CN109408504A - A method of separable topological diagram is filtered out based on adjacency matrix and loop sum - Google Patents
A method of separable topological diagram is filtered out based on adjacency matrix and loop sum Download PDFInfo
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- CN109408504A CN109408504A CN201810915782.XA CN201810915782A CN109408504A CN 109408504 A CN109408504 A CN 109408504A CN 201810915782 A CN201810915782 A CN 201810915782A CN 109408504 A CN109408504 A CN 109408504A
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Abstract
The invention discloses a kind of methods for filtering out separable topological diagram based on adjacency matrix and loop sum.Specific step is as follows by the present invention: according to the corresponding relationship of adjacency matrix and topological diagram, by the number of components and number of degrees of freedom, requirement of the kinematic chain to be integrated, all corresponding adjacency matrix are found out, for the adjacency matrix found out, exclude the adjacent street matrix that there is list degree point, isomorphism and Rigid subchain；Then centainly it is less than the characteristic of the loop sum of inseparable topological diagram according to the loop sum for separating topological diagram, each topological diagram is successively scanned for from low to high according to loop sum, until searching inseparable topological diagram for the first time, so that it is determined that loop sum was less than inseparable topological diagram loop sum is separable topological diagram.The present invention is the method that separable topological diagram is filtered out based on adjacency matrix and loop sum, simple and convenient, and is also a kind of new method that topological diagram is established according to adjacency matrix.
Description
Technical field
The invention belongs to synthesis of mechanism technical fields, and in particular to one kind is filtered out based on adjacency matrix and loop sum can
The method of separated topology figure.
Background technique
The topological structure for determining mechanism is machinery innovation and mechanical concept design stage matter of utmost importance to be solved.In machine
In structure combined process, when synthesis goes out all kinematic chain formation spectrum libraries for meeting number of components and freedom degree requirement, one in spectrum library
As include some inseparable topological diagrams and some separable topological diagrams, and usually needed according to the actual situation from spectrum library
In filter out all inseparable topological diagrams or separable topological diagram, and then find out some new structures for meeting actual requirement
Type.But there is presently no the screening techniques for realizing inseparable topological diagram and separable topological diagram.
Summary of the invention
In view of the deficiencies of the prior art, it is an object of the present invention to provide one kind to be filtered out based on adjacency matrix and loop sum
The method of separable topological diagram, but it is only applicable to the kinematic chain that there is separable topological diagram.
To achieve the goals above, the technical solution of the present invention is as follows:
The present invention is a kind of method for filtering out separable topological diagram based on adjacency matrix and loop sum, and specific steps are such as
Under:
Step 1: according to the number of components for the kinematic chain to be integrated and number of degrees of freedom, requirement, all corresponding adjacent squares are found out
Battle array.
Step 2: the adjacency matrix found out for step 1 excludes the adjacency matrix that there is list degree point.
Step 3: for the adjacency matrix after step 2 is screened, there are the adjacency matrix of isomorphism for exclusion.
Step 4: for the adjacency matrix after step 3 is screened, there are the adjacency matrix of Rigid subchain for exclusion.
Step 5: for the adjacency matrix after step 4 is screened, topological diagram corresponding to each adjacency matrix is drawn.
Step 6: each topological diagram is successively scanned for from low to high according to loop sum, is searched until for the first time
Until inseparable topological diagram, the corresponding loop sum of the inseparable topological diagram is calculated as k, thus to determine loop sum
It is separable topological diagram less than the topological diagram of k, realizes the screening of all separable topological diagrams；Wherein, when search, by ring
Initial value of the loop sum of road sum and that the smallest topological diagram of L difference as search；L=e-v+1, L are independent loop circuit
Number, e are the number of edges in topological diagram, and v is total number of vertex in topological diagram.
The invention has the benefit that the present invention is to filter out separable topology based on adjacency matrix and loop sum
The method of figure, it is simple and convenient, and step 1 therein to step 5 is also a kind of to establish the new of topological diagram according to adjacency matrix
Method.
Detailed description of the invention
Fig. 1 is inseparable topological diagram of 12 component 3DOFs；
Fig. 2 is the separable topological diagram of point of 12 component 3DOFs；
Fig. 3 is the separable topological diagram in side of 12 component 3DOFs；
Fig. 4 is the topological diagram established according to 7 component 2DOF kinematic chains；
Fig. 5 is the separable topological diagram filtered out from Fig. 4 according to loop sum；
Fig. 6 is the topological diagram established according to 9 component 2DOF kinematic chains；
Fig. 7 is the separable topological diagram filtered out from Fig. 6 according to loop sum.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
The determination of total loop number in specific topological diagram: basic ring in topological diagram is 1. determined according to Euler's formula L=e-v+1
The free ring number (loop that elementary cycle is concentrated is denoted as independent loop circuit) that road collection includes, e are the number of edges in topological diagram, and v is to open up
Flutter total number of vertex in figure；2. according to formulaDetermine total loop number in topological diagram, wherein
Collection comprising all loops is combined into total loop collection of topological diagram, is denoted as LS, and the loop number that total loop of topological diagram is concentrated is referred to as total
The rank of loop collection is denoted as Or (LS),It is selected for (independent loop circuit is that elementary cycle concentrates the loop for including) in L independent loop circuit
The number of combinations of i independent loop circuit；I independent loop circuit is selected from L independent loop circuit and carries out " ⊕ " operation, traverses i=2,3 ...,
After L, the arithmetic expression number for being unsatisfactory for calculation condition is μ.
Calculation condition are as follows: (1) at least there are two public vertex for two loops of participation " ⊕ " operation；(2) in " ⊕ " operation
When, two loop corresponding positions element values are 1, and after " ⊕ " operation the corresponding positions of resulting array the case where being still 1 occur and
Only occur twice.
The rule of " ⊕ " operation are as follows: each element and loop of array LP=L (a) ⊕ L (b), i.e. loop array L (a)
The correspondence bit element algebra of array L (b) is summed, and if greater than 0 and be less than the local degree on corresponding positions vertex, LP corresponds to position
Value is 1, is otherwise 0；Wherein the dimension of array LP and the dimension of the two loop array L (a) and L (b) that participate in operation are all the same.
The mathematical description of loop: loop a ties up loop array L (a) with v to indicate, wherein and v is total number of vertex of topological diagram,
Loop array L (a) jth position indicates the relationship on j-th vertex and loop a in topological diagram, j=1,2 ..., v, if j-th of vertex
In loop a, then otherwise it is 0, such as L (1)=[1 0000111100 that the value of loop array L (a) jth position, which is 1,
1] loop being made of the 1st, 6,7,8,9,12 vertex is indicated.
Lower mask body is separable with the point of the inseparable topological diagram (such as Fig. 1) of 12 component 3DOFs and 12 bar 3DOFs
Topological diagram (such as Fig. 2) and 12 bar 3DOFs the separable topological diagram in side (such as Fig. 3) for, to verify separable topology
Total loop number of figure is always less than total loop number of inseparable topological diagram.
As shown in Figure 1 it is the inseparable topological diagram of 12 bar 3DOFs, shares number of edges e=15, number of vertex in this topological diagram
V=12, so the free ring number for including is integrated as L=e-v+1=4 by elementary cycle known to Euler's formula, the rank of total loop collection
(total loop concentrates the total loop number for including)(wherein it is unsatisfactory for operation item
The arithmetic expression of part has: L (1) ⊕ L (3), L (1) ⊕ L (4), L (1) ⊕ L (3) ⊕ L (4), L (2) ⊕ L (3) ⊕ L (4), L (1) ⊕ L
(2) ⊕ L (3) ⊕ L (4), i.e. μ=5), i.e. it include 10 loops in total loop collection LS of this topological diagram, 10 loops specifically indicate
It is as follows:
Elementary cycle collection S { L (1), L (2), L (3), L (4) } is first looked for, wherein elementary cycle concentrates the mathematical description of each loop
Are as follows:
L (1)=[1 0000111100 1]
L (2)=[1 1000100000 1]
L (3)=[0 1111100000 0]
L (4)=[1 1100000011 0]
Other loops in addition to elementary cycle are (this part can be obtained by elementary cycle collection by " ⊕ " operation)
L (5)=L (1) ⊕ L (2)=[1 1000111100 0]
L (6)=L (2) ⊕ L (3)=[1 1111100000 1]
L (7)=L (2) ⊕ L (4)=[1 1100100011 1]
L (8)=L (3) ⊕ L (4)=[1 1111100011 0]
L (9)=L (1) ⊕ L (2) ⊕ L (3)=[1 1111111100 0]
L (10)=L (1) ⊕ L (2) ⊕ L (4)=[1 1100111111 0]
Always loop collection is
LS={ L (1), L (2), L (3), L (4), L (5), L (6), L (7), L (8), L (9), L (10) }
It is illustrated in figure 2 the separable topological diagram of point of 12 bar 3DOFs, shares number of edges e=15, vertex in this topological diagram
Number v=12, so the free ring number for including is integrated as L=e-v+1=4 by elementary cycle known to Euler's formula, total loop collection
Rank (i.e. total loop concentrates the total loop number for including)It (is wherein unsatisfactory for transporting
The arithmetic expression of calculation condition has: L (1) ⊕ L (3), L (1) ⊕ L (4), L (2) ⊕ L (3), L (2) ⊕ L (4), L (1) ⊕ L (2) ⊕ L
(3)、L(1)⊕L(2)⊕L(4)、L(1)⊕L(3)⊕L(4)、L(2)⊕L(3)⊕L(4)、L(1)⊕L(2)⊕L(3)⊕L
(4), i.e. μ=9) i.e. it include 6 loops in total loop collection LS of this topological diagram, 6 loops are specifically expressed as follows:
Elementary cycle collection S { L (1), L (2), L (3), L (4) } is first looked for, wherein elementary cycle concentrates the mathematical description of each loop
Are as follows:
L (1)=[1 0011100000 0]
L (2)=[1 1110100000 0]
L (3)=[0 0100011000 1]
L (4)=[0 0000001111 1]
Other loops in addition to elementary cycle are
L (5)=L (1) ⊕ L (2)=[1 1111000000 0]
L (6)=L (3) ⊕ L (4)=[0 0100011111 1]
Always loop collection is
LS={ L (1), L (2), L (3), L (4), L (5), L (6) }
It is illustrated in figure 3 the separable topological diagram in side of 12 bar 3DOFs, shares number of edges e=15, vertex in this topological diagram
Number v=12, so the free ring number for including is integrated as L=e-v+1=4 by elementary cycle known to Euler's formula, total loop collection
Rank (i.e. total loop concentrates the total loop number for including)(wherein it is unsatisfactory for operation
The arithmetic expression of condition has: L (1) ⊕ L (3), L (1) ⊕ L (4), L (2) ⊕ L (3), L (2) ⊕ L (4), L (1) ⊕ L (2) ⊕ L (3), L
(1) ⊕ L (2) ⊕ L (4), L (1) ⊕ L (3) ⊕ L (4), L (2) ⊕ L (3) ⊕ L (4), L (1) ⊕ L (2) ⊕ L (3) ⊕ L (4), i.e. μ
=9) include 6 loops i.e. in total loop collection LS of this topological diagram, 6 loops are specifically expressed as follows:
Elementary cycle collection S { L (1), L (2), L (3), L (4) } is first looked for, wherein elementary cycle concentrates the mathematical description of each loop
Are as follows:
L (1)=[1 0011100000 0]
L (2)=[1 1110100000 0]
L (3)=[0 0000011001 1]
L (4)=[0 0000001111 1]
Other loops in addition to elementary cycle are
L (5)=L (1) ⊕ L (2)=[1 1111000000 0]
L (6)=L (3) ⊕ L (4)=[0 0000011111 0]
Always loop collection is
LS={ L (1), L (2), L (3), L (4), L (5), L (6) }
In summary for number of components and the identical kinematic chain of number of degrees of freedom, the comprehensive separable topological diagram (packet obtained
Include the separable topological diagram of a little separable topological diagram and side) loop sum be centainly less than the loop of inseparable topological diagram
Sum.
A method of separable topological diagram is filtered out based on adjacency matrix, the specific steps are as follows:
Step 1: according to the number of components for the kinematic chain to be integrated and number of degrees of freedom, requirement, all corresponding adjacent squares are found out
Battle array.
Step 2: the adjacency matrix found out for step 1 excludes the adjacency matrix that there is list degree point.
Step 3: for the adjacency matrix after step 2 is screened, there are the adjacency matrix of isomorphism for exclusion.
Step 4: for the adjacency matrix after step 3 is screened, there are the adjacency matrix of Rigid subchain for exclusion.
Step 5: for the adjacency matrix after step 4 is screened, topological diagram corresponding to each adjacency matrix is drawn.
Step 6: each topological diagram is successively scanned for from low to high according to loop sum, is searched until for the first time
Until inseparable topological diagram, the corresponding loop sum of the inseparable topological diagram is calculated as k, thus to determine loop sum
It is separable topological diagram less than the topological diagram of k, realizes the screening of all separable topological diagrams；Wherein, when search, by ring
Initial value of the loop sum of road sum and that the smallest topological diagram of L difference as search；L=e-v+1, for number of components and certainly
The value of the kinematic chain determined by degree, each topological diagram corresponding L, e, v is equal.
Lower mask body is further illustrated using the synthesis of 7 component 2DOFs and the kinematic chain of 9 component 2DOFs as example
The present invention.
The synthesis of example 1:7 component 2DOF kinematic chain
The topological diagram that 7 component 2DOF kinematic chains obtain after step 1 to step 5 of the present invention (wraps as shown in Figure 4
Containing 4 topological diagrams)；Topological diagram as shown in Figure 4 obtains all separable topological diagrams after step 6 of the present invention screening, such as schemes
(separable topological diagram has 1) shown in 5.
The synthesis of example 2:9 component 2DOF kinematic chain
The topological diagram that 9 component 2DOF kinematic chains obtain after step 1 to step 5 of the present invention (wraps as shown in Figure 6
Containing 40 topological diagrams)；Topological diagram as shown in FIG. 6 obtains all separable topological diagrams after step 6 of the present invention screening, such as
(separable topological diagram has 5) shown in Fig. 7.
Claims (1)
1. a kind of method for filtering out separable topological diagram based on adjacency matrix and loop sum, it is characterised in that: this method tool
Steps are as follows for body:
Step 1: according to the number of components for the kinematic chain to be integrated and number of degrees of freedom, requirement, all corresponding adjacency matrix are found out；
Step 2: the adjacency matrix found out for step 1 excludes the adjacency matrix that there is list degree point；
Step 3: for the adjacency matrix after step 2 is screened, there are the adjacency matrix of isomorphism for exclusion；
Step 4: for the adjacency matrix after step 3 is screened, there are the adjacency matrix of Rigid subchain for exclusion；
Step 5: for the adjacency matrix after step 4 is screened, topological diagram corresponding to each adjacency matrix is drawn；
Step 6: successively scanning for each topological diagram according to loop sum from low to high, can not until searching for the first time
Until isolated topological diagram, the corresponding loop sum of the inseparable topological diagram is calculated as k, thus to determine that loop sum is less than
The topological diagram of k is separable topological diagram, realizes the screening of all separable topological diagrams；Wherein, when search, loop is total
Several initial values with the loop sum of that the smallest topological diagram of L difference as search；L=e-v+1, L are the number of independent loop circuit,
E is the number of edges in topological diagram, and v is total number of vertex in topological diagram.
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| CN102081688A (en) * | 2010-12-24 | 2011-06-01 | 燕山大学 | Method for automatically synthesizing topology embryonic graph of closed loop kinematic chain based on loop theory |
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