CN107944097A - Plane enclosed cuts with scissors the numbering matrix description method of kinematic chain again - Google Patents

Abstract

The invention relates to the field of mechanism kinematic chains, and discloses a method for describing the numbering matrix of a planar closed compound hinge kinematic chain. The components and kinematic pairs of the kinematic chain are numbered, wherein the kinematic pairs are P _n , and an n×n numbering matrix is generated. a. The numbering matrix description method of the planar closed complex hinge kinematic chain of the present invention omits the relationship expression of the topological graph, prevents the loss of information, and the numbering matrix corresponds to the kinematic chain one by one, and can uniquely represent a kinematic chain. The numbering matrix can directly Draw a diagram of the kinematic chain structure.

Description

Numbering Matrix Description Method of Planar Closed Kinematic Chain of Compound Hinge

technical field

The invention relates to the field of mechanism kinematic chains, in particular to a numbering matrix description method of a planar closed compound hinge kinematic chain.

Background technique

The basis of studying mechanism is the characteristic analysis of kinematic chain, and the description of kinematic chain plays a very important role in mechanism. For the traditional representation method, it is generally to transform the kinematic chain diagram into a topological diagram, then convert the topological diagram into a matrix, and perform related operations. However, when drawing a topological diagram of a simplified structure, due to the inclusion of compound hinges, the expression of the topological diagram is cumbersome, and because the drawing methods and forms of the topological diagram are also varied, it is easy to lose part of the information, such as the attributes of kinematic pairs. When the topological map is converted into a matrix, some information is lost in the matrix, such as member numbers and so on. Therefore, there is a need for an expression method to avoid the above problems and prevent the loss of information such as kinematic properties and member numbers.

Contents of the invention

The purpose of the present invention is to address the deficiencies of the above-mentioned technologies, and provide a method for describing the numbering matrix of the planar closed compound hinge kinematic chain, which saves the relationship expression of the topological graph, prevents information loss, and the numbering matrix corresponds to the kinematic chain one by one , can uniquely represent a kinematic chain, and the structure diagram of the kinematic chain can be drawn directly from the numbering matrix.

In order to achieve the above-mentioned purpose, a method for describing the numbering matrix of a planar closed compound hinge kinematic chain designed by the present invention, numbers the components and kinematic pairs of the kinematic chain, wherein the kinematic pair is P _n , and generates an n×n numbering matrix A:

In the formula, n is the number of kinematic pairs, the diagonal elements a _i,j (i=j) of the numbering matrix are all 0, and the other elements a _i,j (i≠j,i=1,..., n; j=1,...,n) is the serial number of the component connecting the kinematic pair P _i and the kinematic pair P _j , when the kinematic pair P _i and the kinematic pair P _j are not connected, a _i,j =0.

Preferably, the element a _i,j of the numbering matrix A is subjected to bool operation, when the element a _i,j =0, the element value remains unchanged, and when the element a _i,j ≠0, the element value takes the value 1, Get the adjacency matrix B.

Preferably, the numbering matrix A is retrieved, a _i,j =0 when the motion pair P _i is not connected to the motion pair P _j , a i, _j =1 when the motion pair P _i is connected to the motion pair P _j , and the motion The association matrix C of the chain, in which the row number represents the component number, and the column number represents the movement pair number, expressing the connection relationship between the movement pair P _n and each component.

Preferably, the numbering matrix A is retrieved. When the component number of the i-row element corresponding to the kinematic pair P _i occurs for k times, the component of the i-row element corresponding to the kinematic pair P _i is a g-element component, g=k+1, and the obtained The property sheet for the kinematic chain components.

Preferably, the indexing matrix A is retrieved. When the component number of the i-column element corresponding to the kinematic pair P _i occurs for k times, the component of the i-row element corresponding to the kinematic pair P _i is a g-element component, and g=k+1 is obtained. The property sheet for the kinematic chain components.

Preferably, the numbering matrix A is retrieved, when there are m or more non-zero and unequal elements a _i,j (i,j=1,2,,...,n) in the row i corresponding to the motion pair P _i value, the hinge at kinematic pair P _i is an m-element complex hinge, where m≥3.

Preferably, the numbering matrix A is retrieved, when there are m or more non-zero and unequal elements in the i-column a _i,j (i,j=1,2,,...,n) corresponding to the motion pair P _i value, the hinge at kinematic pair P _i is an m-element complex hinge, where m≥3.

Preferably, a generalized operation is performed on the row i elements a _i,j (i,j=1,2,...,n) corresponding to the motion pair P _i , and non-zero elements are eliminated, and two of the same component numbers greater than two are reserved , obtain the array code of each motion pair P _i , and then obtain the motion pair type table corresponding to the connection relationship between the array code and the motion pair P _i .

Preferably, generalized operations are performed on the i-column elements a _i,j (i,j=1,2,...,n) corresponding to the motion pair P _i , and non-zero elements are eliminated, and two of the same component numbers greater than two are reserved , obtain the array code of each motion pair P _i , and then obtain the motion pair type table corresponding to the connection relationship between the array code and the motion pair P _i .

Preferably, the component attribute table with the kinematic pair P _i is obtained by searching the connection relationship of the kinematic pair P _i in the kinematic pair type table.

Compared with the prior art, the present invention has the following advantages: the relationship expression of the topological graph is omitted, information loss is prevented, and the numbering matrix corresponds to the kinematic chain one by one, and a kinematic chain can be uniquely represented, and the numbering matrix can be directly drawn Draw a schematic diagram of the kinematic chain.

Description of drawings

Fig. 1 is a schematic structural diagram of a kinematic chain in the numbering matrix description method of the planar closed compound hinge kinematic chain of the present invention.

The components in the figure are numbered as follows:

The first component 1, the second component 2, the third component 3, the fourth component 4, the fifth component 5, the sixth component 6, the seventh component 7, the eighth component 8, the ninth component 9, the tenth component 10, The first exercise pair 11, the second exercise pair 12, the third exercise pair 13, the fourth exercise pair 14, the fifth exercise pair 15, the sixth exercise pair 16, the seventh exercise pair 17, the eighth exercise pair 18, the ninth exercise pair Movement pair 19, tenth movement pair 20, eleventh movement pair 21.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

A method for describing the numbering matrix of the planar closed compound hinge kinematic chain, numbering the components and kinematic pairs of the kinematic chain, where the kinematic pair is P _n , and generating an n×n numbering matrix A:

In the formula, n is the number of kinematic pairs, the diagonal elements a _i,j (i=j) of the numbering matrix are all 0, and the other elements a _i,j (i≠j,i=1,..., n; j=1,...,n) is the serial number of the component connecting the kinematic pair P _i and the kinematic pair P _j , when the kinematic pair P _i and the kinematic pair P _j are not connected, a _i,j =0.

Perform bool operation on the elements a _i,j of the numbering matrix A, when the element a _i,j =0, the element value remains unchanged, when the element a _i,j ≠0, the element value is 1, and the adjacency matrix B is obtained; Retrieve the numbering matrix A, when the kinematic pair P _i and the kinematic pair P _j are not connected, a _i,j =0, when the kinematic pair P _i and the kinematic pair P _j are connected, a _i,j =1, and obtain the association of the kinematic chain Matrix C, where the row number represents the component number, and the column number represents the motion pair number, expressing the connection relationship between the motion pair P _n and each component; the search number matrix A, when the motion pair P _i corresponds to the component number of the i row or i column element The number of occurrences is k, and the component of the i-row element corresponding to the kinematic pair P _i is a g element component, g=k+1, and the attribute table of the kinematic chain component is obtained; the search number matrix A, when the i-row corresponding to the kinematic pair P _i Or there are m or more than m non-zero and unequal values in the elements a _i,j (i,j=1,2,,...,n) of the i column, then the hinge at the kinematic pair P _i is an m-element complex Hinge, where m≥3; perform generalized operations on the i-row or i-column elements a _i,j (i,j=1,2,…,n) corresponding to the motion pair P _i , and eliminate non-zero elements, and for more than 2 2 of the same component numbers are reserved, and the array code of each motion pair P _i is obtained, and then the motion pair type table corresponding to the connection relationship between the array code and the motion pair P _i is obtained; through the connection of the motion pair P _i in the motion pair type table Retrieve the relationship and obtain the attribute table of the component with kinematic pair P _i .

As shown in Figure 1, this figure is a schematic structural diagram of a kinematic chain C ₁ , numbering the components and kinematic pairs of the kinematic chain, including the first kinematic pair 11, the second kinematic pair 12, the third kinematic pair Sub-13, fourth sub-14, fifth sub-15, sixth sub-16, seventh sub-17, eighth sub-18, ninth sub-19, tenth sub-20, eleventh sub-joint 21 and the first component 1, the second component 2, the third component 3, the fourth component 4, the fifth component 5, the sixth component 6, the seventh component 7, and the eighth component 8 connected to the kinematic pair according to the relationship in the figure , the ninth member 9 and the tenth member 10, and generate a 11×11 numbering matrix

numbering matrix The elements a _i,j of kinematic chain C ₁ represent the connection relationship between kinematic pair P _i and kinematic pair P _j , for example, numbering matrix Among them, a ₃ and 4 indicate that the third kinematic pair 13 is connected to the fourth kinematic pair 14 , and the connected member is the fourth member 4 .

numbering matrix It is very concise and contains all the information of the kinematic chain C ₁ , as follows:

1, will number the matrix The element a _{i, j} of the element performs bool operation. When the element a _{i, j} = 0, the element value remains unchanged. When the element a _{i, j} ≠ 0, the element value takes the value 1, and the adjacency matrix is obtained

adjacency matrix It is a matrix representing the adjacent relationship between vertices, and in kinematic chain C ₁ , it represents the connection relationship between kinematic pair and kinematic pair.

2. Retrieve the number matrix When the kinematic pair P _i is not connected to the kinematic pair P _j , a _i,j =0, when the kinematic pair P _i is connected to the kinematic pair P _j , a _i,j =1, to obtain the correlation matrix of the kinematic chain

Express the connection relationship between the kinematic pair P _n and each component, where the row number represents the component number, and the column number represents the kinematic pair number. For example: in numbered matrix The ninth row or the ninth column represents the connection relationship between the ninth kinematic pair 19 and each component, it can be obtained that the ninth kinematic pair 19 is connected with the seventh component 7, the eighth component 8 and the ninth component 9, in the correlation matrix It can be clearly reflected in , a _i,j = 1, and the motion pair P _i is connected to the motion pair P _j .

3. Retrieve number matrix When the component number of the i-row or i-column element corresponding to the kinematic pair P _i occurs for k times, the component of the i-row element corresponding to the kinematic pair P _i is a g element component, g=k+1, and the attribute of the kinematic chain component is obtained table, as shown in the following table:

Assembly number Component properties Assembly number Component properties 1 N ₄ 6 N ₂ 2 N ₃ 7 N ₂ 3 N ₂ 8 N ₂ 4 N ₃ 9 N ₂ 5 N ₂ 10 N ₂

In the table, N _i indicates that the component is an i-element component. In the table, for example, the first component 1 is in the numbering matrix appears 3 times in the first line of , so the first member 1 is a quaternary member.

4. Retrieve number matrix When there are m or more non-zero and unequal values in the i-row or i-column element a _i,j (i,j=1,2,,...,n) corresponding to the motion pair P _i , then the motion pair The hinge at P _i is an m-element complex hinge, where m≥3, in the numbering matrix It can be determined that the third kinematic pair 3 and the ninth kinematic pair 9 are ternary compound hinges.

5. Pair numbering matrix The i row or i column element a _i,j (i,j=1,2,…,n) corresponding to the middle motion pair P _i is subjected to a generalized operation, the non-zero elements are eliminated, and 2 of the same component number greater than 2 are reserved , obtain the array code of each motion pair P _i , and then obtain the motion pair type table corresponding to the connection relationship between the array code and the motion pair P _i . In the array code, if the same component number appears twice, it means that the kinematic pair P _i is a multi-component component, and if it only appears once, it means that the component is a binary component. The number of different component numbers indicates that several components are connected at the kinematic pair P _i , for example, (a, a, b, c) represents that component a, component b, and component c are connected. In this embodiment, the following motion pair type table is obtained:

In this embodiment, in order to better represent the connection relationship of the motion pair P _i , J _XX -XX is used to represent the motion pair attribute, and the meanings represented are as follows:

(1) The number of numbers in the subscript array indicates the number of connected components of the kinematic pair P _i . For example, the first kinematic pair 11 (1,1,2,2) connects the first member 1 and the second member 2, and the number of subscript arrays of the first kinematic pair 11 is 2;

(2) The value of a certain number in the subscript array indicates the number of binary components connected in series by the kinematic pair P _i . When two multi-element components are directly connected on the kinematic pair P _i , the value "0" is used to indicate that, for example, the first component 1 connected by the fifth kinematic pair 15 (1,1,6) is a quaternary component, and the sixth component 6 is a binary component, the sixth component 6 is connected in series with the fifth component 5 of the binary component, the fifth component 5 is connected to the fourth component 4 of the ternary component, and the value of the array is represented by "2". It is stipulated that the median value of the subscript array is arranged from small to large, and the value of the subscript array of the fifth motion pair 15 is "02";

(3) The connection array in the back corresponds to the subscript array, the number of the connection array is equal to the number of the subscript array, and the value of the connection array indicates the type of the connection component at the end of the serial binary component. If the number of binary components in series is the same, the types of connected components at the end are arranged in descending order. For example, the first component 1 connected by the fifth kinematic pair 15 is a quaternary component, and the value of the corresponding connection array is represented by "4", the sixth component 6 connected by the fifth kinematic pair 15 is a binary component, and the sixth The component 6 is connected in series with the fifth component 5 of the binary component and then connected with the fourth component 4 of the ternary component. The value of the corresponding connection array is represented by "3", so the connection array is "43";

(4) The connection member type at the end of the serial binary member in the connection array is a composite hinge, which is represented by "0".

Retrieving the code of the array can get the code of the attribute of the motion pair P _i . For example, the third kinematic pair 13 connects the third component 3 of the binary component, the fourth component 4 of the quadruple component and the eighth component 8 of the binary component, and the array code can be searched to find (2,2,3), (7,8, 9), indicating that the third component 3 of the binary component is connected with the second component 2 of the ternary component, the eighth component 8 of the binary component is connected with the ternary composite hinge, and the code name of the third kinematic pair 13 is J ₀₁₁ -330. Thus, the attribute table of motion pair P _i can be obtained, as shown in the following table:

In the above table, there is a one-to-one correspondence between the kinematic pair type and the kinematic pair attribute code obtained through the kinematic pair connection relationship and the kinematic chain C ₁ , which can uniquely represent the kinematic chain C ₁ .

6. By retrieving the connection relationship of the kinematic pair P _i in the above kinematic pair type table, obtain the component attribute table with the kinematic pair P _i . In this embodiment, use N _i -XX to represent, N _i means that the component is i Meta-component, the following connection array indicates the connection method between this component and binary component, and its rules are as follows:

(1) The number in the array is equal to the elements of the component, such as N ₃ -XXX for the ternary component and N ₄ -XXXX for the quaternary component;

(2) The value of a certain number in the array represents the number of binary components connected in series on the kinematic pair P _i , and when two elements are directly connected on the kinematic pair P _i , the value "0" is used to indicate;

(3) When the kinematic pair P _i is a composite hinge, the composite hinge is regarded as a multi-element component, expressed by the value "-1".

The connection information of the kinematic pair P _i can be retrieved to determine the connection mode of the component with the kinematic pair P _i . For example: the first component 1 is a quaternary component, which appears in the first kinematic pair 11(1,1,2,2), the fourth kinematic pair 14(1,1,4,4), the fifth kinematic pair 15( 1, 1, 6) and the sixth kinematic pair 16 (1, 1, 7), it can be determined that the first kinematic pair kinematic pair 11 and the fourth kinematic pair 14 are connected to the multi-element component, but when judging the sixth kinematic pair of the binary component When component 6 and the seventh component 7 of the binary component, the number of binary components in series cannot be determined, so it is necessary to further search for the seventh kinematic pair 17 (5, 6) connecting the sixth component 6 of the binary component and the second The ninth kinematic pair 19 (7,8,9) of the seventh component 7 of the meta-component, the composite hinge is regarded as a multi-element component, and it can be determined that the kinematic pair element of the seventh component 7 of the binary component in series is 2; for the binary component The sixth component 6 needs to continue searching for the eighth kinematic pair 18 (4, 4, 5) of the fifth component 5 of the serial binary component, and now it can be determined that the kinematic pair element of the serial binary component 6 is 1. From this, it can be obtained that the attributes of the components with kinematic pairs in kinematic chain C ₁ are as follows:

In the formula, N _i indicates that the component is an i-component, and the connection array indicates the connection relationship between components.

Claims (10)

1. A numbering matrix description method of a planar closed compound hinge kinematic chain, characterized in that: the components and kinematic pairs of the kinematic chain are numbered, wherein the kinematic pair is P _n , and an n×n numbering matrix A is generated: In the formula, n is the number of kinematic pairs, the diagonal elements a _i,j (i=j) of the numbering matrix are all 0, and the other elements a _i,j (i≠j,i=1,..., n; j=1,...,n) is the serial number of the component connecting the kinematic pair P _i and the kinematic pair P _j , when the kinematic pair P _i and the kinematic pair P _j are not connected, a _i,j =0. 2. according to the numbering matrix description method of the said plane closed complex hinge kinematic chain of claim 1, it is characterized in that: the element a _i,j of said numbering matrix A is carried out bool operation, when element a _i,j =0 , the element value remains unchanged. When the element a _{i, j} ≠0, the element value takes the value 1, and the adjacency matrix B is obtained. 3. according to the numbering matrix description method of the said planar closed complex hinge kinematic chain of claim 1, it is characterized in that: search numbering matrix A, when kinematic pair P _i and kinematic pair P _j are not connected when a _i,j =0, When the kinematic pair P _i and kinematic pair P _j are connected, a _i,j = 1, and the association matrix C of the kinematic chain is obtained, where the row number represents the component number, and the column number represents the kinematic pair number, expressing the relationship between the kinematic pair P _n and each component connection relationship. 4. according to the numbering matrix description method of the said plane closed compound hinge kinematic chain of claim 1, it is characterized in that: search numbering matrix A, when the number of times that the member numbering of i row element corresponding to kinematic pair P _i appears is k, motion The component of the i row of elements corresponding to the sub-P _i is a g element component, g=k+1, and the attribute table of the kinematic chain component is obtained. 5. according to the numbering matrix description method of the said plane closed compound hinge kinematic chain of claim 1, it is characterized in that: search numbering matrix A, when the number of times that the member numbering of the i column element corresponding to kinematic pair P _i appears is k, motion The component of the i row of elements corresponding to the sub-P _i is a g element component, g=k+1, and the attribute table of the kinematic chain component is obtained. 6. according to the numbering matrix description method of the said planar closed complex hinge kinematic chain of claim 1, it is characterized in that: search numbering matrix A, when kinematic pair P _i corresponding i row element a _{i, j} (i, j=1 ,2,,…,n) there are m or more non-zero and unequal values, then the hinge at kinematic pair P _i is an m-element complex hinge, where m≥3. 7. according to the numbering matrix description method of the said plane closed complex hinge kinematic chain of claim 1, it is characterized in that: search numbering matrix A, when the i column element a _{i corresponding to kinematic pair P i , j} (i, j=1 ,2,,…,n) there are m or more non-zero and unequal values, then the hinge at kinematic pair P _i is an m-element complex hinge, where m≥3. 8. according to the numbering matrix description method of the said planar closed compound hinge kinematic chain of claim 1, it is characterized in that: i row elements a _i,j ( _i ,j=1,2,..., n) Carry out generalized operations, remove non-zero elements, keep 2 of the same component numbers greater than 2, obtain the array code of each motion pair P _i , and then obtain the motion pair type corresponding to the connection relationship between the array code and the motion pair P _i surface. 9. according to the numbering matrix description method of the said plane closed complex hinge kinematic chain of claim 1, it is characterized in that: i column element a _{i corresponding to kinematic pair P i , j} (i, j=1,2,..., n) Carry out generalized operations, remove non-zero elements, keep 2 of the same component numbers greater than 2, obtain the array code of each motion pair P _i , and then obtain the motion pair type corresponding to the connection relationship between the array code and the motion pair P _i surface. 10. The numbering matrix description method of the plane closed compound hinge kinematic chain according to claim 9 is characterized in that: by retrieving the connection relationship of the kinematic pair P _i in the kinematic pair type table, the member with the kinematic pair P _i is obtained attribute table.