A method for analyzing precision of a space large truss mechanism based on equivalent parallel mechanism

Abstract

The application discloses a kind of space large truss mechanism precision analysis method based on equivalent parallel mechanism, it is related to space large truss mechanism precision analysis technical field, comprising the following steps: space large truss mechanism is disassembled into several equivalent parallel mechanisms, establishes single equivalent parallel mechanism model and analyzes its limit error;The relationship between axial total length change and elastic deformation is described by formula, the pose of moving platform is represented;Based on force balance optimization solution, calculate equivalent stiffness coefficient, solve pose change;According to the overall end pose of unit precision cumulative error.This application uses the above-mentioned space large truss mechanism precision analysis method based on equivalent parallel mechanism, uses modular design, each module unit is composed of specific longitudinal beam, transverse frame and cable, when modeling, transverse frame is regarded as base and moving platform respectively, longitudinal beam is assumed to be only axial elastic deformation, simplify model, realize the accurate analysis of the overall precision of space large truss mechanism.

Description

Technical Field

[0001] This invention relates to the field of precision analysis technology for large-scale space truss mechanisms, and in particular to a precision analysis method for large-scale space truss mechanisms based on equivalent parallel mechanisms. Background Technology

[0002] In the field of accuracy analysis methods for large spatial truss mechanisms based on equivalent parallel mechanisms, existing technologies have made certain progress in both theoretical research and practical applications. Theoretically, kinematics, statics, and stiffness analysis have been explored in depth, with kinematic models established using vector methods and matrix methods, and methods for force analysis and stiffness assessment clarified. In practice, these technologies have been applied in areas such as deployable antenna support trusses in aerospace and aircraft model positioning in wind tunnel tests. However, existing technologies still have shortcomings. On the one hand, models are often oversimplified, frequently assuming rigid bodies and zero joint clearances, neglecting complex working conditions and environmental factors. On the other hand, factors affecting accuracy are not fully considered, ignoring the impact of multi-factor coupling and dynamic characteristics on accuracy. Furthermore, optimization methods have limitations, with a single optimization objective, and optimization algorithms are inefficient and inaccurate when dealing with complex systems. Summary of the Invention

[0003] The purpose of this invention is to provide a method for accuracy analysis of large spatial truss mechanisms based on equivalent parallel mechanisms, which solves the problems of numerous influencing factors, complex evolution mechanisms, and difficulty in simplifying models for the accuracy performance of large spatial truss mechanisms.

[0004] To achieve the above objectives, this invention provides a method for accuracy analysis of large spatial truss mechanisms based on equivalent parallel mechanisms, comprising the following steps:

[0005] Step S1: Decompose the large spatial truss mechanism into several equivalent parallel mechanisms, establish a model of a single equivalent parallel mechanism and analyze its limit error;

[0006] Step S2: Accurately quantify the deformation relationship, describe the relationship between the change in total axial length and elastic deformation through formulas, and represent the pose of the moving platform by combining the sliding joint and Lie group elements;

[0007] Step S3: Based on force balance optimization, calculate the equivalent stiffness coefficient according to relevant laws, and solve the pose change with force balance as the objective.

[0008] Step S4: Perform serial error accumulation calculation, and obtain the overall end pose by accumulating the error based on the unit accuracy.

[0009] Preferably, the equivalent parallel mechanism in step S1 includes four longitudinal beams, two transverse frames, and inclined cables. The two transverse frames are respectively set at the upper and lower ends of the four longitudinal beams. The two ends of the inclined cables are respectively connected to the top of one longitudinal beam and the bottom of the adjacent longitudinal beam. There are eight inclined cables.

[0010] Preferably, step S1 includes:

[0011] Each equivalent parallel mechanism's transverse frame is treated as a rigid body. Furthermore, in the established equivalent parallel mechanism model, the two transverse frames are considered as a base and a moving platform, respectively. The four vertices of the base are A... n B n C n and D n The four vertices of the moving platform are A n+1 B n+1 C n+1 and D n+1 ;

[0012] Assuming that the longitudinal beam undergoes only axial elastic deformation under the tension of the stay cables, the relationship between the change in total axial length and elastic deformation under the influence of hinge clearance, member tolerance, and assembly error is calculated using the following formulas (1) and (2):

[0013] τ i =0.5(δL) i -r)(tanh(α2f(δL i )(δL i -r))+1) (1)

[0014] Where, τ i For elastic deformation, r is the total hinge clearance, δL i The change in length of the mechanism link is represented by tanh(), which is the hyperbolic tangent function, and α2 is the weighting coefficient.

[0015] f() is a sign function, represented as:

[0016] f(δL i )=tanh(α1δL i (2)

[0017] Where α1 is the weighting coefficient.

[0018] Preferably, step S2 includes:

[0019] The change in the length of the longitudinal beam is equivalently represented by the translating joint. Due to the change in the length of the longitudinal beam, the body coordinate system of the moving platform will change to a new pose. The pose of the moving platform in the global coordinate system is represented by the Lie group SE(3) elements g0 and g1, respectively. Among them, the Lie group element g eIt is a 4x4 matrix, represented as:

[0020]

[0021] Among them, R e T represents spatial rotation. e Indicates spatial translation;

[0022] Given the initial and final positions of the moving platform, the changes in the lengths of the four branches of the equivalent parallel mechanism are expressed as follows:

[0023] ΔL i =||g e B i -g0B i =R e B i -R0B i +T1-T0||, i=1,2,3,4 (4)

[0024] Among them, B i Let ||·|| represent the coordinates of the endpoints of the moving platform in the global coordinate system, ||·|| represent the L2 norm, R0 represent the spatial rotation matrix of the initial position in the global coordinate system, and T represent the coordinates of the endpoints of the moving platform in the global coordinate system. e T0 represents the spatial translation vector in the global coordinate system, and T0 represents the spatial translation vector of the initial position in the global coordinate system.

[0025] Preferably, step S3 includes:

[0026] Based on the correspondence between elastic deformation and deformation force in Hertz contact and Hooke's law, the equivalent stiffness coefficient k is calculated, representing the stiffness of the longitudinal beam along the axial direction. Thus, the relationship between longitudinal deformation and force in this truss mechanism is obtained as follows:

[0027] F=kτ (5)

[0028] Where F represents the force acting on the truss mechanism;

[0029] The pose change of the equivalent parallel mechanism moving platform is associated with the force on the longitudinal beam through equations (1)-(5), where the force on the longitudinal beam is obtained through force balance constraint calculation.

[0030] Preferably, after establishing a solution model for a unit in step S3, an optimization method is used with pose g. e The equilibrium between the elastic force of the lower mechanism's longitudinal beam and the preload of the stay cables is used as the optimization objective to obtain the positional changes of the equivalent parallel mechanism's moving platform.

[0031] Preferably, step S4 obtains the end pose of the entire large truss mechanism through error accumulation calculation of the series mechanism, expressed as:

[0032]

[0033] Among them, g ei R represents the pose error of the R0th unit, and N represents the number of units constituting the large truss mechanism.

[0034] Therefore, the present invention employs the above-mentioned accuracy analysis method for large spatial truss mechanisms based on equivalent parallel mechanisms, which has the following beneficial effects:

[0035] (1) In terms of product structure, this method adopts modular design. Each module unit consists of specific longitudinal beams, transverse frames and cable stays. When modeling, the transverse frame is equivalent to a rigid body and is regarded as the base and dynamic platform respectively. It is assumed that the longitudinal beam only undergoes axial elastic deformation, which simplifies the model.

[0036] (2) In the process of working, this method first establishes a single unit accuracy analysis model and analyzes the limit error to lay the foundation for the overall analysis; then, the overall accuracy analysis is achieved by accumulating multiple modules, which is consistent with the actual structure of the mechanism; key parameters are calculated using specific formulas and correlations are established to quantify the influencing factors; finally, the dynamic platform pose change is solved with force balance as the optimization goal, and the end pose of the entire truss mechanism is obtained by accumulating the error of the series mechanism, thereby realizing the accurate analysis of the overall accuracy of the large spatial truss mechanism.

[0037] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0038] Figure 1 This is a structural schematic diagram of an embodiment of a spatial large truss mechanism accuracy analysis method based on an equivalent parallel mechanism according to the present invention, wherein (a) is a structural schematic diagram of the equivalent parallel mechanism, and (b) is a coordinate system definition diagram;

[0039] Reference numerals: 1. Longitudinal beam; 2. Transverse frame; 3. Stay cable. Detailed Implementation

[0040] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0041] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0042] Example

[0043] Please see Figure 1 This invention provides a method for accuracy analysis of large spatial truss mechanisms based on equivalent parallel mechanisms, comprising the following steps:

[0044] Step S1: Decompose the large spatial truss mechanism into several equivalent parallel mechanisms. Each equivalent parallel mechanism includes four longitudinal beams 1, two transverse frames 2, and stay cables 3. The two transverse frames 2 are respectively located at the upper and lower ends of the four longitudinal beams 1. The two ends of the stay cables 3 are respectively connected to the top of one longitudinal beam 1 and the bottom of an adjacent longitudinal beam 1. There are eight stay cables 3. Establish a model of a single equivalent parallel mechanism and analyze its limit error.

[0045] Step S2: Accurately quantify the deformation relationship, describe the relationship between the change in total axial length and elastic deformation through formulas, and represent the pose of the moving platform by combining the sliding joint and Lie group elements;

[0046] Step S3: Based on force balance optimization, calculate the equivalent stiffness coefficient according to relevant laws, and solve the pose change with force balance as the objective.

[0047] Step S4: Perform serial error accumulation calculation, and obtain the overall end pose by accumulating the error based on the unit accuracy.

[0048] The specific steps of the above method are as follows:

[0049] like Figure 1 As shown in (a), the transverse frame 2 of each equivalent parallel mechanism is equivalent to a rigid body. In the established equivalent parallel mechanism model, the two transverse frames 2 are respectively regarded as a base and a moving platform, where the four vertices of the base are A... n B n C n and D nThe four vertices of the moving platform are A n+1 B n+1 C n+1 and D n+1 .

[0050] In this embodiment, it is assumed that the longitudinal beam 1 only undergoes axial elastic deformation under the tension of the stay cable 3. The relationship between the change in the total axial length under the influence of hinge clearance, member tolerance, and assembly error and the elastic deformation is calculated by the following formulas (1) and (2):

[0051] τ i =0.5(δL) i -r)(tanh(α2f(δL i )(δL i -r))+1) (1)

[0052] Where, τ i For elastic deformation, r is the total hinge clearance, δL i The change in length of the mechanism link is represented by tanh(), which is the hyperbolic tangent function, and α2 is the weighting coefficient.

[0053] f() is a sign function, represented as:

[0054] f(δL i )=tanh(α1δL i (2)

[0055] Where α1 is the weighting coefficient.

[0056] In this embodiment, as Figure 1 As shown in (b), the change in the length of the longitudinal beam 1 is equivalently represented by the prismatic joint. Due to the change in the length of the longitudinal beam 1, the body coordinate system (O1-x1y1z1) of the moving platform will change to a new pose (Oe-xeyeze). The pose of the moving platform in the global coordinate system is represented by the Lie group SE(3) elements g0 and g1, respectively. Among them, the Lie group element g e It is a 4x4 matrix, represented as:

[0057]

[0058] Among them, R e T represents spatial rotation. e Indicates spatial translation;

[0059] Given the initial and final positions of the moving platform, the changes in the lengths of the four branches of the equivalent parallel mechanism are expressed as follows:

[0060] ΔL i =||g e B i -g0B i =Re B i -R0B i +T1-T0||, i=1,2,3,4 (4)

[0061] Among them, B i Let ||·|| represent the coordinates of the endpoints of the moving platform in the global coordinate system, ||·|| represent the L2 norm, R0 represent the spatial rotation matrix of the initial position in the global coordinate system, and T represent the coordinates of the endpoints of the moving platform in the global coordinate system. e T0 represents the spatial translation vector in the global coordinate system, and T0 represents the spatial translation vector of the initial position in the global coordinate system.

[0062] In this embodiment, based on the correspondence between elastic deformation and deformation force in Hertz contact and Hooke's law, the equivalent stiffness coefficient k is calculated to represent the stiffness of the longitudinal beam 1 along the axial direction. Therefore, the longitudinal deformation and force relationship of the truss mechanism are obtained as follows:

[0063] F=kτ (5)

[0064] Where F represents the force acting on the truss mechanism;

[0065] The pose change of the equivalent parallel mechanism moving platform is correlated with the force on the longitudinal beam 1 through equations (1)-(5), where the force on the longitudinal beam 1 is calculated through force balance constraints. This allows the establishment of a solution model for the element, and the use of optimization methods to determine the pose g. e The equilibrium between the elastic force of the lower mechanism longitudinal beam 1 and the preload of the stay cable 3 is used as the optimization objective to obtain the positional changes of the equivalent parallel mechanism moving platform.

[0066] Finally, the end pose of the entire large truss mechanism is obtained through error accumulation calculation of the series mechanism, and is expressed as:

[0067]

[0068] Among them, g ei R represents the pose error of the R0th unit, and N represents the number of units constituting the large truss mechanism.

[0069] Therefore, the present invention adopts the above-mentioned method for accuracy analysis of large spatial truss mechanisms based on equivalent parallel mechanisms. It adopts a modular design, with each module unit consisting of specific longitudinal beams, transverse frames and cable stays. When modeling, the transverse frames are equivalent to rigid bodies and regarded as the base and moving platform respectively. It is assumed that the longitudinal beams only undergo axial elastic deformation, which simplifies the model and enables accurate analysis of the overall accuracy of large spatial truss mechanisms.

[0070] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for accuracy analysis of large spatial truss mechanisms based on equivalent parallel mechanisms, characterized in that, Includes the following steps: Step S1: Decompose the large spatial truss mechanism into several equivalent parallel mechanisms, establish a model of a single equivalent parallel mechanism and analyze its limit error; Step S2: Accurately quantify the deformation relationship, describe the relationship between the change in total axial length and elastic deformation through formulas, and represent the pose of the moving platform by combining the sliding joint and Lie group elements; Step S3: Based on force balance optimization, calculate the equivalent stiffness coefficient according to relevant laws, and solve the pose change with force balance as the objective. Step S4: Perform serial error accumulation calculation, and obtain the overall end pose by accumulating the error based on the unit accuracy; The equivalent parallel mechanism in step S1 includes four longitudinal beams, two transverse frames, and cable stays. The two transverse frames are respectively set at the upper and lower ends of the four longitudinal beams. The two ends of the cable stays are respectively connected to the top of one longitudinal beam and the bottom of the adjacent longitudinal beam. There are eight cable stays.

2. The accuracy analysis method for large spatial truss mechanisms based on equivalent parallel mechanisms according to claim 1, characterized in that, Step S1 includes: Each equivalent parallel mechanism's transverse frame is treated as a rigid body. Furthermore, in the established equivalent parallel mechanism model, the two transverse frames are considered as a base and a moving platform, respectively. The four vertices of the base are A... n B n C n and D n The four vertices of the moving platform are A n+1 B n+1 C n+1 and D n+1 ; Assuming that the longitudinal beam undergoes only axial elastic deformation under the tension of the stay cables, the relationship between the change in total axial length and elastic deformation under the influence of hinge clearance, member tolerance, and assembly error is calculated using the following formulas (1) and (2): （1） in, For elastic deformation, This represents the total hinge clearance. For changes in the length of the mechanism links, It is the hyperbolic tangent function. These are the weighting coefficients; Functions with positive and negative signs are represented as: （2） in, These are the weighting coefficients.

3. The accuracy analysis method for large spatial truss mechanisms based on equivalent parallel mechanisms according to claim 2, characterized in that, Step S2 includes: The change in the length of the longitudinal beam is equivalently represented by the translation joint. Due to the change in the length of the longitudinal beam, the body coordinate system of the moving platform will change to a new pose. The Lie group SE(3) elements are used respectively. and The pose of the moving platform in the global coordinate system is represented by the Lie group elements. It is a 4x4 matrix, represented as: （3） in, Indicates spatial rotation, Indicates spatial translation; Given the initial and final positions of the moving platform, the changes in the lengths of the four branches of the equivalent parallel mechanism are expressed as follows: （4） in, This represents the coordinates of the endpoint of the moving platform in the global coordinate system, and ||·|| represents the L2 norm. This represents the spatial rotation matrix of the initial position in the global coordinate system. This represents the spatial translation vector in the global coordinate system. The spatial translation vector representing the initial position in the global coordinate system.

4. The accuracy analysis method for large spatial truss mechanisms based on equivalent parallel mechanisms according to claim 3, characterized in that, Step S3 includes: Based on the correspondence between elastic deformation and deformation force in Hertz contact and Hooke's law, the equivalent stiffness coefficient is calculated. , representing the stiffness of the longitudinal beam along the axial direction, yields the following relationship between the longitudinal deformation and force of the truss mechanism: （5） in, Indicates the forces acting on the truss mechanism; The pose change of the equivalent parallel mechanism moving platform is associated with the force on the longitudinal beam through equations (1)-(5), where the force on the longitudinal beam is obtained through force balance constraint calculation.

5. The accuracy analysis method for a large spatial truss mechanism based on an equivalent parallel mechanism according to claim 4, characterized in that: After establishing a solution model for a single element in step S3, an optimization method is used to determine the pose. The equilibrium between the elastic force of the lower mechanism's longitudinal beam and the preload of the stay cables is used as the optimization objective to obtain the positional changes of the equivalent parallel mechanism's moving platform.

6. The accuracy analysis method for a large spatial truss mechanism based on an equivalent parallel mechanism according to claim 5, characterized in that, Step S4 obtains the end pose of the entire large truss mechanism through error accumulation calculation of the series mechanism, which is expressed as: （6） in, Indicates the first The pose error of each unit This indicates the number of units that make up a large truss structure.

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