CN110866293B

CN110866293B - Isomorphism judging method, system, device and medium based on prime number layering matrix

Info

Publication number: CN110866293B
Application number: CN201911051676.2A
Authority: CN
Inventors: 丁佳文; 孙伟; 左惠妍; 胡越; 于普良
Original assignee: Wuhan University of Science and Engineering WUSE
Current assignee: Wuhan University of Science and Engineering WUSE
Priority date: 2019-10-31
Filing date: 2019-10-31
Publication date: 2023-09-12
Anticipated expiration: 2039-10-31
Also published as: CN110866293A

Abstract

The invention relates to isomorphism judging method, system, device and medium based on prime number layering matrix, which respectively acquire layering structures of two motion chains and generate prime number layering matrix of corresponding motion chain according to each layering structure; and sequentially acquiring the number of components, the complex hinge data, the connectivity data and the connection code data of the corresponding motion chain according to each prime number layering matrix, sequentially judging whether the number of components, the complex hinge data, the connectivity data and the connection code data are identical or not, if not, carrying out matrix transformation of a row or a column of exchange on one prime number layering matrix, if so, carrying out isomorphism on the two motion chains, otherwise, carrying out isomorphism on the two motion chains. The prime number layering matrix-based method is simple, convenient and efficient, has small time complexity, can simultaneously consider the reliability of discrimination, is simple to calculate, has small calculation amount and can be labeled, and is applicable to the situation whether complex hinges exist or not.

Description

Isomorphism judging method, system, device and medium based on prime number layering matrix

Technical Field

The invention relates to the field of mechanism kinematic chains, in particular to an isomorphic judging method, system, device and medium based on prime number layering matrix.

Background

The mechanism consists of a component and a kinematic pair, wherein the component is represented by a vertex, and the figure obtained by representing the kinematic pair by a side is called a topological diagram of the mechanism; and the vertexes in the topological graph of the two mechanisms are in one-to-one correspondence, the edges are also in one-to-one correspondence, and the corresponding vertexes and the corresponding edges are in the same connection relation, so that the two mechanisms are isomorphic. In the research process of a planar mechanism kinematic chain, the most critical problem is isomorphism judgment of the kinematic chain. The isomorphism determination of the kinematic chain can enable people to avoid a great number of repeated structures when designing and synthesizing the kinematic chain structure with excellent characteristics, and effectively reduce design time and effort.

Since the last century, since the 60 th century, many students at home and abroad have performed a great deal of effective research work on isomorphism determination of a moving chain, and a great deal of valuable methods have been proposed, such as a feature value and feature vector calculation method based on an adjacency matrix or an association matrix, a congruent loop method, isomorphism determination based on a genetic algorithm, a condensed-rod adjacency matrix method, an adjacency linked list method, a branch code method, and the like, which are proposed on isomorphism determination of a moving chain containing a complex hinge. However, although the feature value and feature vector calculation method based on the adjacent matrix or the associated matrix is simple and direct, when more identical feature values appear again, the calculation amount increases sharply and even fails; the congruent loop method is more efficient when the loops are few and small, but when the vertices are increased and the loops become large, the calculation amount is unacceptable, and the counter-example of failure exists; the isomorphism judgment based on the genetic algorithm is premature and falls into a local solution; the method can solve the situation that the complex hinge is not complex hinge, but when the number of complex hinges is more, the topological structure of the motion chain needs to be increased by more vertexes, and the adjacency matrix also becomes huge; in view of this problem, studies on isomorphism determination of complex hinges proposed by Luo Xianhai and the like solve the problem of increased vertices of a topological graph and use a dynamic modification method therein, but become more complex in algorithm and rule, and the calculation amount is large; the adjacent linked list method describes a motion chain with a complex hinge by means of a double-color topological graph, but the composition analysis is complex and the operation amount is large; the branch code method has larger calculation amount when more components are needed when judging the complex hinge motion chain.

Therefore, the existing method for determining isomorphism of a moving chain cannot simultaneously achieve the reliability, the simplicity in calculation, the small calculation amount and the markability of the determination, and has no universality under the conditions of complex hinge and no complex hinge.

Disclosure of Invention

The invention aims to solve the technical problems of the prior art, and provides a isomorphism judging method, a isomorphism judging system, a isomorphism judging device and a isomorphism judging medium based on prime number layering matrix, which can simultaneously consider judging reliability, simple calculation, less calculation amount and markability, can judge isomorphism of a moving chain through simple calculation, and are applicable to whether a complex hinge exists or not.

The technical scheme for solving the technical problems is as follows:

a prime number layering matrix-based isomorphism judging method comprises the following steps:

step 1: respectively obtaining layered structures corresponding to two motion chains one by one, and generating prime number layered matrixes of the corresponding motion chains according to each layered structure;

step 2: acquiring the number of components of the corresponding moving chains according to each prime number layering matrix, judging whether the number of the components of the two moving chains is the same, if so, executing the step 3, and if not, judging that the two moving chains are heterogeneous;

Step 3: acquiring complex hinge data of the corresponding motion chains according to each prime number layering matrix, judging whether the complex hinge data of the two motion chains are identical, if so, executing the step 4, and if not, judging that the two motion chains are heterogeneous;

step 4: calculating connectivity data and connection code data of the corresponding moving chains according to each prime number layering matrix, judging whether the connectivity data and the connection code data of the two moving chains are identical, if so, executing the step 5, and if not, judging that the two moving chains are heterogeneous;

step 5: and performing matrix transformation of a row or a column of the prime number layering matrix corresponding to one of the motion chains to obtain a transformed prime number layering matrix, judging whether the transformed prime number layering matrix is identical to the prime number layering matrix corresponding to the other motion chain, if so, judging that the two motion chains are isomorphic, and if not, judging that the two motion chains are isomorphic.

The beneficial effects of the invention are as follows: the prime number layering matrix is generated according to a layering structure obtained by the composition principle of the moving chain, and the layering structure of the moving chain comprises the relation among all components in the moving chain, including the connection relation, the distance and the like among all the components, so that the number of the components, the complex hinge data, the connectivity data and the connection code data of two moving chains can be analyzed based on the prime number layering matrix, and whether the two moving chains are isomorphic or not can be judged only through simple calculation through the sequential judgment of the number of the components, the complex hinge data, the connectivity data and the connection code data;

The isomorphism judging method of the moving chain judges isomorphism of the moving chain based on the prime number layering matrix, is simple, convenient and efficient, has small time complexity, can simultaneously consider the reliability, the calculation simplicity, the calculation amount and the markability of the judgment, can judge isomorphism problems of the moving chain through simple calculation, is applicable to the situation whether the moving chain contains a compound hinge or not, effectively reduces design time and energy for designing a synthesized moving chain structure, and is suitable for general popularization; when prime number layering matrixes are generated according to the layering structure of the motion chain, the difference of labels is carried out on each component in the motion chain, so that in step 5, the influence caused by the difference of labels can be effectively avoided by carrying out operation of exchanging rows or exchanging columns on one prime number layering matrix, and the accuracy and the effectiveness of final isomorphism judgment are ensured.

Based on the technical scheme, the invention can also be improved as follows:

further: the specific steps of the step 1 comprise:

step 1.1: selecting one of the kinematic chains, acquiring a corresponding structure diagram, determining all root members in the selected one of the kinematic chains according to the structure diagram, selecting one of the root members, and determining all sub-members corresponding to the selected one of the root members and the distance between the selected one of the root members and each of the sub-members according to the corresponding structure diagram;

Step 1.2: obtaining a sub-layered structure of the selected root member according to the selected root member, all sub-members corresponding to the selected root member and the distances between the selected root member and all the corresponding sub-members;

step 1.3: traversing each root component in the selected one motion chain to obtain a sub-layered structure corresponding to each root component in the selected one motion chain one by one, and obtaining a layered structure of the selected one motion chain according to all the sub-layered structures;

step 1.4: according to a preset prime number matching table, prime number layering matrix definition is obtained, and a prime number layering matrix of a corresponding motion chain is generated according to the prime number layering matrix definition and a layering structure of a selected motion chain;

the prime number layering matrix is defined as:

in one of the kinematic chains, when the ith component is taken as the root component and the jth component is taken as the subcomponent, a _ij Elements representing an ith row and a jth column in the prime number layering matrix of the kinematic chain; k (k) _ij Representing the distance between the ith and jth members in the kinematic chain;representing the distance k between the ith and jth members in the kinematic chain _ij According to the prime numbers corresponding to the prime number matching table;

The preset prime number matching table specifically comprises the following steps:

in a selected kinematic chain, when the ith component is taken as a root component and the jth component is taken as a subcomponent, the distance k between the ith component and the jth component _ij A one-to-one correspondence with each prime number;

step 1.5: and obtaining a prime number layering matrix of another motion chain according to the methods from the step 1.1 to the step 1.4.

Further: in the step 2, the specific implementation of obtaining the number of the components of the corresponding kinematic chain is as follows:

and determining the number of elements which are 0 in each prime number layering matrix according to each prime number layering matrix, and determining the number of elements which are 0 in each prime number layering matrix as the number of corresponding components of the motion chain.

Further: forming a complex hinge by a plurality of target complex hinge components, wherein each target complex hinge component corresponds to one kinematic pair number, and the complex hinge data comprises the complex hinge number and all the kinematic pair numbers forming each complex hinge;

in the step 3, the specific step of acquiring the complex hinge data of the corresponding motion chain includes:

step 3.1: selecting a prime number layering matrix of one of the motion chains, judging whether elements of an ith row and an ith column in the selected prime number layering matrix and elements of the ith row and the ith column are 2 at the same time, if so, in the motion chain corresponding to the selected prime number layering matrix, the jth component is an adjacent component of the ith component, and executing the step 3.2, and if not, in the corresponding motion chain, the jth component is a non-adjacent component of the ith component;

Step 3.2: traversing each element in the ith row of the selected prime number layering matrix, judging all adjacent components adjacent to the ith component in a motion chain corresponding to the selected prime number layering matrix according to the method of the step 3.1, and obtaining the number of the adjacent components of the ith component in the motion chain corresponding to the selected prime number layering matrix according to all the adjacent components adjacent to the ith component;

step 3.3: traversing each row of the selected prime number layering matrix, and obtaining the number of adjacent components corresponding to each component in the motion chain corresponding to the selected prime number layering matrix according to the methods from the step 3.1 to the step 3.2;

step 3.4: respectively judging whether the number of adjacent components corresponding to each component in the motion chain corresponding to the selected prime number layering matrix is larger than 2, if so, determining the corresponding component in the motion chain corresponding to the selected prime number layering matrix as a potential complex hinge component, and executing the step 3.5, if not, determining the corresponding component in the motion chain corresponding to the selected prime number layering matrix as a non-potential complex hinge component;

step 3.5: obtaining all potential complex hinge components in the corresponding motion chain according to the judging method in the step 3.4, and determining the complex hinge number in the corresponding motion chain and all target complex hinge components forming each complex hinge according to all the potential complex hinge components and the selected prime number layering matrix;

Step 3.6: selecting any one complex hinge, and calculating to obtain the number of kinematic pairs corresponding to each target complex hinge component one by one corresponding to the selected complex hinge according to a kinematic pair number calculation formula;

the kinematic pair number calculation formula for calculating the kinematic pair number of the t target complex hinge component in the s complex hinge is as follows:

f _t ^s ＝n _t -N+1；

f _t ^s the number of kinematic pairs of the t target complex hinge component in the s complex hinge is n _t The number of adjacent matrixes corresponding to the t target complex hinge components in the s complex hinge is the number of complex hinges;

step 3.7: traversing all complex hinges in the motion chain corresponding to the selected prime number layering matrix, and obtaining all motion pair numbers forming each complex hinge in the corresponding motion chain according to the method of the step 3.6;

step 3.8: and obtaining the number of the complex hinges in another kinematic chain and all kinematic pairs forming each complex hinge according to the methods from the step 3.1 to the step 3.7.

Further: in the step 3.5, the number of all potential multi-hinge members is greater than or equal to 3;

when the number of all potential multi-hinge members is 3, then the specific steps of determining the number of multi-hinges in the corresponding kinematic chain and forming all target multi-hinge members for each multi-hinge include:

step 3.5.a1: when the 3 potential multi-hinge components are adjacent components each other, and another non-potential multi-hinge component does not exist in the motion chain corresponding to the selected prime number layering matrix and is adjacent to any two potential multi-hinge components each other, the 3 potential multi-hinge components form a multi-hinge, the number of the multi-hinges in the corresponding motion chain is 1, the 3 potential multi-hinge components are all target multi-hinge components of the corresponding multi-hinge, otherwise, the 3 potential multi-hinge components do not form the multi-hinge, and the number of the multi-hinges in the corresponding motion chain is 0;

When the number of all potential multi-hinge members is greater than 3, then the specific steps of determining the number of multi-hinges in the corresponding kinematic chain and forming all target multi-hinge members for each multi-hinge include:

step 3.5.b1: when all the potential multi-hinge components are adjacent to each other, forming a multi-hinge by all the potential multi-hinge components, wherein the number of the multi-hinges in the corresponding motion chain is 1, and all the potential multi-hinge components are target multi-hinge components of the corresponding multi-hinge, otherwise, executing the step 3.5.b2;

step 3.5.b2: selecting any 3 potential multi-hinge members as potential multi-hinge members to be judged, when the 3 potential multi-hinge members to be judged are adjacent members, and one potential multi-hinge member and any two potential multi-hinge members to be judged are adjacent members in the rest potential multi-hinge members, the 3 potential multi-hinge members to be judged form a multi-hinge, and the 3 potential multi-hinge members to be judged are target multi-hinge members of the corresponding multi-hinge, otherwise, the 3 potential multi-hinge members to be judged do not form a multi-hinge;

step 3.5.b3: traversing all potential multi-hinge components, judging all multi-hinges according to the judging method of the step 3.5.b2, and obtaining the corresponding number of the multi-hinges in the motion chain and all target multi-hinge components forming each multi-hinge according to all the multi-hinges.

Further: in the step 3, the specific step of judging whether the complex hinge data of the two motion chains are the same comprises the following steps:

step 3.9: and judging whether the number of the complex hinges of the two moving chains and the number of all the kinematic pairs in the two moving chains are the same, if so, executing the step 4, and if not, judging that the two moving chains are heterogeneous.

Further: in the step 4, the connection data includes a first connection degree of the corresponding kinematic chain and a second connection degree of each component in the corresponding kinematic chain, and the connection code data includes a first connection code of the corresponding kinematic chain and a second connection code of each component in the corresponding kinematic chain;

the specific steps of calculating the connectivity data and the connection code data of the corresponding motion chain include:

step 4.1: selecting prime number layering matrixes of one of the motion chains, and calculating second connectivity corresponding to each component in the motion chain corresponding to the selected prime number layering matrix according to a second connectivity calculation formula;

the second connectivity calculation formula for calculating the second connectivity of the ith component in one of the kinematic chains is:

a second degree of connection for the ith member in one of the kinematic chains, n being the number of members of one of the kinematic chains, a _i1 、a _i2 …a _in All are elements of the ith row in the selected prime number layering matrix;

step 4.2: arranging the elements of each row in the selected prime number layering matrix according to the sequence from large to small to obtain an element sequence of each row, and obtaining a second connection code corresponding to each component one by one according to the element sequence of each row and the second connection degree of the component corresponding to the element sequence of each row one by one;

the second connection code of the ith component in one motion chain is as follows:

a second connection code, a, for the ith member of one of the kinematic chains _imax ,…,a _imin An element sequence in which the elements of the ith row in the selected prime number layering matrix are arranged according to the sequence from big to small;

step 4.3: arranging the second connection degrees of all the components in the motion chain corresponding to the selected prime number layering matrix in a sequence from large to small to obtain a first connection code of the corresponding motion chain; according to all the second connection degrees, calculating to obtain the first connection degree of the corresponding motion chain;

the first connection code of one of the motion chains is:

M ₁ for the first link code of one of the kinematic chains,for the maximum value of all second links in the corresponding kinematic chain, +.>Is the minimum value of all second connectivity in the corresponding kinematic chain;

The specific formula for calculating the first connectivity of one of the kinematic chains is:

wherein S is ¹ A first degree of connectivity for one of the kinematic chains;

step 4.4: obtaining a second connection degree and a second connection code corresponding to each component in another motion chain and a first connection degree and a first connection code of the motion chain according to the methods from the step 4.1 to the step 4.3;

in the step 4, the specific step of determining whether the connectivity data and the connection code data of the two kinematic chains are the same includes:

step 4.5: judging whether the first connection degree of the two kinematic chains is the same, if so, executing the step 4.6, and if not, judging that the two kinematic chains are heterogeneous;

step 4.6: and judging whether the first connection codes of the two moving chains, the second connection degree corresponding to each component in the two moving chains and the second connection code are the same or not, if so, executing the step 5, and if not, judging that the two moving chains are heterogeneous.

According to another aspect of the present invention, there is provided an isomorphic determination system based on a prime number hierarchical matrix, including a matrix generation module, a first determination module, a second determination module, a third determination module, a matrix transformation module, and a fourth determination module:

The matrix generation module is used for respectively acquiring layered structures corresponding to two motion chains one by one and generating prime number layered matrixes of the corresponding motion chains according to each layered structure;

the first judging module is used for acquiring the number of the components of the corresponding moving chain according to each prime number layering matrix and judging whether the number of the components of the two moving chains is the same or not;

the second judging module is used for acquiring complex hinge data of the corresponding motion chains according to each prime number layering matrix and judging whether the complex hinge data of the two motion chains are identical or not when the first judging module judges that the number of the components of the two motion chains is identical;

the third judging module is used for calculating the connectivity data and the connection code data of the corresponding motion chains according to each prime number layering matrix and judging whether the connectivity data and the connection code data of the two motion chains are identical when the second judging module judges that the complex hinge data of the two motion chains are identical;

the matrix transformation module is used for performing matrix transformation of exchange rows or exchange columns on prime number layering matrixes corresponding to one of the motion chains when the third judgment module judges that the connectivity data and the connection code data of the two motion chains are corresponding to the same, so as to obtain a transformed prime number layering matrix;

The fourth judging module is configured to judge whether the prime number layering matrix of the transformation is the same as the prime number layering matrix corresponding to the other motion chain, if yes, judge that the two motion chains are isomorphic, and if no, judge that the two motion chains are isomorphic.

The beneficial effects of the invention are as follows: the prime number layering matrix is generated according to a layering structure obtained by a composition principle of the moving chain, and the layering structure of the moving chain comprises the relation among all components in the moving chain, including the connection relation, the distance and the like among all the components, so that the prime number layering matrix obtained based on the matrix generation module can conveniently analyze the component numbers, the complex hinge data, the connectivity data and the connection code data of two moving chains through a first judgment module, a second judgment module and a third judgment module in sequence, and whether the two moving chains are isomorphic or not can be judged through simple calculation through the sequential judgment of the component numbers, the complex hinge data, the connectivity data and the connection code data;

the isomorphism judging system of the moving chain judges isomorphism of the moving chain based on the prime number layering matrix, is simple, convenient and efficient, has small time complexity, can simultaneously consider the reliability, the calculation simplicity, the calculation amount and the markability of the judgment, can judge isomorphism problems of the moving chain through simple calculation, is applicable to the situation whether the moving chain contains a compound hinge or not, effectively reduces design time and energy for designing a synthesized moving chain structure, and is suitable for general popularization; when prime number layering matrixes are generated according to the layering structure of the moving chain, the difference of labels is carried out on each component in the moving chain, so that operation of exchanging rows or exchanging columns is carried out on one prime number layering matrix through a matrix transformation module, influence caused by the difference of labels can be effectively avoided through judgment of a fourth judgment module, and accuracy and effectiveness of final isomorphism judgment are guaranteed.

According to another aspect of the present invention, there is provided an isomorphism decision device based on a prime number layering matrix, comprising a processor, a memory and a computer program stored in the memory and executable on the processor, the computer program implementing the steps in an isomorphism decision method based on a prime number layering matrix of the present invention when running.

The beneficial effects of the invention are as follows: the isomorphism judgment of the moving chain is realized by the computer program stored in the memory and running on the processor, the prime number layering matrix is based, the method is simple and efficient, the time complexity is low, the reliability, the calculation simplicity, the calculation amount and the markability of the judgment can be simultaneously considered, the isomorphism problem of the moving chain can be judged by simple calculation, the method is applicable to the situation whether the complex hinge exists or not, the design time and the energy are effectively reduced for designing the synthesized moving chain structure, and the method is suitable for general popularization.

According to another aspect of the present invention, there is provided a computer storage medium including: at least one instruction, when executed, implements the steps in a prime number hierarchical matrix based isomorphism decision method of the present invention.

The beneficial effects of the invention are as follows: the isomorphism judgment of the moving chain is realized by executing the computer storage medium containing at least one instruction, the prime number layering matrix is based, the method is simple and efficient, the time complexity is low, the reliability, the simplicity in calculation, the small calculation amount and the markability of the judgment can be simultaneously considered, the isomorphism problem of the moving chain can be judged through simple calculation, the method is applicable to the situation whether the moving chain contains a complex hinge or not, the design time and the energy are effectively reduced for designing the composite moving chain structure, and the method is suitable for general popularization.

Drawings

FIG. 1 is a flow chart of a isomorphic determination method based on prime number layering matrix in a first embodiment of the invention;

FIG. 2 is a flow chart of a prime number layering matrix for generating a kinematic chain according to a first embodiment of the present invention;

FIG. 3 shows a kinematic chain C according to a first embodiment of the invention ₁ Is a simplified structure;

FIG. 4 shows a kinematic chain C according to a first embodiment of the invention ₁ A sub-hierarchical structure diagram corresponding to a third component of the plurality;

FIG. 5 shows a kinematic chain C according to a first embodiment of the invention ₂ Is a simplified structure;

FIG. 6 shows a kinematic chain C according to a first embodiment of the invention ₃ Is a simplified structure;

FIG. 7 is a flow chart of acquiring complex hinge data of a kinematic chain according to a first embodiment of the present invention;

FIG. 8 is a flowchart of step S4 in the first embodiment of the present invention;

fig. 9 is a schematic structural diagram of an isomorphic determining system based on prime number hierarchical matrix in a second embodiment of the invention.

Detailed Description

The principles and features of the present invention are described below with reference to the drawings, the examples are illustrated for the purpose of illustrating the invention and are not to be construed as limiting the scope of the invention.

The present invention will be described below with reference to the accompanying drawings.

In a first embodiment, as shown in fig. 1, a prime number layering matrix-based isomorphism determination method includes the following steps:

s1: respectively obtaining layered structures corresponding to two motion chains one by one, and generating prime number layered matrixes of the corresponding motion chains according to each layered structure;

s2: acquiring the number of components of the corresponding moving chains according to each prime number layering matrix, judging whether the number of the components of the two moving chains is the same, if so, executing S3, and if not, judging that the two moving chains are heterogeneous;

s3: acquiring complex hinge data of the corresponding motion chains according to each prime number layering matrix, judging whether the complex hinge data of the two motion chains are identical, if so, executing S4, and if not, judging that the two motion chains are heterogeneous;

s4: calculating connectivity data and connection code data of the corresponding moving chains according to each prime number layering matrix, judging whether the connectivity data and the connection code data of the two moving chains are identical in correspondence, if so, executing S5, and if not, judging that the two moving chains are heterogeneous;

S5: and performing matrix transformation of a row or a column of the prime number layering matrix corresponding to one of the motion chains to obtain a transformed prime number layering matrix, judging whether the transformed prime number layering matrix is identical to the prime number layering matrix corresponding to the other motion chain, if so, judging that the two motion chains are isomorphic, and if not, judging that the two motion chains are isomorphic.

The isomorphism judging method of the moving chain of the embodiment judges isomorphism of the moving chain based on the prime number layering matrix, is simple, convenient and efficient, has small time complexity, can simultaneously consider the reliability, the calculation is simple, the calculation amount is small and the markability of the judgment, can judge isomorphism of the moving chain through simple calculation, is applicable to the situation whether the moving chain contains a compound hinge or not, effectively reduces design time and energy for designing a synthesized moving chain structure, and is suitable for general popularization.

Preferably, as shown in fig. 2, the specific steps of S1 include:

s1.1: selecting one of the kinematic chains, acquiring a corresponding structure diagram, determining all root members in the selected one of the kinematic chains according to the structure diagram, selecting one of the root members, and determining all sub-members corresponding to the selected one of the root members and the distance between the selected one of the root members and each of the sub-members according to the corresponding structure diagram;

S1.2: obtaining a sub-layered structure of the selected root member according to the selected root member, all sub-members corresponding to the selected root member and the distances between the selected root member and all the corresponding sub-members;

s1.3: traversing each root component in the selected one motion chain to obtain a sub-layered structure corresponding to each root component in the selected one motion chain one by one, and obtaining a layered structure of the selected one motion chain according to all the sub-layered structures;

s1.4: according to a preset prime number matching table, prime number layering matrix definition is obtained, and a prime number layering matrix of a corresponding motion chain is generated according to the prime number layering matrix definition and a layering structure of a selected motion chain;

the prime number layering matrix is defined as:

in a selected kinematic chain, when the ith component is taken as a root component and the jth component is taken as a subcomponent, a _ij Elements representing an ith row and a jth column in the prime number layering matrix of the kinematic chain; k (k) _ij Representing the distance between the ith and jth members in the kinematic chain;representing the distance k between the ith and jth members in the kinematic chain _ij According to the prime numbers corresponding to the prime number matching table;

s1.5: according to the method of S1.1 to S1.4, a prime number layering matrix of another motion chain is obtained.

When any one member of the moving chain is used as a root member, other members of the moving chain form sub-members of the root member, so that each root member of the moving chain can be determined through a structure diagram of the moving chain, and then the distance between each root member and each corresponding sub-member is determined; through the distances, a sub-layered structure corresponding to each root member can be obtained, and all the sub-layered structures form a layered structure of the motion chain; and then according to a preset prime number matching table, prime number layering matrix definition can be obtained, wherein prime numbers comprise prime numbers of 2, 3, 5, 7, 11 … … and the like, the prime number matching table comprises a one-to-one matching relation between the prime numbers and distances between root components and sub-components, the prime number layering matrix definition defines meaning represented by each element in the matrix and comprises the number of root components, the number of root components and the distance between the sub-components and the like, and therefore, based on a layering structure of a moving chain (comprising all distances between all components and all corresponding sub-components), the preset prime number matching table and the obtained prime number layering matrix definition, the prime number layering matrix of the corresponding moving chain is generated, so that analysis and judgment are conveniently carried out according to the prime number layering matrix, and whether two moving chains are isomorphic or not is further judged.

Specifically, the prime number matching table in the present embodiment is shown in table 1.

Table 1 prime number matching table

Distance between root member and subcomponent	Elements in prime/prime hierarchical matrix
		1	2
2	3
		3	5
4	7
		5	11
6	13
		7	17
8	19
		9	23
10	29
		……	……

Specifically, in this embodiment, one of the kinematic chains is C ₁ The known corresponding structure diagram is shown in fig. 3, the sub-layered structure of the third component is obtained according to the methods of S1.1 and S1.2 and is shown in fig. 4, each component is represented by a hollow node, and a solid line between two hollow nodes represents the connection relationship of the two components; in this embodiment, two kinematic chains are respectively kinematic chain C ₂ And a kinematic chain C ₃ Can be combined with a kinematic chain C according to the methods described in S1 to S5 ₁ Respectively making isomorphism decisions, known as kinematic chain C ₂ And a kinematic chain C ₃ The structure diagrams of (a) are shown in fig. 5 and 6 respectively, and the sub-layered structure of each corresponding component can be obtained according to the methods of S1.1 and S1.3, so as to obtain the layered structure corresponding to the kinematic chain.

Specifically, in this embodiment, the kinematic chain C is obtained according to the method of S1.4 ₁ The prime number layering matrix of (a) is:

wherein, in the prime number layering matrixElement a in ₃₄ The value of (2) represents that when the 3 rd component is taken as the root component, the distance between the fourth component and the root component is 1, and the first prime number is represented as 2;

Similarly, the kinematic chain C is obtained ₂ And a kinematic chain C ₃ The prime number layering matrix of (a) is as follows:

preferably, in S2, the specific implementation for obtaining the number of components of the corresponding kinematic chain is:

Since it is defined according to the prime number layering matrix, in each prime number layering matrix, when i=j, element a _ij The number of the components is 0, meaning that when the ith component is taken as a root component, the distance between the ith component and the ith component is 0, and the corresponding element is taken as 0, so that the number of the components can be determined through statistics on the number of the elements of 0 in each prime number layering matrix, the same number of the components is a first necessary condition for judging that two moving chains are in isomorphic relation, when the number of the components is the same, the isomorphic of the two moving chains is possible, and when the number of the components is different, the two moving chains are necessarily isomorphic, therefore, the invention firstly carries out primary judgment on whether the isomorphic problem of the two moving chains through judgment of the number of the components, can carry out primary screening on the isomorphic problem, and is convenient for the subsequent further judgment process.

Specifically, in this embodiment, the number of elements of 0 in the prime number layered matrix of the three kinematic chains is counted, so as to obtain the number of components of the three kinematic chains to be 10.

Preferably, the plurality of target multi-hinge members form a multi-hinge, each target multi-hinge member corresponds to one kinematic pair number, and the multi-hinge data comprises the multi-hinge number and all the kinematic pair numbers forming each multi-hinge;

as shown in fig. 7, in S3, the specific step of acquiring the complex hinge data of the corresponding motion chain includes:

s3.1: selecting a prime number layering matrix of one of the motion chains, judging whether elements of an ith row and an ith column in the selected prime number layering matrix and elements of the ith row and the ith column are 2 at the same time, if so, in the motion chain corresponding to the selected prime number layering matrix, the jth component is an adjacent component of the ith component, executing S3.2, and if not, in the corresponding motion chain, the jth component is a non-adjacent component of the ith component;

s3.2: traversing each element in the ith row of the selected prime number layering matrix, judging all adjacent components adjacent to the ith component in a motion chain corresponding to the selected prime number layering matrix according to the method of S3.1, and obtaining the number of the adjacent components of the ith component in the motion chain corresponding to the selected prime number layering matrix according to all the adjacent components adjacent to the ith component;

S3.3: traversing each row of the selected prime number layering matrix, and obtaining the number of adjacent components corresponding to each component in the motion chain corresponding to the selected prime number layering matrix according to the method of S3.1 to S3.2;

s3.4: respectively judging whether the number of adjacent components corresponding to each component in the motion chain corresponding to the selected prime number layering matrix is larger than 2, if so, determining the corresponding component in the motion chain corresponding to the selected prime number layering matrix as a potential complex hinge component, and executing S3.5, if not, determining the corresponding component in the motion chain corresponding to the selected prime number layering matrix as a non-potential complex hinge component;

s3.5: obtaining all potential complex hinge components in the corresponding motion chain according to the judging method of S3.4, and determining the complex hinge number in the corresponding motion chain and all target complex hinge components forming each complex hinge according to all the potential complex hinge components and a prime number layering matrix;

s3.6: selecting any one complex hinge, and calculating to obtain the number of kinematic pairs corresponding to each target complex hinge component one by one corresponding to the selected complex hinge according to a kinematic pair number calculation formula;

f _t ^s ＝n _t -N+1；

s3.7: traversing all complex hinges in the motion chain corresponding to the selected prime number layering matrix, and obtaining all kinematic pair numbers forming each complex hinge in the corresponding motion chain according to the method of S3.6;

s3.8: the number of complex hinges in the other kinematic chain and the number of all kinematic pairs forming each complex hinge are obtained according to the method of S3.1 to S3.7.

Because the same number of complex hinges and the same number of kinematic pairs forming each complex hinge are the same as the necessary conditions for isomorphism of two kinematic chains, the number of complex hinges needs to be determined, and then the number of kinematic pairs corresponding to each target complex hinge component forming each complex hinge one by one is determined; since the number of the members in the kinematic chain is greater than or equal to 3 and the members must be adjacent to each other, that is, the members greater than or equal to 3 are adjacent to each other, the number of the adjacent members is determined by the prime number layering matrix in the embodiment; further, when the distance k between the ith component and the jth component is based on the prime number matching table _ij When 1, the corresponding prime number is 2, meaning that when element a in prime number layering matrix _ij And a _ji And when the number is 2, the connection relation between the ith component and the jth component is adjacent to each other; therefore, by judging the element of each row 2 in the prime number layering matrix, the adjacent components of the component represented by the row can be judged, and then the number of the adjacent components corresponding to the represented component is judged, when the number of the adjacent components is more than 2, the adjacent components represented by the row and other components are adjacent to each other, and the situation of double hinging is possible;

the embodiment comprehensively judges the situation of possibly forming the complex hinge based on the prime number layering matrix according to the situation that each row of elements are 2, namely a potential complex hinge component possibly forming the complex hinge is obtained; further analyzing based on all the potential multi-hinge components to obtain the number of multi-hinges forming the multi-hinges and all target multi-hinge components forming each multi-hinge; finally, calculating the number of kinematic pairs corresponding to each target compound hinge member according to the number of compound hinges and a kinematic pair number calculation formula; the judging step only needs to carry out simple calculation and analysis based on prime number layering matrix, so that accurate complex hinge data (complex hinge number and all kinematic pairs) can be obtained, a basis is provided for further isomorphism judgment in the follow-up process, the method is simple and effective, and the judging result is accurate; when the number of the complex hinges is 0, it means that the motion chain does not contain the complex hinges, so the embodiment is applicable to the situation of whether the motion chain contains the complex hinges or not, and has higher universality.

Preferably, in S3.5, the number of all potential multiple hinge members is greater than or equal to 3;

s3.5.a1: when the 3 potential multi-hinge components are adjacent components in pairs, and one non-potential component does not exist in the motion chain corresponding to the selected prime number layering matrix and is adjacent to any two potential multi-hinge components, the 3 potential multi-hinge components form a multi-hinge, the number of the multi-hinges in the corresponding motion chain is 1, the 3 potential multi-hinge components are target multi-hinge components of the corresponding multi-hinge, otherwise, the 3 potential multi-hinge components do not form the multi-hinge, and the number of the multi-hinges in the corresponding motion chain is 0;

s3.5.b1: when all the potential multi-hinge components are adjacent to each other in pairs, forming a multi-hinge by all the potential multi-hinge components, wherein the number of the multi-hinges in the corresponding motion chain is 1, and all the potential multi-hinge components are target multi-hinge components of the corresponding multi-hinge, otherwise, executing S3.5.b2;

S3.5.b2: selecting any 3 potential multi-hinge members as potential multi-hinge members to be judged, when the 3 potential multi-hinge members to be judged are adjacent members, and one potential multi-hinge member and any two potential multi-hinge members to be judged are adjacent members in the rest potential multi-hinge members, the 3 potential multi-hinge members to be judged form a multi-hinge, and the 3 potential multi-hinge members to be judged are target multi-hinge members of the corresponding multi-hinge, otherwise, the 3 potential multi-hinge members to be judged do not form a multi-hinge;

s3.5.b3: traversing all potential multi-hinge components, judging all multi-hinges according to a judging method of S3.5.b2, and obtaining the corresponding number of multi-hinges in a motion chain and all target multi-hinge components forming each multi-hinge according to all the multi-hinges.

Since the number of potential multi-hinge members constituting the multi-hinge must be greater than or equal to 3, when the number is equal to 3, the 3 potential multi-hinge members are adjacent to each other in pairs, and when another member is not present in the corresponding motion chain and any two potential multi-hinge members are adjacent to each other, the 3 potential multi-hinge members form a structure without self-ring, which can only be a multi-hinge; when the number of the potential multi-hinge components forming the multi-hinge is larger than 3 through judging the number of the adjacent components, two situations exist, one is that all the potential multi-hinge components larger than 3 form the same multi-hinge, the number of the multi-hinge is 1, and the other is that among the potential multi-hinge components larger than 3, three potential multi-hinge components form one multi-hinge, and the other three potential multi-hinge components form the other multi-hinge, namely the number of the multi-hinge is larger than 1; therefore, for the first case, judging whether all the potential multi-hinge members are adjacent members or not, for the second case, selecting any three potential multi-hinge members, and adopting a similar judging step as that when the number of the potential multi-hinge members is 3; the judging step of the embodiment can accurately judge the number of the complex hinges forming the complex hinges and the number of all the kinematic pairs forming each complex hinge, has simple theory and accurate and effective result, and provides basis for subsequent further judgment.

Specifically, the present embodiment judges the kinematic chain C through the steps S3.1 to S3.5 ₁ The number of the potential multi-hinge members is 5, and the corresponding 5 potential multi-hinge members are not all in a mutually adjacent member relation, so that the motion chain C is obtained according to the method from S3.5.b2 to S3.5.b3 ₁ The 3 rd, 4 th and 10 th members form a double hinge, the chain C ₁ The number of the complex hinges is 1, and the 3 rd component, the 4 th component and the 10 th component are all 3 target complex hinge components corresponding to the complex hinges; then according to the method from S3.6 to S3.7, the kinematic pairs corresponding to the 3 target compound hinge components one by one are calculatedNumber average 3, i.e. kinematic chain C ₁ Comprising 3 three pairs of bars; similarly, for the kinematic chain C ₂ And a kinematic chain C ₃ The same analysis and judgment are carried out, and the corresponding structure diagram is combined to obtain the kinematic chain C ₂ And a kinematic chain C ₃ Each comprising only one complex hinge and each comprising 3 triple bars.

Preferably, in S3, the specific step of determining whether the complex hinge data of the two motion chains are identical includes:

s3.9: and judging whether the number of the complex hinges of the two moving chains and the number of all the kinematic pairs in the two moving chains are the same, if so, executing the step 4, and if not, judging that the two moving chains are heterogeneous.

When the complex hinge data of the two moving chains are identical, that is, the same number of complex hinges (when the number of the complex hinges is 0, the two moving chains do not contain complex hinges) and the number of kinematic pairs forming each complex hinge are identical, it can be stated that the two moving chains may have the same structure and connection relationship, and the two moving chains may have the isomorphic relationship, so that the subsequent judging step can be performed; the isomorphism problem can be further judged by simple analysis and calculation based on prime number layering matrixes of two motion chains.

Specifically, in this embodiment, the number of the complex hinges of the three kinematic chains is 1, and each of the three kinematic chains includes 3 pairs of rods, so that the number of the complex hinges of the three kinematic chains and the number of all the kinematic pairs forming the complex hinges are identical.

Preferably, in S4, the connection data includes a first connection degree of the corresponding kinematic chain and a second connection degree of each member in the corresponding kinematic chain, and the connection code data includes a first connection code of the corresponding kinematic chain and a second connection code of each member in the corresponding kinematic chain;

as shown in fig. 8, the specific steps of calculating the connectivity data and the connectivity code data of the corresponding kinematic chain include:

S4.1: selecting prime number layering matrixes of one of the motion chains, and calculating second connectivity corresponding to each component in the motion chain corresponding to the selected prime number layering matrix according to a second connectivity calculation formula;

s4.2: arranging the elements of each row in the selected prime number layering matrix according to the sequence from large to small to obtain an element sequence of each row, and obtaining a second connection code corresponding to each component one by one according to the element sequence of each row and the second connection degree of the component corresponding to the element sequence of each row one by one;

s4.3: arranging the second connection degrees of all the components in the motion chain corresponding to the selected prime number layering matrix in a sequence from large to small to obtain a first connection code of the corresponding motion chain; according to all the second connection degrees, calculating to obtain the first connection degree of the corresponding motion chain;

The first connection code of one of the motion chains is:

wherein S is ¹ A first degree of connectivity for one of the kinematic chains;

s4.4: obtaining a second connection degree and a second connection code corresponding to each component in the other moving chain and a first connection degree and a first connection code of the moving chain according to the methods from S4.1 to S4.3;

as shown in fig. 8, in S4, the specific step of determining whether the connectivity data and the connection code data of two motion chains are the same includes:

s4.5: judging whether the first connection degree of the two kinematic chains is the same, if so, executing S4.6, and if not, judging that the two kinematic chains are heterogeneous;

s4.6: and judging whether the first connection codes of the two moving chains, the second connection degree corresponding to each component in the two moving chains and the second connection code are the same or not, if so, executing S5, and if not, judging that the two moving chains are heterogeneous.

Based on the determination of the multi-hinge data, it can be primarily explained that two moving chains may have the same structure and connection relationship, so in this embodiment, by calculating and analyzing the first connection degree and the second connection code of the two moving chains and the second connection degree and the second connection code corresponding to each member in each moving chain, the accurate connection relationship between each member in the two moving chains can be accurately determined, and when the first connection degree and the second connection code of the two moving chains and the second connection degree and the second connection code corresponding to each member in the two moving chains are completely the same, the two moving chains have the completely same connection relationship, so that the two moving chains are most likely to be in the isomorphic relationship; similarly, the embodiment can accurately and efficiently judge the isomorphism problem of the moving chain by simple calculation and analysis based on the prime number layering matrix.

Specifically, in the present embodiment, in S4.1, for the kinematic chain C ₁ The third component of (a) is prime number layering matrixThe second connectivity of the third member is calculated as:

then in S4.2, pairThe third row elements of the sequence are arranged in the order from big to small, and the obtained element sequence is 5,3,3,3,3,3,3,2,2,2,0; thus, the second connection code for the third member is:

since the element with 0 in the prime number layering matrix does not play a role in calculating the second connectivity and the first connectivity of the subsequent motion chain, and is necessarily located at the rear end of the element sequence when each row of elements are arranged in order from large to small, for convenience of description, the element with 0 in the prime number layering matrix may be omitted when S4.1 to S4.4 are performed, that is, the second connection code of the third member may be written as:

/>

specifically, in the present embodiment, the kinematic chain C is obtained according to the method of S4.1 to S4.4 ₁ And the second connection degree and the second connection code corresponding to each component, and summarizing all the information together to obtain:

similarly, a kinematic chain C is obtained ₂ And a kinematic chain C ₃ The summary information of (2) is as follows:

/>

according to the judging method of S4.5 to S4.6, the kinematic chain C can be seen from the summarized information ₃ With the kinematic chain C ₁ Kinematic chain C ₂ The first links of (C) are not equal, so that the kinematic chain C ₃ With the kinematic chain C ₁ Kinematic chain C ₂ Homoisomerism, further, kinematic chain C ₁ With the kinematic chain C ₂ The first connection degree and the first connection code of the chain are the same, the number of the component is ignored, and the second connection degree and the second connection code are also the same, so that the motion chain C ₁ With the kinematic chain C ₂ And most likely in a homogenous relationship.

Specifically, in this embodiment S5, and the kinematic chain C ₁ With the kinematic chain C ₂ The corresponding prime number layering matrix can be completely transformed into identical ones by exchanging rows and exchanging columnsMatrix, therefore, motion chain C ₁ With the kinematic chain C ₂ Is a isomorphic kinematic chain.

In a second embodiment, as shown in fig. 9, an isomorphic determining system based on prime number layering matrix includes a matrix generating module, a first determining module, a second determining module, a third determining module, a matrix transforming module and a fourth determining module:

The isomorphism judging system of the moving chain judges isomorphism of the moving chain based on the prime number layering matrix, is simple, convenient and efficient, has small time complexity, can simultaneously consider the reliability, the simplicity in calculation, the small calculation amount and the markability of the judgment, can judge isomorphism problems of the moving chain through simple calculation, is applicable to the situation whether the moving chain contains a compound hinge or not, effectively reduces design time and energy for designing a synthesized moving chain structure, and is suitable for general popularization.

The third embodiment, based on the first embodiment and the second embodiment, further discloses a isomorphic determining device based on a prime number layering matrix, which comprises a processor, a memory and a computer program stored in the memory and capable of running on the processor, wherein the computer program realizes the specific steps S1 to S5 shown in fig. 1 when running.

The isomorphism judgment of the moving chain is realized by the computer program stored in the memory and running on the processor, the prime number layering matrix is based, the method is simple and efficient, the time complexity is low, the reliability, the calculation simplicity, the calculation amount and the markability of the judgment can be simultaneously considered, the isomorphism problem of the moving chain can be judged by simple calculation, the method is applicable to the situation whether the complex hinge exists or not, the design time and the energy are effectively reduced for designing the synthesized moving chain structure, and the method is suitable for general popularization.

The present embodiment also provides a computer storage medium having at least one instruction stored thereon, which when executed, implements the specific steps of S1 to S5.

The isomorphism judgment of the moving chain is realized by executing the computer storage medium containing at least one instruction, the prime number layering matrix is based, the method is simple and efficient, the time complexity is low, the reliability, the simplicity in calculation, the small calculation amount and the markability of the judgment can be simultaneously considered, the isomorphism problem of the moving chain can be judged through simple calculation, the method is applicable to the situation whether the moving chain contains a complex hinge or not, the design time and the energy are effectively reduced for designing the composite moving chain structure, and the method is suitable for general popularization.

In this embodiment, details of S1 to S5 are not fully described in detail in the first embodiment and fig. 1 to 8, and detailed descriptions thereof are omitted.

The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims

1. The isomorphism judging method based on the prime number layering matrix is characterized by comprising the following steps of:

step 4: calculating connectivity data and connection code data of the corresponding moving chains according to each prime number layering matrix, judging whether the connectivity data and the connection code data of the two moving chains are identical in correspondence, if so, executing the step 5, and if not, judging that the two moving chains are heterogeneous;

Step 5: performing matrix transformation of a row or a column of exchange on a prime number layering matrix corresponding to one of the motion chains to obtain a transformed prime number layering matrix, judging whether the transformed prime number layering matrix is identical to a prime number layering matrix corresponding to the other motion chain, if so, judging that the two motion chains are isomorphic, and if not, judging that the two motion chains are isomorphic;

the specific steps of the step 1 include:

the prime number layering matrix is defined as:

the preset prime number matching table specifically comprises the following steps: in a selected kinematic chain, when the ith component is taken as a root component and the jth component is taken as a subcomponent, the distance k between the ith component and the jth component _ij A one-to-one correspondence with each prime number;

2. The isomorphism determination method based on prime number hierarchical matrix according to claim 1, wherein in the step 2, the specific implementation of obtaining the number of components of the corresponding kinematic chain is as follows:

3. The isomorphism determination method based on prime number layering matrix according to claim 1, wherein a plurality of target complex hinge components form a complex hinge, each target complex hinge component corresponds to one kinematic pair number, and the complex hinge data comprises the complex hinge number and all kinematic pair numbers forming each complex hinge;

f _t ^s ＝n _t -N+1；

4. A prime number layering matrix-based isomorphism determination method according to claim 3, wherein in the step 3.5, the number of all potential complex hinge members is greater than or equal to 3;

step 3.5.a1: when the 3 potential multi-hinge components are adjacent components in pairs, and one non-potential multi-hinge component does not exist in the motion chain corresponding to the selected prime number layering matrix, and the non-potential multi-hinge components are adjacent components with any two potential multi-hinge components, the 3 potential multi-hinge components form a multi-hinge, the number of the multi-hinges in the corresponding motion chain is 1, the 3 potential multi-hinge components are target multi-hinge components of the corresponding multi-hinge, otherwise, the 3 potential multi-hinge components do not form the multi-hinge, and the number of the multi-hinges in the corresponding motion chain is 0;

5. The isomorphism determination method based on prime number hierarchical matrix according to claim 3, wherein in the step 3, the specific step of determining whether the complex hinge data of two motion chains are identical comprises:

6. The isomorphism determination method based on prime number layering matrix according to claim 2, wherein in the step 4, the connection data includes a first connection degree of a corresponding motion chain and a second connection degree of each component in the corresponding motion chain, and the connection code data includes a first connection code of the corresponding motion chain and a second connection code of each component in the corresponding motion chain;

The first connection code of one of the motion chains is:

M ₁ for the first link code of one of the kinematic chains,for the maximum value of all second links in the corresponding kinematic chain, +.>To correspond toThe minimum of all second connectivity in the kinematic chain;

wherein S is ¹ A first degree of connectivity for one of the kinematic chains;

7. The isomorphic judging system based on the prime number layering matrix is characterized by comprising a matrix generating module, a first judging module, a second judging module, a third judging module, a matrix transformation module and a fourth judging module:

The fourth judging module is used for judging whether the prime number layering matrix of the transformation is the same as the prime number layering matrix corresponding to the other motion chain, if so, judging that the two motion chains are isomorphic, and if not, judging that the two motion chains are isomorphic;

the matrix generation module is specifically configured to perform the following steps:

the prime number layering matrix is defined as:

8. An isomorphic determining device based on a prime number layering matrix, comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, the computer program when run implementing the method steps of any one of claims 1 to 6.

9. A computer storage medium, the computer storage medium comprising: at least one instruction which, when executed, implements the method steps of any of claims 1 to 6.