A six-dimensional force sensor based on planar strain sensing elements

CN122192599APending Publication Date: 2026-06-12HANGZHOU ZHIGAN MICROELECTRONICS CO LTD

Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
HANGZHOU ZHIGAN MICROELECTRONICS CO LTD
Filing Date
2026-04-29
Publication Date
2026-06-12

AI Technical Summary

Technical Problem

Existing six-dimensional force sensor strain gauges require a large number of plates, and the side mounting and lead wire binding operations are difficult, resulting in low production efficiency and making it difficult to achieve industrialization.

Method used

A three-beam structure based on a plane strain sensing unit is adopted, and full-bridge chips are symmetrically arranged on the upper or lower surface of the main beam. Combined with glass micro-fusion technology, automated chip mounting and connection are performed, simplifying the chip mounting and lead wire process.

🎯Benefits of technology

The sensor has achieved miniaturization, reducing the difficulty and cost of mounting, improving production efficiency, and ensuring the sensor's high strength and thermal stability, making it suitable for industrial production processes.

✦ Generated by Eureka AI based on patent content.

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Abstract

The application provides a six-dimensional force sensor based on a plane strain sensing unit and belongs to the technical field of six-dimensional force sensors.The elastic body main part comprises a loading platform, a main beam, a floating beam and a shell, one end of the main beam is connected to the central loading platform, the other end of the main beam is connected to the floating beam, the floating beam is arranged orthogonally to the main beam, the end of the floating beam away from the main beam is connected to the shell, and the upper surface or the lower surface of the main beam is provided with six plane strain sensing units, and the six plane strain sensing units are respectively used for measuring forces Fx, Fy and Fz in three directions in space and moments Mx, My and Mz in three directions;the six-dimensional force sensor is prepared by adopting the plane strain sensing unit and a corresponding fixing process, the difficulties caused by the side surface pasting of the chip and the side wall lead binding are avoided, the six-dimensional force sensor has the advantages of small number of pasted pieces, simple process, high pasting precision, low manufacturing cost and the like, and is convenient for highly automated industrial production.
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Description

Technical Field

[0001] This invention relates to the field of six-dimensional force sensor technology, and more specifically, to a six-dimensional force sensor based on a plane strain sensing unit. Background Technology

[0002] Six-dimensional force sensors represent the cutting edge of force measurement technology. They can simultaneously detect forces (Fx, Fy, Fz) in three orthogonal directions and moments (Mx, My, Mz) in three directions in three-dimensional space, providing the most comprehensive force information. In a six-dimensional force sensor, strain gauges, as the core sensing element, are typically mounted on an elastic body structure using adhesive or fixed methods. When an external load is applied to the sensor, the elastic body deforms, causing the strain gauge to deform synchronously, resulting in a change in its resistance. By detecting this change in resistance, the applied force or moment can be indirectly calculated. Currently, the most widely used type is the metal foil strain gauge, which works based on the strain effect of metallic materials. However, it suffers from limitations such as limited sensitivity and insufficient ability to detect micro-strain, making it difficult to meet the demands of high-precision measurement scenarios. In contrast, semiconductor strain gauges utilize the piezoresistive effect of semiconductor materials, where the resistivity changes significantly under stress. Their sensitivity can be tens of times that of metal foil strain gauges, while also possessing superior dynamic response characteristics and lower mechanical hysteresis. Therefore, in high-precision mechanical measurement applications such as precision robot operation, aerospace testing, and medical instruments, semiconductor strain gauges are gradually replacing traditional metal strain gauges, becoming a key technology path to achieve higher sensing accuracy.

[0003] The most common structures for six-dimensional force sensor elastomers are three-beam and four-beam structures. Typically, strain gauges are attached to the top, bottom, and sides of the main beam of the elastomer, converting the resistance change caused by deformation under stress into a voltage signal output. Strain gauges are usually attached to the top and bottom surfaces of the main beam to measure Fz, Mx, and My, while strain gauges are attached to the left and right sides to measure Fx, Fy, and Mz. This approach presents challenges due to the difficulty of attaching the strain gauges to the sides and binding the leads. Conventional methods require attaching 24 strain gauges, with the strain gauge leads forming six Wheatstone bridges on the circuit board to measure Fx, Fy, Fz, Mx, My, and Mz respectively. The attaching and bridging processes are extremely cumbersome, requiring manual operation, resulting in low efficiency, poor attaching accuracy, and poor product consistency, hindering the industrial production of six-dimensional force sensors.

[0004] How to invent a six-dimensional force sensor based on a plane strain sensing unit to solve these problems has become an urgent issue for those skilled in the art. Summary of the Invention

[0005] The present invention aims to solve the problems of existing six-dimensional force sensors, such as the excessive number of strain gauges, the difficulty in side mounting and lead wire binding of strain gauges, and the cumbersome process of bridging the lead wires to the circuit board, which makes the entire process difficult to carry out in industrial production.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: This invention provides a three-beam structure six-dimensional force sensor based on planar technology, including a sensor body. The sensor body includes an upper cover plate, an elastic body, and a lower cover plate arranged sequentially from top to bottom. The main body of the elastic body includes a central loading platform, a main beam, a floating beam, and a shell. One end of the main beam is connected to the central loading platform, and the other end of the main beam is connected to the floating beam. The floating beam is orthogonal to the main beam, and the end of the floating beam facing away from the main beam is connected to the shell. The main beam has six plane strain sensing units on its upper or lower surface. These six plane strain sensing units are used to measure the forces Fx, Fy, and Fz in three directions and the moments Mx, My, and Mz in three directions.

[0007] Preferably, the elastomer material is stainless steel (including but not limited to 316L stainless steel), and its structure includes three ear-shaped grooves and three arc-shaped grooves evenly distributed around the circumference, forming a force-measuring structure of three main beams plus three floating beams.

[0008] Preferably, the optimal dimensions of the main body of the elastic body are obtained through an AI+CAE simulation optimization platform based on the sensor range. The diameter of the elastic body is 4 to 200 mm, the beam depth is not less than 0.5 mm, the width of the main beam is not less than 0.3 mm, and the width of the floating beam is not less than 0.1 mm.

[0009] Preferably, it also includes a signal acquisition module and a terminal, with six plane strain sensing units electrically connected to the input terminal of the signal acquisition module, and the output terminal of the signal acquisition module electrically connected to the terminal.

[0010] Preferably, the terminal uses a nonlinear decoupling algorithm based on machine learning for signal decoupling.

[0011] Preferably, the plane strain sensing unit is a full-bridge chip.

[0012] Preferably, the size of the full-bridge chip is 0.1 to 1 mm, and each full-bridge chip contains four semiconductor strain gauges (the materials of the semiconductor strain gauges include, but are not limited to, silicon, silicon carbide, and gallium nitride) to form a Wheatstone bridge.

[0013] Preferably, the full-bridge chip integrates a temperature sensing function, which can acquire temperature signals while acquiring six-dimensional force signals, and perform corresponding temperature compensation based on the temperature signals.

[0014] Preferably, the six plane strain sensing units (such as full-bridge chips) are disposed on the upper or lower surface of the main beam, and two plane strain sensing units (such as full-bridge chips) are symmetrically arranged on a single surface of each main beam along its axial direction.

[0015] Preferably, the full-bridge chip is attached and fixed to the upper or lower surface of the main beam using a chip mounter and a glass micro-melting process.

[0016] Preferably, the position of the plane strain sensing unit patch is determined by using an AI+CAE simulation optimization platform, and the distance between the edge of the plane strain sensing unit and the edge of the central loading stage is not less than 0.1 mm.

[0017] The beneficial effects of this invention are: (1) Compared with traditional six-dimensional force sensors, the planar strain sensing unit (such as a full-bridge chip with a size of 0.1 to 1 mm) used in this invention requires significantly less mounting space. Combined with the simplified patch layout selected on the upper or lower surface of the main beam, it is more conducive to the miniaturization design of the sensor structure, and is particularly suitable for six-dimensional force sensors with millimeter-level size. By using the glass micro-melting process to directly sinter the sensing unit on the corresponding surface (i.e., the upper or lower surface) of the elastomer, not only is the operational difficulty of traditional side patch and lead bonding avoided, but also a high-strength and high-thermal-stability connection between the chip and the substrate is achieved, overcoming the problems of poor thermal stability and easy aging failure of traditional adhesive bonding processes.

[0018] (2) A simplified patch layout is selected on the upper or lower surface of the main beam. A total of 6 plane strain sensing units (such as full-bridge chips) can realize six-dimensional force signal sensing. Compared with the traditional method of pasting 24 discrete strain gauges and manually assembling them, it greatly reduces the difficulty of patching, process complexity and manufacturing cost. It avoids the difficulties of side mounting and side wall lead binding. At the same time, it has the advantages of fewer patches, simple patching process and low manufacturing cost. Moreover, the full-bridge chip pasting process is fully automated, which greatly saves manpower, improves the production efficiency of the patching process and realizes industrialized process production.

[0019] (3) Unlike the traditional method of first pasting strain gauges and then assembling a Wheatstone bridge, this invention directly uses plane strain sensing units (such as full-bridge chips). While ensuring the output signal and output sensitivity, it greatly reduces the space and difficulty of pasting strain gauges. The output of the six plane strain sensing units represents the output signals of the six six-dimensional force components respectively. It can also synchronously collect temperature signals and realize temperature compensation, thereby simplifying the hardware structure while ensuring the accuracy and environmental adaptability of six-dimensional force measurement.

[0020] (4) This invention achieves extreme simplification of the structure, patching, and bridging of the six-dimensional force sensor, facilitating highly automated industrial production. The sensor adopts the simplest three-beam structure of the six-dimensional force sensor. Using a patching machine, six full-bridge chips are respectively pasted on the upper or lower surface of the main beam at specified positions through glass micro-melting process. The pasting process is extremely simple and fully automated. The lead wires of the full-bridge chips are connected to the circuit board to form a Wheatstone bridge. This method is also simpler than the traditional method of forming six Wheatstone bridges with 24 strain gauges. Therefore, this invention achieves extreme simplification of the structure, patching, and bridging of the six-dimensional force sensor, facilitating highly automated industrial production. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0022] Figure 1 This is a schematic diagram of the elastomer structure of the present invention; Figure 2 This is a schematic diagram of the sensor appearance of the present invention; Figure 3 This is a schematic diagram of the patch position of the plane strain sensing unit of the present invention (taking surface mount as an example). Figure 4 This is the Mises stress diagram under full-scale loading of Fx according to the present invention; Figure 5 This is the Mises stress diagram under full-scale loading of Fy according to the present invention; Figure 6 This is the Mises stress diagram under full-scale loading of Fz according to the present invention; Figure 7 This is the Mises stress diagram under full-scale loading of Mx according to the present invention; Figure 8 This is the Mises stress diagram under full-scale loading of My according to the present invention; Figure 9This is the Mises stress diagram under full-scale loading of Mz according to the present invention; Figure 10 This is a curve showing the stress variation along the patch path when the Fx is fully loaded according to the present invention; Figure 11 This is a curve showing the stress variation along the patch path when the Fy is fully loaded according to the present invention; Figure 12 This is a curve showing the stress variation along the patch path when the Fz is fully loaded according to the present invention; Figure 13 This is a curve showing the stress variation along the patch path when the Mx is fully loaded according to the present invention; Figure 14 This is a curve showing the stress variation along the patch path when My is fully loaded according to the present invention; Figure 15 This is a curve showing the stress variation along the patch path when the Mz full-scale load of the present invention is applied.

[0023] In the figure: 1. Central loading platform; 2. Main beam; 3. Floating beam; 4. Shell; 5. Upper cover plate; 6. Elastomer; 7. Lower cover plate; 8. Plane strain sensing unit. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] General Description The planar strain sensing unit 8 described in this invention refers to a miniature sensing module that integrates multiple strain sensing elements into one unit using microfabrication or film deposition processes, directly forming a Wheatstone bridge or similar detection circuit and outputting strain-related electrical signals. Its implementation includes, but is not limited to: a semiconductor full-bridge chip; a pressure-sensitive unit formed using micro / nano fabrication processes such as nanoimprinting fabricated by microelectromechanical systems (MEMS); a thin-film strain bridge directly formed on the surface of the main beam by physical or chemical vapor deposition (such as sputtering); or a thick-film metal strain bridge formed on the surface of the main beam by printing and sintering processes. The following describes the preferred embodiments in detail. It is understood that the following description using a full-bridge chip as an example of the planar strain sensing unit 8 is merely a preferred embodiment of this invention. Any other technical means capable of achieving the same "integrated, planar" strain detection function, such as a thin-film strain bridge directly sputtered on the surface of the main beam 2 or a thick-film strain bridge formed by printing and sintering, utilizes the same concept of this invention, namely, replacing the traditional multi-piece discrete side-mounted patches by setting a small number of integrated sensing units on a single surface of the main beam. Therefore, all should fall within the protection scope of this invention. Example 1

[0026] Please see Figure 1 and Figure 2 The present invention provides a six-dimensional force sensor based on a plane strain sensing unit, which mainly includes an elastic body 6, an upper cover plate 5 and a lower cover plate 7; the elastic body 6 is the core sensitive component of the sensor, which is made of stainless steel through integrated machining and has good mechanical properties and stability.

[0027] The main structure of the elastic body 6 includes: a central loading platform 1, three main beams 2 evenly distributed around the circumference, three floating beams 3 corresponding one-to-one with the main beams 2 and orthogonally connected, and an annular shell 4; the inner end of each main beam 2 is connected to the central loading platform 1, and the outer end is connected to the corresponding floating beam 3; the other end of the floating beam 3 is fixedly connected to the inner wall of the shell 4. This structure is formed by opening three circumferentially distributed ear-shaped grooves and three arc-shaped grooves on the shell 4, which constitutes a classic three-beam force measurement model.

[0028] The present invention will be described in detail below through embodiments. One of the key improvements of the present invention lies in the selection and arrangement of the strain sensing element, namely, the use of a plane strain sensing unit 8. In this embodiment, a full-bridge chip is used as a preferred form of the plane strain sensing unit 8 for description. Please refer to the following... Figure 3This invention abandons the large (typically 2-5 mm) discrete metal foil strain gauges used in traditional six-dimensional force sensors. Traditional methods require up to 24 strain gauges, which is not only cumbersome but also severely restricts sensor miniaturization. The sensor design of this invention fully considers miniaturization requirements. The full-bridge chip is a pre-integrated miniaturized device with planar dimensions of 0.1 mm × 0.1 mm to 1 mm × 1 mm, preferably 0.3 mm × 0.3 mm. Each full-bridge chip is internally integrated with four semiconductor silicon strain gauges in a Wheatstone full-bridge circuit configuration. Due to the use of ultra-small (0.1-1 mm) full-bridge chips and the requirement of only 6 chips, the elastic body 6 structure can be made very compact. Through CAE simulation and optimization, the overall diameter of the elastic body 6 can be controlled within 4-10 mm, preferably 8 mm; the beam depth is 0.5-3 mm, preferably 2 mm; the main beam 2 width is 0.3-1.5 mm, preferably 1 mm; and the floating beam 3 width is 0.1-0.5 mm, preferably 0.3 mm. mm, this miniaturized design solves the urgent need for miniaturized six-dimensional force sensors in the narrow spaces of humanoid robots' dexterous hands and fingertips.

[0029] Traditional methods for measuring six-dimensional force require strain gauges to be attached to the upper and lower surfaces and left and right sides of the main beam 2 to obtain strain information in different directions. This results in complex gauge placement, difficult wiring, and a total of up to 24 gauges. In this embodiment, the full-bridge chip is mounted on the upper or lower surface of the main beam 2. As a preferred implementation, two full-bridge chips can be symmetrically mounted along the axial direction on a single surface (e.g., the upper surface) of each main beam 2, for a total of six chips mounted on the three main beams 2 (see [link to documentation]). Figure 3 (Taking the full-bridge chip mounted on the upper surface of the main beam 2 as an example), this layout avoids the process difficulty of mounting and wire bonding on narrow sidewalls. The number of chips is reduced from the traditional 24 to 6, which not only simplifies the mounting process and reduces manufacturing costs, but also makes fully automated mounting possible.

[0030] Furthermore, this embodiment employs a glass micro-fusion process to fix the full-bridge chip to a predetermined position on the upper or lower surface of the main beam 2. This process specifically includes: applying a low-temperature glass slurry to the predetermined position on the corresponding surface (upper or lower surface, taking the upper surface as an example) of the cleaned main beam 2; precisely placing the full-bridge chip on the slurry; and then sintering it in a controlled atmosphere furnace at a temperature lower than the tempering temperature of the elastomer 6 material. This allows the glass slurry to melt, flow, and wet the chip and substrate. After cooling, a strong connection with high strength, high insulation, and matching coefficients of thermal expansion is formed. Compared to traditional adhesive processes, which typically have poor thermal stability and are prone to aging, creep, or failure in high or low temperature environments, leading to sensor performance drift or even complete malfunction, the glass micro-fusion layer exhibits excellent high-temperature resistance, aging resistance, and thermal stability. Its connection strength is far superior to adhesives, ensuring long-term reliability and signal stability of the sensor in harsh environments. Furthermore, this process has good consistency and is highly suitable for integration with automated production equipment.

[0031] In this embodiment, the mounting position of the full-bridge chip has been carefully optimized. Based on the "AI+CAE simulation optimization platform", the stress field of the elastomer 6 under six-dimensional load is accurately simulated and analyzed (refer to...). Figures 4-9 To maximize output sensitivity and reduce interdimensional coupling, the optimal mounting position for each chip is determined. In a preferred embodiment, the distance d between the edge of the full-bridge chip closest to the edge of the central loading stage 1 and the edge of the central loading stage 1 is optimized to 0.4 mm (see [link to relevant documentation]). Figure 3 , Figures 10-15 ). Example 2

[0032] Based on Example 1, the full-bridge chip in this example can also integrate a temperature sensing element (such as a diffusion resistor) for real-time monitoring of the chip temperature, providing a signal for subsequent temperature compensation. The output signals (analog voltages) of the six full-bridge chips are connected to the flexible circuit board through micro-welded leads, and then input to the signal acquisition module for amplification and analog-to-digital conversion. The signal acquisition module simultaneously acquires the output voltage of the full-bridge (representing strain) and the resistance change of the temperature sensing element (representing temperature), and sends the data to the terminal processing system, which has signal decoupling and temperature compensation capabilities.

[0033] The terminal processing system of this invention includes a signal processing algorithm. Preferably, a data-driven method based on machine learning is used for nonlinear decoupling. In one specific embodiment, for the coupling relationship between the six strain voltage signals, the terminal uses a backpropagation (BP) neural network optimized by a genetic algorithm (GA) to establish a nonlinear mapping model from the six original voltage signals to the real six-dimensional force / torque. This model can accurately map the complex nonlinear relationship between them. This method effectively overcomes the problem of insufficient accuracy of traditional linear algebra-based decoupling methods under complex nonlinear coupling, and improves the measurement accuracy and anti-interference capability of the sensor. At the same time, the system performs real-time digital temperature compensation on the six strain signals based on the real-time acquired temperature signal, effectively suppressing the measurement drift caused by changes in ambient temperature, and ensuring that the sensor maintains stable measurement accuracy and reliability across the entire temperature range. Example 3

[0034] In this embodiment, a preferred implementation of the plane strain sensing unit 8 is described in detail below using a full-bridge chip. The leads on each full-bridge chip terminal are connected to a flexible printed circuit board (FPCB) through micro-welding technology, and then the signals are collected and connected to the sensor's signal acquisition module. After the elastomer 6 is assembled with the upper cover plate 5 and the lower cover plate 7, the output of the signal acquisition module is connected to an external terminal through a connector. The entire chip mounting, welding, and bridging process can be completed by high-precision automated equipment, realizing a fundamental transformation from manual production to industrialized process production.

[0035] Because it adopts the simplest three-beam configuration, the sensing elements are reduced to six standardized plane strain sensing units 8 (full-bridge chips in this example), all of which are mounted on an easily operable plane. Combined with glass micro-melting, a process suitable for mass sintering, the assembly process of the entire sensor is greatly simplified. In addition, in the traditional manufacturing process, manually pasting dozens of strain gauges and manually assembling wires are the main bottlenecks, resulting in low efficiency and poor consistency. However, the process route described in this invention (precision dispensing, automatic chip pick-and-place, automated sintering, and laser micro-welding of leads) can be highly integrated into an automated production line, achieving minimal manual intervention from the loading of the elastomer 6 to the unloading of the finished sensor. This manufacturing method not only significantly improves production efficiency and reduces labor costs and skill dependence, but more importantly, it ensures high consistency and reliability of product performance, meeting the needs of large-scale commercial applications of six-dimensional force sensors.

[0036] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A six-dimensional force sensor based on a plane strain sensing unit, comprising a sensor body, characterized in that, The sensor body includes an upper cover plate (5), an elastic body (6), and a lower cover plate (7) arranged sequentially from top to bottom. The main body of the elastic body (6) includes a central loading platform (1), a main beam (2), a floating beam (3), and a shell (4). One end of the main beam (2) is connected to the central loading platform (1), and the other end of the main beam (2) is connected to the floating beam (3). The floating beam (3) is orthogonal to the main beam (2), and the end of the floating beam (3) away from the main beam (2) is connected to the shell (4). Among them, the upper or lower surface of the main beam (2) is provided with a total of six plane strain sensing units (8). The six plane strain sensing units (8) are used to measure the forces Fx, Fy, Fz in three directions and the torques Mx, My, Mz in three directions.

2. A six-dimensional force sensor based on a plane strain sensing unit according to claim 1, characterized in that, The elastic body (6) is made of stainless steel and its structure includes three ear-shaped grooves and three arc-shaped grooves evenly distributed around the circumference, forming a force measuring structure of three main beams (2) plus three floating beams (3).

3. A six-dimensional force sensor based on a plane strain sensing unit according to claim 1, characterized in that, The diameter of the elastic body (6) is 4 to 200 mm, the beam depth is not less than 0.5 mm, the width of the main beam (2) is not less than 0.3 mm, and the width of the floating beam (3) is not less than 0.1 mm.

4. A six-dimensional force sensor based on a plane strain sensing unit according to claim 1, characterized in that, It also includes a signal acquisition module and a terminal. Six plane strain sensing units (8) are electrically connected to the input end of the signal acquisition module, and the output end of the signal acquisition module is electrically connected to the terminal. The terminal uses a nonlinear decoupling algorithm based on machine learning to decouple the signal.

5. A six-dimensional force sensor based on a plane strain sensing unit according to claim 1, characterized in that, The plane strain sensing unit (8) is a full-bridge chip.

6. A six-dimensional force sensor based on a plane strain sensing unit according to claim 5, characterized in that, The full-bridge chip has a size of 0.1 to 1 mm, and each full-bridge chip contains four semiconductor strain gauges to form a Wheatstone bridge.

7. A six-dimensional force sensor based on a plane strain sensing unit according to claim 5, characterized in that, The full-bridge chip integrates a temperature sensing function, which can acquire temperature signals while collecting six-dimensional force signals, and perform corresponding temperature compensation based on the temperature signals.

8. A six-dimensional force sensor based on a plane strain sensing unit according to claim 1, characterized in that, The six plane strain sensing units (8) are disposed on the upper or lower surface of the main beam (2), and two plane strain sensing units (8) are symmetrically arranged on a single surface of each main beam (2) along its axial direction.

9. A six-dimensional force sensor based on a plane strain sensing unit according to claim 5, characterized in that, The full-bridge chip is attached and fixed to the upper or lower surface of the main beam (2) using a chip mounter and a glass micro-melting process.

10. A six-dimensional force sensor based on a plane strain sensing unit according to claim 1, characterized in that, The distance between the edge of the plane strain sensing unit and the edge of the central loading stage (1) is not less than 0.1 mm.