Workpiece geometric feature recognition and position relation judgment method for automatic assembly process

Abstract

The invention provides a workpiece geometric feature recognition and position relation judgment method for an automatic assembly process, and provides a systematized analysis and processing scheme for geometric features and position information in a product design model. According to the method, the geometric features of the three-dimensional design model are accurately recognized, the relative position relation of the workpiece is extracted, and related data are efficiently organized and stored, so that accurate analysis of the geometric features and the position relation is realized. The system obtains key process information in the assembling process through geometric topology information analysis and position relation derivation, and therefore planning and optimization of the assembling process are supported. The method aims at solving the technical problems of geometric feature recognition and position relation analysis in the automatic assembly process, and an innovative solution is provided for achieving intelligent and efficient assembly process reasoning and resource allocation.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent manufacturing, and particularly relates to a method for identifying geometric features of workpieces and judging positional relationships in an automated assembly process. Background Art

[0002] In modern manufacturing, automated assembly is an important means to improve production efficiency and product consistency. Especially in high-precision fields such as aerospace, automotive manufacturing, and precision electronics, the requirements for assembly accuracy and reliability are particularly strict. The key to achieving precise automated assembly lies in the accurate identification of workpiece geometric features, reasonable layout, and accurate positional relationship judgment. These tasks directly affect the operation path, workpiece positioning, and assembly method selection during the assembly process, and are related to the quality and efficiency of the entire automated assembly system. However, traditional assembly processes usually rely on human experience and simple geometric relationship judgment methods, which cannot meet the requirements of the automated assembly system for comprehensive extraction and refined analysis of workpiece geometric information. Especially when dealing with complex three-dimensional workpiece models, due to the workpiece having various geometric features such as cylinders, cones, spheres, toroidal coils, and polygonal planes, as well as various spatial positional relationships, it is difficult for manual analysis to be accurate and comprehensive within a limited time, and the efficiency is low.

[0003] To address this problem, the currently common method is to manually identify geometric information and perform assembly planning through 3D modeling software based on the CAD design model of the workpiece. However, these methods have significant defects in complex assembly process scenarios: on the one hand, due to the lack of a systematic geometric information extraction and structured storage method, the processing of workpiece geometric feature data is complex and difficult to analyze; on the other hand, existing geometric analysis methods are difficult to quickly judge the relative positional relationships between multiple workpieces, thus affecting the accuracy and controllability of automated assembly.

[0004] Therefore, the existing technology still needs to be improved. Summary of the Invention

[0005] In view of the above deficiencies of the prior art, the purpose of the present invention is to provide a method for identifying geometric features of workpieces and judging positional relationships in an automated assembly process, aiming to solve the problem that existing geometric analysis methods in the prior art are difficult to quickly judge the relative positional relationships between multiple workpieces, thus affecting the accuracy and controllability of automated assembly.

[0006] To achieve the above purpose, the present invention adopts the following technical solutions:

[0007] A method for identifying geometric features of workpieces and judging positional relationships in an automated assembly process, the method comprising the following steps:

[0008] Step 1: Obtain the CAD design model of the workpiece, and extract geometric information based on the STEP file of the workpiece design model. First, extract the geometric topology information of entities, faces, lines, and points in sequence according to the preset hierarchical structure, providing basic data for subsequent assembly process reasoning and analysis of the positional relationship between workpieces;

[0009] Step 2: During the extraction process of the mating surface attribute information of the workpiece design model, classify the faces extracted from the workpiece geometric information, and conduct detailed identification and extraction according to the specific geometric feature attributes of various mating surfaces. First, the system automatically identifies various mating surfaces, including cylindrical surfaces, conical surfaces, spherical surfaces, toroidal coil surfaces, toroidal planes, and polygonal planes, through keyword recognition and attribute discrimination techniques. Finally, this structured data will be stored in a JSON file for further data processing and invocation;

[0010] Step 3: In the case where the geometric attribute information of the mating surface of the workpiece design model is incomplete, generate a complete geometric feature description through analysis and completion techniques to ensure the accuracy and integrity of the mating surface geometric information. First, extract the high-level characterization information of the mating surface, and perform attribute calculation and derivation based on preset rules. Classify and store the complemented workpiece mating surface information in a JSON file to form a complete workpiece geometric description database;

[0011] Step 4: When processing the workpiece data in the JSON file, since each workpiece usually has an independent local coordinate system, standardize these local coordinate systems for unified spatial analysis and positional relationship judgment;

[0012] Step 5: After completing the conversion between local and global coordinate systems, calculate the relative positional relationship between different workpieces based on the unified global coordinate information for positional relationship judgment. These relative positional relationships include perpendicular, parallel, coaxial adjacency, coaxial separation, coaxial partial overlap, containment, and being contained.

[0013] Furthermore, the geometric information extraction based on the STEP file of the workpiece design model in Step 1 includes:

[0014] Step 1-1: Parse each entity of the workpiece from the STEP file, and then extract its corresponding face information. Each face includes its geometric shape attributes, and further parse the edges and endpoints connected to this face;

[0015] Step 1-2: All the extracted geometric data will be stored in a JSON file according to the hierarchical structure to ensure data readability and structured management.

[0016] Furthermore, the method for identifying the geometric attributes of the mating surface in Step 2 is:

[0017] Step 2-1: For different types of mating surfaces, extract and record the corresponding geometric properties. Different surfaces require different attribute information to form a systematic mating surface data structure;

[0018] Step 2-2: Extract the attribute information of the cylindrical surface. The attribute information of the cylindrical surface includes the mating surface ID, the workpiece ID it belongs to, the bottom radius, the height, the concavity and convexity, the axis endpoint coordinates, and the axis vector;

[0019] Step 2-3: Extract the attribute information of the conical surface. The attribute information of the conical surface includes the mating surface ID, the workpiece ID it belongs to, the bottom radius, the top radius, and the axis endpoint coordinates;

[0020] Step 2-4: Extract the attribute information of the spherical surface. The attribute information of the spherical surface includes the mating surface ID, the workpiece ID it belongs to, the center point coordinates of the sphere, and the radius information;

[0021] Step 2-5: Extract the attribute information of the toroidal coil surface. The attribute information of the toroidal coil surface includes the mating surface ID, the workpiece ID it belongs to, the inner and outer radii, the center point, the axis vector, and the normal vector information;

[0022] Step 2-6: Extract the attribute information of the toroidal plane. The attribute information of the toroidal plane includes the mating surface ID, the workpiece ID it belongs to, the inner and outer radii, the center point, and the normal vector attribute;

[0023] Step 2-7: Extract the attribute information of the polygonal plane. The attribute information of the polygonal plane includes the mating surface ID, the workpiece ID it belongs to, the normal vector, the component edge IDs, including the inner edge ID, the outer edge ID, and the total ID information. In the edges, the edge ID, the axis endpoint coordinates, and the direction vector information are required.

[0024] Further, the generation of the complete geometric feature description in Step 3 includes:

[0025] Step 3-1: For the cylindrical surface, its completion process includes extracting the axis endpoints, calculating the height of the cylinder, and determining the concavity and convexity of the surface. First, obtain one of the axis endpoints, that is, the given center point of the cylindrical surface, and extract the maximum control point of the B-spline curve in its direction as the other axis endpoint according to the mating surface axis vector; determine the height of the cylindrical surface through regular calculations using the two known axis endpoints. In addition, for the special expression of the cylindrical surface, based on the rules, the cylindrical surface generatrix needs to be segmented according to the data law to realize the extraction and completion of the upper and lower bottom surface information of the cylindrical surface;

[0026] Step 3-2: In other mating surfaces, for the missing axis endpoints, height, and normal vector attributes, the same completion process as in Step 3-1 is also carried out.

[0027] Further, the step for judging the concavity and convexity of the workpiece in Step 3-1 is to judge by the normal vector N of the mating surface and the direction vector N1 is achieved within the included angle range as follows:

[0028] First, convert the point P, the center point P 0 and the axis direction Axis_direction on the mating surface into NumPy arrays. Then, use the right-hand rule to calculate N 1 through the cross product of the normal vector N e and the axis vector Vec:

[0029] N e = N 1 × Vec;

[0030] Calculate the vector P 0 from point P to the center P Vec , and obtain the tangent vector P Vec through the cross product. It can accurately describe the geometric properties at point P in the local coordinate system and be used in subsequent steps to judge the concavity and convexity of the cylindrical surface, as well as other geometric calculations:

[0031] P Vec = P - P 0 ;

[0032] P Vec = P Vec × Axis_direction;

[0033] Next, according to the properties of the cylindrical surface, determine the direction vector N 2 , and calculate the final direction vector N through the cross product. The cylindrical surface can be an inner surface or an outer surface. The inner surface refers to the surface facing the inside of the cylinder, and its normal vector points inward; the outer surface refers to the surface facing the outside of the cylinder, and the normal vector points outward. When calculating N 2 , use the tangent vector R Vec and the axial vector Axis_direction of the cylinder to calculate the direction vector perpendicular to these two vectors through the cross product formula. Subsequently, calculate the final normal vector N through the cross product of the normal vectors N e and N 2 . This vector is geometrically perpendicular to N e and N 2 , effectively describing the normal relationship at point P and providing a basis for subsequent concavity and convexity judgment:

[0034] N 2 = R Vec × Axis_direction;

[0035] N = N e × N 2 ;

[0036] Subsequently, the dot product is used to calculate the angle between N and N 1 and convert it to degrees;

[0037] Finally, the concavity and convexity are judged according to the range of the included angle θ: if the included angle θ is between 0 and 90 degrees, it represents a convex surface; if the included angle θ is between 90 and 180 degrees, it represents a concave surface:

[0038]

[0039] Furthermore, in the fourth step, since the workpiece is usually modeled or designed in its own local coordinate system, its coordinate system is standardized and reflects the local geometric features. However, in the entire product, the actual position and orientation of the workpiece will change due to the difference from the coordinate system to which the assembly belongs. Therefore, it is necessary to uniformly process the workpiece coordinate system, that is, by calculating the rotation matrix of the workpiece to the product coordinate system to achieve the complete conversion of the coordinate system and provide a basis for subsequent accurate position judgment, specifically including:

[0040] First, obtain the origin of the coordinate system and its direction vectors. The direction vectors include the X-axis, Y-axis, and Z-axis. These direction vectors describe the spatial orientation of the workpiece in its own reference system. To ensure that these direction vectors are unit vectors, thereby improving the accuracy of the conversion and maintaining mathematical orthogonality, these direction vectors are normalized. The formula for normalization is:

[0041]

[0042] where v is the direction vector to be normalized, v′ is the normalized unit vector, and ||v|| represents the modulus of the vector, that is, the Euclidean norm, and the calculation formula is:

[0043]

[0044] Use these normalized direction vectors to construct the rotation matrix of the local coordinate system:

[0045] R local =[X local Y local Z local ;

[0046] X local Y local Z local are the normalized direction vectors of the local coordinate system on the X-axis, Y-axis, and Z-axis respectively. This rotation matrix describes the directional relationship between the local coordinate system and the global coordinate system, thereby realizing the conversion of the local coordinate system to the global coordinate system;

[0047] Next, it is also necessary to construct the rotation matrix of the global coordinate system:

[0048] R global = [X global Y global Z global ;

[0049] X local Y local Z local are the normalized direction vectors of the global coordinate system on the X-axis, Y-axis, and Z-axis respectively. By multiplying the rotation matrix R golbal of the global coordinate system with the inverse matrix of the rotation matrix of the local coordinate system the complete transformation matrix T is obtained:

[0050]

[0051] This transformation matrix is used to convert the points in the local coordinate system to the global coordinate system, and can accurately describe how the workpiece in the local coordinate system is positioned and oriented in the global coordinate system.

[0052] Furthermore, the method for calculating the relative position relationship of the workpiece in step five is as follows:

[0053] Step 5-1: First, determine which parts are in contact. For the parts determined to be in contact, further analyze the positional relationship of their respective faces to ensure the accuracy of position judgment;

[0054] Step 5-2: For the parts in contact and the respective faces within the same part, specifically determine their positional relationships, which include: perpendicular, parallel, coaxial separation, coaxial adjacency, coaxial partial overlap, inclusion, and being included, in order to establish an accurate geometric position description and provide reliable data support for subsequent assembly operations.

[0055] Furthermore, the method for judging the contact of workpiece parts in step 5-1 is as follows:

[0056] After obtaining the complete set of attribute information, it is necessary to first determine whether they are the same part. The positional relationship of the same part can be directly judged using rules, while the positional relationship of different parts needs to first determine whether they are in contact. First, calculate the vector between the center points of the two workpieces:

[0057]

[0058] where and are the center point coordinates of workpiece 1 and workpiece 2 respectively;

[0059] Next, project this vector onto the axis direction of the workpiece, and calculate the distance along the axis direction of the workpiece:

[0060]

[0061] Let the heights of workpiece 1 and workpiece 2 be h 1 and h 2 , calculate the vertical distance from the center vector to the axis where the workpiece is located:

[0062]

[0063] Combined with the mating surface radii R 1 and R 2 , and the heights h 1 and h 2 of workpiece 1 and workpiece 2, the maximum allowable distance is obtained:

[0064]

[0065] On this basis, if d Per1 ≤d max1 , d Per2 ≤d max2 , d Axis1 <d max3 , and there is a case where R 1 and R 2 are equal, then it is determined that the workpieces are in contact.

[0066] Furthermore, in step 5-2, when judging the spatial relationship between workpieces, corresponding calculation rules are set to finally realize the judgment of the positional relationship, where the positional relationship includes perpendicular, parallel, coaxial separation, coaxial adjacency, coaxial partial overlap, inclusion, and being included. Specifically:

[0067] 5-2-1. Judgment of perpendicular relationship:

[0068] When detecting the perpendicular relationship between each surface, different vector calculation methods should be adopted according to different geometric shapes. Specifically, based on the dot product relationship of the axis vectors or normal vectors of the geometric bodies, the accurate judgment of the perpendicular relationship can be realized. The following describes three cases of the perpendicular relationship judgment:

[0069] 1) Between a three-dimensional body and a three-dimensional body: When both geometric bodies are three-dimensional bodies, the judgment can be made through their respective axis vectors. Let the axis vectors of three-dimensional body A and three-dimensional body B be and The dot product of the two is defined as If |d A |≈0, then it is determined that the two geometric bodies are perpendicular to each other;

[0070] 2) Between a three-dimensional body and a two-dimensional plane: When one geometric body is a three-dimensional body and the other is a two-dimensional plane, the axis vector of the three-dimensional body and the normal vector of the two-dimensional plane are used to determine the perpendicular relationship. Let the axis vector of the three-dimensional body be The normal vector of the two-dimensional plane is The dot product of the two is defined as If |d| ≈ 1, it is determined that the three-dimensional body and the two-dimensional plane are perpendicular to each other;

[0071] 3) Between two-dimensional planes: When both geometric bodies are two-dimensional planes, their perpendicular relationship is judged by using their respective normal vectors. Let the normal vectors of plane A and plane B be and Then their dot product is defined as If |d n | ≈ 0, it is determined that the two planes are perpendicular to each other;

[0072] 5-2-2. Judgment of parallel and coaxial relationships:

[0073] When detecting the parallel relationship between each face, different vector calculation methods should be adopted according to different geometric shapes. Similarly, the following describes three cases of judging the parallel relationship:

[0074] 1) Between three-dimensional bodies: For the axial vector relationship between two three-dimensional bodies, first perform a cross product operation on the axial vectors of the two objects. If the cross product result is the zero vector, that is Then it is determined that the axial vectors of the two objects are parallel; otherwise, it is determined to be a non-parallel relationship;

[0075] 2) Between a three-dimensional body and a two-dimensional plane: If one object is a three-dimensional body and the other is a two-dimensional plane, then calculate the dot product between the axial vector of the three-dimensional body and the normal vector of the plane. If the dot product Then it is judged that the axial vector of the three-dimensional body is perpendicular to the normal vector of the plane, indicating that this three-dimensional body is parallel to the two-dimensional plane; otherwise, it is determined to be a non-parallel relationship;

[0076] 3) Between two-dimensional planes: If both objects are two-dimensional planes, then judge by calculating the cross product result of the normal vectors of the two planes. If the cross product Then it is determined that the two planes are parallel; otherwise, it is determined to be a non-parallel relationship;

[0077] After judging parallel, it is also necessary to judge whether the two planes are coaxial. Judge the perpendicular distance L of the vector connecting the center points projected onto the R 1 or R 2 axial vector. Whether it is 0. When it is not 0, it is simply parallel. When it is 0, it is coaxial; h For the coaxial situation, judge the intersection, inclusion, partial overlap or adjacency relationship through the following method:

[0078] Calculate the projection distance L of the center connection of the two objects to an axis and half of the sum of the object heights

[0079] ​ Relationship:

[0080] If then the two objects are judged to be coaxially separated; if then the two objects are judged to be adjacent; if further judge whether L is less than half of the height difference between the objects

[0081] If then the higher object contains the lower object; if then the lower object is contained by the higher object;

[0082] In all judgment steps, a predetermined error tolerance is introduced to consider small errors in numerical calculations and ensure the accuracy of the position relationship judgment.

[0083] Furthermore, when judging the spatial relationship between workpieces, for the spheres in the assembly, most of them are hemispherical structures, and the axial vectors and normal vectors of the spheres usually lack clear physical meanings. Therefore, the geometric relationship is judged by comparing the center points of the hemispheres with the axial endpoints of the corresponding faces: if the center point is exactly equal to a certain axial endpoint, it is judged to be coaxially adjacent; if the center point is inconsistent with only one of the two axial endpoints and is far apart, it is judged to be coaxially separated; if the center point is inconsistent with only one of the two axial endpoints and the value of the center point is between the two axial endpoints, it is judged to be coaxially partially overlapping.

[0084] The technical solution adopted by the present invention has the following beneficial effects:

[0085] The present invention organically organizes and stores the geometric features and position information in the three-dimensional design model in the knowledge graph, realizing the effective association and convenient retrieval of data. The system obtains the relative position relationship of the workpieces through accurate geometric feature recognition, and then supports the reasoning of the assembly process. In this process, the product design model is parsed to identify the geometric features and the relative position relationship of the workpieces to extract key assembly information. The purpose of the present invention is to provide a method for identifying geometric features and judging position relationships of workpieces to improve the intelligent level of the automated assembly process. Brief Description of the Drawings

[0086] Figure 1 is the overall flow chart of the present invention;

[0087] Figure 2 is the technical roadmap of the present invention;

[0088] Figure 3 is the flow chart for extracting geometric information of the present invention;

[0089] Figure 4 is the part ontology and attribute information diagram of the present invention;

[0090] Figure 5 It is a diagram of the geometric feature recognition result of the present invention;

[0091] Figure 6 It is a diagram of the specific parameters of the mating surface extracted by the present invention;

[0092] Figure 7 It is a diagram of the specific parameters of the positional relationship of the present invention;

[0093] Figure 8 It is a flowchart for judging the complete geometric attribute information of the workpiece of the present invention;

[0094] Figure 9 It is a schematic diagram for judging the coaxiality of geometric bodies of the present invention. Specific embodiments

[0095] To make the objectives, technical solutions and effects of the present invention clearer and more definite, the following further elaborates the present invention by way of examples with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0096] The following combines the attached Figure 1 - attached Figure 9 , and further describes the specific embodiments of the present invention. The following examples are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention.

[0097] The present invention is a framework method for accurately identifying the geometric features of workpieces and judging the positional relationship, and proposes an improved geometric topology information extraction and global position analysis technology. For complex workpiece structures, geometric feature extraction, mating surface attribute analysis and calculation of the positional relationship between workpieces are completed in sequence. The entire process is as Figure 1 and Figure 2 shown, and is illustrated by taking the parsing of the STEP file of a typical workpiece design model as an example. Others such as assembly models or structural component models are equally applicable.

[0098] The present invention belongs to the field of computer-aided design and intelligent manufacturing, and relates to geometric information extraction and topological analysis methods. Specifically, it relates to a method for identifying the geometric features of workpieces and judging the positional relationship in an automated assembly process, including geometric topology parsing, mating surface classification and attribute extraction, calculation and judgment of the relative positional relationship between workpieces.

[0099] The present invention first inputs the STEP file of the workpiece design model and parses its geometric topology information; according to the hierarchical structure, it gradually extracts the topological data of SHELL (solid), FACE (surface), EDGE (line), and POINT (point) to describe the basic geometric features of the workpiece. Then, it classifies the extracted FACE geometric information, identifies various mating surface types such as cylindrical surfaces, conical surfaces, multi-planar surfaces, spherical surfaces, and toroidal coils, and completes the geometric attribute data according to the characteristics of each type of surface to generate a complete geometric description of the workpiece. For the assembly relationship between workpieces, the present invention further unifies the local coordinate systems of each workpiece to the global coordinate system to ensure the position analysis of different workpieces in the same coordinate framework. By calculating the relative position relationship, it determines whether there are coaxial, adjacent, inclusion, or other spatial relationships between workpieces, thereby providing accurate data support for assembly process reasoning and path planning, facilitating direct calls in subsequent assembly simulation and digital twin optimization, and effectively improving the model application efficiency.

[0100] In an alternative example of the application, a method for identifying geometric features and judging position relationships of workpieces is provided, including the following steps:

[0101] Step 1: Obtain the CAD design model of the workpiece, extract geometric information based on the STEP file of the workpiece design model, and sequentially extract the geometric topology information of the solid, surface, line, and point according to the preset hierarchical structure to provide basic data for subsequent assembly process reasoning and position relationship analysis between workpieces. Specifically: Parse each SHELL of the workpiece from the STEP file, and then extract the corresponding FACE information. Each surface includes its geometric shape attributes, and further parse the connected edges (LOOP / EDGE) and end points (POINT); all the extracted geometric data will be stored in a JSON file according to the hierarchical structure to ensure the readability and structured management of the data;

[0102] Step 2: During the extraction process of the mating surface attribute information of the workpiece design model, classify the surfaces extracted from the workpiece geometric information, and carefully identify and extract them according to the specific geometric feature attributes of each type of mating surface. The system automatically identifies various mating surfaces, including cylindrical surfaces, conical surfaces, spherical surfaces, toroidal coil surfaces, toroidal planes, and polygonal planes, through keyword recognition and attribute discrimination techniques. Finally, this structured data will be stored in a JSON file for further processing and calling of the data. The geometric information extraction process is as Figure 3 shown.

[0103] Specifically, for different types of mating surfaces, corresponding geometric attributes are extracted and recorded. Different surfaces require different attribute information to form a systematic mating surface data structure, specifically including: The attribute information of a cylindrical surface includes the mating surface ID, the ID of the workpiece it belongs to, the bottom radius, the height, the concavity and convexity, the coordinates of the axis endpoints, and the axis vector; The attribute information of a conical surface includes the mating surface ID, the ID of the workpiece it belongs to, the bottom radius, the top radius, and the axis endpoint coordinates; The attribute information of a spherical surface includes the mating surface ID, the ID of the workpiece it belongs to, the coordinates of the center point of the sphere, and the radius information; The attribute information of an annular coil surface includes the mating surface ID, the ID of the workpiece it belongs to, the inner and outer radii, the center point, the axis vector, and the normal vector information; The attribute information of an annular plane includes the mating surface ID, the ID of the workpiece it belongs to, the inner and outer radii, the center point, and the normal vector attribute; The attribute information of a polygonal plane includes the mating surface ID, the ID of the workpiece it belongs to, the normal vector, the IDs of the constituent edges, including the inner edge ID, the outer edge ID, and the total ID information. In the edges, the edge ID, the coordinates of the axis endpoints, and the direction vector information are required, specifically as Figure 6 shown.

[0104] Step 3: In the case where the geometric attribute information of the mating surface of the workpiece design model is incomplete, generate a complete geometric feature description through analysis and complementation techniques to ensure the accuracy and integrity of the mating surface geometric information, extract the high-level characterization information of the mating surface, and perform calculation and derivation of attributes based on preset rules. Classify and store the complemented workpiece mating surface information in a JSON file to form a complete workpiece geometric description database.

[0105] The method for complementing the geometric attribute information for different mating surfaces is as follows: For a cylindrical surface, its complementation process includes extracting the axis endpoints, calculating the height of the cylinder, and determining the concavity and convexity of the surface. First, obtain one of the axis endpoints, that is, the center point of the given cylindrical surface, and extract the maximum control point of the B-spline curve in its direction as the other axis endpoint based on the axis vector of the mating surface; Calculate the height of the cylindrical surface through regular calculations using the two known axis endpoints. In addition, for special expression methods of the cylindrical surface, such as 10 circles and 10 lines, on the basis of the rules, the cylindrical surface generatrix needs to be segmented according to the data law to realize the extraction and complementation of the upper and lower bottom surface information of the cylindrical surface; In other mating surfaces, for the missing axis endpoints, height, and normal vector attributes, similar complementation processing is also performed.

[0106] Step 3 specifically includes:

[0107] Specifically, the concavity and convexity can be realized by judging the included angle range between the normal vector N of the mating surface and the direction vector N 1 as follows: First, convert the points P, the center point P 0 on the mating surface, and the axis direction Axis_direction into NumPy arrays. Then, use the right-hand rule to pass through the normal vector N 1The cross product of the axis vector Vec calculates N e .

[0108] N e =N 1 ×Vec calculates the distance from point P to center P 0 The vector P Vec , and obtain the tangent vector R through the cross product Vec It can accurately describe the geometric characteristics of point P in the local coordinate system and be used in subsequent steps to determine the concavity and convexity of the cylindrical surface and other geometric calculations.

[0109] P Vec =PP 0

[0110] R Vec =P Vec ×Axis_direction

[0111] Next, according to the nature of the cylindrical surface (inner surface or outer surface), determine the direction vector N 2 The final direction vector N is calculated by the cross product. The inner surface refers to the surface facing the inside of the cylinder, and its normal vector points inward; the outer surface refers to the surface facing the outside of the cylinder, and its normal vector points outward. 2 When using the tangent vector R Vec and the axial vector Axis_direction of the cylinder, and the direction vector perpendicular to these two vectors is calculated by the cross product formula. e and N 2 The final normal vector N is calculated by the cross product of e and N 2 , which effectively describes the normal relationship at point P and provides a basis for subsequent concavity and convexity judgment.

[0112] N 2 =R Vec ×Axis_direction

[0113] N=N e ×N 2

[0114] Then, the dot product is used to calculate N and N 1 The angle between the two surfaces is calculated and converted into degrees. Finally, the convexity is determined based on the range of the angle: if the angle is between 0 and 90 degrees, it is convex; if the angle is between 90 and 180 degrees, it is concave.

[0115]

[0116] Finally, the geometric feature recognition results achieved by the method in Step 3 are as Figure 5 shown.

[0117] Step 4: When processing the workpiece data in the JSON file, since each workpiece usually has an independent local coordinate system, in order to perform unified spatial analysis and position relationship judgment, it is necessary to standardize these local coordinate systems.

[0118] Step 4 specifically includes:

[0119] Since workpieces are usually modeled or designed in their own local coordinate systems, their coordinate systems are standardized and reflect local geometric features. However, in the entire product, the actual position and orientation of the workpieces will vary due to their different relationships with the coordinate system to which the assembly belongs. Therefore, it is necessary to uniformly process the workpiece coordinate systems. That is, by calculating the rotation matrix of the workpiece to the product coordinate system, the complete transformation of the coordinate system can be achieved, providing a basis for subsequent accurate position judgment. Specifically, first, it is necessary to obtain the origin of the coordinate system and its direction vectors (X-axis, Y-axis, and Z-axis), and these direction vectors describe the spatial positioning of the workpiece in its own reference system. To ensure that these direction vectors are unit vectors, thereby improving the accuracy of the transformation and maintaining mathematical orthogonality, it is necessary to normalize them. The formula for normalization is:

[0120]

[0121] where v is the direction vector to be normalized, v′ is the normalized unit vector, and ||v|| represents the modulus of the vector (i.e., the Euclidean norm), and the calculation formula is:

[0122]

[0123] Using these normalized direction vectors (X-axis, Y-axis, and Z-axis) to construct the rotation matrix, R local =[X local Y local Z local . This rotation matrix describes the directional relationship between the local coordinate system and the global coordinate system, thus realizing the transformation of the local coordinate system to the global coordinate system. Next, it is also necessary to construct the rotation matrix of the global coordinate system, R global =[X global Y global Z global . Then, by multiplying the rotation matrix of the global coordinate system by the inverse matrix of the rotation matrix of the local coordinate system, the complete transformation matrix T is obtained.

[0124]

[0125] This transformation matrix is used to convert points in the local coordinate system to the global coordinate system, and can accurately describe how the workpiece in the local coordinate system is positioned and oriented in the global coordinate system.

[0126] Step Five: After completing the conversion between the local and global coordinate systems, based on the unified global coordinate information, the relative position relationships between different workpieces can be calculated. These relative position relationships include various geometric relationships such as perpendicular, parallel, coaxial adjacency, coaxial separation, coaxial partial overlap, inclusion, and being included.

[0127] Step Five specifically includes:

[0128] The part body and attribute information diagram of the present invention is as Figure 4 shown. First, it is necessary to determine which parts are in contact. For the parts determined to be in contact, we further analyze the positional relationships of their respective faces to ensure the accuracy of position judgment; for the parts in contact and the faces within the same part, their positional relationships are determined in detail. The positional relationships include: perpendicular, parallel, coaxial separation, coaxial adjacency, coaxial partial overlap, inclusion, and being included, so as to establish an accurate geometric position description and provide reliable data support for subsequent assembly operations. The flowchart for judging the complete geometric attribute information of the workpiece is as Figure 8 shown, and specifically includes the following methods:

[0129] The method for judging the contact of workpiece parts is:

[0130] After obtaining the complete set of attribute information, it is necessary to first determine whether they are the same part. The positional relationships of the same part can be directly judged using rules, while for different parts, it is necessary to first determine whether they are in contact. First, calculate the vector between the center points of the two workpieces

[0131]

[0132] where and are the center point coordinates of workpiece 1 and workpiece 2 respectively. Then, project this vector onto the axis direction where the workpieces are located, and calculate the distance

[0133]

[0134] Let the heights of workpiece 1 and workpiece 2 be h 1 and h 2 respectively, and calculate the perpendicular distance from the center vector to the axis where the workpieces are located

[0135]

[0136] Combined with the radii R 1 and R 2, and the workpiece height h 1 and h 2 , the maximum allowable distance can be obtained On this basis, if d Per1 ≤d max1 、d Per2 ≤d max2 、d Axis1 <d max3 and there is a case where R 1 and R 2 are equal, it is determined that the workpiece is in contact.

[0137] Among them, the method for judging the positional relationship of workpiece parts is specifically as follows:

[0138] When judging the spatial relationship between workpieces, corresponding calculation rules are set to finally realize the judgment of the positional relationship. The positional relationships include perpendicular, parallel, coaxial separation, coaxial adjacency, coaxial partial overlap, inclusion, being included, and the judgment rules for the relative positional relationship of workpieces.

[0139] 1. Judgment of perpendicular relationship

[0140] When detecting the perpendicular relationship between each surface, different vector calculation methods should be adopted according to different geometric shapes. Specifically, based on the dot product relationship of the axis vectors or normal vectors of the geometric bodies, the accurate judgment of the perpendicular relationship can be realized. The following describes three cases of the judgment of the perpendicular relationship:

[0141] 1) Between three-dimensional bodies: When both geometric bodies are three-dimensional bodies, the perpendicular relationship can be judged by their respective axis vectors. Let the axis vectors of three-dimensional body A and three-dimensional body B be and The dot product of the two is defined as If |d A |≈0, it is determined that the two geometric bodies are perpendicular to each other.

[0142] 2) Between a three-dimensional body and a two-dimensional plane: When one geometric body is a three-dimensional body and the other is a two-dimensional plane (such as a polygonal plane), the axis vector of the three-dimensional body and the normal vector of the two-dimensional plane are used to judge the perpendicular relationship. Let the axis vector of the three-dimensional body be The normal vector of the two-dimensional plane is The dot product of the two is defined as If |d|≈1, it is determined that the three-dimensional body and the two-dimensional plane are perpendicular to each other.

[0143] 3) Between two-dimensional planes: When both geometric bodies are two-dimensional planes, their perpendicular relationship is judged by using their respective normal vectors. Let the normal vectors of plane A and plane B be and Then their dot product is defined as If |d n | ≈ 0, it is determined that the two planes are perpendicular to each other;

[0144] 2. Judgment of parallel and coaxial relationships

[0145] When detecting the parallel relationship between each surface, different vector calculation methods should be adopted according to different geometric shapes. Similarly, the following describes three cases of judging the parallel relationship:

[0146] 1) Between three-dimensional objects: For the axial vector relationship between two three-dimensional objects, first perform a cross product operation on the axial vectors of the two objects. If the cross product result is a zero vector, that is it is determined that the axial vectors of the two objects are parallel; otherwise, it is determined as a non-parallel relationship;

[0147] 2) Between a three-dimensional object and a two-dimensional plane: If one object is a three-dimensional object and the other is a two-dimensional plane, then calculate the dot product between the axial vector of the three-dimensional object and the normal vector of the plane. If the dot product it is determined that the axial vector of the three-dimensional object is perpendicular to the normal vector of the plane, indicating that this three-dimensional object is parallel to the two-dimensional plane; otherwise, it is determined as a non-parallel relationship;

[0148] 3) Between two-dimensional planes: If both objects are two-dimensional planes, then judge by calculating the cross product result of the normal vectors of the two planes. If the cross product it is determined that the two planes are parallel; otherwise, it is determined as a non-parallel relationship;

[0149] After determining parallelism, it is also necessary to judge whether the two planes are coaxial. Judge the perpendicular distance L of the vector connecting the center points projected onto the axial vector of R 1 or R 2 Whether it is 0. When it is not 0, it is simply parallel, as shown in h (A); when it is 0, it is coaxial, as shown in Figure 9 (B). For the coaxial case, judge the intersection, inclusion, partial overlap or adjacency relationship through the following method: Figure 9 (B). For the coaxial case, judge the intersection, inclusion, partial overlap or adjacency relationship through the following method:

[0150] Calculate the relationship between the projection distance L of the line connecting the centers of the two objects onto an axis and half of the sum of the object heights :

[0151] If it is determined that the two objects are coaxially separated; if it is determined that the two objects are adjacent; if Further judge whether L is less than half of the height difference of the objects If the higher object contains the lower object; if Then the lower object is contained by the higher object. A predetermined error tolerance is introduced in all judgment steps to account for small errors in numerical calculations and ensure the accuracy of the position relationship judgment.

[0152] Specifically, for the spheres in the assembly, they are mostly hemispherical structures, and the axial vectors and normal vectors of the spheres usually lack clear physical meanings. Therefore, the geometric relationship is judged by comparing the center points of the hemispheres with the axial endpoints of the corresponding faces: if the center point is exactly equal to a certain axial endpoint, it is determined to be coaxially adjacent; if the center point is inconsistent with only one of the two axial endpoints and is far apart, it is determined to be coaxially separated; if the center point is inconsistent with only one of the two axial endpoints and the value of the center point is between the two axial endpoints, it is determined to be coaxially partially overlapping. The position relationship judgment results are as Figure 7 shown. The first row and the first column are the ID numbers of all faces, and each position relationship is the relationship between its corresponding row ID and column ID.

[0153] The beneficial technical effects of the present invention at least include;

[0154] The present invention is a framework method for accurately identifying the geometric features of workpieces and judging the position relationship, and proposes a method for identifying the geometric features of workpieces and judging the position relationship based on the analysis of geometric topology information and the analysis of mating surface attributes. By parsing the STEP file of the workpiece design model, the geometric topology information of SHELL (solid), FACE (face), EDGE (line), and POINT (point) is extracted layer by layer, and classified and attribute-complemented to solve the problems of identifying the geometric features of complex workpieces and judging the position relationship. The present invention also combines the unified processing of the local coordinate system and the global coordinate system to ensure the accurate analysis of the spatial position relationship between workpieces.

[0155] The improvement points of the present invention are mainly reflected in the accurate extraction of workpiece geometric information and the method for judging the position relationship. On the basis of the existing geometric analysis and topological analysis technologies, combined with the mating surface classification and attribute-complementation technologies, the processing methods of the local and global coordinate systems are unified. By improving and optimizing the existing process, the present invention proposes a new framework that can efficiently complete the identification of geometric features and the judgment of position relationships. Verified by experiments, the method provided by this application performs excellently in the accuracy of geometric information extraction and the reliability of position relationship judgment, and can provide efficient data support for assembly process planning and path optimization.

[0156] Other embodiments of the present invention will be readily apparent to those skilled in the art upon consideration of the specification and practice of the solutions disclosed herein. The present invention is intended to cover any variations, uses, or adaptations of the present invention, which follow the general principles of the present invention and include known common knowledge or conventional technical means in the technical field not disclosed in this disclosure. The specification and examples are only regarded as exemplary, and the true scope and spirit of the present invention are pointed out by the claims.

Claims

1. A method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process, characterized in that: The method comprises the following steps: Step 1: Obtain the CAD design model of the workpiece, extract geometric information based on the STEP file of the workpiece design model, and extract the geometric topological information of entities, surfaces, lines, and points in sequence according to the preset hierarchical structure to provide basic data for subsequent assembly process reasoning and position relationship analysis between workpieces; Step 2: In the process of extracting the mating surface attribute information of the workpiece design model, the faces extracted from the workpiece geometric information are classified, and the specific geometric feature attributes of each type of mating surface are carefully identified and extracted. The system automatically identifies various types of mating surfaces, including cylindrical surfaces, conical surfaces, spherical surfaces, toroidal coil surfaces, torus planes, and polygonal planes, through keyword recognition and attribute discrimination technology. Finally, these structured data will be stored in a JSON file for further processing and calling of the data; Step 3: When the geometric attribute information of the mating surface of the workpiece design model is incomplete, a complete geometric feature description is generated through analysis and completion technology to ensure the accuracy and completeness of the geometric information of the mating surface, extract the high-level representation information of the mating surface, and calculate and derive the attributes based on preset rules. The completed workpiece mating surface information is classified and stored in a JSON file to form a complete workpiece geometry description database; Step 4: When processing the workpiece data in the JSON file, since each workpiece usually has an independent local coordinate system, these local coordinate systems are standardized and spatial analysis and position relationship judgment are performed uniformly; Step 5: After completing the conversion between the local and global coordinate systems, the relative position relationships between different workpieces are calculated based on the unified global coordinate information, and the position relationship judgment is performed. These relative position relationships include vertical, parallel, coaxial adjacency, coaxial separation, coaxial partial overlap, inclusion, and being included.

2. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 1, characterized in that: Extracting geometric information based on the STEP file of the workpiece design model in step 1 includes: Step 1-1: parse each entity of the workpiece from the STEP file, and then extract its corresponding surface information, each surface including its geometric shape attributes, and further parse the edges and endpoints connected to the surface; Step 1-2: All extracted geometric data will be stored in a JSON file in a hierarchical structure to ensure data readability and structured management.

3. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 1, characterized in that: The method for identifying the geometric properties of the mating surface in step 2 is: Step 2-1: For different types of mating surfaces, extract and record corresponding geometric attributes. Different surfaces require different attribute information to form a systematic mating surface data structure; Step 2-2: extracting the attribute information of the cylindrical surface, the attribute information of the cylindrical surface includes the mating surface ID, the workpiece ID, the bottom radius, the height, the concavity, the axis endpoint coordinates and the axis vector; Step 2-3: extract the attribute information of the conical surface, which includes the matching surface ID, the workpiece ID, the bottom radius, the top radius and the axis endpoint coordinates; Step 2-4: extracting the attribute information of the spherical surface, which includes the matching surface ID, the workpiece ID, the coordinates of the spherical center point and the radius information; Step 2-5: extracting the attribute information of the annular coil surface, the attribute information of the annular coil surface includes the matching surface ID, the workpiece ID, the inner and outer radius, the center point, the axis vector and the normal vector information; Step 2-6: extract the attribute information of the annular plane, the attribute information of the annular plane includes the matching surface ID, the workpiece ID, the inner and outer radius, the center point and the normal vector attribute; Step 2-7: Extract the attribute information of the polygonal plane. The attribute information of the polygonal plane includes the mating surface ID, the workpiece ID, the normal vector, the constituent edge ID, including the inner edge ID, the outer edge ID and the total ID information. The edge ID, the axis endpoint coordinates and the direction vector information are required in the edge.

4. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 1, characterized in that: The step 3 in which a complete geometric feature description is generated by the completion technology includes: Step 3-1: For the cylindrical surface, the completion process includes extracting the axis endpoints, calculating the cylinder height, and determining the surface concavity. First, obtain one of the axis endpoints, that is, the center point of the given cylindrical surface, and extract the maximum control point of the B-spline curve in its direction as the other axis endpoint based on the axis vector of the matching surface; determine the height of the cylindrical surface by regular calculation through the known two axis endpoints. In addition, the special expression of the cylinder requires the segmentation of the cylindrical generatrix based on the rules and data rules to realize the extraction and completion of the upper and lower bottom surface information of the cylinder; Step 3-2: For other mating surfaces, the missing axis endpoints, heights, and normal vector attributes are also completed as in step 3-1.

5. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 4, characterized in that: The step of judging the concavity and convexity of the workpiece in step 3-1 is achieved by judging the angle range between the normal vector N of the mating surface and the direction vector N1, and the process is as follows: First, convert the point P, center point P0 and axis direction Axis_direction on the mating surface into NumPy arrays. Then, use the right-hand rule to calculate N through the cross product of the normal vector N1 and the axis vector Vec. e : N e =N1×Vec; Calculate the vector P from point P to center P0 Vec , and obtain the tangent vector R through the cross product Vec , which can accurately describe the geometric characteristics at point P in the local coordinate system and is used in subsequent steps to determine the concavity and convexity of the cylindrical surface and other geometric calculations: P Vec =P-P0; P Vec =P Vec ×Axis_direction; Next, according to the properties of the cylindrical surface, the direction vector N2 is determined, and the final direction vector N is calculated by the cross product. The cylindrical surface is the inner surface or the outer surface. The inner surface refers to the surface facing the inside of the cylinder, and its normal vector points inward; the outer surface refers to the surface facing the outside of the cylinder, and its normal vector points outward. When calculating N2, the tangent vector R is used Vec and the axial vector Axis_direction of the cylinder, and the direction vector perpendicular to these two vectors is calculated by the cross product formula. Then, the normal vector N e The cross product of and N2 calculates the final normal vector N, which is geometrically perpendicular to N e and N2, effectively describe the normal relationship at point P, providing a basis for subsequent concavity and convexity judgment: N2=R Vec ×Axis_direction; N=N e ×N2; Then, the angle between N and N1 is calculated using the dot product and converted into degrees; Finally, the convexity is determined based on the range of the angle θ: if the angle θ is between 0 and 90 degrees, it is convex; if the angle θ is between 90 and 180 degrees, it is concave:

6. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 1, characterized in that: In step 4, since the workpiece is usually modeled or designed in its own local coordinate system, its coordinate system is standardized and reflects the local geometric features. However, in the entire product, the actual position and direction of the workpiece will change due to the difference in the coordinate system to which the assembly belongs. Therefore, the workpiece coordinate system needs to be unified, that is, by calculating the rotation matrix from the workpiece to the product coordinate system, to achieve a complete conversion of the coordinate system, providing a basis for subsequent accurate position judgment, specifically including: First, the origin of the coordinate system and its direction vectors are obtained. The direction vectors include the X-axis, Y-axis, and Z-axis. These direction vectors describe the spatial positioning of the workpiece in its own reference system. In order to ensure that these direction vectors are unit vectors, thereby improving the accuracy of the conversion and maintaining mathematical orthogonality, these direction vectors are normalized. The normalization formula is: Where v is the direction vector to be normalized, v′ is the normalized unit vector, and ||v|| represents the modulus of the vector, i.e., the Euclidean norm, and the calculation formula is: Use these normalized direction vectors to construct the rotation matrix for the local coordinate system: R local =[X local Y local Z local ]; X local Y local Z local are respectively the normalized direction vectors of the local coordinate system on the X-axis, Y-axis, and Z-axis. The rotation matrix describes the direction relationship between the local coordinate system and the global coordinate system, thereby realizing the transformation from the local coordinate system to the global coordinate system; Next, we also need to construct the rotation matrix of the global coordinate system: R glocal =[X glocal Y glocal Z glocal ]; X global Y global Z global They are the normalized direction vectors of the global coordinate system on the X-axis, Y-axis, and Z-axis, respectively. By transforming the rotation matrix R of the global coordinate system global Multiply by the inverse of the local rotation matrix Get the complete transformation matrix T: This transformation matrix is ​​used to transform points in the local coordinate system into the global coordinate system, and can accurately describe how the workpiece in the local coordinate system is positioned and oriented in the global coordinate system.

7. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 1, characterized in that: The method for calculating the relative position relationship of the workpiece in step 5 is: Step 5-1: First determine which parts are in contact with each other. For the parts that are determined to be in contact, further analyze the position relationship of each surface to ensure the accuracy of position determination; Step 5-2: For the contacting parts and the various surfaces inside the same part, determine their positional relationships in detail. The positional relationships include: vertical, parallel, coaxial separation, coaxial adjacency, coaxial partial overlap, inclusion and being included, so as to establish an accurate geometric position description and provide reliable data support for subsequent assembly operations.

8. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 7, characterized in that: The method for determining the contact between workpiece parts in step 5-1 is: After obtaining the complete set attribute information, it is necessary to determine whether they are the same part. The position relationship of the same part can be directly determined using rules, while the position relationship of different parts needs to be determined whether they are in contact. First, the vector between the center points of the two workpieces is calculated: in and They are the center point coordinates of workpiece 1 and workpiece 2 respectively; Next, project the vector to the axis direction where the workpiece is located , calculate the distance along the workpiece axis: Let the heights of workpiece 1 and workpiece 2 be h1 and h2 respectively, and calculate the vertical distance from the center vector to the axis where the workpiece is located: Combining the radii R1 and R2 of the mating surfaces of workpiece 1 and workpiece 2, and the heights h1 and h2 of workpiece 1 and workpiece 2, the maximum allowable distance is obtained: On this basis, if d Per1 ≤d max1 ,d Per2 ≤d max2 ,d Axis1 <d max3 , and if R1 and R2 are equal, it is judged that the workpieces are in contact.

9. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 7, characterized in that: In step 5-2, when judging the spatial relationship between workpieces, corresponding calculation rules are set to finally realize the position relationship judgment, where the position relationship includes vertical, parallel, coaxial separation, coaxial adjacency, coaxial partial overlap, inclusion, and being included, specifically: 5-2-1. Vertical relationship judgment: When detecting the perpendicular relationship between the faces, different vector calculation methods should be used according to the different geometric forms. Specifically, the dot product relationship between the axis vector or normal vector of the geometric body can be used to accurately determine the perpendicular relationship. The following describes three situations for determining the perpendicular relationship: Between three-dimensional bodies: When two geometric bodies are three-dimensional bodies, they can be judged by their respective axis vectors. Suppose the axis vectors of three-dimensional body A and three-dimensional body B are and The dot product of the two is defined as If |d A |≈0, then the two geometric bodies are considered perpendicular to each other; Between a 3D body and a 2D plane: When one geometric body is a 3D body and the other is a 2D plane, the axis vector of the 3D body and the normal vector of the 2D plane are used to determine the perpendicular relationship. Let the axis vector of the 3D body be The normal vector of a two-dimensional plane is The dot product of the two is defined as If |d|≈1, the three-dimensional body and the two-dimensional plane are determined to be perpendicular to each other; Between two-dimensional planes: When both geometric bodies are two-dimensional planes, their vertical relationship is determined by their respective normal vectors. Suppose the normal vectors of plane A and plane B are and Then its dot product is defined as If |d n |≈0, then the two planes are considered perpendicular to each other; 5-2-2. Determination of parallel and coaxial relationship: When detecting the mutual parallel relationship between various faces, different vector calculation methods should be used according to different geometric forms. Similarly, the following describes three situations of parallel relationship judgment: Between three-dimensional bodies: For the axis vector relationship between two three-dimensional bodies, first perform a cross product operation on the axis vectors of the two objects. If the cross product result is a zero vector, that is, If the axis vectors of the two objects are parallel, it is determined that they are in a non-parallel relationship; otherwise, Between a 3D body and a 2D plane: If one object is a 3D body and the other is a 2D plane, calculate the dot product between the axis vector of the 3D body and the normal vector of the plane. If the dot product If the axis vector of the three-dimensional body is perpendicular to the normal vector of the plane, it means that the three-dimensional body is parallel to the two-dimensional plane; otherwise, it is considered as a non-parallel relationship. Between two-dimensional planes: If both objects are two-dimensional planes, the cross product of the normal vectors of the two planes is used to determine if the cross product is If the two planes are parallel, they are considered to be non-parallel. After determining whether the two surfaces are parallel, it is necessary to determine whether they are coaxial and the vertical distance L of the projection of the center point connecting vector to the R1 or R2 axis vector. b Is it 0? If it is not 0, it is simply parallel. If it is zero, it is coaxial. For the case of co-axis, the intersection, inclusion, partial overlap or adjacency relationship is determined in the following ways: Calculate the projection distance L of the line connecting the centers of the two objects to an axis and half of the sum of the object heights Relationship: like Then the two objects are judged to be coaxially separated; if Then the two objects are judged to be adjacent; if Further determine whether L is less than half of the object height difference like Then the higher object contains the lower object; if Then the lower object is contained by the higher object; A predetermined error tolerance is introduced in all judgment steps to take into account small errors in numerical calculations and ensure the accuracy of positional relationship judgment.

10. The method for identifying geometric features and determining positional relationships of workpieces in an automated assembly process according to claim 9, characterized in that: When judging the spatial relationship between workpieces, the spheres in the assembly are mostly hemispherical structures, and the axis vectors and normal vectors of the spheres usually lack clear physical meanings. Therefore, the geometric relationship is judged by comparing the center point of the hemisphere with the axis endpoints of the corresponding surface: if the center point is completely equal to an axis endpoint, it is judged to be coaxially adjacent; if the center point is inconsistent with only one of the two axis endpoints and the distance is far, it is judged to be coaxially separated; if the center point is inconsistent with only one of the two axis endpoints and the value of the center point is between the two axis endpoints, it is judged to be partially overlapping coaxially.

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