A hobeman ring and its design method and application

Abstract

The application relates to the field of mechanical structure design, in particular to a Hobelman ring and a design method and application thereof. The design method comprises the following steps: S1, providing a first angled rod and a second angled rod, and the middle part and both ends of the first angled rod and the second angled rod are provided with pivot holes; the middle part pivot holes of the first angled rod and the second angled rod are hingedly connected to form a module capable of rotating around the middle part hinged point; the two adjacent end pivot holes of two same modules are correspondingly connected and hingedly connected to form a folding unit; meanwhile, the rod angles of the first angled rod and the second angled rod are obtained; S2, the number of the folding units required for forming the Hobelman ring is calculated according to the rod angles, and whether the Hobelman ring can be constructed is judged. The application solves the technical problem that the existing idealized model is disconnected with the physical reality.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical structure design, in particular to a Hoberman ring and its design method and application. BACKGROUND

[0002] In the fields of aerospace, large-scale construction, and robotics, the demand for deployable structures is growing. Deployable structures can transform between a compact, retracted state and a fully expanded, working state, thereby greatly improving space utilization, transportation convenience, and functional diversity.

[0003] Chuck Hoberman invented the Hoberman sphere in 1990. This structure is composed of hinged, tilting strut units, which allows all units to be synchronized radially scaled by a single degree of freedom. In addition, the sphere maintains its overall geometry throughout the entire expansion and retraction process.

[0004] In recent years, the Hoberman sphere principle has been applied to the design of deployable antennas and solar cell arrays in the aerospace field. In the field of robotics, it has driven the development of new robotic systems, including snake swallowing robots, and has applications in human-computer interaction and adaptive infrastructure.

[0005] Despite the extensive research on Hoberman rings, existing design methods for Hoberman rings still have deficiencies in design theory. Existing Hoberman ring models are generally idealized point-line models, such as (Bai et al. Journal of Mechanical Engineering Science, 227(12): 2795-2809 (2013)), which ignore the manufacturing constraints of the angled bar (such as the angled bar width, pivot hole diameter) and simplify it to a pure geometric structure composed of two line segments without width. Although this point-line model can simplify the structure and derive the geometric relationship of the structure during expansion and contraction, it is convenient for mathematical calculation and improves the efficiency of theoretical analysis.

[0006] As shown in Figure 1 , the idealization of the above technology leads to differences between theoretical design (as shown in Figure 1 (a)) and actual manufacturing (as shown in Figure 1 (b)). In actual engineering, the following shortcomings exist:

[0007] 1. Low prediction accuracy: This difference can lead to inaccurate performance prediction in engineering practice.

[0008] 2. Risk of structural interference: Unexpected geometric interference may occur during the movement of the structure, or even assembly failure.

[0009] 3. High R&D costs and long cycle: Because there are differences between theoretical models and actual manufacturing, the design process relies heavily on repeated trials and corrections of physical prototypes.

[0010] 4. Unable to handle complex designs in actual manufacturing: This idealized model cannot handle complex kinematic problems dominated by physical constraints such as the width of the angled rod. For example, designers cannot determine the final folding and unfolding geometry of the structure actually manufactured solely through theoretical models, nor can they optimize or explore more complex combinations of design parameters solely through point-line theoretical models. Summary of the Invention

[0011] Therefore, the technical problem to be solved by the present invention is to overcome the problems in the prior art, thereby providing a Hobman ring and its design method and application.

[0012] Firstly, a design method for a Hobmann ring is provided, including the following steps:

[0013] S1. Provide a first angled rod and a second angled rod, with pivot holes provided in the middle and at both ends of the first angled rod and the second angled rod; hinge the pivot holes in the middle of the first angled rod and the second angled rod to form a module that can rotate about the middle hinge point;

[0014] By connecting the pivot holes at adjacent ends of two identical modules in pairs and pivoting them together, a folding unit is formed.

[0015] At the same time, obtain the length of the first angled rod. Short rod length pole angle and bar width And the length of the second angled rod Short rod length pole angle and bar width ,in ≥ , ≤ , < / 2;

[0016] S2, based on the rod angle and pole angle Calculate the number of folding units required to construct the Hobmann ring. And determine whether it can be constructed into a Hobermann ring; if for integer, the Hobbing ring can be assembled; otherwise, the Hobbing ring cannot be assembled.

[0017] In one embodiment of the present application, the number of folding units required to constitute a Hobbing ring is calculated according to the rod angle and the rod angle . The formula is:

[0018] ;

[0019] ;

[0020] wherein, is the number of folding units; is the included angle formed by the corresponding connecting line of the two end pivot holes of the first angled rod and the second angled rod in the module; is the rod angle of the first angled rod; is the rod angle of the second angled rod.

[0021] In one embodiment of the present application, the step S3 of calculating the determination parameter of the Hobbing ring in the folded state is further included, and the relative size of the determination parameter and the rod width is judged, so as to judge the folding state of the Hobbing ring; if , the Hobbing ring is in the first folded state; if , the Hobbing ring is in the second folded state; if , the first folded state and the second folded state of the Hobbing ring coexist.

[0022] In one embodiment of the present application, the formula of the determination parameter of the Hobbing ring in the folded state is:

[0023] ;

[0024] wherein, is the determination parameter; is the long rod length; is the short rod length; is the rod angle of the first angled rod; is the rod angle of the second angled rod; is the vertical distance from the center of the end pivot hole of the first angled rod to the outer edge of the profile of the first angled rod or the vertical distance from the center of the end pivot hole of the second angled rod to the outer edge of the profile of the second angled rod.

[0025] In one embodiment of the present application, the step S4 of calculating the circumscribed circle radius of the Hobbing ring in the first folded state or the second folded state according to the determination result of the step S3 is further included. .

[0026] In one embodiment of the present application, the formula for calculating the circumscribed circle radius of the Hobbleman ring in the first folded state or the second folded state is:

[0027] ;

[0028] ;

[0029] ;

[0030] ;

[0031] ;

[0032] wherein, R is the circumscribed circle radius of the Hobbleman ring in the first folded state or the second folded state; L is the distance from the center of the Hobbleman ring to the center of the first outermost pivot point in the first folded state; L is the distance from the center of the Hobbleman ring to the center of the second outermost pivot point in the first folded state; L is the distance from the center of the Hobbleman ring to the center of the first outermost pivot point in the second folded state; L is the distance from the center of the Hobbleman ring to the center of the second outermost pivot point in the second folded state; is the decision parameter; L is the long rod length; L is the short rod length; is the rod angle of the first angled rod; is the rod angle of the second angled rod; is the vertical distance from the center of the first angled rod end pivot hole to the outer edge of the first angled rod profile or the vertical distance from the center of the second angled rod end pivot hole to the outer edge of the second angled rod profile; L is the rod width of the first angled rod or the second angled rod.

[0033] In one embodiment of the present application, the step of: S5, calculating the circumscribed circle radius of the Hobbleman ring in the unfolded state .

[0034] In one embodiment of the present application, the formula for calculating the circumscribed circle radius of the Hobbleman ring in the unfolded state is:

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] wherein, R is the circumscribed circle radius of the Hobson ring in the unfolded state; D is the distance from the Hobson ring center to the center of the first outermost pivot point; D is the distance from the Hobson ring center to the center of the second outermost pivot point; D is the distance from the Hobson ring center to the center of the third outermost pivot point; L is the length of the long rod; L is the length of the short rod; is the rod angle of the first angled rod; is the rod angle of the second angled rod; is the vertical distance from the center of the first angled rod end pivot hole to the outer edge of the first angled rod profile or the vertical distance from the center of the second angled rod end pivot hole to the outer edge of the second angled rod profile; is the rod width of the first angled rod or the second angled rod.

[0040] In one embodiment of the present application, the step of calculating the radius expansion ratio is further included: S6, evaluating the structural performance of the designed Hobson ring by this parameter.

[0041] In one embodiment of the present application, the formula for calculating the radius expansion ratio is:

[0042] ;

[0043] wherein, R is the radius expansion ratio of the Hobson ring; R is the circumscribed circle radius of the Hobson ring in the first folded state or the second folded state; R is the circumscribed circle radius of the Hobson ring in the unfolded state.

[0044] In a second aspect, a Hobson ring is provided, which is designed by the design method of the Hobson ring as described above and is arranged to be freely foldable and unfoldable.

[0045] In a third aspect, the application of the Hobson ring as described above in aerospace, solar energy, portable devices, building structures or robots is provided.

[0046] The above technical solutions of the present application have the following beneficial effects compared with the prior art:

[0047] The Hobson ring design method improves the accuracy and reliability of the design; by introducing the actual manufacturing constraints such as rod width, pivot point diameter, etc., the motion limits and geometric interference of the structure can be accurately predicted in the initial stage of design, avoiding the performance deviation between the traditional idealized model and the actual product, and reducing the trial and error cost of the physical prototype.

[0048] The Hobson ring design method improves the assembly efficiency; through modular design, each component can be quickly assembled, improving the research and development efficiency and the first assembly success rate.

[0049] The Hobson ring design method enhances the generality of the design; the configuration of the angled rod is expanded from symmetric to asymmetric, greatly widening the design space.

[0050] The Hobson ring design method improves the design efficiency; the present application provides a complete set of analytical formulas, so that designers do not need to rely on time-consuming dynamic simulation software or physical prototypes to quickly evaluate the performance of different design schemes through analytical formulas, and the design efficiency is improved by orders of magnitude. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to make the content of the present application more easily understood, the present application will be further described in detail below according to specific embodiments of the present application and in conjunction with the accompanying drawings.

[0052] Figure 1 is a schematic diagram of the present point line model and the actual model.

[0053] Figure 2 is a schematic diagram of the basic angled rod in the present application.

[0054] Figure 3 is an exploded schematic diagram of the fastener in the present application.

[0055] Figure 4 is a structural schematic diagram of the first fastening element in the present application from the first perspective and the second perspective.

[0056] Figure 5 is a structural schematic diagram of the second fastening element in the present application from the first perspective and the second perspective.

[0057] Figure 6 is a structural schematic diagram of the first angled rod and the second angled rod in the present application and a model schematic diagram.

[0058] Figure 7 is a structural schematic diagram of the first angled rod and the second angled rod in the present application and a model schematic diagram.

[0059] Figure 8is a structure diagram and a model diagram showing that the middle and end portions of the first and second angle forming rods are pivotally connected by fasteners in the present application;

[0060] Figure 9 is an assembly diagram of the Hobelman ring assembled by a plurality of identical folding units in the present application.

[0061] Figure 10 is a diagram of the Hobelman ring assembled in the present application.

[0062] Figure 11 is a diagram and a partial enlarged diagram of the Hobelman ring in the first folding state in the present application.

[0063] Figure 12 is a diagram and a partial enlarged diagram of the Hobelman ring in the second folding state in the present application.

[0064] Figure 13 is a diagram of the Hobelman ring in the first and second folding states in the present application.

[0065] Figure 14 is a diagram and a partial enlarged diagram of the Hobelman ring in the unfolded state in the present application.

[0066] Figure 15 is a diagram of the Hobelman ring in the unfolded state in the present application.

[0067] Figure 16 is a diagram of the Hobelman ring in the first folding state and the unfolded state in the present application.

[0068] Figure 17 is a diagram of the Hobelman ring in different parameters.

[0069] Description of the drawing reference signs in the specification:

[0070] 10, base angle forming rod; 101, first angle forming rod; 102, second angle forming rod; 103, side edge; 104, circular arc;

[0071] 20, pivot hole;

[0072] 30, fastener; 301, first fastening element; 302, second fastening element. DETAILED DESCRIPTION

[0073] The present application will be further described in conjunction with the drawings and specific embodiments so that those skilled in the art can better understand the present application and implement it, but the embodiments are not limiting to the present application.

[0074] In the design of the Hobmann ring, the use of an idealized point-line model neglects actual manufacturing constraints such as member width and pivot hole diameter, leading to discrepancies between theoretical design and actual manufacturing. This discrepancy causes unexpected geometric interference during structural motion, reduces prediction accuracy, and increases the likelihood of assembly failure. Furthermore, key performance indicators, including the accuracy of kinematic behavior, assembly reliability, and design process efficiency, are adversely affected. Specifically, the theoretical model fails to accurately reflect the actual hinge point positions and spatial relationships between members.

[0075] For example, in the design of deployable satellite antennas, Hobmann rings are used to achieve compact storage and deployment capabilities. During the theoretical design phase, the point-line model predicts that the structure can deploy smoothly. However, due to the width of the rods in actual manufacturing, physical collisions occur between the rods during the movement of the folding units, preventing the structure from fully deploying or retracting. This interference phenomenon prevents the antenna from achieving its intended operating state, necessitating redesign and remanufacturing of the prototype, thus extending the development cycle and increasing the complexity of design iterations.

[0076] If the aforementioned issues are not addressed, the Hobman ring may face the risk of functional failure in practical engineering applications, affecting the overall performance and reliability of the system. Consequently, the design process will heavily rely on repeated testing and correction of physical prototypes, leading to excessive consumption of R&D resources, hindering project progress, and ultimately limiting the potential for widespread adoption of this technology in demanding fields such as aerospace.

[0077] In this regard, combined with Figures 6 to 16 This embodiment proposes a design method for a Hobman ring, including the following steps:

[0078] S1. A first angled rod 101 and a second angled rod 102 are provided, and pivot holes 20 are provided in the middle and at both ends of the first angled rod 101 and the second angled rod 102; the pivot holes 20 in the middle of the first angled rod 101 and the second angled rod 102 are hinged to form a module that can rotate about the middle hinge point, such as... Figure 7 As shown;

[0079] By pivoting the adjacent ends of two identical modules with their pivot holes 20 aligned and connected in pairs, a folding unit is formed, as shown below. Figure 8 As shown;

[0080] At the same time, such as Figure 6 As shown, the length of the long rod of the first angled rod 101 is obtained. Short rod length pole angle and bar width and the length of the second angled rod 102 Short rod length pole angle and the width of the rod wherein ≥ , ≤ , < / 2;

[0081] S2, calculating the number of folding units required to form the Hobelman ring according to the rod angle and the rod angle , and determining whether it can be formed into a Hobelman ring; if is an integer of , then it can be assembled into a Hobelman ring, as shown in Figure 9 ; otherwise, it cannot be assembled into a Hobelman ring;

[0082] S3, calculating the determination parameter of the Hobelman ring in the folded state and determining the relative size of the determination parameter and the width of the rod , and further determining the folding state of the Hobelman ring; if , then the Hobelman ring is in the first folded state, as shown in Figure 11 ; if , then the Hobelman ring is in the second folded state, as shown in Figure 12 ; if , then the first folded state and the second folded state of the Hobelman ring coexist;

[0083] S4, calculating the circumscribed circle radius of the Hobelman ring in the first folded state or the second folded state according to the determination result of step S3 ;

[0084] S5, calculating the circumscribed circle radius of the Hobelman ring in the unfolded state ;

[0085] S6, calculating the radius deployment ratio to evaluate the structural performance of the Hobelman ring designed by this parameter.

[0086] In this embodiment, the design method of the Hobelman ring is realized by providing a first angled rod 101 and a second angled rod 102. The first angled rod 101 refers to a bent rod-shaped member with a rod angle ; the second angled rod 102 refers to a bent rod-shaped member with a rod angle .

[0087] Further, the middle part and both ends of the first angled rod 101 and the second angled rod 102 are provided with a pivot hole 20, which is a positioning hole for realizing hinged connection.

[0088] Thus, the middle pivot hole in the first angled bar 101 and the second angled bar 102 is hinged by the fastener 30 to form a module that can rotate around the middle hinge point, and the center of rotation of the module is defined as the geometric center of the middle pivot hole. Specifically, in combination with Figure 3 and Figure 4 , the fastener 30 includes a first fastening element 301 and a second fastening element 302 that are threadedly connected, wherein the inner wall of the first fastening element 301 is provided with multiple threads, and the outer wall of the second fastening element 302 is provided with multiple threads. When the first fastening element 301 and the second fastening element 302 are tightened relative to each other, the threads of the first fastening element 301 and the threads of the second fastening element 302 engage to achieve threaded connection. The fastener 30 can ensure that the bar members can rotate freely and are reliably connected.

[0089] In practical applications, the long bar length , the short bar length , the bar angle , and the bar width of the first angled bar 101, and the long bar length , the short bar length , the bar angle , and the bar width of the second angled bar 102 refer to the process of determining these physical size parameters, which can be directly obtained by using measuring tools to obtain the actual values of the bar samples.

[0090] The present embodiment incorporates the bar width and other actual manufacturing parameters, avoiding the structural interference risk and prediction accuracy problems caused by the idealized point-line model in the background art that ignores physical constraints, thereby ensuring the assembly feasibility and kinematic accuracy of the Hobelman ring.

[0091] As shown in Figure 6 , it should be noted that:

[0092] The long bar length and the short bar length are the distances from the center of the middle pivot hole to the centers of the two end pivot holes, as shown in Figure 6 (b). In the present application, it is allowed that and are not equal, i.e. ≥ , to cover asymmetric angled bar configurations.

[0093] The bar included angle is the included angle between the center lines of the long bar and the short bar of the first angled bar 101, as shown in Figure 6 (b).

[0094] The bar included angle The angle between the lines connecting the centers of the long and short members of the second angled member 102, such as... Figure 6 As shown in (b).

[0095] The member width 2R is defined as the finite width of the member, such as... Figure 6 As shown in (b), < / 2. Furthermore, It is the vertical distance from the center of the pivot hole 20 at the end of the rod to the outer edge of the rod profile, i.e., half the width of the rod.

[0096] Pivot hole diameter The diameter of the pivot hole 20 opened at the middle and both ends of the angled rod is, for example... Figure 6 As shown in (b).

[0097] This design method integrates actual manufacturing parameters with geometric constraints to construct a Hobmann ring design process that takes into account the physical entity.

[0098] This embodiment further proposes a method based on the rod angle. and pole angle Calculate the number of folding units required to construct the Hobmann ring. The formula is:

[0099] ;

[0100] ;

[0101] in, The number of folding units; The included angle is formed by the lines connecting the corresponding pivot holes at both ends of the first angled rod 101 and the second angled rod 102 in the module. The angle of the first angled rod 101; The angle of the second angled rod 102.

[0102] Specifically, such as Figure 7 As shown in (b), the included angle formed by the lines connecting the corresponding pivot holes at both ends of the first angled rod 101 and the second angled rod 102 in the module is . ;like Figure 8 As shown in (b), the included angle formed by the lines connecting the corresponding pivot holes at both ends of the first angled rod 101 and the second angled rod 102 in the folding unit is . .

[0103] This embodiment further proposes a decision parameter for calculating the Hobman ring in the folded state. The formula is:

[0104] ;

[0105] wherein, is the determining parameter; is the long rod length; is the short rod length; is the rod angle of the first angled rod 101; is the rod angle of the second angled rod 102; is the vertical distance from the center of the end pivot hole of the first angled rod 101 to the outer edge of the profile of the first angled rod 101 or the vertical distance from the center of the end pivot hole of the second angled rod 102 to the outer edge of the profile of the second angled rod 102.

[0106] It is to be noted that the embodiment calculates the determining parameter and judges the relative size of the determining parameter and the rod width , so as to predict which kind of folding state the structure is in at the design stage.

[0107] The embodiment further proposes a formula for calculating the circumradius of the Hobelman ring in the first folding state (as shown in (a) of Figure 13 or the second folding state (as shown in (b) of Figure 13 ):

[0108] ;

[0109] ;

[0110] ;

[0111] ;

[0112] ;

[0113] wherein, is the circumradius of the Hobelman ring in the first folding state or the second folding state; is the distance from the center of the Hobelman ring to the center of the first outermost pivot point in the first folding state, i.e. the line segment OA in (a) of Figure 13 ; is the distance from the center of the Hobelman ring to the center of the second outermost pivot point in the first folding state, i.e. the line segment OB in (a) of Figure 13 ; is the distance from the center of the Hobelman ring to the center of the first outermost pivot point in the second folding state, i.e. the line segment OA in (b) of Figure 13 ; is the distance from the center of the Hobelman ring to the center of the second outermost pivot point in the second folding state, i.e. the line segment OB in (b) of Figure 13 ; for determining the parameter; for determining the long rod length; for determining the short rod length; for determining the rod angle of the first angled rod 101; for determining the rod angle of the second angled rod 102; for determining the vertical distance from the center of the end pivot hole of the first angled rod 101 to the outer edge of the profile of the first angled rod 101 or the vertical distance from the center of the end pivot hole of the second angled rod 102 to the outer edge of the profile of the second angled rod 102; for determining the rod width of the first angled rod 101 or the second angled rod 102.

[0114] It should be noted that due to the different parameters of the angled rods, the Hobble Ring will appear in two different folded states. As shown in Figure 11 , when the short rod arc 104 is in tangential contact with the long rod side edge 103, the folding is completed, reaching the first folded state F1. As shown in Figure 12 , when contracted to the centermost, the two long rod arcs 104 are in tangential contact, then reaching the second folded state F2.

[0115] The present embodiment can directly calculate the circumscribed circle radius of the Hobble Ring in the folded and unfolded states through the mathematical formula of the geometric parameters of the angled rods, so that the designer can quickly design and optimize to achieve a specific radius target.

[0116] In combination with Figure 15 , the present embodiment further proposes a formula for calculating the circumscribed circle radius of the Hobble Ring in the unfolded state as follows:

[0117] ;

[0118] ;

[0119] ;

[0120] ;

[0121] Among them, is the circumscribed circle radius of the Hobble Ring in the unfolded state; is the distance from the center of the Hobble Ring to the center of the first outermost pivot point; is the distance from the center of the Hobble Ring to the center of the second outermost pivot point; is the distance from the center of the Hobble Ring to the center of the third outermost pivot point; is the long rod length; is the short rod length; is the rod angle of the first angled rod 101; is the rod angle of the second angled rod 102; is the vertical distance from the center of the end pivot hole of the first angled rod 101 to the outer edge of the profile of the first angled rod 101 or the vertical distance from the center of the end pivot hole of the second angled rod 102 to the outer edge of the profile of the second angled rod 102; is the rod width of the first angled rod 101 or the second angled rod 102.

[0122] In combination Figure 16 , the embodiment further proposes a formula for calculating the radius expansion ratio as follows:

[0123] ;

[0124] wherein, is the Hobemian ring radius expansion ratio; is the circumscribed circle radius of the Hobemian ring in the first folded state or the second folded state; is the circumscribed circle radius of the Hobemian ring in the unfolded state.

[0125] It should be noted that when the Hobemian ring is unfolded to the state as shown in Figure 14 , the short rod arc 104 is in tangential contact with the short rod side edge 103, then the unfolding is completed, reaching the unfolded state of the Hobemian ring.

[0126] The embodiment further proposes that the design method further comprises the step of: S7, repeating steps S1-S6 to adjust and optimize the parameters so as to meet the design requirements.

[0127] From the above:

[0128] First, a model of the parameterized basic angled rod 10 is established, as shown in Figure 2 . Unlike the point-line model in the prior art, the geometric parameters of the basic angled rod 10 defined by the present application additionally introduce the rod width and the pivot point diameter which can reflect the actual physical size and manufacturing constraints. The present application also includes basic geometric parameters such as long rod length , short rod length , rod angle , wherein ≥ , < / 2. This definition fully considers the rod entity size in the modeling stage, thereby improving the consistency of the model and the entity structure.

[0129] Then, the kinematic model of the Hobelman loop is constructed. Based on the aforementioned angled link 10, a modular and bottom-up assembly approach is adopted. First, two angled links with different angles are combined into a module using fasteners 30 through the pivot holes 20 in the middle of the links. Then, two identical modules are assembled into a folding unit using the pivot holes 20 at the ends. Finally, multiple identical folding units are assembled into a closed Hobelman loop through the pivot holes at the ends.

[0130] Finally, the structural performance of the Hobelman loop is analyzed. The geometric configuration of the Hobelman loop in the fully expanded state and the final collapsed state is analyzed, and an analytical function relationship between the circumscribed circle radius of the Hobelman loop and the aforementioned defined geometric parameters is further established. This function relationship can be used to quantitatively predict the influence of different design parameters on the size change of the Hobelman loop, providing a parameterized design basis for actual manufacturing.

[0131] In combination Figure 17 The embodiment also discloses a Hobelman loop designed using the aforementioned design method of the Hobelman loop, which is set to be freely foldable and unfoldable. Figure 17 The Hobelman loops in the examples cover combinations of symmetry and asymmetry, different link lengths, and different angles, to verify the accuracy of the design method provided by the present application.

[0132] The embodiment also discloses an application of the aforementioned Hobelman loop designed using the design method in aerospace, solar energy, portable devices, building structures, or robots.

[0133] Specifically, the core innovation of the embodiment is that the Hobelman loop designed using the aforementioned design method is applied to specific engineering fields, effectively bridging the gap between theoretical models and actual manufacturing, and solving the engineering practice problems caused by the idealized point-line model ignoring physical constraints such as link width and pivot hole size, achieving reliable deployment and efficient operation in the fields of aerospace, solar energy, building structures, or robots.

[0134] Overall, this application scheme integrates the precise modeling of actual manufacturing constraints, enabling the Hobelman loop to achieve reliable and efficient performance in key engineering scenarios, significantly improving the feasibility of practical applications.

[0135] Obviously, the above embodiments are only examples for clear illustration, and do not limit the embodiments. For ordinary skilled persons in the art, other different forms of changes or variations can be made based on the above description. Here, it is not necessary or possible to exhaust all embodiments. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. A method for designing a Hopperman ring, characterized in that, Includes the following steps: S1. Provide a first angled rod (101) and a second angled rod (102), wherein pivot holes (20) are provided in the middle and at both ends of the first angled rod (101) and the second angled rod (102); the pivot holes (20) in the middle of the first angled rod (101) and the second angled rod (102) are hinged to form a module that can rotate about the middle hinge point; Pivot the pivot holes (20) at adjacent ends of two identical modules to form a folding unit; At the same time, the length of the first angled rod (101) is obtained. Short rod length pole angle and bar width and the length of the second angled rod (102) Short rod length pole angle and bar width ,in ≥ , ≤ , < / 2; S2, based on the rod angle and pole angle Calculate the number of folding units required to construct the Hobmann ring. And determine whether it can be constructed into a Hobermann ring; if for If the integers are equal to a certain value, they can be assembled into a Hobermann ring; otherwise, they cannot be assembled into a Hobermann ring. According to the pole angle and pole angle Calculate the number of folding units required to construct the Hobmann ring. The formula is: ； ； in, The number of folding units; The included angle is formed by the lines connecting the corresponding pivot holes at both ends of the first angled rod (101) and the second angled rod (102) in the module; The angle of the first angled rod (101); The angle of the second angled rod (102); S3. Calculate the criteria for the Hobman ring in the folded state. And determine the judgment parameters. With the width of the rod The relative size of the Hobman ring is used to determine its folding state; if Then the Hobermann ring is in the first folded state; if Then the Hobmann ring is in the second folded state; if Then the first folded state and the second folded state of the Hobermann ring coexist; Calculate the decision parameters of the Hobman ring in the folded state. The formula is: ； in, For determination parameters; The length of the long rod; This refers to the length of the short rod; The angle of the first angled rod (101); The angle of the second angled rod (102); It is the vertical distance from the center of the pivot hole at the end of the first angled rod (101) to the outer edge of the profile of the first angled rod (101) or the vertical distance from the center of the pivot hole at the end of the second angled rod (102) to the outer edge of the profile of the second angled rod (102); S4. Based on the determination result of step S3, calculate the circumcircle radius of the Hobman ring in the first folded state or the second folded state. ; S5. Calculate the radius of the circumcircle of the Hobmann ring in its unfolded state. ; S6. Calculate the radius expansion / contraction ratio and evaluate the structural performance of the Hobman ring designed with this parameter. The formula for calculating the radius expansion / contraction ratio is: ； in, The expansion-contraction ratio of the Hobmann ring radius; The radius of the circumcircle of the Hobmann ring in the first or second folded state; Let be the radius of the circumcircle of the Hobmann ring in its unfolded state.

2. The design method of the Hopperman ring according to claim 1, characterized in that, The formula for calculating the circumcircle radius of the Hobmann ring in its first or second folded state is: ； ； ； ； ； in, The radius of the circumcircle of the Hobmann ring in the first or second folded state; The distance from the center of the Hobmann ring in its first folded state to the center of the first outermost pivot point; The distance from the center of the Hobmann ring in its first folded state to the center of the second outermost pivot point; The distance from the center of the Hobmann ring in the second folded state to the center of the first outermost pivot point; The distance from the center of the Hobmann ring in the second folded state to the center of the second outermost pivot point; For determination parameters; The length of the long rod; This refers to the length of the short rod; The angle of the first angled rod (101); The angle of the second angled rod (102); It is the vertical distance from the center of the pivot hole at the end of the first angled rod (101) to the outer edge of the profile of the first angled rod (101) or the vertical distance from the center of the pivot hole at the end of the second angled rod (102) to the outer edge of the profile of the second angled rod (102); The width of the first angled member (101) or the second angled member (102).

3. The design method of the Hopperman ring according to claim 1, characterized in that, The formula for calculating the circumcircle radius of a Hoppermann ring in its unfolded state is: ； ； ； ； in, Let be the radius of the circumcircle of the Hobmann ring in its unfolded state; The distance from the center of the Hopperman ring to the center of the first outermost pivot point; The distance from the center of the Hopperman ring to the center of the second outermost pivot point; This is the distance from the center of the Hopperman ring to the center of the third outermost pivot point; The length of the long rod; This refers to the length of the short rod; The angle of the first angled rod (101); The angle of the second angled rod (102); It is the vertical distance from the center of the pivot hole at the end of the first angled rod (101) to the outer edge of the profile of the first angled rod (101) or the vertical distance from the center of the pivot hole at the end of the second angled rod (102) to the outer edge of the profile of the second angled rod (102); The width of the first angled member (101) or the second angled member (102).

4. A Hobermann ring, characterized in that, Designed using the design method of the Hobman ring as described in any one of claims 1-3, it is configured to be freely foldable and unfoldable.

5. The application of the Hobmann ring of claim 4 in aerospace, solar energy, portable devices, building structures or robotics.

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