Motion subtree system, it is possible to achieve input space cylindrical coordinatess data, arm end executive component and prime mover position The functions such as inverse, output end component displacement, speed and accelerating curve are being calculated just.

For achieving the above object, technical scheme provided by the present invention is：A kind of motion for Delta parallel manipulators Characteristic analysis system, including the man machine interface and algorithm two large divisions that are made by Visual Basic language；The man machine interface Mode interface and data output interface are being calculated just including integration motion subtree interface, cylindrical coordinatess inverse mode interface, cylindrical coordinatess； The algorithm includes the just calculation algorithm and inverse algorithm based on interspace analytic geometry, and displacement, speed, accelerating curve show Algorithm and its module；The system can carry out being related to arm end executive component and prime mover phase according to positive and negative computation algorithm Mutually the positive inverse of position relationship, exports end component body dynamics information, in the way of curve and form with the shape of space equation Formula describes Delta parallel manipulators B joint triangle correlation geometric properties information, and makes TXT format system simulation calculus numbers According to list, wherein, the B joints are the joint of the upper arm with underarm junction of Delta parallel manipulator arms.

Manipulator arm length input, the final actuating element space whole story can be carried out in the case where motion subtree interface is integrated The relative angle of operation of the input of position cylindrical coordinatess, the angular displacement driver corresponding with whole story position cylindrical coordinatess is exported, relative motion Characteristic information output services；

Each arm length and final actuating element whole story position coordinateses, system are input in the case where motion subtree interface is integrated By the just calculation integrated according to inside and inverse algorithm, the corner that inverse is obtained and shows angular displacement driver is first passed through, then Based on the inverse result, it is assumed that final actuating element is, with straightway as track, three angular displacements to be calculated and displayed and drives The whole story angular displacement numerical value of dynamic device, based on being assumed by this, is calculated and is drawn out in the specified time according to even acceleration-at the uniform velocity-even Three coordinate direction displacement of final actuating element, speed and accelerating curve during retarded motion mode.

Manipulator arm length input, final actuating element space whole story position can be carried out under cylindrical coordinatess inverse mode interface Put cylindrical coordinatess input, the relative angle of operation output of the angular displacement driver comprising two kinds of feasible solutions, three angular displacement drivers turn Angle-time curve output services；

Each arm length and final actuating element position coordinateses are input at cylindrical coordinatess inverse mode interface, can be calculated full Two groups of solutions of sufficient condition, one of which solution are not attainable singular solution, due to adopting the inverse based on interspace analytic geometry Algorithm, algorithm are related to trigonometric function equation in itself, thus generate the singular solution, and input final actuating element whole story position is sat Mark, the angular displacement that can calculate and draw out three angular displacement drivers change over curve.

Just calculating in cylindrical coordinatess and can carry out under mode interface the input of angular displacement driver whole story corner；B joints triangle geometry Feature is exported, including B₁B₂B₃The output of oscillating bearing plane equation, B₁B₂The output of middle vertical plane equation, B joint △ B₁B₂B₃Three length of sides Output, B joint △ B₁B₂B₃Circumradius is exported and B joint △ B₁B₂B₃Unfaithful intention coordinate is exported, B₁、B₂、B₃Represent respectively The B joints of three groups of arms of Delta parallel manipulators；The D point coordinates output of final actuating element center and relative motion feature are believed Breath output services；

The whole story numerical value that mode interface is input into three angular displacement driver angles is being calculated just in cylindrical coordinatess, system will be according to just calculating Algorithm is according to B₁B₂B₃Oscillating bearing plane equation, B₁B₂And B₂B₃Middle vertical plane equation, B joint △ B₁B₂B₃Three length of sides, B joints Place △ B₁B₂B₃Circumradius and B joint △ B₁B₂B₃The order of unfaithful intention coordinate is calculated, and abundant display systems were calculated Journey, finally draws the coordinate of final actuating element center D points, and calculates and draw out three coordinate direction position of final actuating element Shifting, speed and accelerating curve.

Manipulator arm length input, inertia of respectively rolling over input, each arm quality can be carried out under data output interface Input, the final actuating element whole story position coordinateses input, require movement time input, the angular displacement driver whole story angle output, The output of angular displacement driver Mean Speed, guiding system simulation calculus data list work；

Each arm length is input under data output interface, roll over inertia and arm, final actuating element quality, end End executive component whole story position coordinateses and run time, system will be according to final actuating element with straightway as track, angular displacement The hypothesis of the even acceleration of driver-at the uniform velocity-uniformly accelerated motion mode is calculated and be shown angular displacement driver uniform motion stage speed, Some segmentations in record motor process, the coordinate of each segmentation, speed and accekeration, and output TXT data forms are provided Function.

The integration motion subtree interface and cylindrical coordinatess are just being calculated mode interface and are being owned by exporting final actuating element three The function of coordinate direction displacement, speed and accelerating curve, which employs the Graphics graphic plotting modes in VB programs, and The function being adjusted to the scale for showing curve relative coordinates axle, the cylindrical coordinatess inverse mode interface and cylindrical coordinatess are provided Just calculate mode interface and provide the interface just calculated with inverse phase separation.

The inverse is the locus cylindrical coordinatess for being input into final actuating element, calculates motor movement angle by algorithm Degree, its algorithm are as follows：

Inside program using cylindrical coordinatess calculate, self-defined angle initial value be 30 degree, below variable declaration：l₁For OA distances, l₂ For upper arm lengths, l₃For lower arm lengths, l₄For the distance of three oscillating bearings of final actuating element centre-to-centre spacing, dx is that end performs The angle variables of element central definition, dy are the radius variable of final actuating element center definition, during dz is final actuating element The height variable of heart definition,For upper arm and horizontal direction angle, opA, opB, opC areThree constants of equation, by known bar Part is calculated；

Rectilinear motion mode is calculated：

If from (θ₁, r1, h1) and move to (θ₂, r2, h2), motor is just in uniform rotation cylindrical coordinatess

Cartesian coordinate

If D point coordinates is D (θ_D, r_D, h_D)

Design coordinate branching program

Descartes

Wherein scope r_D≤ 131.18, h_D≤244.18

To 2 points of applications distances formula of BC (whereinFor unknown number)

Launch

Abbreviation 1

Abbreviation 2

Abbreviation 3

Three groups of same processes of arm application carry out abbreviation

Solve above-mentioned trigonometric function equation opA sin θs+opB cos θ+opC=0

Using formula

Can solve

The inverse data just at last by obtaining, it is assumed that final actuating element is even from space starting point in a linear fashion Accelerate, at the uniform velocity, in the case of even deceleration, during calculating after displacement, speed and acceleration, can with selectivity output calculate data or Shown in the form of s-t, v-t, a-t figure, its algorithm is as follows：

Cylindrical coordinatess

Cartesian coordinate

Distance of the space a little away from B1, B2, B3 is equal, and B1, B2, B3 represent three groups of handss of Delta parallel manipulators respectively The B joints of arm,

Determine B1, B2, the B3 circumscribed circle center of circle

Circumradius

Semicircle is long

Heron's formula

Wherein abc is three length of sides, by obtained by space length formula；

Circumscribed circle central coordinate of circle formula is as follows：

Radius

Increment is defined using the method for direction vector

If 2 points (x1, y1, z1) and (x2, y2, z2), its direction vector is (x2-x1, y2-y1, z2-z1)

All directions increment may be defined as

Circular cylindrical coordinate divides into 2 points of (θ₁,r₁,h₁) and (θ₂,r₂,h₂)

Direction vector (r₂cosθ₂-r₁cosθ₁,r₂sinθ₂-r₁sinθ₁,h₂-h₁)

It is as follows that direction vector turns circular cylindrical coordinate：

Direction increment should be：

Defined in program, direction vector is vic, i.e. vector v ictor

The cylindrical coordinatess that cartesian coordinate is represented be dex, dey, dez

Then there is initial value dex=r₁cosθ₁, dey=r₁sinθ₁, dez=h₁

There are all directions increment deltax, deltay, deltaz

And be definite value

Equation array：

B arrays are directly adopted, is conveniently checked, conversion array is first replaced with bb and bbb

B plane equations are solved, has then tried to achieve B1B2, B2B3, B3B1 direction cosine matrix

According to triangle excenter property, unfaithful intention O should be in planeThree plane crossing places

Ternary linear function is solved again

Attached direction cosines seek method：

Using vector method, it is known that hand exercise characteristic is only translation, therefore willCan to hand center translation certain distance The feature geometries body of similar ball is formed,

Three translation vectors areTranslation distance is l₄If, translation vector be MOVE (3,3)

MOVE matrixes are

B points are made matrix addition, note paying back toward vector translation；

Translation transformation adopts four-matrix multiplication transformations

B point coordinates need to increase one-dimensional, and basic skills is as follows：

Triangle circumcenter coordinate is asked for according to said method

Semi-perimeter

Heron's formula

Circumradius

The direction vector for asking for OD straight line expression formulas, vertical plane B1B2B3 and D excessively can represent that direction vector advancesLength, as D point position.

The system includes Delta parallel manipulator single armed set feature input modules, can change interior by the module Portion calculates the size characteristic with Delta parallel manipulators, and then can be used to calculate the Delta parallel manipulators with acceleration as index The optimal solution of handss.

The system includes result of calculation display module, and the result of calculation display module defines frame with scale, can Display of the figure line in coordinate is controlled by defining scale size.

The present invention compared with prior art, has the advantage that and beneficial effect：

The system can effectively realize the motion subtree of Delta parallel manipulators, it is possible to achieve input space post is sat Inverse, output end component body dynamics information, Delta are just being calculated in mark data, arm end executive component and prime mover position The functions such as parallel manipulator B joint triangle correlation geometric properties information, system simulation calculation data list；Wrap inside the system The output data listing function of the triangle geometry feature of joint containing B, angular displacement driver geometric properties etc., can be in parallel for Delta Robot movement feature analysiss provide convenient approach, the determination of Delta construction geometry relations and optimization are provided for the later stage Foundation；Cylindrical coordinatess inverse mode interface and cylindrical coordinatess are just being calculated mode interface and are providing the man machine interface just calculated with inverse phase separation, Can use as the teaching software of colleges and universities' training student study parallel manipulator, make student's profound understanding parallel manipulator positive and negative Calculate meaning；The system can change each arm length of parallel manipulator, with reference to the simulation calculus result data list of the system, can To coordinate statistical method solution to be able to the mechanical hand length optimal solution of the minimum condition of acceleration.

Description of the drawings

Schematic diagrams of the Fig. 1 for Delta parallel manipulators.

Fig. 2 is the integration motion subtree surface chart comprising result of calculation.

Fig. 3 is the cylindrical coordinatess inverse mode surface chart comprising result of calculation.

Fig. 4 is that the cylindrical coordinatess comprising result of calculation are just calculating mode surface chart.

Fig. 5 is the data output interface figure comprising result of calculation.

Data list document maps of the Fig. 6 for data output interface result of calculation.

Specific embodiment

With reference to specific embodiment, the invention will be further described.

The motion subtree system for Delta parallel manipulators described in the present embodiment, including by Visual Man machine interface and algorithm two large divisions that Basic language makes；Wherein, the man machine interface includes integrating motion subtree circle Face (SIM interfaces), cylindrical coordinatess inverse mode interface (Cylindrical Coordinate-Inverse Solution interfaces), Cylindrical coordinatess are just calculating mode interface (Cylindrical Coordinate-Positive Solution interfaces) and data output circle Face (Motor interfaces)；The algorithm includes the just calculation algorithm and inverse algorithm based on interspace analytic geometry, and displacement, speed, Accelerating curve display algorithm and its module.

The system can carry out being related to arm end executive component and prime mover mutual alignment according to positive and negative computation algorithm The positive inverse of relation, exports end component body dynamics information in the way of curve and form, is described in the form of space equation Delta parallel manipulators B joint triangle correlation geometric properties information, and TXT format system simulation calculus data lists are made, Wherein, the B joints are the joint of the upper arm with underarm junction of Delta parallel manipulator arms, as shown in Figure 1.

Manipulator arm length input, the final actuating element space whole story can be carried out in the case where motion subtree interface is integrated The relative angle of operation of the input of position cylindrical coordinatess, the angular displacement driver corresponding with whole story position cylindrical coordinatess is exported, relative motion The work such as characteristic information (curve) output；

Each arm length and final actuating element whole story position coordinateses, system are input in the case where motion subtree interface is integrated By the just calculation integrated according to inside and inverse algorithm, the corner that inverse is obtained and shows angular displacement driver is first passed through, then Based on the inverse result, it is assumed that final actuating element is, with straightway as track, three angular displacements to be calculated and displayed and drives The whole story angular displacement numerical value of dynamic device, based on being assumed by this, is calculated and is drawn out in the specified time according to even acceleration-at the uniform velocity-even Three coordinate direction displacement of final actuating element, speed and accelerating curve during retarded motion mode, as shown in Figure 2.

Manipulator arm length input, final actuating element space whole story position can be carried out under cylindrical coordinatess inverse mode interface Put cylindrical coordinatess input, the relative angle of operation output of the angular displacement driver comprising two kinds of feasible solutions, three angular displacement drivers turn The work such as angle-time curve output；

Each arm length and final actuating element position coordinateses are input at cylindrical coordinatess inverse mode interface, can be calculated full Two groups of solutions of sufficient condition, one of which solution are not attainable singular solution, due to adopting the inverse based on interspace analytic geometry Algorithm, algorithm are related to trigonometric function equation in itself, thus generate the singular solution, and input final actuating element whole story position is sat Mark, the angular displacement that can calculate and draw out three angular displacement drivers change over curve, as shown in Figure 3.

Just calculating in cylindrical coordinatess and can carry out under mode interface the input of angular displacement driver whole story corner；B joints triangle geometry Feature is exported, including B₁B₂B₃The output of oscillating bearing plane equation, B₁B₂The output of middle vertical plane equation, B joint △ B₁B₂B₃Three length of sides Output, B joint △ B₁B₂B₃Circumradius is exported and B joint △ B₁B₂B₃Unfaithful intention coordinate is exported, B₁、B₂、B₃Represent respectively The B joints of three groups of arms of Delta parallel manipulators；The D point coordinates output of final actuating element center and relative motion feature are believed The work such as breath (curve) output；

The whole story numerical value that mode interface is input into three angular displacement driver angles is being calculated just in cylindrical coordinatess, system will be according to just calculating Algorithm is according to B₁B₂B₃Oscillating bearing plane equation, B₁B₂And B₂B₃Middle vertical plane equation, B joint △ B₁B₂B₃Three length of sides, B joints Place △ B₁B₂B₃Circumradius and B joint △ B₁B₂B₃The order of unfaithful intention coordinate is calculated, and abundant display systems were calculated Journey, finally draws the coordinate of final actuating element center D points, and calculates and draw out three coordinate direction position of final actuating element Shifting, speed and accelerating curve, as shown in Figure 4.

Manipulator arm length input, inertia of respectively rolling over input, each arm quality can be carried out under data output interface Input, the final actuating element whole story position coordinateses input, require movement time input, the angular displacement driver whole story angle output, The work such as the output of angular displacement driver Mean Speed, guiding system simulation calculus data list；

Each arm length is input under data output interface, roll over inertia and arm, final actuating element quality, end End executive component whole story position coordinateses and run time, system will be according to final actuating element with straightway as track, angular displacement The hypothesis of the even acceleration of driver-at the uniform velocity-uniformly accelerated motion mode is calculated and be shown angular displacement driver uniform motion stage speed, Some segmentations in record motor process, the coordinate of each segmentation, speed and accekeration, and output TXT data forms are provided Function, as shown in Figure 5 and Figure 6.

The integration motion subtree interface and cylindrical coordinatess are just being calculated mode interface and are being owned by exporting final actuating element three The function of coordinate direction displacement, speed and accelerating curve, which employs the Graphics graphic plotting modes in VB programs, root According to the feature of the display packing, to allow users to preferably observe curve, the method for drafting is provided to be sat to showing that curve is relative The function that the scale of parameter is adjusted.The cylindrical coordinatess inverse mode interface and cylindrical coordinatess are just being calculated mode interface and are just being provided Calculate and interface that inverse is separated, can use as the teaching software of colleges and universities training students study parallel manipulator, allow student The positive inverse meaning of profound understanding parallel manipulator.

The inverse is the locus cylindrical coordinatess for being input into final actuating element, calculates motor movement angle by algorithm Degree.Its algorithm is as follows：

Inside program using cylindrical coordinatess calculate, self-defined angle initial value be 30 degree, below variable declaration：l₁For OA distances, l₂ For upper arm lengths, l₃For lower arm lengths, l₄For the distance of three oscillating bearings of final actuating element centre-to-centre spacing, dx is that end performs The angle variables of element central definition, dy are the radius variable of final actuating element center definition, during dz is final actuating element The height variable of heart definition,For upper arm and horizontal direction angle, opA, opB, opC areThree constants of equation, by known bar Part is calculated；

Rectilinear motion mode is calculated：

If from (θ₁, r1, h1) and move to (θ₂, r2, h2), motor is just in uniform rotation

Cylindrical coordinatess

Cartesian coordinate

If D point coordinates is D (θ_D, r_D, h_D)

Design coordinate branching program

Descartes

Wherein scope r_D≤ 131.18, h_D≤244.18

To 2 points of applications distances formula of BC (whereinFor unknown number)

Launch

Abbreviation 1

Abbreviation 2

Abbreviation 3

Three groups of same processes of arm application carry out abbreviation

Solve above-mentioned trigonometric function equation opA sin θs+opB cos θ+opC=0

Using formula

Can solve

During inverse, in the locus post of the size characteristic and final actuating element of user input Delta parallel manipulator After coordinate, the starting point coordinate and terminal point coordinate of input are converted into space vector by system, bring the utilization of motor corner unknown number into The joint part coordinate of space geometry relation calculating machine handss arm, by this calculated three coordinate respectively with origin coordinates Point-to-point transmission coordinate formula is constituted with terminal point coordinate.Two groups of resulting three ternary quadratic equations will be obtained by a set of abbreviation step To the reasonable calculating formula with regard to motor corner tangent.Final calculation result is drawn by triangulation.By this algorithm meter Motor movement angle is calculated, in Industry Control, can be by the angle information and other relative motion characteristic inputs be transported Dynamic control module, reaches the control end component purpose that path is moved according to the rules.

The inverse data just at last by obtaining, it is assumed that final actuating element is even from space starting point in a linear fashion Accelerate, at the uniform velocity, in the case of even deceleration, during calculating after displacement, speed and acceleration, can with selectivity output calculate data or Shown in the form of s-t, v-t, a-t figure.Its algorithm is as follows：

Cylindrical coordinatess

Cartesian coordinate

Distance of the space a little away from B1, B2, B3 is equal, and B1, B2, B3 represent three groups of handss of Delta parallel manipulators respectively The B joints of arm,

Determine B1, B2, the B3 circumscribed circle center of circle

Circumradius

Semicircle is long

Heron's formula

Wherein abc is three length of sides, by obtained by space length formula；

Circumscribed circle central coordinate of circle formula is as follows：

Radius

Increment is defined using the method for direction vector

If 2 points (x1, y1, z1) and (x2, y2, z2), its direction vector is (x2-x1, y2-y1, z2-z1)

All directions increment may be defined as

Circular cylindrical coordinate divides into 2 points of (θ₁,r₁,h₁) and (θ₂,r₂,h₂)

Direction vector (r₂cosθ₂-r₁cosθ₁,r₂sinθ₂-r₁sinθ₁,h₂-h₁)

It is as follows that direction vector turns circular cylindrical coordinate：

Direction increment should be：

Defined in program, direction vector is vic, i.e. vector v ictor

The cylindrical coordinatess that cartesian coordinate is represented be dex, dey, dez

Then there is initial value dex=r₁cosθ₁, dey=r₁sinθ₁, dez=h₁

There are all directions increment deltax, deltay, deltaz

And be definite value

Equation array：

B arrays are directly adopted, is conveniently checked, conversion array is first replaced with bb and bbb

B plane equations are solved, has then tried to achieve B1B2, B2B3, B3B1 direction cosine matrix

According to triangle excenter property, unfaithful intention O should be in planeThree plane crossing places are again Secondary solution ternary linear function

Attached direction cosines seek method：

Using vector method, it is known that hand exercise characteristic is only translation, therefore willCan to hand center translation certain distance The feature geometries body of similar ball is formed,

Three translation vectors areTranslation distance is l₄If, translation vector be MOVE (3,3)

MOVE matrixes are

B points are made matrix addition, note paying back toward vector translation；

Translation transformation adopts four-matrix multiplication transformations

B point coordinates need to increase one-dimensional, and basic skills is as follows：

Triangle circumcenter coordinate is asked for according to said method

Semi-perimeter

Heron's formula

Circumradius

The direction vector for asking for OD straight line expression formulas, vertical plane B1B2B3 and D excessively can represent that direction vector advancesLength, as D point position.

When just calculating, using gained inverse data as initial data, according to user-defined motion mode (defined in this program For even acceleration, at the uniform velocity, uniformly retarded motion feature), it is assumed that final actuating element moves to end from space starting point with straight path Thus point, can set up the motion vector in three joints.Joint motion vector is stored by matrix, and will be carried out Discrete processes, dispersion degree are determined by precision prescribed is calculated.To obtain serial on motion vector, the start-stop of joint using this method A series of coordinates between point.Every group of joint coordinates be all with final actuating element as the centre of sphere, lower pole segments length is as radius Point on ball.Articulare circumcentre of a triangle and circumradius are calculated by Heron's formula, unfaithful intention and end is it is easy to show that Executive component line is perpendicular to 3 points of place planes.Height coordinate can be drawn using the mode of solution space triangle, passed through Simple geometry calculates two other coordinate.Speed and acceleration are calculated also through similar form.Displacement, speed during calculating After acceleration, data can be calculated with selectivity output or be shown in the form of s-t, v-t, a-t figure.

The way of output of figure addend evidence can allow user to be more convenient to be apparent from just calculating and inverse algorithm flow, deeply Know from experience algorithm essence, preferable teaching efficiency can be reached.

Additionally, present system also provides Delta parallel manipulators single armed set feature input module and result of calculation show Module, can change internal calculation Delta parallel manipulator by the Delta parallel manipulator single armed set feature input modules The size characteristic of handss, and then can be used to calculate the optimal solution of the Delta parallel manipulators with acceleration as index, it is designer Determine that arm size provides foundation.And the result of calculation display module defines frame with scale, definition ratio can be passed through Chi size controls display of the figure line in coordinate.

Embodiment described above is only present pre-ferred embodiments, not limits the practical range of the present invention with this, therefore The change made by all shapes according to the present invention, principle, all should cover within the scope of the present invention.

Claims (8)

1. a kind of motion subtree system for Delta parallel manipulators, it is characterised in that：Including by Visual Basic Man machine interface and algorithm two large divisions that language makes；The man machine interface includes integrating motion subtree interface, cylindrical coordinatess Inverse mode interface, cylindrical coordinatess are just calculating mode interface and data output interface；The algorithm is included based on interspace analytic geometry Just algorithm and inverse algorithm, and displacement, speed, accelerating curve display algorithm and its module；The system being capable of basis Positive and negative computation algorithm carries out the positive inverse for being related to arm end executive component and prime mover mutual alignment relation, with curve and table The mode of lattice exports end component body dynamics information, and Delta parallel manipulators B joint triangle is described in the form of space equation Shape correlation geometric properties information, and make TXT format system simulation calculus data lists, wherein, the B joints be Delta simultaneously The upper arm of connection manipulator arm and the joint of underarm junction；The inverse is that the locus post for being input into final actuating element is sat Mark, calculates motor movement angle by algorithm, and its algorithm is as follows：

Inside program using cylindrical coordinatess calculate, self-defined angle initial value be 30 degree, below variable declaration：l₁For OA distances, l₂For upper Arm lengths, l₃For lower arm lengths, l₄For the distance of three oscillating bearings of final actuating element centre-to-centre spacing, dx is final actuating element The angle variables of center definition, radius variables of the dy for the definition of final actuating element center, dz are fixed for final actuating element center The height variable of justice,For upper arm and horizontal direction angle, opA, opB, opC areThree constants of equation, by known conditions meter Draw；

Rectilinear motion mode is calculated：

If from (θ₁, r1, h1) and move to (θ₂, r2, h2), motor is just in uniform rotation

Cylindrical coordinatess

Cartesian coordinate

If D point coordinates is D (θ_D, r_D, h_D)

Design coordinate branching program

Descartes

Wherein scope r_D≤ 131.18, h_D≤244.18

To 2 points of applications distances formula of BC, whereinFor unknown number

$\begin{array}{c}{\[r_D{\mathrm{cos\θ}}_D+l_{4}cos\mathrm{\θ}-(l_1+l_{2}cos{\∂}_1)cos0\]}^2+{\[r_D{\mathrm{sin\θ}}_D+l_{4}sin0-(l_1+l_{2}cos{\∂}_1)sin0\]}^2+{(h_D-l_{2}sin{\∂}_1)}^2\\ =l_3^2\end{array}$

Launch

$\begin{array}{c}{\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)}^2+{\[\left(l_1+l_2\cos {\∂}_1\right)\cos 0\]}^2-2\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)\left(l_1+l_2\cos {\∂}_1\right)\cos 0\\ +{\left(r_D{\mathrm{sin\θ}}_D+l_4\sin 0\right)}^2+{\[\left(l_1+l_2\cos {\∂}_1\right)\sin 0\]}^2-2\left(r_D{\mathrm{sin\θ}}_D+l_4\sin 0\right)\left(l_1+l_2\cos {\∂}_1\right)\sin 0\\ +h_D^2+{\left(l_2\sin {\∂}_1\right)}^2-2h_D{l}_2\sin {\∂}_1-l_3^2=0\end{array}$

Abbreviation 1

$\begin{array}{c}{\left(l_1+l_2\cos {\∂}_1\right)}^2+{\left(l_2\sin {\∂}_1\right)}^2-2\[r_D{\mathrm{cos\θ}}_D\cos 0+l_4{\cos }^{2}0+r_D{\mathrm{sin\θ}}_D\sin 0+l_4{\sin }^{2}0\]\left(l_1+l_2\cos {\∂}_1\right)\\ -2h_D{l}_2\sin {\∂}_1+{\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)}^2+{\left(r_D{\mathrm{sin\θ}}_D+l_4\sin 0\right)}^2+h_D^2-l_3^2=0\end{array}$

Abbreviation 2

$\begin{array}{c}{l}_1^2+l_2^2+2l_1{l}_{2}cos{\∂}_1-2(r_D{\mathrm{cos\θ}}_{D}cos0+r_D{\mathrm{sin\θ}}_{D}sin0+l_4^2)(l_{2}cos{\∂}_1+l_1)-h_D{l}_{2}sin{\∂}_1+\\ \mathrm{......}\end{array}$

Abbreviation 3

$\begin{array}{c}2l_2(r_D{\mathrm{cos\θ}}_{D}cos0+r_D{\mathrm{sin\θ}}_{D}sin0+l_4^2+l_1)cos{\∂}_1-2h_D{l}_{2}sin{\∂}_1+l_1^2+l_2^2\\ -2l_1\left(r_D{\mathrm{cos\θ}}_D\cos 0+r_D{\mathrm{sin\θ}}_D+{l_4}^2\right)+{\left(r_D{\mathrm{cos\θ}}_D+l_4\cos 0\right)}^2+{\left(r_D{\mathrm{sin\θ}}_D+R_4\sin 0\right)}^2+h_D^2-l_3^2=0\end{array}$

Three groups of same processes of arm application carry out abbreviation

Solve above-mentioned trigonometric function equation opA sin θs+opB cos θ+opC=0

Using formula

$tan\left(\frac{\∂}{2}\right)=\frac{A\±\sqrt{A^2+B^2-C^2}}{B-C}$

Can solve

The inverse data just at last by obtaining, it is assumed that final actuating element adds from space starting point is even in a linear fashion Speed, at the uniform velocity, in the case of even deceleration, during calculating after displacement, speed and acceleration, can with selectivity output calculate data or with The form of s-t, v-t, a-t figure shows that its algorithm is as follows：

Cylindrical coordinatess

Cartesian coordinate

Distance of the space a little away from B1, B2, B3 is equal, and B1, B2, B3 represent the B of three groups of arms of Delta parallel manipulators respectively Joint,

Determine B1, B2, the B3 circumscribed circle center of circle

Circumradius

Semicircle is long

Heron's formula

$R=\frac{abc}{\sqrt{(a+b+c)(a+b-c)(a-b+c)(-a+b+c)}}$

Wherein abc is three length of sides, by obtained by space length formula；

Circumscribed circle central coordinate of circle formula is as follows：

$A=\sqrt{{(Xa-Xb)}^2+{(Ya-Yb)}^2}$

$B=\sqrt{{(Xa-Xc)}^2+{(Ya-Yc)}^2}$

$C=\sqrt{{(Xb-Xc)}^2+{(Yb-Yc)}^2}$

$Y=\frac{A+B+C}{2}$

$X=\sqrt{Y(Y-A)(Y-B)(Y-C)}$

Radius

Increment is defined using the method for direction vector

If 2 points (x1, y1, z1) and (x2, y2, z2), its direction vector is (x2-x1, y2-y1, z2-z1)

All directions increment may be defined as

Circular cylindrical coordinate divides into 2 points of (θ₁,r₁,h₁) and (θ₂,r₂,h₂)

Direction vector (r₂cosθ₂-r₁cosθ₁,r₂sinθ₂-r₁sinθ₁,h₂-h₁)

It is as follows that direction vector turns circular cylindrical coordinate：

$\left(\arctan \left(\frac{r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1}{r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1}\right),\sqrt{{\left(r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1\right)}^2+{\left(r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1\right)}^2},h_2-h_1\right)$

Direction increment should be：

$\left(\arctan \right(\frac{r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1}{r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1}),\frac{\sqrt{{(r_2{\mathrm{cos\θ}}_2-r_1{\mathrm{cos\θ}}_1)}^2+{(r_2{\mathrm{sin\θ}}_2-r_1{\mathrm{sin\θ}}_1)}^2}}{n},\frac{h_2-h_1}{n})$

Defined in program, direction vector is vic, i.e. vector v ictor

The cylindrical coordinatess that cartesian coordinate is represented be dex, dey, dez

Then there is initial value dex=r₁cosθ₁, dey=r₁sinθ₁, dez=h₁

There are all directions increment deltax, deltay, deltaz

And be definite value

$deltaz=\frac{h_2-h_1}{n}$

Equation array：

B arrays are directly adopted, is conveniently checked, conversion array is first replaced with bb and bbb

B plane equations are solved, has then tried to achieve B1B2, B2B3, B3B1 direction cosine matrixAccording to three Angular unfaithful intention property, unfaithful intention O should be in planeThree plane crossing places solve ternary first power again Journey

Attached direction cosines seek method：

$cos{\∂}_1=\frac{x_{B2}-x_{B1}}{\left|B1B2\right|}$

${\mathrm{cos\β}}_1=\frac{y_{B2}-y_{B1}}{\left|B1B2\right|}$

${\mathrm{cosv}}_1=\frac{z_{B2}-z_{B1}}{\left|B1B2\right|}$

Using vector method, it is known that hand exercise characteristic is only translation, therefore willCan be formed to hand center translation certain distance The feature geometries body of similar ball,

Three translation vectors areTranslation distance is l₄If, translation vector be MOVE (3,3) MOVE matrixes be

B points are made matrix addition, note paying back toward vector translation；

Translation transformation adopts four-matrix multiplication transformations

B point coordinates need to increase one-dimensional, and basic skills is as follows：

$\left[\begin{array}{cccc}x& y& z& 1\end{array}\right]\×\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ m& n& p& 1\end{array}\right]=\left[\begin{array}{cccc}x+m& y+n& z+p& 1\end{array}\right]$

Triangle circumcenter coordinate is asked for according to said method

Semi-perimeter

Heron's formula

Circumradius

The direction vector for asking for OD straight line expression formulas, vertical plane B1B2B3 and D excessively can represent that direction vector advances Length, as D point position.

2. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Manipulator arm length input, final actuating element space whole story position can be carried out in the case where motion subtree interface is integrated Cylindrical coordinatess input, the relative angle of operation of the angular displacement driver corresponding with whole story position cylindrical coordinatess are exported, relative motion feature Information output works；

It is input into each arm length and final actuating element whole story position coordinateses in the case where motion subtree interface is integrated, system will be by The just calculation integrated according to inside and inverse algorithm, first pass through the corner that inverse is obtained and shows angular displacement driver, then with this Based on inverse result, it is assumed that final actuating element is, with straightway as track, three angular displacement drivers to be calculated and displayed Whole story angular displacement numerical value, based on being assumed by this, calculate and draw out in the specified time according to even acceleration-at the uniform velocity-even deceleration Three coordinate direction displacement of final actuating element, speed and accelerating curve during motion mode.

3. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Manipulator arm length input, final actuating element space whole story position column can be carried out under cylindrical coordinatess inverse mode interface Coordinate input, the relative angle of operation output of the angular displacement driver comprising two kinds of feasible solutions, three angular displacement drivers corner-when Between relation curve output services；

Each arm length and final actuating element position coordinateses are input at cylindrical coordinatess inverse mode interface, can be calculated and be met bar Two groups of solutions of part, one of which solution are not attainable singular solution, due to adopting the inverse algorithm based on interspace analytic geometry, Algorithm is related to trigonometric function equation in itself, thus generates the singular solution, is input into final actuating element whole story position coordinateses, can The angular displacement for calculating and drawing out three angular displacement drivers changes over curve.

4. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Just calculating in cylindrical coordinatess and can carry out under mode interface the input of angular displacement driver whole story corner；B joints triangle geometry feature is defeated Go out, including B₁B₂B₃The output of oscillating bearing plane equation, B₁B₂The output of middle vertical plane equation, B joint △ B₁B₂B₃The output of three length of sides, B Joint △ B₁B₂B₃Circumradius is exported and B joint △ B₁B₂B₃Unfaithful intention coordinate is exported, B₁、B₂、B₃Delta is represented respectively The B joints of three groups of arms of parallel manipulator；The D point coordinates output of final actuating element center and relative motion characteristic information are exported Work；

The whole story numerical value that mode interface is input into three angular displacement driver angles is being calculated just in cylindrical coordinatess, system will be according to just algorithm According to B₁B₂B₃Oscillating bearing plane equation, B₁B₂And B₂B₃Middle vertical plane equation, B joint △ B₁B₂B₃Three length of sides, B joint △ B₁B₂B₃Circumradius and B joint △ B₁B₂B₃The order of unfaithful intention coordinate is calculated, abundant display systems calculating process, most The coordinate of final actuating element center D points is drawn afterwards, and is calculated and drawn out three coordinate direction displacement of final actuating element, speed Degree and accelerating curve.

5. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：Can carry out under data output interface manipulator arm length input, inertia of respectively rolling over input, each arm mass input, Final actuating element whole story position coordinateses are input into, require movement time input, the output of angular displacement driver whole story angle, angular displacement The output of driver Mean Speed, guiding system simulation calculus data list work；

Each arm length is input under data output interface, inertia is rolled over and arm, final actuating element quality, end are held Units whole story position coordinateses and run time, system will be according to final actuating elements with straightway as track, and angular displacement drives The hypothesis of the even acceleration of device-at the uniform velocity-uniformly accelerated motion mode is calculated and be shown angular displacement driver uniform motion stage speed, record Some segmentations in motor process, the coordinate of each segmentation, speed and accekeration, and the function of output TXT data forms is provided.

6. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：The integration motion subtree interface and cylindrical coordinatess are just being calculated mode interface and are being owned by exporting three coordinate side of final actuating element To the function of displacement, speed and accelerating curve, the Graphics graphic plotting modes in VB programs are which employs, and provides right Show the function that the scale of curve relative coordinates axle is adjusted；The cylindrical coordinatess inverse mode interface and the cylindrical coordinatess just side of calculation Formula interface provides just calculates the interface being separated with inverse.

7. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：The system includes Delta parallel manipulator single armed set feature input modules, can change internal calculation by the module With the size characteristic of Delta parallel manipulators, and then can be used to calculating Delta parallel manipulators with acceleration as index most Excellent solution.

8. a kind of motion subtree system for Delta parallel manipulators according to claim 1, its feature exist In：The system includes result of calculation display module, and the result of calculation display module defines frame with scale, can be by fixed Adopted scale size controls display of the figure line in coordinate.