A bistable linear drive

By using a bistable linear drive device, rapid linear motion is achieved by utilizing the difference in thermal expansion coefficients of two layers of metal sheets. This solves the shortcomings of existing devices in terms of response speed and energy consumption, and provides a high-efficiency, low-energy linear motion solution.

CN119195999BActive Publication Date: 2026-02-13FUZHOU UNIV
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Patent Information

Application Number
CN202411381127.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-30
Publication Date
2026-02-13
Estimated Expiration
2044-09-30

AI Technical Summary

Technical Problem

Existing linear drive devices are inadequate in terms of efficient linear motion output, response speed, and anti-interference capability. They perform poorly, especially in environments requiring rapid response, and are also complex in structure and have high energy consumption.

Method used

The device employs a bistable linear drive mechanism, comprising a bubble assembly, a rotating assembly, and a linear motion component. It utilizes the difference in thermal expansion coefficients of the two-layer metal sheets to achieve rapid linear motion through curvature changes caused by heating. It features a simple structure, low energy consumption, and good anti-interference performance.

Benefits of technology

It achieves fast-response linear motion output, reduces energy consumption, improves the device's anti-interference capability, and has a compact structure, is easy to manufacture, and has good economic benefits.

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Abstract

The application relates to a bistable linear driving device which comprises a water bubble assembly, a rotating assembly and a linear motion part; the water bubble assembly comprises a shell and a double-layer metal sheet, the shell is composed of a fan-shaped bottom plate and an arc-shaped constraint ring, the length of the double-layer metal sheet is greater than the arc length of the arc-shaped constraint ring, the two ends of the double-layer metal sheet are fixed at the two ends of the arc-shaped constraint ring, and the double-layer metal sheet is bent inward to form a water bubble structure; the rotating assembly comprises a rotating base plate and two sets of clamping piece heating assemblies, the rotating base plate is rotationally connected with the fan-shaped bottom plate, the two sets of clamping piece heating assemblies are fixedly connected on the left and right sides of the lower part of the rotating base plate, and the heating pieces and motion transmission parts are respectively clamped on the two sides of the inwardly bent double-layer metal sheet; the linear motion part comprises a guide sleeve and a sliding rod, a guide block is arranged on the rotating base plate and is slidably embedded in a sliding groove on the guide sleeve, a sliding rod guide seat is arranged on the fan-shaped bottom plate, the front end of the sliding rod is fixedly connected with the guide sleeve, and the rear part is in sliding fit with the sliding rod guide seat. The device has the advantages of simple structure, low energy consumption, fast response speed and good anti-interference performance.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of linear driving devices, in particular to a bistable linear driving device. BACKGROUND

[0002] In many industrial application scenarios, linear driving devices are widely used in mechanical equipment, robots and industrial production lines, etc. However, the existing linear driving devices face many challenges in design, especially in situations that require efficient linear motion output. Traditional linear driving devices, such as linear motors, hydraulic cylinders, etc., although they can provide certain output force and displacement, their structures are often complex and slow in response speed. In addition, such devices usually cannot achieve rapid displacement output in a short time and need continuous external energy input to maintain their working state. In environments such as the presence of magnetic field interference, dust, low precision requirements but fast response speed requirements, etc., the adaptability of traditional linear driving devices is limited.

[0003] Bistable structure, by using the inherent stress of materials or structures, switches between two stable states, and does not need continuous energy input to maintain the stable state. This unique feature makes it very suitable for low energy consumption, anti-interference, fast response application scenarios, especially in the field of micro robots, micro controllers, etc. It shows great potential. However, in the prior art, the application of bistable structure in linear driving devices is relatively rare, which to some extent limits its popularization and application in wider industrial scenarios. SUMMARY

[0004] The purpose of the present application is to provide a bistable linear driving device, which has simple structure, low energy consumption, fast response speed and good anti-interference performance.

[0005] In order to achieve the above object, the technical scheme adopted by the present application is: a bistable linear driving device, comprising a water bubble assembly, a rotating assembly and a linear motion part; the water bubble assembly comprises a shell and a double-layer metal sheet, the shell is composed of a fan-shaped bottom plate and an arc-shaped constraint ring arranged on the outer peripheral part of the shell, the length of the double-layer metal sheet is greater than the arc length of the arc-shaped constraint ring, the double-layer metal sheet is arranged in the shell and its two ends are fixed at the two ends of the arc-shaped constraint ring respectively, so as to form a water bubble structure by inward bending; the rotating assembly comprises a rotating base plate and two sets of clamping piece heating assemblies, the rotating center part of the rotating base plate is rotationally connected with the center position of the fan-shaped bottom plate, the two sets of clamping piece heating assemblies are fixedly connected on the left and right sides of the lower part of the rotating base plate respectively, and the heating pieces and the motion transmission parts of the clamping piece heating assemblies are clamped on the two sides of the inwardly bent double-layer metal sheet respectively; the linear motion part comprises a guide sleeve and a slide rod, a guide block is arranged on the middle part of the rotating base plate, a sliding groove is formed in the guide sleeve, the guide block is slidingly embedded in the sliding groove and can slide up and down in the sliding groove, a slide rod guide seat is arranged on the fan-shaped bottom plate, the front end of the slide rod is fixedly connected with the guide sleeve, and the rear part is slidingly matched with the slide rod guide seat.

[0006] Further, the water bubble assembly comprises two pressing blocks, and the two ends of the double-layer metal sheet are fixedly connected with the two ends of the arc-shaped constraint ring through the pressing blocks.

[0007] Further, an arc-shaped sliding groove is formed on the rotating base plate in the circumferential direction, which is used for conveniently adjusting the installation position of the clamping piece heating assembly on the rotating base plate, and the clamping piece heating assembly is fixedly installed on the arc-shaped sliding groove of the rotating base plate.

[0008] Further, the clamping piece heating assembly comprises a mounting frame, a ceramic heating piece, a first screw, a first nut and a first bearing; the mounting frame is composed of a horizontal part and a vertical part connected to the lateral lower part of the horizontal part, the ceramic heating piece is installed on the vertical part to heat the double-layer metal sheet on the lateral side; the mounting frame is arranged on the lower side of the rotating base plate, the first screw passes through the rotating base plate and the horizontal part downward and is matched with the first nut, so as to fixedly connect the mounting frame with the lower part of the rotating base plate; the first bearing is installed on the lower part of the first nut, and the outer side surface thereof is in contact with the double-layer metal sheet on the lateral side, so as to clamp the double-layer metal sheet between the ceramic heating piece and the first bearing;

[0009] Further, the connecting wire of the ceramic heating piece passes through the horizontal part of the mounting frame and the rotating base plate upward and is connected with an external power supply.

[0010] Further, the center position of the fan-shaped bottom plate is provided with a rotating connecting seat, and the rotating center part of the rotating base plate is rotationally connected with the rotating connecting seat through a second bearing; the lower part of the rotating base plate is connected with a horizontally arranged second bearing, and the upper and lower sides of the second bearing are in contact with the fan-shaped bottom plate and the rotating base plate respectively, so as to support the rotating base plate and reduce the friction force of relative movement between the rotating base plate and the fan-shaped bottom plate.

[0011] Further, the water bubble structure formed by inward bending of the double-layer metal sheet has a positive curvature region and a negative curvature region; the thermal expansion coefficients of the inner and outer layers of the double-layer metal sheet are different, and by energizing the heating sheet on one side, the double-layer metal sheet is heated locally to introduce a curvature opposite to it; the boundary driving angle β of the loading section increases with the increase of temperature, and the midpoint deflection first increases and then decreases until it is equal to the midpoint deflection corresponding to the unstable configuration with the same boundary driving angle β of the loading section, at which time the strain energy reaches a maximum value, the loading section jumps, and the water bubble structure jumps and rolls; the rotating assembly transmits the rotating motion of the water bubble structure to the linear motion member, so that the linear motion member rapidly extends and retracts.

[0012] Further, the double-layer metal sheet with different thermal expansion coefficients of the inner and outer layers introduces a boundary angle after heating, and the configuration of the loading section of the double-layer metal sheet is determined by the following equation set:

[0013]

[0014]

[0015] θ(o1)=β,θ(o2)=-β,x(o1)=0,y(o1)=0,y(o2)=0,x(o2)=d ls

[0016] Wherein, K is the bending stiffness of the double-layer metal sheet, s represents the natural coordinate arc length of the water bubble, o1 and o2 are respectively the left and right endpoints of the loading section of the double-layer metal sheet, the x-axis is coincident with the vector formed by o1 and o2, the y-axis conforms to the right-hand rule, θ(s) represents the angle between the tangent line at the point with arc length s on the loading section and the x-axis, x and y are the Cartesian coordinates of any point on the loading section, F x , F y respectively represent the internal force of the loading section along the x-axis direction and the internal force along the y-axis direction, d ls represents the distance between the two ends of the loading section, and β represents the boundary driving angle of the two ends of the loading section.

[0017] The critical loading curvature of the bistable linear driving device is determined by the following formula:

[0018]

[0019] Wherein, κ crThe critical loading curvature required for the jump of the loading section is proportional to the factor and the critical driving angle c The critical driving angle required for the jump of the loading section is proportional to the factor and the critical driving angle ls The length of the loading section is proportional to the factor and the critical driving angle

[0020] Further, the radius of the arc-shaped constraint ring is reduced and the loading position is increased, so that the critical loading curvature of the bistable linear driving device is increased cr The higher loading temperature is required, but the output power of the bistable linear driving device is improved.

[0021] Compared with the prior art, the present application has the following beneficial effects:

[0022] (1) The present application adopts an efficient bistable telescopic mechanism, which realizes the rapid output linear motion of the bistable state by utilizing the characteristics of the local loading section jump driving bubble structure roll, and improves the response speed of the system;

[0023] (2) The bistable structure of the present application has a lower energy consumption feature, and the present application utilizes thermal excitation to trigger the jump of the loading section, and the overall boundary of the bubble can be moved, so that the required loading temperature is lower, while retaining the characteristics of the bistable jump, the input cost can be effectively reduced;

[0024] (3) The present application has simple structure, easy to manufacture, compact structure design, low manufacturing cost, good economic efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0025] Figure 1 The device structure diagram of the embodiment of the present application.

[0026] Figure 2 The device structure explosion diagram of the embodiment of the present application.

[0027] Figure 3 The driving principle diagram of the embodiment of the present application.

[0028] Figure 4 The local double-layer metal sheet jump diagram in the embodiment of the present application.

[0029] Figure 5 The midpoint deflection and strain energy of the local double-layer metal sheet in the embodiment of the present application change with the boundary angle.

[0030] Figure 6 The critical load changes with the loading position and the constraint radius in the embodiment of the present application.

[0031] Figure 7 The stall torque diagram in the embodiment of the present application. DETAILED DESCRIPTION

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0034] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0035] like Figures 1-2 As shown, this embodiment provides a bistable linear drive device, including a bubble assembly 1, a rotating assembly 2, and a linear motion component 3. The bubble assembly 1 includes a shell and a double-layer metal sheet 4. The shell is composed of a fan-shaped base plate 5 and an arc-shaped constraint ring 6 disposed on its outer periphery. The length of the double-layer metal sheet 4 is greater than the arc length of the arc-shaped constraint ring 6. The double-layer metal sheet 4 is disposed inside the shell and its two ends are respectively fixed to the two ends of the arc-shaped constraint ring 6, thereby bending inward to form a bubble structure. The rotating assembly 2 includes a rotating base plate 7 and two sets of clamp heating assemblies. The rotation center of the rotating base plate 7 is rotatably connected to the center position of the fan-shaped base plate 5. Next, the two sets of clamp heating assemblies are fixedly connected to the left and right sides of the lower part of the rotating base plate, and the heating plates and motion transmission components of the clamp heating assemblies are respectively clamped on both sides of the inwardly bent double-layer metal sheet; the linear motion component includes a guide sleeve 8 and a slide rod 9. A guide block 10 is provided in the middle of the rotating base plate 7. A slide groove 13 is opened in the guide sleeve 8. The guide block 10 is slidably embedded in the slide groove 13 and can slide up and down in it. A slide rod guide seat 11 is provided on the fan-shaped base plate 5. The front end of the slide rod 9 is fixedly connected to the guide sleeve 8, and the rear end is slidably engaged with the slide rod guide seat 11, thereby realizing the directional extension and retraction of the linear motion component.

[0036] In this embodiment, the bubble assembly includes two pressure blocks 12, and the two ends of the double-layer metal sheet are respectively fixedly connected to the two ends of the arc-shaped constraint ring through the pressure blocks.

[0037] In this embodiment, an arc-shaped groove 14 is formed along the circumference of the rotating base plate 7 to facilitate the adjustment of the installation position of the clamp heating assembly on the rotating base plate, so as to ensure that the heating plate and motion transmission component of the clamp heating assembly are clamped on both sides of the inwardly bent double-layer metal plate, and the clamp heating assembly is fixedly installed on the arc-shaped groove 14 of the rotating base plate 7.

[0038] In the embodiment, the clamping heating assembly comprises a mounting frame 15, a ceramic heating sheet 16, a first screw 17, a first nut 18 and a first bearing 19. The mounting frame 15 is composed of a horizontal part and a vertical part connected to the lateral lower part of the horizontal part. The ceramic heating sheet 16 is installed on the vertical part to heat the double-layer metal sheet beside it. The mounting frame 15 is arranged on the lower side of the rotating base plate. The first screw 17 passes through the rotating base plate and the horizontal part downward and cooperates with the first nut 18 to fix the mounting frame on the lower part of the rotating base plate. The first bearing 19 is installed on the lower part of the first nut 18 and its outer side is in contact with the double-layer metal sheet beside it, so as to clamp the double-layer metal sheet 4 between the ceramic heating sheet 16 and the first bearing 19.

[0039] In the embodiment, the connecting wire of the ceramic heating sheet 16 passes through the horizontal part of the mounting frame and the rotating base plate upward and is connected with the external power supply.

[0040] In the embodiment, the center position of the fan-shaped base plate 5 is provided with a rotating connecting seat 20. The rotating center part of the rotating base plate 7 is rotatably connected with the rotating connecting seat 20 through a second bearing 21. The lower part of the rotating base plate 7 is connected with a horizontally arranged second bearing 21. The upper and lower sides of the second bearing 21 are in contact with the fan-shaped base plate and the rotating base plate respectively to support the rotating base plate and reduce the friction force between the rotating base plate and the fan-shaped base plate.

[0041] As shown in the figure, one part of the double-layer metal sheet 4 is attached to the inner wall of the arc-shaped constraint ring 6, and the other part is pre-bent towards the constraint center direction to form a water bubble structure. The water bubble structure has a positive curvature region and a negative curvature region. Figure 3

[0042] The thermal expansion coefficients of the inner and outer layers of the double-layer metal sheet 4 are different. By energizing the heating sheet on one side, the local double-layer metal sheet is heated to introduce a curvature opposite to it. The boundary driving angle β of the loading section increases with the increase of temperature. The midpoint deflection first increases and then decreases until it is equal to the midpoint deflection corresponding to the unstable configuration with the same boundary driving angle β. At this time, the strain energy reaches a maximum value, the loading section jumps, and the water bubble structure jumps and rolls. The rotating assembly transmits the rotational motion of the water bubble structure to the linear motion part to make the linear motion part quickly stretch and contract.

[0043] The double-layer metal sheet with different thermal expansion coefficients of the inner and outer layers introduces a boundary angle after heating. The configuration of the double-layer metal sheet in the loading section is determined by the following equation set:

[0044]

[0045]

[0046] ​θ(o1)=β, θ(o2)=-β, x(o1)=0, y(o1)=0, y(o2)=0, x(o2)=d ls

[0047] Where K is the bending stiffness of the double-layer metal sheet, s represents the natural coordinate arc length of the bubble, o1 and o2 are the left and right endpoints of the loading segment of the double-layer metal sheet, the x-axis coincides with the vector formed by o1 and o2, the y-axis follows the right-hand rule, θ(s) represents the angle between the tangent at the point s away from o1 on the loading segment and the x-axis, and x and y are the Cartesian coordinates of any point on the loading segment. x F y Let d represent the internal forces along the x-axis and y-axis of the loaded segment, respectively. ls β represents the distance between the two ends of the loading segment, and β represents the boundary driving angle at both ends of the loading segment.

[0048] The critical loading curvature of a bistable linear drive is determined by the following formula:

[0049]

[0050] Among them, κ cr The critical loading curvature required for the loading segment to undergo a jump, where ε is the scaling factor and β is the critical loading curvature. c The critical drive angle s represents the angle required for the loading segment to change direction. ls Indicates the length of the loaded segment.

[0051] like Figures 4-5 As shown, in this embodiment, the coefficient of thermal expansion of the upper layer of the double-layer metal sheet 4 is smaller than that of the lower layer. By energizing the ceramic heating element 7 on the right side, the double-layer metal sheet is heated locally, introducing a curvature opposite to that of the lower layer. The driving angle β of the loading segment increases with increasing temperature, and the deflection δ at the midpoint of the loading segment... m The deflection is gradually increased and then decreased until it equals the midpoint deflection of the unstable configuration. At this point, the loading segment switches from stable state I to stable state II, and the bubble structure rolls clockwise. The rotating component transmits the rotational motion of the bubble structure to the linear motion component, causing it to extend rapidly. By energizing the ceramic heating element on the left, the linear motion component retracts rapidly, achieving linear motion output from the bistable structure.

[0052] Reducing the radius of the arc-shaped constraint ring and increasing the loading position (midpoint of the heating element) makes the critical loading curvature κ of the bistable linear drive device more responsive. cr Increasing the load requires a higher loading temperature, but it can improve the output power of the bistable linear drive.

[0053] Preferably, select such as Figure 6The bistable linear drive device corresponding to the constraint radius 2 and loading position 2 shown has a large critical load and high output power, while the critical load is small.

[0054] like Figure 7 As shown, the stall torque of this device increases with the increase of the loading temperature. When the heating temperature is 120℃, the output force of the bistable linear output device is 1.03N.

[0055] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A bi-stable linear drive apparatus, characterized by, The application relates to a double-layer metal sheet water bubble assembly, a rotating assembly and a linear motion component. The water bubble assembly comprises a shell and a double-layer metal sheet, the shell is composed of a fan-shaped bottom plate and an arc-shaped constraint ring arranged on the outer peripheral portion of the shell, the length of the double-layer metal sheet is greater than the arc length of the arc-shaped constraint ring, the double-layer metal sheet is arranged in the shell and the two ends of the double-layer metal sheet are fixed on the two ends of the arc-shaped constraint ring respectively, so that the double-layer metal sheet is bent inward to form a water bubble structure; the rotating assembly comprises a rotating base plate and two sets of clamping piece heating assemblies, the rotating center portion of the rotating base plate is rotationally connected with the center position of the fan-shaped bottom plate, the two sets of clamping piece heating assemblies are fixedly connected on the left and right sides of the lower portion of the rotating base plate respectively, and the heating pieces and the motion transmission components of the clamping piece heating assemblies are clamped on the two sides of the inwardly bent double-layer metal sheet respectively; the linear motion component comprises a guide sleeve and a sliding rod, a guide block is arranged on the middle portion of the rotating base plate, a sliding groove is formed in the guide sleeve, the guide block is slidably embedded in the sliding groove and can slide up and down in the sliding groove, a sliding rod guide seat is arranged on the fan-shaped bottom plate, the front end of the sliding rod is fixedly connected with the guide sleeve, and the rear portion is slidably matched with the sliding rod guide seat. The water bubble structure formed by the inward bending of the double-layer metal sheet has a positive curvature region and a negative curvature region; the thermal expansion coefficients of the inner and outer layers of the double-layer metal sheet are different, the heating piece on one side is electrified to heat the local double-layer metal sheet and introduce the curvature opposite to the curvature, the boundary driving angle beta of the loading section increases with the temperature rise, the midpoint deflection first increases and then decreases until the midpoint deflection corresponding to the unstable configuration with the same boundary driving angle beta is equal, at this time, the strain energy reaches the maximum value, the loading section jumps, and the water bubble structure jumps and rolls; the rotating assembly transmits the rotating motion of the water bubble structure to the linear motion component, so that the linear motion component rapidly extends and retracts; θ(ol) = β, θ(02) = -β, x(ol) = 0, y(ol) = 0, y(02) = 0, x(02) = d ls wherein K is the bending stiffness of the double-layer metal sheet, s represents the natural coordinate arc length of the bubble, o1 and o2 are respectively the left and right endpoints of the loading segment of the double-layer metal sheet, the x-axis is coincident with the vector formed by o1 and o2, the y-axis conforms to the right-hand rule, θ(s) represents the included angle between the tangent at the point on the loading segment with an arc length of s from o1 and the x-axis, x and y are the Cartesian coordinates of any point on the loading segment, F x , F y respectively represent the internal force of the loading segment along the x-axis direction and the internal force along the y-axis direction, d ls represents the distance between the two ends of the loading segment, and β represents the boundary driving angle of the two ends of the loading segment. The double-layer metal sheet with different thermal expansion coefficients of the inner and outer layers introduces the boundary angle after heating, and the configuration of the double-layer metal sheet of the loading section is determined by the following equation set: wherein κ cr is the critical loading curvature needed for the jump to occur in the loading segment, ε is a scaling factor, β c represents the critical driving angle needed for the jump to occur in the loading segment, s ls represents the length of the loading segment.

2. A bi-stable linear drive according to claim 1, characterised in that, The critical loading curvature of the bistable linear driving device is determined by the following formula:

3. A bi-stable linear drive according to claim 1, characterised in that, The water bubble assembly comprises two pressing blocks, and the two ends of the double-layer metal sheet are fixedly connected on the two ends of the arc-shaped constraint ring through the pressing blocks.

4. A bi-stable linear drive according to claim 1, characterised in that, An arc-shaped sliding groove is formed on the rotating base plate in the circumferential direction, which is used for conveniently adjusting the installation position of the clamping piece heating assembly on the rotating base plate.

5. A bi-stable linear drive according to claim 4, wherein, The clamping piece heating assembly comprises a mounting frame, a ceramic heating piece, a first screw, a first nut and a first bearing; the mounting frame is composed of a horizontal portion and a vertical portion connected to the lateral lower portion of the horizontal portion, the ceramic heating piece is mounted on the vertical portion to heat the double-layer metal sheet on the lateral side; the mounting frame is arranged on the lower side of the rotating base plate, the first screw passes through the rotating base plate and the horizontal portion downward and is matched with the first nut, so as to fixedly connect the mounting frame on the lower portion of the rotating base plate; the first bearing is mounted on the lower portion of the first nut, and the outer side surface thereof is in contact with the double-layer metal sheet on the lateral side, so as to clamp the double-layer metal sheet between the ceramic heating piece and the first bearing. The connecting wire of the ceramic heating piece passes through the horizontal portion of the mounting frame and the rotating base plate upward and is connected with the external power supply.

6. A bi-stable linear drive according to claim 1, characterised in that, The center position of the fan-shaped bottom plate is provided with a rotating connecting seat, and the rotating center part of the rotating base plate is connected with the rotating connecting seat through a second bearing. The lower part of the rotating base plate is connected with a horizontally arranged second bearing, and the upper and lower sides of the second bearing are respectively in contact with the fan-shaped bottom plate and the rotating base plate, so as to support the rotating base plate and reduce the friction force between the rotating base plate and the fan-shaped bottom plate.

7. A bi-stable linear drive according to claim 1, wherein Decreasing the radius of the arc-shaped constraint ring and increasing the loading position make the critical loading curvature K of the bistable linear driving device smaller cr Increasing, higher loading temperature is needed, but the output power of the bistable linear driving device can be improved.

Citation Information

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