A Configuration Synthesis Method for the Planetary Gear Mechanism of a Floor Grinder Based on Graph Theory

Abstract

The present invention provides a configuration synthesis method for the planetary gear mechanism of a floor grinding machine based on graph theory. This method first deeply analyzes the planetary gear mechanism to determine the quantitative relationship of basic elements, and obtains a new quantitative relationship of elements through high pair-low substitution. Then, it uses adjacency matrix interpolation to generate the adjacency matrices of all configurations, and on this basis, eliminates various unreasonable monochromatic topological graphs. According to the method of the canonical adjacency matrix set, the configuration synthesis of monochromatic topological graphs is carried out, and combined with the length requirement of the longest transmission chain of the planetary gear mechanism, the monochromatic topological graphs that do not meet the conditions are excluded. Finally, the position points suitable for high pairs and compound hinges are selected to generate a multicolor topological graph. After carrying out canonical point numbering and one-to-one correspondence verification on the multicolor topological graph, the entire configuration synthesis process is completed. This method realizes the configuration synthesis of complex planetary gear transmission coefficients, ensuring comprehensiveness and high efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of planetary gears, and particularly relates to a synthetic method for the configuration of a planetary gear mechanism of a floor grinding machine based on graph theory, which is particularly applicable to the configuration design and optimization of complex planetary gear transmission systems.

Background Art

[0002] Due to its advantages such as compact structure, large transmission ratio, and strong load-bearing capacity, planetary gear mechanisms are widely used in fields such as automotive transmissions, wind power generation units, aerospace equipment, and industrial robots. However, with the complication of application scenarios, the configuration design of planetary gear mechanisms faces more and more challenges. Traditional configuration design methods mainly rely on empirical formulas and trial-and-error methods, lacking systematic theoretical support, resulting in low design efficiency, insufficient innovation, and difficulty in meeting the requirements of high complexity and high performance.

[0003] In recent years, graph theory, as a powerful mathematical tool, has gradually been applied in the configuration design of mechanical systems. Graph theory can abstract complex mechanical structures into combinations of nodes and edges, thereby providing a systematic and visual analysis method.

[0004] In view of this, the inventor of this case conducted in-depth research on the above problems, and thus this case was born.

Summary of the Invention

[0005] The present invention aims to solve the technical problems existing in the prior art. The present invention provides a synthetic method for the configuration of a planetary gear mechanism of a floor grinding machine based on graph theory, which realizes the synthetic configuration of complex planetary gear transmission coefficients and ensures comprehensiveness and high efficiency.

[0006] The present invention is implemented as follows: A synthetic method for the configuration of a planetary gear mechanism of a floor grinding machine based on graph theory:

[0007] (1) Analyze the planetary gear mechanism to obtain the quantitative relationship of basic elements, obtain a new quantitative relationship according to the substitution of higher pairs with lower pairs, and use adjacency matrix interpolation to obtain the adjacency matrices of all configurations;

[0008] (2) Delete the monochromatic topological graphs containing discrete points, and delete the non-conforming monochromatic topological graphs according to higher pairs and compound hinges;

[0009] (3) Calculate all loops of each monochromatic topological graph, that is, each monochromatic topological graph corresponds to a loop set, and delete the separable monochromatic topological graphs through the loop set;

[0010] (4) Calculate the independent loops through the loop sets of the remaining monochromatic topological graphs, and judge and delete the monochromatic topological graphs containing rigid sub-chains;

[0011] (5)Conduct the configuration synthesis of the monochromatic topological graph according to the method of the canonical adjacency matrix set; define the set composed of all the canonical adjacency matrices of a kinematic chain as the canonical adjacency matrix set of the kinematic chain;

[0012] (6)Delete the monochromatic topological graphs that do not meet the conditions in combination with the length requirement of the longest transmission chain of the planetary gear mechanism, select the position points suitable for the higher pairs and compound hinges, and generate the polychromatic topological graph;

[0013] (7)Conduct the configuration synthesis of the polychromatic topological graph according to the canonical labeling method; the canonical labeling method includes the canonical vertex labeling of the perimeter loop and the canonical vertex labeling of the inner sub-chain.

[0014] Further, in step (1), first analyze the planetary gear mechanism to obtain the number of components, lower pairs, higher pairs and compound hinges, then conduct the substitution of higher pairs with lower pairs, and then judge the number of components, lower pairs and compound hinges. Draw a graph with components and compound hinges as vertices and lower pairs as edges; according to the number of components, lower pairs, higher pairs and compound hinges, generate the corresponding zero matrix, then insert a 1 at the longest side of the upper triangular matrix, insert a 1 at the remaining positions of the upper triangular matrix, which is related to the number of components, lower pairs, higher pairs and compound hinges, and then make the lower triangular matrix symmetric according to the upper triangular matrix, so as to obtain the adjacency matrices of all configurations.

[0015] Further, in step (2), exclude the graphs containing vertices with a degree of 1 or less, that is, according to the adjacency matrix, search for the number of non-zero elements in each row (or column) by row (or column). If the number of non-zero elements in a certain row (or column) is 0 or 1, then delete the monochromatic topological graph, and delete the monochromatic topological graphs with degrees of points that do not meet the requirements according to the number of higher pairs and compound hinges.

[0016] Further, in step (3), obtain all the loop sets through the adjacency matrix, and delete the separable monochromatic topological graphs, that is, delete the monochromatic topological graphs in which two loops are related by only one point or one edge.

[0017] Further, in step (4), use the loop set to calculate the independent loops by using the loop θ, operation calculation, and conduct the discrimination of the rigid sub-chain. If then it does not contain a rigid sub-chain, where ω i is the active factor group, r = 1, 2,..., v, and v is the number of independent loops.

[0018] Further, in step (5), draw the perimeter monochromatic topological graph of the kinematic chain, obtain the canonical perimeter monochromatic topological graph set through the perimeter monochromatic topological graph, and then obtain the canonical adjacency matrix set corresponding to the canonical perimeter monochromatic topological graph. Judge whether the intersection of the canonical adjacency matrix sets of two kinematic chains is non-empty. If it is non-empty, then they are isomorphic.

[0019] Further, in step (6), the length of the longest transmission chain of the planetary gear transmission mechanism is determined, and a reasonable monochromatic topological graph is screened out according to the length. Then, based on the existence relationship between the higher pair and the compound hinge, that is, the higher pair is a point with a degree of 2, and the degree of the point of the compound hinge is analyzed according to the actual planetary gear transmission mechanism, and coloring is performed to obtain a multicolor topological graph.

[0020] Further, in step (7), the above-mentioned canonical labeling method is continued to be used to canonical label the multicolor topological graph, and it is judged whether the position points of the higher pair and the compound hinge correspond one by one. If they correspond one by one, they are isomorphic; otherwise, they are non-isomorphic.

[0021] The present invention has the following effective effects compared with the existing technology: The configuration synthesis method proposed by the present invention can systematically and comprehensively solve the problem of the configuration synthesis of complex planetary gear transmission mechanisms. By means of computer programming, the automation of configuration synthesis can be realized, reducing the phenomenon of low efficiency and easy omission during manual mechanism synthesis, and improving the efficiency and accuracy of configuration synthesis.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be further described below with reference to the accompanying drawings in conjunction with embodiments.

[0023] Figure 1 It is a flowchart of the configuration synthesis method of the planetary gear mechanism of the floor grinding machine based on graph theory of the present invention.

[0024] Figure 2 It is a kinematic schematic diagram of an embodiment of the present invention.

[0025] Figure 3 It is a monochromatic topological graph corresponding to the kinematic schematic diagram of an embodiment of the present invention.

[0026] Figure 4 It is a modified monochromatic topological graph corresponding to the kinematic schematic diagram of an embodiment of the present invention.

[0027] Figure 5 It is a monochromatic topological graph containing discrete points of the present invention.

[0028] Figure 6 It is a separable monochromatic topological graph of the present invention.

[0029] Figure 7 It is a monochromatic topological graph containing a rigid sub-chain of the present invention.

[0030] Figure 8 It is a monochromatic topological graph for calculating the case of an independent loop of the present invention.

[0031] Figure 9 It is the original monochromatic topological graph for calculating the case of the canonical adjacency matrix set of the present invention.

[0032] Figure 10 It is the canonical monochromatic topological graph of the case of calculating the canonical adjacency matrix set of the present invention.

[0033] Figure 11 It is the result of the synthesis of the monochromatic topological graph configuration.

[0034] Figure 12 It is the result of the monochromatic topological graph screened according to the transmission chain.

[0035] Figure 13 It is the polychromatic topological graph after adding higher pairs and compound hinges.

[0036] Figure 14 It is the result of the synthesis of the polychromatic topological graph configuration.

Specific Embodiment

[0037] In order to better understand the technical solution of the present invention, the technical solution of the present invention will be described in detail below in conjunction with the accompanying drawings of the specification and specific embodiments.

[0038] Refer to Figure 1-14 As shown, the present invention provides a method for synthesizing the configuration of the planetary gear mechanism of a floor grinding machine based on graph theory:

[0039] (1) Analyze the planetary gear mechanism to obtain the quantitative relationship of the basic elements. According to the substitution of higher pairs with lower pairs, obtain the new quantitative relationship of the elements, and use the adjacency matrix interpolation to obtain the adjacency matrices of all configurations.

[0040] (2) Delete the monochromatic topological graphs containing discrete points, and delete the non-conforming monochromatic topological graphs according to the higher pairs and compound hinges.

[0041] (3) Calculate all the loops of each monochromatic topological graph, that is, each monochromatic topological graph corresponds to a loop set. Through the loop set, delete the separable monochromatic topological graphs.

[0042] (4) Calculate the independent loops through the loop sets of the remaining monochromatic topological graphs, and judge and delete the monochromatic topological graphs containing rigid sub-chains.

[0043] (5) Conduct configuration synthesis according to the method of the canonical adjacency matrix set.

[0044] (6) Combine the length requirement of the longest transmission chain of the planetary gear mechanism to delete the non-conforming monochromatic topological graphs, select the position points suitable for the higher pairs and compound hinges, and generate the polychromatic topological graph.

[0045] (7) Conduct configuration synthesis on the polychromatic topological graph according to the canonical labeling method.

[0046] Preferably, in step (1), first analyze the planetary gear mechanism to obtain the number of components, lower pairs, higher pairs, and compound hinges, then perform the substitution of higher pairs with lower pairs, and then determine the number of components, lower pairs, and compound hinges. Take the components and compound hinges as vertices and the lower pairs as edges to draw a graph. In the embodiment of the present invention, a planetary gear mechanism with 5 components, 8 lower pairs, 3 higher pairs, and 1 compound hinge is taken as an example, and with reference to Figure 2-4 as shown, it is the kinematic diagram and monochromatic topological graph of this embodiment of the present invention. Generate a 9*9 zero matrix, then insert n1 1s into the longest side of the upper triangular matrix, insert 11 - n1 1s into the remaining positions of the upper triangular matrix, where the range of n1 is from 6 to 11, and then make the lower triangular matrix symmetric to the upper triangular matrix, thus obtaining the adjacency matrices of all configurations.

[0047] Preferably, with reference to Figure 5 as shown, in step (2), exclude the monochromatic topological graphs containing vertices with a degree of 1 or less, that is, according to the adjacency matrix, search for the number of non-zero elements in each row (or column) by row (or column). If the number of non-zero elements in a certain row (or column) is 0 or 1, then delete this monochromatic topological graph, and delete the monochromatic topological graphs whose degrees of points do not conform according to the number of higher pairs and compound hinges.

[0048] Preferably, with reference to Figure 6 as shown, in step (3), obtain all loop sets through the adjacency matrix, and delete the separable monochromatic topological graphs according to the relationship between the loops in the loop set, that is, delete the monochromatic topological graphs in which two loops are related by only one point or one edge.

[0049] Preferably, in step (4), use the loop set to calculate independent loops by using loop θ operation.

[0050] Suppose a certain configuration monochromatic topological graph contains loop 1 as 1, 2, 3, 8, 7, 1; then L(1) = [0, 1, 1, 0, 0, 0, 1, 1, 1]; N[L(a)] represents the number of vertices in loop L(a). For example, the above N[L(1)] = 5; the "θ" operation of the loop is defined as L(a)θL(b), and the operation result is denoted as p(aθb).

[0051] The "θ" operation rule: Each element of the array of loop L(a) is algebraically subtracted from the corresponding element of loop L(b). If the difference is greater than 0, the value of the corresponding bit of p(aθb) is 1; otherwise, its value is 0, that is

[0052]

[0053] where b a (i) is the i-th element of the array of loop L(a); where b b(i) is the i-th element of the ring L(b) array; where p(aθb) i is the value of the i-th element after the "θ" operation of ring L(a) and L(b).

[0054] Of the loop The operation is defined as The operation result is denoted as

[0055] Operation rule: Compare each element of the ring L(a) array with the corresponding element of the ring L(b). If both are 1, then The value of the corresponding bit is 1; otherwise its value is 0, that is

[0056]

[0057] where b a (i) is the i-th element of the ring L(a) array; where b b (i) is the i-th element of the ring L(b) array; where is the value of the i-th element after the operation of ring L(a) and the operation.

[0058] Of the loop The operation is defined as The operation result is denoted as LP.

[0059] Operation rule: Algebraically sum each element of the ring L(a) array with the corresponding element of the ring L(b). If the sum is greater than 0 and less than the local degree of the corresponding vertex, the value of the corresponding bit of LP is 1; otherwise its value is 0, that is

[0060]

[0061] where b a (i) is the i-th element of the ring L(a) array; where b b (i) is the i-th element of the ring L(b) array; where d l (i) is the local degree of the i-th vertex. If the resulting array LP is also a loop, it can be used to represent, indicating a combined loop formed by ring L(a) and ring L(b).

[0062] Local degree of vertex: After the following processing of the corresponding monochromatic topological graph, the degree of the obtained vertex is its local degree.

[0063] 1. Remove the vertices that are not in any operation loop and the connection relationships corresponding to these vertices in the monochromatic topological graph.

[0064] 2. Remove the internal connection relationship of each loop participating in the operation.

[0065] Loop Existence conditions for the operation:

[0066] 1. The two loops participating in the operation have at least two common points, that is

[0067] 2. During the operation, the following situation occurs and only occurs 2 times. The corresponding bit elements of the two loops are 1 and The corresponding bit element of the resulting array after the operation is still 1.

[0068] Of loop L(a) and L(b) The operation of the loop only makes sense when the 2 existence conditions for its operation are met. At this time Otherwise, LP has no meaning.

[0069] Loop Properties of the operation:

[0070] Loop The loop operation satisfies the commutative law, that is

[0071] Loop The loop operation satisfies the associative law, that is

[0072] Loop The loop operation satisfies the self-cancellation law, that is θ is an n-dimensional 0 array, and n is the number of vertices of the monochromatic topological graph.

[0073] Loop The loop operation satisfies the absorption law, that is

[0074] For a monochromatic topological graph with the number of vertices v, the number of edges e, and the number of independent loops L, the following Euler relationship exists among the three: L = e - v + 1. In the embodiment of the present invention, L = 3. By using the loop set and the loop operation, its independent loops can be calculated.

[0075] Refer to Figure 7 As shown, select the loop set {L(1), L(2), L(3)}, L(1) = [1, 0, 1, 0, 0, 0, 1, 1, 1], L(2) = [0, 1, 0, 1, 1, 1, 1, 0, 0], L(3) = [1, 1, 1, 1, 0, 0, 1, 0, 0]; the remaining loop set is {L(4), L(5), L(6)}, L(4) = [1, 0, 0, 1, 1, 1, 1, 1, 1], L(5) = [1, 1, 0, 1, 0, 0, 1, 1, 1], L(6) = [1, 0, 1, 1, 1, 1, 1, 0, 0].

[0076]

[0077] It can be seen that the loop set {L(1), L(2), L(3)} is the independent loop of this monochromatic topological graph.

[0078] Refer to Figure 8 As shown, given the independent loops {L(1), L(2), L(3)} of the monochromatic topological graph, L(1) = [0, 0, 0, 0, 1, 1, 1, 1, 0], L(2) = [0, 0, 0, 1, 1, 0, 1, 1, 0], L(3) = [1, 1, 1, 1, 0, 0, 1, 1, 1], through the discrimination of rigid sub-chains, if then it does not contain a rigid sub-chain, where ω i is the active factor group, r = 1, 2,..., v, and v is the number of independent loops. The steps are as follows:

[0079] Step 4.1. Determine the independent loops {L(1), L(2), L(3)}, L(1) = [0, 0, 0, 0, 1, 1, 1, 1, 0], L(2) = [0, 0, 0, 1, 1, 0, 1, 1, 0], L(3) = [1, 1, 1, 1, 0, 0, 1, 1, 1].

[0080] Step 4.2. Select the loop L1(1) = L(1), and obtain its active factor ω1 = N[L1(1)] - 3;

[0081] L1(1) = L(1) = [0, 0, 0, 0, 1, 1, 1, 1, 0], ω1 = N[L1(1)] - 3 = 1.

[0082] Step 4.3. Select the loop L1(2) = L(2), and obtain its active factor relative to the first loop, ω2 = N[P(2)] - 1, where P(2) = L1(2) θ L1(1); L1(2) = L(2) = [0, 0, 0, 1, 1, 0, 1, 1, 0], P(2) = [0, 0, 0, 1, 0, 0, 0, 0, 0], ω2 = N[P(2)] - 1 = 0.

[0083] Step 4.4. Select the loop L1(3) = L(3), and obtain its active factor relative to the previous two loops, ω3 = N[P(3)] - 1, where P(3) = L1(3) θ P(2) θ L1(1); L1(3) = L(3) = [1, 1, 1, 1, 0, 0, 1, 1, 1], P(3) = [1, 1, 1, 0, 0, 0, 0, 0, 1]; ω3 = N[P(3)] - 1 = 3.

[0084] Judge Furthermore, judge whether it contains a rigid sub-chain.

[0085] ω1 - 1 = 0, ω1 + ω2 - 2 = -1 ≤ 0, ω1 + ω2 + ω3 - 3 = 1, so referring to Figure 5 contains a rigid sub-chain.

[0086] Preferably, referring to Figure 9 As shown, in step (5), obtain the canonical sequence string of the kinematic chain loop. The canonical sequence string of the loop is only related to the degree of the vertices. According to the loop number, write down the degree corresponding to the vertex at the corresponding position of the vertex. Let the one with the largest degree be the first one, which is the canonical sequence string. Figure 6 The configuration monochromatic topological graph contains loop 1 as 2, 7, 6, 5, 1, 4, 3, 2, and the corresponding degrees are 3, 3, 2, 2, 4, 2, 2. Then the canonical sequence string is 4223322.

[0087] Define the longest canonical sequence string as the canonical degree sequence of the perimeter loop of the kinematic chain, and the corresponding loop is the perimeter loop of the kinematic chain.

[0088] Perimeter monochromatic topological graph of the kinematic chain: When making a representative of the monochromatic topological graph of the kinematic chain, follow the following rules:

[0089] 1. Place the perimeter loop on the outermost periphery to form a regular polygon.

[0090] 2. Place the remaining vertices not on the perimeter loop inside the regular polygon.

[0091] The above can obtain the perimeter monochromatic topological graph of the kinematic chain.

[0092] Canonical vertex labeling of the perimeter monochromatic topological graph: Canonical vertex labeling of the perimeter loop and canonical vertex labeling of the inner sub-chain.

[0093] Canonical vertex labeling of the perimeter loop:

[0094] 1. Label from small to large according to the canonical degree sequence of the perimeter loop. Figure 6 The canonical sequence string of the perimeter loop of the configuration monochromatic topological graph is 4223322, then the corresponding vertex labels are 1, 2, 3, 4, 5, 6, 7.

[0095] 2. If the starting point corresponding to the canonical degree sequence is not unique, then select the vertex connected to the largest inner sub-chain among these vertices as the starting vertex for canonical labeling.

[0096] Description of the inner sub-chain: If an inner sub-chain is connected to the vertices with canonical labels m and n (m ≤ n) on the perimeter loop, then this inner sub-chain is represented by the array [m, n], and at the same time this inner sub-chain is also called the [m, n] sub-chain.

[0097] Level of the inner sub-chain: For two inner sub-chains ISC1[m1, n1] and ISC2[m2, n2], we stipulate that the level of the inner sub-chain with more vertices is higher than that of the inner sub-chain with fewer vertices. If the number of vertices contained in these two inner sub-chains is equal, then, if m1 < m2, the level of the inner sub-chain ISC1 is higher, and vice versa; if m1 = m2 and n1 < n2, the level of the inner sub-chain ISC1 is higher, and vice versa.

[0098] Canonical vertex labeling of the inner sub-chain: Labeling is carried out according to the level of the inner sub-chain.

[0099] The monochromatic topological graph obtained after canonical vertex labeling is the canonical perimeter monochromatic topological graph of the kinematic chain, and its corresponding adjacency matrix is the canonical adjacency matrix.

[0100] Refer to Figure 10 As shown in the reference Figure 9 The monochromatic topological graph obtained after canonical vertex labeling with reference to

[0101] Define the set composed of all canonical adjacency matrices of a kinematic chain as the canonical adjacency matrix set of the kinematic chain.

[0102] Isomorphism discrimination based on the canonical adjacency matrix set: A necessary and sufficient condition for two kinematic chains A and B to be isomorphic is that the intersection of their canonical adjacency matrix sets is non-empty. Refer to Figure 11 As shown, the configuration synthesis result of the monochromatic topological graph in the embodiment of the present invention.

[0103] Preferably, in step (6), in combination with the length requirement of the longest transmission chain of the planetary gear mechanism, delete the monochromatic topological graphs that do not meet the conditions, select the position points suitable for the higher pairs and compound hinges, and generate a multi-color topological graph; the length of the longest transmission chain in the embodiment of the present invention is 7, there is only one compound hinge and its degree is 3 and there are 3 higher pairs, that is, delete the monochromatic topological graphs with a length not equal to 7 in the monochromatic topological graph (refer to Figure 12 As shown), and then generate a multi-color topological graph according to the degrees of the higher pairs and compound hinges, and the condition that there cannot be directly connected edges in the topological graph (refer to Figure 13 As shown), where the red points represent compound hinges and the green points represent higher pairs.

[0104] Preferably, in step (7), once again according to the canonical labeling method, perform canonical labeling on the multi-color topological graph, and perform configuration synthesis according to the one-to-one correspondence between the higher pairs and compound hinges. If they are in one-to-one correspondence, they are isomorphic, otherwise they are not isomorphic. Refer to Figure 13 As shown, the configuration synthesis result of the multi-color topological graph in the embodiment of the present invention.

[0105] The configuration synthesis method of planetary gear mechanism based on graph theory in the present invention first analyzes the planetary gear mechanism to obtain the quantitative relationship of basic elements, obtains the new quantitative relationship of elements according to the substitution of higher pairs with lower pairs, uses the interpolation of adjacency matrices to obtain the adjacency matrices of all configurations, deletes the graphs containing discrete points based on these adjacency matrices, calculates all the loops contained in each graph so that each graph has a loop set, deletes the separable graphs according to the loop set and calculates the independent loops of the remaining graphs, judges whether there are rigid sub-chains by the independent loops, deletes the graphs containing rigid sub-chains, conducts configuration synthesis according to the method of canonical adjacency matrix set, and then excludes the non-conforming monochromatic topological graphs in combination with the length requirement of the longest transmission chain of the planetary gear mechanism. Finally, the position points suitable for higher pairs and compound hinges are selected to generate a multi-color topological graph. After carrying out canonical point numbering and one-to-one correspondence verification on the multi-color topological graph, the entire configuration synthesis process is completed. It can systematically, comprehensively and effectively solve the problem of configuration synthesis of complex planetary gear transmission mechanisms. By means of computer programming, the automation of configuration synthesis can be realized, reducing the phenomenon of low efficiency and easy omission during manual mechanism synthesis, and improving the efficiency and accuracy of configuration synthesis.

[0106] Although the specific embodiments of the present invention have been described above, those skilled in the art of this technology should understand that the specific embodiments we described are illustrative rather than used to limit the scope of the present invention. Equivalent modifications and changes made by those skilled in the art in accordance with the spirit of the present invention should be covered by the scope protected by the claims of the present invention.

Claims

1. A synthetic method for the configuration of the planetary gear mechanism of a floor grinding machine based on graph theory, characterized in that: (1) Analyze the planetary gear mechanism to obtain the basic element quantity relationship. According to the high pair-low pair substitution, obtain the new element quantity relationship, and use the adjacency matrix interpolation to obtain the adjacency matrices of all configurations. Draw a monochromatic topological graph based on the adjacency matrix. (2) Delete the monochromatic topological graphs containing discrete points. According to the adjacency matrix, search for the number of non-zero elements in each row or column by row or column. If the number of non-zero elements in a certain row or column is 0 or 1, then delete the monochromatic topological graph, and delete the monochromatic topological graphs whose degrees of points do not conform according to the number of high pairs and compound hinges. (3) Calculate all the loops of each monochromatic topological graph, that is, each monochromatic topological graph corresponds to a loop set. Through the loop set, delete the separable monochromatic topological graphs. (4) Calculate the independent loops through the loop sets of the remaining monochromatic topological graphs, and judge and delete the monochromatic topological graphs containing rigid sub-chains. (5) Conduct the configuration synthesis of the monochromatic topological graph according to the method of the canonical adjacency matrix set; define the set composed of all the canonical adjacency matrices of a kinematic chain as the canonical adjacency matrix set of the kinematic chain. (6) Combine the length requirements of the longest transmission chain of the planetary gear mechanism to delete the monochromatic topological graphs that do not meet the conditions, select the position points suitable for high pairs and compound hinges, and generate a multicolored topological graph. (7) Conduct the configuration synthesis of the multicolored topological graph according to the canonical labeling method; the canonical labeling method includes the canonical vertex labeling of the perimeter loop and the canonical vertex labeling of the inner sub-chain.

2. The synthesis method of the planetary gear mechanism configuration of the floor grinding machine based on graph theory according to claim 1, characterized in that: In step (1), first analyze the planetary gear mechanism to obtain the number of components, lower pairs, higher pairs and compound hinges, then conduct the high pair-low pair substitution, and then judge the number of components, lower pairs and compound hinges. Use the components and compound hinges as vertices and the lower pairs as edges to draw a graph. Generate the corresponding zero matrix according to the number of components, lower pairs, higher pairs and compound hinges, then insert n1 1s into the longest side of the upper triangular matrix, insert 11 - n1 1s into the remaining positions of the upper triangular matrix. n1 is related to the number of components, lower pairs, higher pairs and compound hinges, and then make the lower triangular matrix symmetric to the upper triangular matrix, so as to obtain the adjacency matrices of all configurations.

3. The method for the configuration synthesis of the planetary gear mechanism of the floor grinding machine based on graph theory according to claim 1, wherein: In step (3), obtain all the loop sets through the adjacency matrix, and delete the separable monochromatic topological graphs, that is, delete the monochromatic topological graphs in which two loops are related by only one point or one edge.

4. The method for the configuration synthesis of the planetary gear mechanism of the floor grinding machine based on graph theory according to claim 1, wherein: In step (5), draw the perimeter monochromatic topological graph of the kinematic chain, use the canonical labeling method, that is, obtain the canonical perimeter monochromatic topological graph set through the perimeter monochromatic topological graph, and then obtain the canonical adjacency matrix set corresponding to the canonical perimeter monochromatic topological graph, and judge whether the intersection of the canonical adjacency matrix sets of two kinematic chains is non-empty. If it is non-empty, then they are isomorphic.

5. The synthetic method of the planetary gear mechanism configuration of the floor grinding machine based on graph theory according to claim 1, wherein: In step (6), judge the length of the longest transmission chain of the planetary gear transmission mechanism, screen out the reasonable monochromatic topological graphs by length, and conduct coloring according to the existence relationship of high pairs and compound hinges, that is, the high pair is a point with a degree of 2, and analyze the degree of the point of the compound hinge according to the actual planetary gear transmission mechanism, so as to obtain a multicolored topological graph.

6. The synthetic method for the planetary gear mechanism configuration of the floor grinding machine based on graph theory according to claim 1, wherein: In step (7), the multi-color topological graph is subjected to canonical labeling, and it is judged whether the position points of the higher pairs and the compound hinges correspond one by one. If they correspond one by one, they are isomorphic; otherwise, they are non-isomorphic.

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