CN106113042A - The geometry solving method of parallel institution instantaneous axis - Google Patents
The geometry solving method of parallel institution instantaneous axis Download PDFInfo
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- CN106113042A CN106113042A CN201610590067.4A CN201610590067A CN106113042A CN 106113042 A CN106113042 A CN 106113042A CN 201610590067 A CN201610590067 A CN 201610590067A CN 106113042 A CN106113042 A CN 106113042A
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- space
- parallel institution
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
- B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators
Abstract
The present invention proposes a kind of geometry solving method of parallel institution instantaneous axis, comprises the steps: to draw out the structure diagram of parallel institution, and draws out the kinematic pair of each side chain；Calculate the degree of freedom space of each side chain；According to Generalized Dual rule, solve the constraint space of each side chain；According to the constraint space of each side chain, solve parallel institution moving platform constraint space；Further according to Generalized Dual rule, solve the instantaneous axis of parallel institution moving platform.The present invention proposes a kind of geometry solving method of parallel institution instantaneous axis, changes complicated algebraic operation for simple geometric operation, reduces computational complexity.Make result of calculation more directly perceived.
Description
Technical field
The present invention relates to path adaptation technical field, particularly to a kind of geometry solving method of parallel institution instantaneous axis.
Background technology
Instantaneous axis is a very important concept in parallel robot.Can be in the hope of the rotary shaft of its moving platform by instantaneous axis
Line and speed.At present, the method solving employing algebraically mostly of instantaneous axis, main method has: by Jacobian matrix and input speed
Degree is solved the instantaneous axis of moving platform and is solved by attitude matrix.
Solved by the method for Jacobi:
Wherein, J is that the spinor of parallel robot moving platform is expressed, and ω is the Jacobian matrix of robot,For input angle speed
Degree.Instantaneous axis is solved by the method for attitude matrix:
Wherein, A represents the matrix of 4 × 4, is the attitude matrix of linkage platform, andFor the derivative of this matrix, A-1
Meet AA-1=Ι.
From above two method for solving it can be seen that the major defect of the method for solving of existing instantaneous axis and deficiency are:
Amount of calculation is bigger, and solving result is the most directly perceived.
Such as the patent of invention of Chinese patent CN 102107431A, this invention provides a kind of parallel robot, but, this
Major defect and the deficiency of the method for solving of bright parallel robot instantaneous axis are: amount of calculation is bigger, and solving result is the most straight
See.
Summary of the invention
The purpose of the present invention is intended at least solve one of described technological deficiency.
To this end, it is an object of the invention to propose the geometry solving side of a kind of solving result parallel institution instantaneous axis intuitively
Method.
To achieve these goals, the present invention provides a kind of geometry solving method of parallel institution instantaneous axis, including walking as follows
Rapid:
Step S1, according to the structure of parallel institution, draws out the structure diagram of parallel institution, and draws out each side chain
Kinematic pair；
Step S2, according to being drawn out the kinematic pair of each side chain, calculates the degree of freedom space of each side chain；
Step S3, according to Generalized Dual rule, solves the constraint space of each side chain；
Step S4, according to the constraint space of each side chain, solves parallel institution moving platform constraint space；
Step S5, further according to Generalized Dual rule, solves the instantaneous axis of parallel institution moving platform.
Further, in step sl, when drawing out the kinematic pair of each side chain, utilize different colours, different directions, have
Straight line without arrow makes a distinction.
Further, in step s 2, described degree of freedom space is the set comprising multiple kinematic pair spinor line；
One vector $ in described degree of freedom spacefIt is expressed as:
$f=$1∩$2∩...∩$i...∩$n；
Wherein, n is all side chain kinematic pair number summations, and $ represents the spinor of kinematic pair.
Further, in step s 2, the spinor that revolute pair is corresponding is expressed as:
Wherein, s is the unit vector of spinor axis direction, can represent with the cosine in three directions, and r is this spinor axis
On any point；So, the geometric expression of its correspondence is a line, and this line is the axis through revolute pair.
Further, in step s 2, the spinor that moving sets is corresponding is expressed as:
Wherein, s represents the direction of moving sets, and its geometric expression is the two ends lines with arrow；
Further, described Generalized Dual rule meets following condition:
The all of force constraint line phases with its dual constraint space of every rotational freedom line in A, degree of freedom space
Hand over or parallel；Vice versa；
Every moving direction line in B, degree of freedom space is all vertical with all of force constraint line in its dual constraint space；
Otherwise, the even mensuration line of each constraint in constraint space hangs down with all rotational freedom lines in its antithesis degree of freedom space
Directly；
Moving direction line in C, degree of freedom space can be any with the even amount line of direction of the constraint in its dual constraint space
Configuration；
The general motion axis of screw in degree of freedom space meets with the general wrench of a force system axis in its dual constraint space:
pF+pC=dFCtanαFC, F=1,2 ..., n；C=1,2 ..., 6-n；
Wherein pFFor the pitch of kinematic screw, p in degree of freedom spaceCFor the pitch of restraining forces spiral, d in constraint spaceFC
It is the common vertical line distance of two spirals, αFCIt it is the angle of two spirals.
Further, meet antithesis according to the vector in the vector degree of freedom space in Generalized Dual rule constraint space to close
System.That is:
Wherein, $fOne vector in expression degree of freedom space, and $cIt it is the vector in constraint space.
Further, in step s 5, according to Generalized Dual rule, try to achieve and the vector $ in constraint spacecThe arrow of antithesis
Amount $1,$2,$3...$i, then utilize parallelogram law, the above-mentioned vector obtained that solves synthesized, then after synthesis
Vector is the instantaneous axis of parallel institution moving platform.
The present invention proposes a kind of geometry solving method of parallel institution instantaneous axis, changes complicated algebraic operation in order to simply
Geometric operation, reduce computational complexity.Make result of calculation more directly perceived.
Aspect and advantage that the present invention adds will part be given in the following description, and part will become from the following description
Obtain substantially, or recognized by the practice of the present invention.
Accompanying drawing explanation
Above-mentioned and/or the additional aspect of the present invention and advantage are from combining the accompanying drawings below description to embodiment and will become
Substantially with easy to understand, wherein:
Fig. 1 a-Fig. 1 g is the geometric expression schematic diagram of common kinematic pair；
Fig. 2 is the overall flow figure of the present invention；
Fig. 3 is parallelogram law schematic diagram；
Fig. 4 is instantaneous axis geometry solving flow chart of the present invention.
Detailed description of the invention
Embodiments of the invention are described below in detail, and the example of described embodiment is shown in the drawings, the most from start to finish
Same or similar label represents same or similar element or has the element of same or like function.Below with reference to attached
The embodiment that figure describes is exemplary, it is intended to is used for explaining the present invention, and is not considered as limiting the invention.
Method of geometry is related operation based on spinor, is a kind of geometric expression of algebraic operation in spinor.
First introducing some basic concepts, parallel institution typically has several side chains, and every side chain all can have kinematic pair,
First the geometric expression of each kinematic pair is introduced:
For revolute pair (R) specific in mechanism, its 1 degree of freedom, by the redness coincided with pivot center
Straight line characterizes, as shown in (Fig. 1 a), these two ends without the straight line of arrow, not only there is as pivot center direction attribute and
And also there is position attribution；Moving sets (P) common in mechanism also only have 1 degree of freedom, with one parallel with moving direction and
The straight line of two ends band arrow characterizes, as (shown in (Fig. 1 b), owing to moving movement only has direction attribute, so this freedom of movement
Degree line the most only has direction attribute.
A common class pure rolling pair in mechanism, as secondary in meshed gears, friction free cam is secondary, and this kinematic pair also only has
1 degree of freedom, its transient motion is considered as two Objects around As contact lines and does relatively pure rolling, can with one with contact line weight
The two ends closed characterize, as (shown in (Fig. 1 c), with rotational motion, this symbol represents that symbol is the same not only without the red straight line of arrow
There is direction attribute but also there is position attribution.
Hooke's hinge (U) common in mechanism has 2 rotational freedoms, as (shown in (Fig. 1 d), respectively with two respectively with
Pivot center overlaps and the two ends intersected characterize without the straight line of arrow, the intersection point of two straight lines and Hooke's hinge center superposition；Mechanism
In common cylindrical pair (C) have mobile and rotate 2 degree of freedom, as shown in (Fig. 1 e), respectively with one and cylindrical pair rotation
The two ends of dead in line characterize its rotational motion without arrow straight line, then with a two ends band arrow parallel with cylindrical pair pivot center
Head straight line characterizes its moving movement.
Spherical pair (S) common in mechanism has 3 rotational freedoms, as shown in (Fig. 1 f), with three non-coplanar but converge
The two ends meeting at space common point represent without arrow straight line, and this space common point overlaps with spherical pair central point；In mechanism common
Planar contact pair (E) there are 1 rotational freedom and 2 one-movement-freedom-degrees, as shown in (Fig. 1 h), with two parallel with plane but phase
The two ends band arrow straight line and the two ends perpendicular with plane that are not parallel to each other represent without arrow straight line.
This geometric expression and their spinor algebra express one_to_one corresponding.
The present invention provides a kind of geometry solving method of parallel institution instantaneous axis, with reference to accompanying drawing 2-3, comprises the steps:
Step S1, according to the structure of parallel institution, draws out the structure diagram of parallel institution, and draws out each side chain
Kinematic pair；
When drawing out the kinematic pair of each side chain, different colours, different directions, straight line with or without arrow is utilized to carry out district
Point.
The collection of illustrative plates symbol with power that moves represents
Such as, rotating symbol straight line and represent, this straight line coincides with the rotating shaft of revolute pair.Moving sets band arrow
Line represents, its direction is consistent with the direction of movement.
Step S2, according to being drawn out the kinematic pair of each side chain, calculates the degree of freedom space of each side chain；
This line chart constitutes the degree of freedom space of each side chain, similar to the formation of vector space in linear algebra, freely
Degree space refers to the space opened by object of which movement spinor, is the set comprising multiple motion spinor line, and it characterizes object
The space motion allowed, seek common ground available degree of freedom space to each revolute pair.
One vector $ in degree of freedom spacefIt is expressed as:
$f=$1∩$2∩...∩$i...∩$n, (1)；
Wherein, n is all side chain kinematic pair number summations, and $ represents the spinor of kinematic pair.
Spinor corresponding to revolute pair is expressed as:
Wherein, s is the unit vector of spinor axis direction, can represent with the cosine in three directions, and r is this spinor axis
On any point；So, the geometric expression of its correspondence is a line, and this line is the axis through revolute pair.
Painted revolute pair spinor line is the most correct to use above-mentioned formula (2) may determine that.
The spinor that moving sets is corresponding is expressed as:
Wherein, s represents the direction of moving sets, and its geometric expression is the two ends lines with arrow；
Painted revolute pair spinor line is the most correct to use above-mentioned formula (3) may determine that.
Other kinematic pair can be regarded as the linear combination that both basic exercises are secondary.
Step S3, according to Generalized Dual rule, solves the constraint space of each side chain；
Generalized Dual rule meets following condition:
The all of force constraint line phases with its dual constraint space of every rotational freedom line in A, degree of freedom space
Hand over or parallel；Vice versa；
Every moving direction line in B, degree of freedom space is all vertical with all of force constraint line in its dual constraint space；
Otherwise, the even mensuration line of each constraint in constraint space hangs down with all rotational freedom lines in its antithesis degree of freedom space
Directly；
Moving direction line in C, degree of freedom space can be any with the even amount line of direction of the constraint in its dual constraint space
Configuration；
The general motion axis of screw in degree of freedom space meets with the general wrench of a force system axis in its dual constraint space:
pF+pC=dFCtanαFC, F=1,2 ..., n；C=1,2 ..., 6-n；(4)；
Wherein pFFor the pitch of kinematic screw, p in degree of freedom spaceCFor the pitch of restraining forces spiral, d in constraint spaceFC
It is the common vertical line distance of two spirals, αFCIt it is the angle of two spirals.
Step S4, according to the constraint space of each side chain, solves parallel institution moving platform constraint space；
Vector according to the vector degree of freedom space in Generalized Dual rule constraint space meets duality relation.I.e. retrain
Amassing of the vector in the vector degree of freedom space in space is 0:
Formula is:
Wherein, $fOne vector in expression degree of freedom space, and $cIt it is the vector in constraint space.
Step S5, further according to Generalized Dual rule, solves the instantaneous axis of parallel institution moving platform.
According to Generalized Dual rule, try to achieve and the vector $ in constraint spacecThe vector $ of antithesis1,$2,$3...$i, then profit
By parallelogram law, as shown in Figure 4, synthesize the above-mentioned vector obtained that solves, then the vector after synthesis is in parallel
The instantaneous axis of mechanism's moving platform.
The present invention proposes a kind of geometry solving method of parallel institution instantaneous axis, changes complicated algebraic operation in order to simply
Geometric operation, reduce computational complexity.Make result of calculation more directly perceived.
Although above it has been shown and described that embodiments of the invention, it is to be understood that above-described embodiment is example
Property, it is impossible to be interpreted as limitation of the present invention, those of ordinary skill in the art is without departing from the principle of the present invention and objective
In the case of above-described embodiment can be changed within the scope of the invention, revise, replace and modification.The scope of the present invention
Extremely it is equal to by claims and limits.
Claims (8)
1. the geometry solving method of a parallel institution instantaneous axis, it is characterised in that comprise the steps:
Step S1, according to the structure of parallel institution, draws out the structure diagram of parallel institution, and draws out the motion of each side chain
Secondary；
Step S2, according to being drawn out the kinematic pair of each side chain, calculates the degree of freedom space of each side chain；
Step S3, according to Generalized Dual rule, solves the constraint space of each side chain；
Step S4, according to the constraint space of each side chain, solves parallel institution moving platform constraint space；
Step S5, further according to Generalized Dual rule, solves the instantaneous axis of parallel institution moving platform.
The geometry solving method of a kind of parallel institution instantaneous axis the most as claimed in claim 1, it is characterised in that: in step sl,
When drawing out the kinematic pair of each side chain, different colours, different directions, straight line with or without arrow is utilized to make a distinction.
The geometry solving method of a kind of parallel institution instantaneous axis the most as claimed in claim 1, it is characterised in that: in step s 2,
Described degree of freedom space is the set comprising multiple kinematic pair spinor line；
One vector $ in described degree of freedom spacefIt is expressed as:
$f=$1∩$2∩...∩$i...∩$n；
Wherein, n is all side chain kinematic pair number summations, and $ represents the spinor of kinematic pair.
The geometry solving method of a kind of parallel institution instantaneous axis the most as claimed in claim 1, it is characterised in that: in step s 2,
Spinor corresponding to revolute pair is expressed as:
Wherein, s is the unit vector of spinor axis direction, can represent with the cosine in three directions, and r is on this spinor axis
Any point；So, the geometric expression of its correspondence is a line, and this line is the axis through revolute pair.
The geometry solving method of a kind of parallel institution instantaneous axis the most as claimed in claim 1, it is characterised in that: in step s 2,
The spinor that moving sets is corresponding is expressed as:
Wherein, s represents the direction of moving sets, and its geometric expression is the two ends lines with arrow.
The geometry solving method of a kind of parallel institution instantaneous axis the most as claimed in claim 1, it is characterised in that: described Generalized Dual
Rule meets following condition:
Every rotational freedom line in A, degree of freedom space all intersect with all of force constraint line in its dual constraint space or
Parallel；Vice versa；
Every moving direction line in B, degree of freedom space is all vertical with all of force constraint line in its dual constraint space；Instead
It, the even mensuration line of each constraint in constraint space is vertical with all rotational freedom lines in its antithesis degree of freedom space；
Moving direction line in C, degree of freedom space can be with arbitrary disposition with the even amount line of direction of the constraint in its dual constraint space；
The general motion axis of screw in degree of freedom space meets with the general wrench of a force system axis in its dual constraint space:
pF+pC=dFC tanαFC, F=1,2 ..., n；C=1,2 ..., 6-n；
Wherein pFFor the pitch of kinematic screw, p in degree of freedom spaceCFor the pitch of restraining forces spiral, d in constraint spaceFCIt is two spiral shells
The common vertical line distance of rotation, αFCIt it is the angle of two spirals.
The geometry solving method of a kind of parallel institution instantaneous axis the most as claimed in claim 1, it is characterised in that: according to Generalized Dual
The vector in the vector degree of freedom space in rule constraint space meets duality relation.That is:
Wherein, $fOne vector in expression degree of freedom space, and $cIt it is the vector in constraint space.
The geometry solving method of a kind of parallel institution instantaneous axis the most as claimed in claim 1, it is characterised in that: in step s 5,
According to Generalized Dual rule, try to achieve and the vector $ in constraint spacecThe vector $ of antithesis1,$2,$3...$i, then utilize parallel four
Limit shape rule, synthesizes the above-mentioned vector obtained that solves, then the instantaneous axis that vector is parallel institution moving platform after synthesis.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112936289A (en) * | 2021-03-24 | 2021-06-11 | 太原科技大学 | Method for judging virtual constraints and number thereof in mechanism based on continuity of over-constraints |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5427531A (en) * | 1992-10-20 | 1995-06-27 | Schlumberger Technology Corporation | Dynamic simulation of mechanisms |
| CN102968665A (en) * | 2012-12-05 | 2013-03-13 | 苏州大学 | Forward kinematics solving method of parallel robot |
| CN103034123A (en) * | 2012-12-11 | 2013-04-10 | 中国科学技术大学 | Dynamic model parameter identification based parallel robot control method |
| CN103472724A (en) * | 2013-09-16 | 2013-12-25 | 江苏大学 | Real-time control dynamics modeling method for multi-freedom-degree parallel mechanism |
| CN103500367A (en) * | 2013-10-08 | 2014-01-08 | 北京理工大学 | 3-PRS (Prismatic-Revolute-Spherical) parallel robot positioning accuracy optimization method based on interval analysis |
-
2016
- 2016-07-25 CN CN201610590067.4A patent/CN106113042B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5427531A (en) * | 1992-10-20 | 1995-06-27 | Schlumberger Technology Corporation | Dynamic simulation of mechanisms |
| CN102968665A (en) * | 2012-12-05 | 2013-03-13 | 苏州大学 | Forward kinematics solving method of parallel robot |
| CN103034123A (en) * | 2012-12-11 | 2013-04-10 | 中国科学技术大学 | Dynamic model parameter identification based parallel robot control method |
| CN103472724A (en) * | 2013-09-16 | 2013-12-25 | 江苏大学 | Real-time control dynamics modeling method for multi-freedom-degree parallel mechanism |
| CN103500367A (en) * | 2013-10-08 | 2014-01-08 | 北京理工大学 | 3-PRS (Prismatic-Revolute-Spherical) parallel robot positioning accuracy optimization method based on interval analysis |
Non-Patent Citations (1)
| Title |
|---|
| 陈子明，黄真，曹文熬: "《空间少自由度并联机构瞬时螺旋运动轴线曲面的几何表示方法》", 《燕山大学学报》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112936289A (en) * | 2021-03-24 | 2021-06-11 | 太原科技大学 | Method for judging virtual constraints and number thereof in mechanism based on continuity of over-constraints |
| CN112936289B (en) * | 2021-03-24 | 2022-11-04 | 太原科技大学 | Method for judging virtual constraints and number of virtual constraints in mechanism based on continuity of overconstrained |
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