CN107944097A - Plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again - Google Patents
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Abstract
The present invention relates to mechanism kinematics chain field, discloses a kind of numbering matrix description method that plane enclosed cuts with scissors kinematic chain again, the component and kinematic pair of kinematic chain are numbered, wherein kinematic pair is Pn, and generate n × n numbering matrix As.The numbering matrix description method that plane enclosed of the present invention cuts with scissors kinematic chain again eliminates the relationship expression of topological diagram, information is prevented to lose, and numbering matrix is corresponded with kinematic chain, can uniquely represent a kinematic chain, kinematic chain structure diagram can be directly drawn by numbering matrix.
Description
Technical field
The present invention relates to mechanism kinematics chain field, and in particular to a kind of plane enclosed cuts with scissors the numbering matrix description of kinematic chain again
Method.
Background technology
The basis that research institution is learned is kinematic chain signature analysis, and the description of kinematic chain plays extremely important in theory of mechanisms
Role.For traditional method for expressing, kinematic chain schematic diagram is usually changed into topological diagram, then topological diagram is converted into square
Battle array, and carry out relevant computing.And when drawing topological diagram to structure diagram, due to comprising compound hinges, causing topological graph expression
It is comparatively laborious, and the technique of painting due to topological diagram and form are also diversified, are easily lost a part of information, such as kinematic pair
Attribute etc., when topological diagram is converted into matrix, a part of information, such as rod piece numbering etc. are lost in matrix again.Therefore need
A kind of expression, avoids the above problem, prevents the loss of the information such as movement sub-attribute and rod piece numbering.
The content of the invention
Deficiency of the purpose of the present invention aiming at above-mentioned technology, there is provided a kind of plane enclosed cuts with scissors the numbering square of kinematic chain again
Battle array description method, eliminates the relationship expression of topological diagram, it is therefore prevented that and information is lost, and numbering matrix is corresponded with kinematic chain,
It can uniquely represent a kinematic chain, kinematic chain structure diagram can directly be drawn by numbering matrix.
To achieve the above object, a kind of plane enclosed designed by the present invention cuts with scissors the numbering matrix description side of kinematic chain again
Method, is numbered the component and kinematic pair of kinematic chain, and wherein kinematic pair is Pn, and generate n × n numbering matrix As：
In formula, n be kinematic pair quantity, the diagonal entry a of numbering matrixi,j(i=j) be 0, numbering matrix its
Its element ai,j(i ≠ j, i=1 ..., n；J=1 ..., n) it is connection kinematic pair PiWith kinematic pair PjComponent numbering, work as movement
Secondary PiWith kinematic pair PjWhen not connecting, ai,j=0.
Preferably, by the element a of the numbering matrix Ai,jBool computings are carried out, as element ai,jWhen=0, element value is not
Become, as element ai,jWhen ≠ 0, element value value 1, obtains adjacency matrix B.
Preferably, numbering matrix A is retrieved, as kinematic pair PiWith kinematic pair PjA when not connectingi,j=0, as kinematic pair PiWith
Kinematic pair PjA when having connectioni,j=1, the incidence matrix C of kinematic chain is obtained, wherein line number represents component numbering, and row number represents fortune
Dynamic secondary numbering, expressive movement secondary PnWith the connection relation of each component.
Preferably, numbering matrix A is retrieved, as kinematic pair PiThe number that the component numbering of corresponding i row elements occurs is k,
Kinematic pair PiThe component of corresponding i row elements is g member components, g=k+1, obtains the attribute list of kinematic chain component.
Preferably, numbering matrix A is retrieved, as kinematic pair PiThe number that the component numbering of corresponding i column elements occurs is k,
Kinematic pair PiThe component of corresponding i row elements is g member components, g=k+1, obtains the attribute list of kinematic chain component.
Preferably, numbering matrix A is retrieved, as kinematic pair PiCorresponding i row elements ai,j(i, j=1,2, ..., n) in have m
A and more than m non-zero and unequal value, then kinematic pair PiThe hinge at place is the multiple hinge of m members, wherein m >=3.
Preferably, numbering matrix A is retrieved, as kinematic pair PiCorresponding i column elements ai,j(i, j=1,2, ..., n) in have m
A and more than m non-zero and unequal value, then kinematic pair PiThe hinge at place is the multiple hinge of m members, wherein m >=3.
Preferably, to kinematic pair PiCorresponding i row elements ai,j(i, j=1,2 ..., n) carries out broad sense computing, rejects non-zero
Element, retains 2 to the identical components numbering more than 2, obtains each kinematic pair PiArray code name, and then obtain array generation
Number with kinematic pair PiThe corresponding kinematic pair type list of connection relation.
Preferably, to kinematic pair PiCorresponding i column elements ai,j(i, j=1,2 ..., n) carries out broad sense computing, rejects non-zero
Element, retains 2 to the identical components numbering more than 2, obtains each kinematic pair PiArray code name, and then obtain array generation
Number with kinematic pair PiThe corresponding kinematic pair type list of connection relation.
Preferably, by kinematic pair P in kinematic pair type listiConnection relation retrieved, obtain band kinematic pair Pi's
Structure attribute table.
Compared with prior art, the present invention has the following advantages：Eliminate the relationship expression of topological diagram, it is therefore prevented that information is lost
Lose, and numbering matrix is corresponded with kinematic chain, can uniquely represent a kinematic chain, movement can be directly drawn by numbering matrix
Chain structure schematic diagram.
Brief description of the drawings
Fig. 1 is the structural representation that plane enclosed of the present invention cuts with scissors a kinematic chain in the numbering matrix description method of kinematic chain again
Figure.
Each part numbers are as follows in figure：
First component 1, second component 2, the 3rd component 3, the 4th component 4, the 5th component 5, the 6th component 6, the 7th component
7th, the 8th component 8, the 9th component 9, the tenth component 10, the first kinematic pair 11, the second kinematic pair 12, the 3rd kinematic pair the 13, the 4th
Kinematic pair 14, the 5th kinematic pair 15, the 6th kinematic pair 16, the 7th kinematic pair 17, the 8th kinematic pair 18, the 9th kinematic pair 19,
Ten kinematic pairs 20, the 11st kinematic pair 21.
Embodiment
The present invention is described in further detail with specific embodiment below in conjunction with the accompanying drawings.
A kind of plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again, and the component and kinematic pair of kinematic chain are compiled
Number, wherein kinematic pair is Pn, and generate n × n numbering matrix As：
In formula, n be kinematic pair quantity, the diagonal entry a of numbering matrixi,j(i=j) be 0, numbering matrix its
Its element ai,j(i ≠ j, i=1 ..., n；J=1 ..., n) it is connection kinematic pair PiWith kinematic pair PjComponent numbering, work as movement
Secondary PiWith kinematic pair PjWhen not connecting, ai,j=0.
By the element a of numbering matrix Ai,jBool computings are carried out, as element ai,jWhen=0, element value is constant, as element ai,j
When ≠ 0, element value value 1, obtains adjacency matrix B；Numbering matrix A is retrieved, as kinematic pair PiWith kinematic pair PjWhen not connecting
ai,j=0, as kinematic pair PiWith kinematic pair PjA when having connectioni,j=1, the incidence matrix C of kinematic chain is obtained, wherein line number represents structure
Part is numbered, and row number represents kinematic pair numbering, expressive movement secondary PnWith the connection relation of each component；Numbering matrix A is retrieved, works as movement
Secondary PiThe number that the component numbering of corresponding i rows or i column elements occurs is k, kinematic pair PiThe component of corresponding i row elements is g members
Component, g=k+1, the attribute list of acquirement kinematic chain component；Numbering matrix A is retrieved, as kinematic pair PiCorresponding i rows or i column elements
ai,jThere are m and more than m non-zero and unequal value in (i, j=1,2, ..., n), then kinematic pair PiThe hinge at place is multiple for m members
Hinge, wherein m >=3；To kinematic pair PiCorresponding i rows or i column elements ai,j(i, j=1,2 ..., n) carries out broad sense computing, rejects non-
Neutral element, retains 2 to the identical components numbering more than 2, obtains each kinematic pair PiArray code name, and then obtain array
Code name and kinematic pair PiThe corresponding kinematic pair type list of connection relation；By to kinematic pair P in kinematic pair type listiConnection close
System is retrieved, and obtains band kinematic pair PiStructure attribute table.
With reference to shown in Fig. 1, which is a kinematic chain C1Structure diagram, the component and kinematic pair of kinematic chain are compiled
Number, which includes the first kinematic pair 11, the second kinematic pair 12, the 3rd kinematic pair 13, the movement of the 4th kinematic pair the 14, the 5th
Secondary 15, the 6th kinematic pair 16, the 7th kinematic pair 17, the 8th kinematic pair 18, the 9th kinematic pair 19, the tenth kinematic pair the 20, the 11st
Kinematic pair 21 and connect the first component 1 of above-mentioned kinematic pair, second component 2, the 3rd component 3, the 4th component by relation in figure
4th, the 5th component 5, the 6th component 6, the 7th component 7, the 8th component 8, the 9th component 9 and the tenth component 10, and generate 11 × 11
Numbering matrix
Numbering matrixElement ai,jRepresent kinematic chain C1Kinematic pair PiWith kinematic pair PjConnection relation, for example, compile
Number matrixMiddle a3,4Represent that the 3rd kinematic pair 13 is connected with the 4th kinematic pair 14, the component of connection is the 4th component 4.
Numbering matrixIt is very succinct, contain kinematic chain C1Full detail, it is as follows：
1st, will numbering matrixElement ai,jBool computings are carried out, as element ai,jWhen=0, element value is constant, works as element
ai,jWhen ≠ 0, element value value 1, obtains adjacency matrix
Adjacency matrixThe matrix of neighbouring relations between expression vertex, in kinematic chain C1Middle expression kinematic pair and kinematic pair
Connection relation.
2nd, numbering matrix is retrievedAs kinematic pair PiWith kinematic pair PjA when not connectingi,j=0, as kinematic pair PiAnd fortune
Dynamic secondary PjA when having connectioni,j=1, obtain the incidence matrix of kinematic chain
Expressive movement secondary PnWith the connection relation of each component, wherein line number represents component numbering, and row number represents kinematic pair
Numbering.Such as：In numbering matrixIn the 9th row or the 9th row represent company between the 9th kinematic pair 19 and each component
Relation is connect, the 9th kinematic pair 19 can be obtained and be connected with the 7th component 7, the 8th component 8 and the 9th component 9, in incidence matrix
In can clearly embody, ai,j=1, kinematic pair PiWith kinematic pair PjIt is connected.
3rd, numbering matrix is retrievedAs kinematic pair PiThe component of corresponding i rows or i column elements numbers the number occurred
K, kinematic pair PiThe component of corresponding i row elements is g member components, g=k+1, the attribute list of kinematic chain component is obtained, such as following table institute
Show：
| Component is numbered | Structure attribute | Component is numbered | Structure attribute |
| 1 | N4 | 6 | N2 |
| 2 | N3 | 7 | N2 |
| 3 | N2 | 8 | N2 |
| 4 | N3 | 9 | N2 |
| 5 | N2 | 10 | N2 |
In table, NiExpression component is i member components, and in table, such as first component 1 is in numbering matrixThe first row in
Occur 3 times, so first component 1 is quaternary component.
4th, numbering matrix is retrievedAs kinematic pair PiCorresponding i rows or i column elements ai,j(i, j=1,2, ..., n) in have
M and more than m non-zero and unequal value, then kinematic pair PiThe hinge at place is the multiple hinge of m members, wherein m >=3, in numbering matrixIt can be determined that the 3rd kinematic pair 3 and the 9th kinematic pair 9 are that ternary is cut with scissors again.
5th, to numbering matrixMiddle kinematic pair PiCorresponding i rows or i column elements ai,j(i, j=1,2 ..., n) carry out broad sense
Computing, rejects nonzero element, retains 2 to the identical components numbering more than 2, obtains each kinematic pair PiArray code name,
And then obtain array code name and kinematic pair PiThe corresponding kinematic pair type list of connection relation.In array code name, for phase isomorphism
Part numbering occurs 2 times, illustrates kinematic pair PiIt is a polynary component to go out, and is only occurred 1 time, and it is a binary structure to illustrate the component
Part.Differing component numbering quantity represents several components in kinematic pair PiPlace be connected, for example, (a, a, b, c) represent component a,
Component b, component c are connected.In the present embodiment, following kinematic pair type list is obtained：
In the present embodiment, in order to more preferably represent kinematic pair PiConnection relation, use JXX- XX represents movement sub-attribute, its
The meaning of representative is as follows：
(1) number of number represents kinematic pair P in subscript arrayiThe number of connecting elements.For example, the first kinematic pair 11
(1,1,2,2) first component 1 and second component 2 are connected, the number of the subscript array of the first kinematic pair 11 is 2；
(2) value that certain in subscript array counts represents kinematic pair PiThe number of connection series connection bicomponent element.Two polynary structures
Part is in kinematic pair PiOn when being connected directly, represented with numerical value " 0 ", such as the first structure of the 5th kinematic pair 15 (1,1,6) connection
Part 1 is a quaternary component, and the 6th component 6 is a bicomponent element, and the 6th component 6 is connected with the 5th component 5 of bicomponent element, the
The 4th component 4 of five components 5 connection ternary component, the value of array are represented with " 2 ".Regulation subscript array intermediate value by arranging from small to large
Row, the value of 15 subscript array of the 5th kinematic pair is " 02 "；
(3) the connection array of back is corresponding with subscript array, connects the number of array and the number phase of subscript array
Deng the value for connecting array represents the connecting elements type of series connection bicomponent element end.If bicomponent element number of connecting is identical, end
Connecting elements type, according to arranging from big to small.Such as the 5th kinematic pair 15 connect first component 1 be a quaternary component,
The value of corresponding connection array just represents that the 6th component 6 of the 5th kinematic pair 15 connection is a bicomponent element with " 4 ", the 6th
Component 6 is connected with the 5th component 5 of bicomponent element followed by the 4th component 4 of ternary component is connected, and the value of corresponding connection array uses " 3 "
Represent, then connection array is " 43 "；
(4) the connecting elements type for connecting bicomponent element end of connecting in array is that compound hinges is represented with " 0 ".
Array code name is retrieved, kinematic pair P can be obtainediAttribute code name.Such as the 3rd kinematic pair 13 connection two
First the 3rd component 3 of component, the 4th component 4 of quaternary component and the 8th component 8 of bicomponent element, retrieve array code name, can find (2,
2,3), (7,8,9), represent that the 3rd component 3 of bicomponent element is connected with ternary component second component 2, the 8th component 8 of bicomponent element and
Tri compound hinge is connected, and the code name of the 3rd kinematic pair 13 is J011-330.Thus, it is possible to obtain kinematic pair PiAttribute list, such as
Shown in following table：
In upper table, the kinematic pair type, movement sub-attribute code name and the kinematic chain C that are obtained by kinematic pair connection relation1It is
Correspondingly, kinematic chain C can be uniquely represented1。
6th, by kinematic pair P in above-mentioned kinematic pair type listiConnection relation retrieved, obtain band kinematic pair Pi's
Structure attribute table, in the present embodiment, uses Ni- XX represents, NiExpression component is i member components, and connection array representation below should
The connection mode of component and bicomponent element, its rule are as follows：
(1) number in array is equal with the element of component, if ternary component is N3- XXX, quaternary component are N4-XXXX；
(2) value that certain in array counts represents kinematic pair PiThe number of the bicomponent element of upper series connection, two polynary in the fortune
Dynamic secondary PiOn when being connected directly, use numerical value " 0 " to represent；
(3) as kinematic pair PiWhen being compound hinges, by compound hinges as a polynary component, represented with numerical value " -1 ".
To kinematic pair PiLink information just retrieve, you can determine band kinematic pair PiThe connection mode of component.Such as：The
One component 1 is a quaternary component, appears in the first kinematic pair 11 (1,1,2,2), the 4th kinematic pair 14 (1, Isosorbide-5-Nitrae, 4), the 5th
In kinematic pair 15 (1,1,6) and the 6th kinematic pair 16 (1,1,7), it may be determined that the first kinematic pair kinematic pair 11 and the 4th kinematic pair
14 are connected with polynary component, but when judging the 6th component 6 of bicomponent element and seven component 7 of bicomponent element, can not be true
Surely the number of series connection bicomponent element, it is therefore desirable to further the 7th movement for carrying out retrieval connection the 6th component 6 of bicomponent element
Secondary 17 (5,6) and the 9th kinematic pair 19 (7,8,9) for connecting the 7th component 7 of bicomponent element, it is one polynary that compound hinges, which is regarded,
Component, it may be determined that series connection the 7th component 7 of bicomponent element pairing element be 2；Needed for the 6th component 6 of bicomponent element
Continue the 8th kinematic pair 18 (4,4,5) of retrieval series connection the 5th component 5 of bicomponent element, it now is possible to determine series connection bicomponent element 6
Pairing element be 1.Thus, kinematic chain C1The attribute of component with kinematic pair such as following table：
In formula, NiExpression component is i member components, connects the connection relation between array representation component.
Claims (10)
1. a kind of plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again, it is characterised in that：To the component and fortune of kinematic chain
Dynamic pair is numbered, and wherein kinematic pair is Pn, and generate n × n numbering matrix As：
In formula, n be kinematic pair quantity, the diagonal entry a of numbering matrixi,j(i=j) it is 0, other members of numbering matrix
Plain ai,j(i ≠ j, i=1 ..., n；J=1 ..., n) it is connection kinematic pair PiWith kinematic pair PjComponent numbering, as kinematic pair Pi
With kinematic pair PjWhen not connecting, ai,j=0.
2. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：By described in
The element a of numbering matrix Ai,jBool computings are carried out, as element ai,jWhen=0, element value is constant, as element ai,jWhen ≠ 0, element
It is worth value 1, obtains adjacency matrix B.
3. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：Retrieval is compiled
Number matrix A, as kinematic pair PiWith kinematic pair PjA when not connectingi,j=0, as kinematic pair PiWith kinematic pair PjA when having connectioni,j=
1, the incidence matrix C of kinematic chain is obtained, wherein line number represents component numbering, and row number represents kinematic pair numbering, expressive movement secondary Pn
With the connection relation of each component.
4. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：Retrieval is compiled
Number matrix A, as kinematic pair PiThe number that the component numbering of corresponding i row elements occurs is k, kinematic pair PiCorresponding i row elements
Component is g member components, g=k+1, obtains the attribute list of kinematic chain component.
5. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：Retrieval is compiled
Number matrix A, as kinematic pair PiThe number that the component numbering of corresponding i column elements occurs is k, kinematic pair PiCorresponding i row elements
Component is g member components, g=k+1, obtains the attribute list of kinematic chain component.
6. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：Retrieval is compiled
Number matrix A, as kinematic pair PiCorresponding i row elements ai,j(i, j=1,2, ..., n) in have m and more than m it is non-zero and unequal
Value, then kinematic pair PiThe hinge at place is the multiple hinge of m members, wherein m >=3.
7. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：Retrieval is compiled
Number matrix A, as kinematic pair PiCorresponding i column elements ai,j(i, j=1,2, ..., n) in have m and more than m it is non-zero and unequal
Value, then kinematic pair PiThe hinge at place is the multiple hinge of m members, wherein m >=3.
8. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：To movement
Secondary PiCorresponding i row elements ai,j(i, j=1,2 ..., n) carries out broad sense computing, nonzero element is rejected, to identical more than 2
Component numbering retains 2, obtains each kinematic pair PiArray code name, and then obtain array code name and kinematic pair PiConnection relation
Corresponding kinematic pair type list.
9. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 1, it is characterised in that：To movement
Secondary PiCorresponding i column elements ai,j(i, j=1,2 ..., n) carries out broad sense computing, nonzero element is rejected, to identical more than 2
Component numbering retains 2, obtains each kinematic pair PiArray code name, and then obtain array code name and kinematic pair PiConnection relation
Corresponding kinematic pair type list.
10. plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again according to claim 9, it is characterised in that：Pass through
To kinematic pair P in kinematic pair type listiConnection relation retrieved, obtain band kinematic pair PiStructure attribute table.
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| CN110851925A (en) * | 2019-10-31 | 2020-02-28 | 武汉科技大学 | Planetary gear train isomorphism determination method, system and medium based on improved adjacency matrix |
| CN110852022A (en) * | 2019-10-31 | 2020-02-28 | 武汉科技大学 | Circuit model-based planetary gear train isomorphism determination method, system and medium |
| CN111008359A (en) * | 2019-11-11 | 2020-04-14 | 武汉科技大学 | Hamming number kinematic chain isomorphism judgment method based on prime number asymmetric adjacent matrix |
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| CN110826214A (en) * | 2019-10-31 | 2020-02-21 | 武汉科技大学 | Planetary gear train isomorphism judgment method, system and medium based on prime number layering |
| CN110851926A (en) * | 2019-10-31 | 2020-02-28 | 武汉科技大学 | Planetary gear train isomorphism judgment method, system and medium based on traversal loop |
| CN110851925A (en) * | 2019-10-31 | 2020-02-28 | 武汉科技大学 | Planetary gear train isomorphism determination method, system and medium based on improved adjacency matrix |
| CN110852022A (en) * | 2019-10-31 | 2020-02-28 | 武汉科技大学 | Circuit model-based planetary gear train isomorphism determination method, system and medium |
| CN110852022B (en) * | 2019-10-31 | 2023-05-23 | 武汉科技大学 | Planetary gear train isomorphism judging method, system and medium based on circuit model |
| CN110826214B (en) * | 2019-10-31 | 2023-08-11 | 武汉科技大学 | Prime number layering-based planetary gear train isomorphism judging method, system and medium |
| CN110851926B (en) * | 2019-10-31 | 2023-09-01 | 武汉科技大学 | Planetary gear train isomorphism judging method, system and medium based on traversal loop |
| CN110851925B (en) * | 2019-10-31 | 2024-02-20 | 武汉科技大学 | Planetary gear train isomorphism judging method, system and medium based on improved adjacency matrix |
| CN111008359A (en) * | 2019-11-11 | 2020-04-14 | 武汉科技大学 | Hamming number kinematic chain isomorphism judgment method based on prime number asymmetric adjacent matrix |
| CN111104563A (en) * | 2019-11-11 | 2020-05-05 | 武汉科技大学 | Kinematic chain isomorphism judgment method based on prime number asymmetric adjacent matrix |
| CN111008359B (en) * | 2019-11-11 | 2023-09-19 | 武汉科技大学 | Hamming number kinematic chain isomorphism judging method based on prime number asymmetric adjacency matrix |
| CN111104563B (en) * | 2019-11-11 | 2024-04-16 | 武汉科技大学 | Method for determining isomorphism of kinematic chain based on prime number asymmetric adjacency matrix |
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