Six-degree-of-freedom vibration simulation system interference detection method based on generalized Stewart platform

Abstract

The invention discloses a six-degree-of-freedom vibration simulation system interference detection method based on a generalized Stewart platform. The method comprises the following steps: determining an interference detection structure; regarding a to-be-detected structure as a cylinder, and obtaining configuration parameters, geometric parameters and interference information of the to-be-detected structure; and detecting the to-be-detected structure according to a preset rule and obtaining a detection result. Wherein the interference detection structure must comprise an actuating branch chain; the configuration parameters of the to-be-detected structure must uniquely and completely describe the central axis vector and starting point information of the to-be-detected structure; the geometric parameters comprise the maximum radius and the height of the to-be-detected structure; the interference information needs to be reasonably arranged in combination with the space required by actual installation; the preset rule comprises the distance between the cylinders. According to the invention, the spacing of each structure can be detected in the theoretical design stage of the vibration simulation system, and the situations of structural interference and insufficient mounting spacing are avoided, so that the theoretical design result has high engineering feasibility.

Description

Technical Field

[0001] The present invention belongs to the technical field of interference detection of six-degree-of-freedom vibration simulation systems, and specifically relates to an interference detection method for six-degree-of-freedom vibration simulation systems based on a generalized Stewart platform. The method can be used in the theoretical simulation stage to detect the spacing between components of the vibration simulation system, thereby avoiding structural interference and insufficient installation spacing, and making the theoretical design results highly engineering feasible. Background Art

[0002] In modern industry and engineering, the generalized Stewart platform is used in a variety of fields, including six-degree-of-freedom vibration simulation systems and vibration isolation systems, due to its high precision, high rigidity, heavy-load capacity, and wide range of motion. This type of mechanism is typically composed of a static platform, a dynamic platform, and multiple actuator branches, enabling complex three-dimensional motion. However, the design process of a generalized Stewart platform is extremely complex, involving multiple disciplines such as system dynamics and structural optimization. During the preliminary design phase, ensuring the rational spatial layout of the mechanism's components and preventing theoretical design results from being directly applicable to engineering are key issues in the design of generalized Stewart platforms.

[0003] The traditional physical prototype method directly manufactures the relevant structures, assembles them and observes whether there is interference. This method is the simplest and most intuitive, but the trial-and-error cycle is long and the cost is high, and it can no longer meet current engineering needs; the projection method obtains the relative positions of each component by solving the spatial vector equations converted from the kinematic equations of the parallel mechanism. This method can be used for interference detection in the theoretical design stage, but the calculation is complex and not universal for different types of mechanisms; the traditional theoretical distance detection method simplifies it into the calculation of the distance between two straight lines in space. The calculation results are relatively conservative and have a large gap with the actual situation. Therefore, it is necessary to design an interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform. It is used to detect the spacing between the components of the vibration simulation system in the theoretical simulation stage to avoid structural interference and insufficient installation spacing, so that the theoretical design results have a high degree of engineering feasibility. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides an interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform, comprising: determining an interference detection structure; treating the structure to be detected as a cylinder to obtain configuration parameters, geometric parameters and interference information of the structure to be detected; and detecting the structure to be detected according to preset rules and obtaining detection results.

[0005] The specific technical solution is: an interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform, including:

[0006] determining a structure to be detected, wherein the structure to be detected includes an actuating branch chain;

[0007] The actuating branch chain of the structure to be detected is regarded as a cylinder, and the configuration parameters, geometric parameters and interference information of the structure to be detected are obtained; the configuration parameters of the structure to be detected describe the central axis vector and starting point information of the structure to be detected; the geometric parameters include: the maximum radius and height of the structure to be detected; the interference information is reasonably set according to the actual installation space required;

[0008] The structure to be inspected is inspected according to preset rules and an inspection result is obtained. The preset rules include the distance between cylinders.

[0009] Compared with other existing six-degree-of-freedom vibration simulation system interference detection methods based on the generalized Stewart platform, the advantages of the present invention are:

[0010] (1) The present invention fully considers the installation environment requirements in the actual installation environment, making the interference detection basis more realistic. The final physical object can meet various assembly and layout requirements, greatly improving the engineering feasibility of the theoretical design results;

[0011] (2) The present invention optimizes the interference detection process and incorporates the traditional spacing calculation method into it, so that the shortest spacing of the structure to be detected can be quickly calculated in some relatively simple situations. In large-scale optimization models, the detection speed and efficiency can be greatly improved;

[0012] (3) The present invention regards the interference detection structure as a cylinder, taking into account a more comprehensive spatial interference detection situation. Without affecting the detection accuracy, it greatly reduces the burden of structural details on calculations and improves the efficiency of interference detection. At the same time, the present invention can make the upper limit of the optimization model with the goal of minimizing the envelope of the vibration simulation system and the constraint of non-interference in structural space higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flow chart of interference detection of the present invention;

[0014] Figure 2 Schematic diagram of the structure of the generalized Stewart platform of the present invention;

[0015] Figure 3 A schematic diagram of variables in an embodiment of the present invention;

[0016] Figure 4 A schematic diagram of theoretical interference detection geometry according to an embodiment of the present invention;

[0017] Figure 5 Schematic diagram of three distance detection situations of the present invention;

[0018] Figure 63. It is a comparison chart of the traditional detection method of an embodiment of the present invention and the optimization results of the present invention.

[0019] Among them, the accompanying drawings are marked as: 201—static platform, 202—actuating branch chain, 203—moving platform, 301—upper hinge distribution angle, 302—upper hinge distribution circle radius, 303—lower hinge distribution circle radius, 304—lower hinge distribution angle, 305—actuating branch chain length, 306—actuating branch chain height, 307—body coordinate system, 308—geodetic coordinate system, 309—starting point, 310—central axis vector, 2021—actuator, 2022—actuating hinge, 2023—actuating transmission rod. DETAILED DESCRIPTION

[0020] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other. To achieve the above-mentioned objectives, the present invention adopts the following technical solutions.

[0021] Among the related technologies, the traditional physical prototype method directly manufactures the relevant structures, assembles them and observes whether there is any interference in the vibration simulation system. This method is the simplest and most intuitive, but the trial-and-error cycle is long and the cost is high, and it can no longer meet current engineering needs; the projection method obtains the relative positions of each component by solving the spatial vector equations converted from the kinematic equations of the vibration simulation system. This method can be used for interference detection in the theoretical design stage, but the calculation is complex and the versatility for the same type of different mechanisms is insufficient; the traditional theoretical distance detection method simplifies the distance between the structures to be tested to the distance between the center axes of the two structures to be tested. The calculation results are relatively conservative and are quite different from the actual situation.

[0022] like Figures 1 to 6 As shown, the present invention provides an interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform, comprising: determining a structure to be detected; obtaining configuration parameters, geometric parameters, and interference information of the structure to be detected; and detecting the structure to be detected according to three distance detection conditions according to preset rules and steps, calculating the distance between the structures to be detected, and obtaining interference detection results. Following the preset rules and steps can reduce computing resource consumption in some cases and improve interference detection efficiency. This method can be used in the theoretical simulation stage to detect whether the spacing between the structures of the six-degree-of-freedom vibration simulation system of the generalized Stewart platform is sufficient, avoiding structural interference and insufficient installation spacing, and making the theoretical design results highly feasible for engineering.

[0023] The following will be combined Figure 1A flowchart illustrating theoretical interference detection in some embodiments of the present invention is provided. The interference detection method includes:

[0024] Determine the structure to be tested, which must include an actuating branch chain, which may include: air springs, auxiliary supports, and lifting rings;

[0025] Treat the structure to be detected as a cylinder and obtain its configuration parameters, geometric parameters, and interference information. The configuration parameters must be able to uniquely and completely describe the central axis vector and starting point information of the structure to be detected; the interference information is set based on the actual installation space required.

[0026] According to the preset rule steps, the structures to be detected are detected according to three situations respectively and the distance between the structures to be detected is calculated to obtain the detection results. The preset rule steps can reduce the computing resource consumption in some situations and improve the detection efficiency. The three situations comprehensively consider the interference situations that may occur in the three-dimensional space after the structures to be detected are simplified into cylinders. The preset rules include the distance between the cylinders.

[0027] The following is an example of the appeal process:

[0028] like Figure 2 As shown, the six-degree-of-freedom vibration simulation system of the generalized Stewart platform must include three parts: a static platform 201, an actuating branch 202 and a dynamic platform 203. The static platform 201 and the dynamic platform 203 are parallel to each other, and the actuating branch 202 is located between the static platform 201 and the dynamic platform 203. The actuating branch 202 may include: an actuator 2021, an actuating hinge 2022, and an actuating transmission rod 2023, wherein the actuating transmission rod 2023 is arranged between the two actuating hinges 2022 to form a combination of an actuating transmission structure, and the actuating transmission structure is concentrically assembled along the central axis of the actuator 2021. Some vibration simulation systems may require structures such as air springs, auxiliary supports and hanging rings, which are also located between the static platform 201 and the dynamic platform 203. Structural interference in the six-degree-of-freedom vibration simulation system of the generalized Stewart platform occurs in the space between the static platform 201 and the dynamic platform 203. The structure to be tested must include multiple actuating branches 202, which may include air springs, auxiliary supports, and lifting rings depending on actual use requirements.

[0029] The configuration parameters of the structure to be detected must be able to uniquely and completely describe the axis vector and starting point information;

[0030] In some embodiments, as Figure 3As shown, the configuration parameters of the structure to be tested must be able to uniquely and completely describe the axis vector and starting point information. Taking the actuating branch 202 as an example, the parameter combination includes but is not limited to: upper hinge distribution angle 301, upper hinge distribution circle radius 302, lower hinge distribution circle radius 303, lower hinge distribution angle 304, actuating branch length 305 and actuating branch height 306;

[0031] The upper hinge distribution angle 301 is the angle between the vector from the origin to the end point of the actuating branch and the X axis in the body coordinate system 307. ;

[0032] The radius of the upper hinge distribution circle 302 is the distance from the origin to the end point of the actuating branch in the body coordinate system 307. ;

[0033] The radius of the lower hinge point distribution circle 303 is the distance from the origin to the starting point of the actuating branch chain in the geodetic coordinate system 308. ;

[0034] The lower hinge distribution angle 304 is the angle between the vector from the origin to the starting point of the actuating branch and the X axis in the geodetic coordinate system 308. ;

[0035] The actuation branch chain length 305 is the distance between the actuation branch chain end execution point and the actuation branch chain starting point. ;

[0036] The height 306 of the actuating branch chain is the vertical distance between the end execution point of the actuating branch chain and the starting point of the actuating branch chain. ;

[0037] Preferably, the origin of the geodetic coordinate system 308 is the point on the bottom surface where the sum of the distances from the starting points of the six actuating branches is the smallest. The Z-axis direction is the normal vector of the bottom surface. The X-axis direction can be determined according to engineering requirements, and the Y-axis direction is determined by the Cartesian right-hand rule. The origin of the body coordinate system 307 is the intersection of the Z-axis of the geodetic coordinate system 308 and the upper surface. The directions of the remaining axes are preferably consistent with the geodetic coordinate system 308.

[0038] The geometric parameters of the structure to be detected include: the maximum radius of the structure to be detected , height of the structure to be tested ;

[0039] In some embodiments, as Figure 4The figure shows a simplified geometric model of an interference detection case. In this case, the structure to be detected is six actuating branches 202 and an air spring. The actuating branches 202 are composed of actuators 2021 and actuating transmission rods 2023. The structure to be detected is regarded as a cylinder. The configuration position is determined based on the axis vector and starting point information of each structure to be detected. Then, according to the geometric parameters: the maximum radius of the structure to be detected , height of the structure to be tested , calculate and get the minimum spacing and position between the structures to be detected, such as Figure 4 Shown in the black dotted box.

[0040] Further, combined Figure 2 and Figure 3 The configuration and geometric parameters in can completely and uniquely represent the vector and starting point information of the six actuators 2021 and the actuation transmission structure, and the steps include:

[0041] Based on the geodetic coordinate system 308, the upper hinge point distribution angle 301 and upper hinge distribution circle radius 302 solves the coordinates of the execution point of the actuation branch chain 202 ; According to the distribution angle of the lower hinge point 304 and lower hinge distribution circle radius 303 Solve the coordinates of the starting point 309 of the actuating branch chain 202 , ;

[0042] According to the execution point of the actuation branch chain 202 and the coordinates of the starting point 309 of the actuating branch chain 202 The median axis vector 310 of the actuating branch chain 202 can be obtained and is expressed as , ;

[0043] The height of the actuator 2021 is , the height of the actuating transmission structure is , then the starting point of the actuator 2021 can be deduced ,vector ; Starting point of actuating transmission rod 2023 ,vector .

[0044] The interference information of the structure to be inspected must be selected in combination with the actual installation space required, including: wrench operation space, structural processing error and cable space;

[0045] like Figure 5As shown in the figure, the structure to be detected is regarded as a cylinder, and the distance between the structures to be detected can be simplified into the following three cases, including: the distance between cylindrical surfaces in space, the distance between circular surfaces in space and cylindrical surfaces, and the distance between circular surfaces in space;

[0046] Furthermore, the minimum spacing between the spatial cylindrical surfaces, the spatial circular surfaces and the cylindrical surfaces, and the spatial circular surfaces and the circular surfaces can be constructed by constructing parametric equations based on their starting points, vectors, and structural information, and their distance formulas can be solved by the parametric equations. Finally, the minimum spacing value can be determined by algorithms such as the conjugate gradient method, the Lagrange multiplier method, and the interior point method, or the minimum distance value can be obtained by a numerical method.

[0047] The calculation basis of the parametric equation of a point on the space circular surface is:

[0048] ;

[0049] Where, , is the variable of the equation is a point on the circular surface of space, is the center of the circular surface in space, is the radius of the circular surface in space;

[0050] The calculation basis of the parametric equation of a point on a spatial cylindrical surface is:

[0051] ;

[0052] Where, and is the variable of the equation, is a point on the cylindrical surface in space, is the unit vector in the direction of the center axis of the space cylinder, is the height of the cylindrical surface in space;

[0053] Distance formula The calculation formula is:

[0054] ;

[0055] Where, and are the parameter equations of the structure to be tested, , You can take a point on the cylindrical surface of space or a point on the circular surface of space, and then use the conjugate gradient method, Lagrange multiplier method and interior point method to numerically calculate the minimum spacing value in each case. , or .

[0056] The preset interference detection step includes:

[0057] Calculate the distance between the central axes of two cylinders whose structures are to be simplified If the two endpoints of the line segment representing the distance are inside the two central axis segments, then the shortest distance between the two structures to be detected is ,in is the radius of the cylinder being measured, and the distance The calculation basis is:

[0058] when hour:

[0059] ;

[0060] when hour:

[0061] ;

[0062] In the formula is the medial axis vector, Any point on the central axis can be Coincidence refers to the coordinates of the execution point of the actuating branch chain.

[0063] If the endpoint of the shortest distance line segment between the central axis segments of the structure to be detected is not on the central axis, it is necessary to calculate the distance between the two cylindrical surfaces of the structure to be detected based on the parametric equations of the spatial straight line and the circular surface. ; Calculate the distance between the two cylindrical surfaces of the structure to be detected and the two circular surfaces of the other structure to be detected , respectively calculate the distance between the two circular surfaces of the two structures to be detected and the two circular surfaces of the other structure to be detected , at this time the shortest distance between the two structures to be detected ;

[0064] In some embodiments, when the number of structures to be detected is n, the number of operations required to use the preset interference detection step is The range is ,This step can greatly reduce the number of operations and improve the ,efficiency of interference detection.

[0065] Preferably, to improve detection accuracy, the structure to be detected can be subdivided and stacked. For example, the actuation transmission structure can be composed of an actuation transmission rod 2023 arranged on two actuation hinges 2022. The more stacked the structure, the higher the detection accuracy, but at the same time, the longer the computing time and the more resources required.

[0066] The interference information of the structure to be detected will be used as a judgment threshold. When the shortest distance is less than the threshold, it is judged that the structure interferes. Otherwise, the structure meets the requirements.

[0067] In some embodiments, in two optimization models that both aim to minimize the envelope of the generalized Stewart platform, one model uses a traditional spatial distance detection method, and the other uses the spatial interference detection method of the present invention. The traditional spatial distance detection method simplifies the distance between cylinders into the distance between two straight lines in space. The calculation result is relatively conservative and has a large gap with the actual situation. The spatial distance detection method of the present invention is more comprehensive and takes various situations into consideration. Figure 4 and Figure 6 As shown, the model using the method of the present invention can achieve more precise interference detection of the structure to be detected. In the final optimized platform configuration result, at the minimum spacing, the starting point and direction unit vectors of the two structures to be detected are:

[0068] , ;

[0069] , ;

[0070] The maximum radius of the structure to be detected is , the height is , because the design uses M4 hexagon socket bolts for structural installation, sufficient space is reserved according to the size of the corresponding L-shaped wrench, and the interference judgment threshold Based on the parametric equations of the straight line and the circular surface in space, the shortest distance between the two structures to be detected is ; Based on the traditional theoretical distance detection method, the shortest distance between the two structures to be detected is ;

[0071] From the above formula, we can get If the traditional theoretical distance detection method is used as the basis for interference detection, this configuration will be judged as interference. However, if Figure 4 As shown, no interference occurs in this case. The method of the present invention can significantly improve accuracy without significantly extending the calculation time, significantly raising the upper limit of the results of the optimization model mentioned above, and enabling the design of a more compact six-degree-of-freedom vibration simulation system based on a generalized Stewart platform.

[0072] It should be understood that the above-described specific embodiments of the present invention are merely illustrative or illustrative of the principles of the present invention and do not constitute limitations of the present invention. Therefore, any modifications, equivalent substitutions, improvements, etc. made without departing from the spirit and scope of the present invention are intended to be included within the scope of protection of the present invention. In addition, the appended claims are intended to cover all variations and modifications that fall within the scope and metes and bounds of the appended claims, or equivalents thereof.

Claims

1. A six-degree-of-freedom vibration simulation system interference detection method based on a generalized Stewart platform, characterized in that: include: determining a structure to be detected, wherein the structure to be detected includes an actuating branch chain; The actuating branch chain of the structure to be detected is regarded as a cylinder, and the configuration parameters, geometric parameters and interference information of the structure to be detected are obtained; the configuration parameters of the structure to be detected describe the central axis vector and starting point information of the structure to be detected; the geometric parameters include: the maximum radius and height of the structure to be detected; the interference information is reasonably set according to the actual installation space required; The structure to be inspected is inspected according to preset rules and an inspection result is obtained. The preset rules include the distance between cylinders.

2. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 1, characterized in that: The structure to be detected also includes: an air spring, an auxiliary support or a hanging ring; the actuating branch chain includes an actuator and an actuating transmission structure; the actuating transmission structure includes an actuating hinge and an actuating transmission rod; the actuating transmission structure is arranged above the actuator, and the actuating transmission structure is concentrically assembled along the central axis of the actuator.

3. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 2, characterized in that: The six-degree-of-freedom vibration simulation system of the generalized Stewart platform includes: a static platform, an actuating branch chain and a dynamic platform. The static platform and the dynamic platform are parallel to each other, and the actuating branch chain is located between the static platform and the dynamic platform.

4. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 1, characterized in that: The medial axis vector and starting point information described by the configuration parameters of the structure to be tested are expressed in the same coordinate system. The configuration parameters include: upper hinge distribution angle, upper hinge distribution circle radius, lower hinge distribution circle radius, lower hinge distribution angle, actuation branch length, and actuation branch height. The upper hinge distribution angle is the angle between the vector from the origin to the end point of the actuating branch and the X axis in the body coordinate system. ; The radius of the upper hinge distribution circle is the distance from the origin to the end point of the actuating branch in the body coordinate system. ; The radius of the lower hinge point distribution circle is the distance from the origin to the starting point of the actuating branch chain in the geodetic coordinate system. ; The lower hinge distribution angle is the angle between the vector from the origin to the starting point of the actuating branch and the X axis in the geodetic coordinate system. ; The length of the actuating branch chain is the distance between the end execution point of the actuating branch chain and the starting point of the actuating branch chain. ; The height of the actuating branch chain is the vertical distance between the end execution point of the actuating branch chain and the starting point of the actuating branch chain. .

5. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 4, characterized in that: The geometric parameters include: the maximum radius of the structure to be detected , height of the structure to be tested .

6. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 5, characterized in that: The vector and starting point information of the actuator and actuation transmission structure are expressed through configuration parameters and geometric parameters, including: Based on the geodetic coordinate system, the upper hinge point distribution angle and the radius of the upper hinge distribution circle Solve the coordinates of the execution point of the actuation branch chain ; According to the distribution angle of the lower hinge point and the radius of the lower hinge point distribution circle Solve the coordinates of the starting point of the actuating branch chain , ; According to the execution point of the actuation branch chain and the coordinates of the starting point of the actuating branch chain The medial axis vector of the actuating branch chain can be obtained and recorded as , ; Actuator height is , the height of the actuating transmission structure is , then the actuator starting point can be deduced ,vector ; Starting point of the actuating transmission rod ,vector .

7. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 1, characterized in that: The interference information is combined with the actual installation space required, including wrench operation space, structural processing error and cable space, to make a reasonable selection.

8. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 6, characterized in that: The structures to be detected are regarded as cylinders, and the distances between the structures to be detected can be summarized into the following three cases: the distance between cylindrical surfaces in space, the distance between circular surfaces in space and cylindrical surfaces, and the distance between circular surfaces in space.

9. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 8, characterized in that: The structure to be tested is tested according to the preset rules and steps and the test results are obtained, including: Calculate the distance between the central axes of two cylinders whose structures are to be simplified If the two endpoints of the line segment representing the distance are inside the two central axis segments, then the shortest distance between the two structures to be detected is ,in are the radius of the two structures to be detected, and the distance The calculation basis is: when hour: ； when hour: ； In the formula is the medial axis vector, Any point on the central axis can be Coincidence refers to the coordinates of the execution point of the actuating branch chain; If the endpoint of the shortest distance line segment between the central axis segments of the structure to be detected is not on the central axis, it is necessary to calculate the distance between the two cylindrical surfaces of the structure to be detected based on the parametric equations of the spatial straight line and the circular surface. , respectively calculate the distance between the two cylindrical surfaces of the structure to be detected and the two circular surfaces of the other structure to be detected , calculate the distance between the two circular surfaces of the two cylinders and the two circular surfaces of another cylinder respectively , at this time the shortest distance between the two structures to be detected ; The interference information of the structure to be detected will be used as a judgment threshold. When the shortest distance is less than the threshold, it is judged that the structure interferes. Otherwise, the structure meets the requirements.

10. The interference detection method for a six-degree-of-freedom vibration simulation system based on a generalized Stewart platform according to claim 9, characterized in that: Calculate the distance between the two cylindrical surfaces of the structure to be detected based on the parametric equations of the cylindrical surface and the circular surface in space , respectively calculate the distance between the two cylindrical surfaces of the structure to be detected and the two circular surfaces of the other structure to be detected , respectively calculate the distance between the two circular surfaces of the two structures to be detected and the two circular surfaces of the other structure to be detected , the specific calculation method is: The calculation basis of the parametric equation of a point on the space circular surface is: ； Where, and is the variable of the equation, is a point on the circular surface of space, is the center of the circular surface in space, is the radius of the circular surface in space; The calculation basis of the parametric equation of a point on a spatial cylindrical surface is: ； Where, and is the variable of the equation, is a point on the center axis of the cylindrical surface in space, is the unit vector in the direction of the center axis of the space cylinder, is the height of the cylindrical surface in space; Distance formula The calculation basis is: ； Where, and are the parameter equations of the structure to be tested, , You can take a point on the cylindrical surface or a point on the circular surface, and then find the minimum spacing value in each case. , or .

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