Integrally-formed six-dimensional force sensor based on low-coupling flexible hinge
By using a one-piece molded six-dimensional force sensor based on a low-coupling flexible hinge, the force coupling problem of existing six-dimensional force sensors is solved, achieving efficient and accurate torque detection, which is suitable for robotics, aerospace and industrial automation.
Patent Information
- Application Number
- CN202511248467.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-09-03
- Publication Date
- 2025-11-07
AI Technical Summary
Existing six-dimensional force sensors suffer from force coupling, resulting in low calibration efficiency, complex decoupling algorithms, and structural defects that cause wear and poor dynamic response, failing to meet the force control accuracy requirements of high-end equipment.
A one-piece molded six-dimensional force sensor based on a low-coupling flexible hinge is adopted. Through topology-optimized flexible mechanism and one-piece molded structure, combined with a signal processing system, low-coupling output and high-precision detection are achieved.
It significantly reduces interdimensional coupling, simplifies the calibration process, improves dynamic response and long-term stability, meets the requirements of high-precision detection, and reduces costs and time consumption.
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Figure CN120907715A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of force sensing, in particular to an integrally formed six-dimensional force sensor based on a low-coupling flexible hinge. BACKGROUND
[0002] A six-dimensional force sensor, also known as a six-dimensional force / torque sensor, is a key sensing device that can simultaneously detect three-dimensional orthogonal forces (Fx / Fy / Fz) and three-dimensional torques (Mx / My / Mz). The core principle is to convert mechanical quantities into electrical signals (such as strain gauge resistance changes) through elastic body deformation, and then restore multi-dimensional force information through decoupling algorithms. Such sensors are core sensing elements in fields such as precise robot operation (such as surgical robots, humanoid foot control), aerospace thrust testing, industrial automation, etc., directly affecting the control accuracy and safety of the system.
[0003] Current mainstream six-dimensional force sensors generally have force coupling phenomena (i.e. force in one direction causing abnormal output in other directions), causing the following serious problems: (1) Extremely low calibration efficiency: Traditional six-dimensional force sensors are forced to use full combination calibration methods (Full-Factorial Calibration) due to dimensional force coupling effects. Taking a sensor with a range of ±500N as an example, according to the international standard ISO376: Load needs to be applied to 6 dimensions (Fx / Fy / Fz / Mx / My / Mz); Each dimension requires at least 5 load points (such as 0%, 25%, 50%, 75%, and 100% range); The full combination test point is as high as 5 6 =15,625 times, even if orthogonal experimental design is used to simplify the combination space, more than 2,000 effective load combination tests are still required.
[0004] In actual engineering, even if a full-automatic six-dimensional force loading platform (such as Kistler Type 9129AA) is used, the single "loading-stabilization-acquisition" process takes ≥120 seconds, the total time consumption is >70 hours (nearly 3 days), and the equipment cost is more than US$2 million.
[0005] (2) Decoupling algorithm is complex: Coupling errors need to rely on high-dimensional matrix compensation (such as a 6*6 coupling matrix). The algorithm has poor real-time performance (usually more than 1ms delay), and factors such as temperature drift and creep require repeated calibration on site.
[0006] To solve the problem of force coupling, people have invented "uncoupled" six-dimensional force sensors. However, existing "uncoupled" six-dimensional force sensor schemes have structural defects and performance degradation problems, such as: (1)Patent with publication number CN102323000A (publication date: 2012.01.18) discloses a "safety type no force coupling six-dimensional force sensor", which keeps point contact between the spherical end face of the guide rod at both ends and the inner side of the elastic body, and keeps line contact between the cylindrical side face of the guide rod at both ends and the surface of the elastic body. The guide rod applies external force to the elastic body through point contact and line contact, so as to cause strain of the strain gauge pasted on the elastic body, and the external force and torque are measured by measuring the resistance value of the strain gauge. The invention completely eliminates the coupling between the components from the structure, and avoids complex decoupling algorithm. However, since the elastic bodies in each direction (Fx / Fy / Fz) are independently processed and then assembled on the lower plate, rather than being integrally formed, the relative position accuracy of the multiple elastic bodies and the guide rod needs to be ensured during assembly, and the machining error will significantly magnify the stress distribution deviation in the strain gauge area. The spherical end of the guide rod is in point contact with the Fx elastic body, and the side face is in line contact with the Fy / Fz elastic body. Under long-term dynamic load (such as robot walking), the contact surface is worn due to sliding friction (especially in dusty environment), which causes the change of spherical curvature, leading to the shift of contact point and the drift of Fx measurement, and the concave marks in the line contact area cause the nonlinearity of contact stiffness, which further leads to the increase of Fy / Fz coupling error. Although the patent uses GCr15 bearing steel, it does not design wear compensation or sealing protection, and the actual service life is limited. The point / line contact between the guide rod and the elastic body in the patent will produce coulomb friction (especially when the pre-tightening force is too high), and part of the mechanical energy will be converted into heat energy loss under high-frequency excitation, the equivalent damping ratio of the system increases, leading to the decrease of resonance frequency, and the transient force such as robot foot impact cannot be captured (typical frequency width needs to be greater than 200Hz). Moreover, the sliding interface has static friction-dynamic friction conversion (Stribeck effect), and small force change cannot drive sliding, which is easy to appear dead zone (DeadZone) in low load area (such as small force cannot be detected), leading to micro-force control failure; the step response has hysteresis, and the repeatability accuracy decreases (may be greater than 1%FS). Therefore, in view of the above problems of the patent, it is urgent to design an integrally formed elastic body without sliding friction, and to realize low coupling output between each component.
[0007] (2) Patent with publication number CN107131983A (publication date: 2017.09.05) discloses "a dual-eye structure uncoupled six-dimensional force sensor", which is characterized in that a No. 1 dual-eye structure through hole is opened in the lower platform sensitive beam, and a No. 2 dual-eye structure through hole is opened in the upper platform sensitive beam; each four strain gauges on the surface of the through hole form a set of Wheatstone full bridge; eight sets of Wheatstone full bridges are used to realize the measurement of six-dimensional force information, and the uncoupled output of the force dimension is realized. However, in this design, the upper platform sensitive beam is opened in the horizontal direction, and the lower platform sensitive beam is opened in the vertical direction. Under the action of the Z-direction force Fz, the upper and lower layers deform uncoordinatedly to generate a parasitic bending moment Mx / My, and the actual measurement coupling degree may be large; all sensitive beams are concentrated and fixed on the center hub to form a rigid force transmission core, and stress in any direction causes the hub to deflect slightly, which amplifies the false strain signal in other directions (such as Fx causing My drift) through the lever effect. Therefore, although the six-dimensional force sensor with the dual-eye structure has innovation in reducing the bending modulus of the through hole and improving the sensitivity, the uncoupling is not thorough enough, and the actual measurement coupling degree may not be ideal.
[0008] With the leap of high-end equipment in force control precision requirements, the existing sensor has seriously restricted the development of the industry, for example: (1) Robot safety risk of losing control: in the walking of biped robots, a coupling error of the foot sensor of more than 3% may cause the attitude to be misjudged as falling down.
[0009] (2) Loss of precision manufacturing yield: due to the coupling of Z-direction force and Mx, the chip rate of a semiconductor wafer handling robot increases by 0.15%, resulting in an annual loss of more than 200 million US dollars in the industry.
[0010] (3) Failure of emerging scenarios: a minimally invasive surgical robot needs to detect a tissue reaction force of less than 0.1 N, and requires a coupling degree of less than 0.5%. The dead zone and temperature drift of the existing sensor cannot meet this requirement.
[0011] In view of the current market demand and the status quo of six-dimensional force sensors, developing a six-dimensional force sensor with low coupling at the physical layer, one-piece molding, and no friction and wear is the only way to break through the three bottlenecks of calibration efficiency, dynamic response, and long-term stability, and is also a strategic demand for the national high-end equipment to be self-controllable.
[0012] Therefore, a one-piece molding six-dimensional force sensor based on a low-coupling flexible hinge is provided to overcome the above problems. SUMMARY
[0013] The purpose of the present application is to provide a one-piece molding six-dimensional force sensor based on a low-coupling flexible hinge to solve the problems raised in the background art.
[0014] To solve the above technical problems, the application provides a one-piece six-dimensional force sensor based on a low-coupling flexible hinge, which is used for synchronously detecting three-dimensional orthogonal forces Fx, Fy and Fz and three-dimensional moments Mx, My and Mz, and comprises a one-piece elastic body, which sequentially comprises a base, a flexible hinge layer and a force input platform from bottom to top. The base is a rigid base, and the main plane is disc-shaped. The flexible hinge layer comprises 12 flexible hinges, 12 rectangular strain beams and bosses / pillars for supporting the strain beams and the flexible hinges, wherein 8 flexible hinges are horizontally arranged and symmetrically arranged along the +Fx / -Fx and +Fy / -Fy directions, each direction has two flexible hinges, the axes of the flexible hinges are parallel to the x / y axes, the positions of the flexible hinges are close to the periphery of the base, and the force input ends of the flexible hinges face the center of the disc, the force output ends of the 8 horizontally arranged flexible hinges are rigidly connected with one horizontal rectangular strain beam respectively, and the horizontal rectangular strain beam is rigidly connected with the base through the pillar; 4 flexible hinges are vertically arranged, arranged along the 45°, 135°, 225° and 315° directions of the base plane and parallel to the z axis, the positions of the flexible hinges are close to the periphery of the base and located on the same central circle, and the force input ends of the flexible hinges are close to the force input platform, and the force output ends of the flexible hinges are rigidly connected with one vertical rectangular strain beam respectively, and the vertical rectangular strain beam is rigidly connected with the base through the boss. Each flexible hinge comprises a force guide rod, a force isolation sleeve, a topologically optimized flexible mechanism, an inner ring and an outer ring, the force guide rod is a thin solid cylinder, the force isolation sleeve is a hollow cylinder, the shape of the force isolation sleeve includes but is not limited to a circle and a square, the flexible mechanism is rigidly connected between the force guide rod and the force isolation sleeve, the inner ring is rigidly connected with the force guide rod, the outer ring is rigidly connected with the force isolation sleeve, the outer diameter of the outer ring is greater than the outer diameter of the inner ring, and there is a gap between the outer ring and the inner ring, forming a limit overload protection mechanism, and the limit overload protection mechanism further comprises a structure form of outward protruding mechanism and inward protruding mechanism: the outward protruding mechanism of the force guide rod and the inward protruding mechanism of the force isolation sleeve; the opposite pre-contact surfaces between the two are concentric curved surfaces with gaps; the radius of the curved surface of the protruding mechanism of the force isolation sleeve is greater than the radius of the curved surface of the protruding mechanism of the force guide rod. The force isolation sleeves of all the flexible hinges are rigidly connected with the base through the pillars. The main plane of the force input platform is parallel to the main plane of the base, and the lower surface of the force input platform is provided with 12 force output rods, wherein two horizontal force output rods are arranged along the +Fx / -Fx and +Fy / -Fy directions respectively, and four vertical force output rods are arranged along the Fz direction, and the ends of the force output rods are rigidly connected with the force guide rods of the corresponding flexible hinges respectively. Each of the rectangular strain beams is symmetrically pasted with two foil strain gauges along the axial centerline to form a half-bridge circuit, and two groups of half-bridge circuits in the same direction are connected in series to form a full-bridge output, and the strain gauges of the twelve rectangular strain beams form six full-bridge outputs, which correspond to the detection of +Fx / -Fx / +Fy / -Fy / Fz12 / Fz34 dimensions respectively.
[0015] Further, the flexible mechanism is a cross-shaped S-type elastic arm, a honeycomb structure, a spiderweb structure or a multi-layer concentric ring structure, and is topologically optimized, and the objective function is to maximize the ratio of radial flexibility to axial stiffness, wherein the radial flexibility C_radial≥10 -4 m / N, the ratio of axial stiffness to radial stiffness K_axial / K_radial≥10 4 , and the constraint condition is that the maximum stress of the flexible mechanism under external force is <0.2σ_yield, and σ_yield is the yield strength of the flexible mechanism material.
[0016] Further, among the eight horizontally arranged flexible hinges, two flexible hinges in the +Fx direction and two flexible hinges in the -Fx direction are symmetric about the y-axis, and two flexible hinges in the +Fy direction and two flexible hinges in the -Fy direction are symmetric about the x-axis; the axes of the four vertically arranged flexible hinges all pass through the line connecting the center of the base and the center of the force input platform, and the included angle between adjacent two vertical flexible hinges is 90°.
[0017] Further, the force input platform is provided with eight screw holes at the top end for rigidly connecting the external force applying component and the force input platform by bolts for the input of external forces Fx / Fy / Fz; the aspect ratio of the rectangular strain beam is >5:1, and all the strain beams are located outside the circumference of the base.
[0018] Further, the elastomer is integrally formed by selective laser melting additive manufacturing or overall machining, and the material is AlSi10Mg aluminum alloy, stainless steel or polyether ether ketone; when SLM additive manufacturing is adopted and the material is AlSi10Mg aluminum alloy, the printing layer thickness is 30μm, and after forming, the material is subjected to solid solution treatment at 530℃ / 6h and aging treatment at 160℃ / 8h, the yield strength of the material is ≥280MPa, the elastic modulus is ≥70GPa, and the fatigue life of the flexible hinge is >10 7 times of cycles.
[0019] Further, the strain factor GF of the foil strain gauge is approximately 2, which is highly sensitive to axial elastic strain and has very low response to shear strain; after the signals of the six full-bridge outputs are conditioned, the elastic modulus E and the cross-sectional area A of the rectangular strain beam are combined to calculate the tension / compression force on the beam by the formula F=EAε / k, wherein ε is the axial strain and k is the structure coefficient, and then the external forces Fx / Fy / Fz are decoupled.
[0020] Further, the gap size between the inner ring and the outer ring is determined by finite element simulation, the simulation calculates the critical deformation according to the material yield limit, to ensure that when Fx / Fy increases to the contact between the inner ring and the outer ring, the contact surface stress is less than 0.8 times the material yield strength; the contact surface of the inner ring and the outer ring is a circular surface, so as to reduce the jam caused by sliding friction when contacting.
[0021] Further, a signal processing system is also included, the signal processing system takes STM32G474RET6 MCU as a core, is equipped with 24-bit sigma-delta type ADC, the ADC has 6-channel synchronous sampling function, the skew between channels is less than 1ns, the sampling rate is 10kSPS, and sampling data is read through SPI; the MCU amplifies the strain gauge voltage signal through the built-in PGA, and inputs the ADC after being treated by a 2-order Butterworth anti-aliasing filter; The signal processing system also has a temperature compensation function, and the compensation formula is: Vcomp=Vraw*[1+α*(T-T0)], Wherein Vcomp is the compensated voltage, Vraw is the original voltage, alpha is the channel temperature coefficient, T is the real-time temperature, T0 is the reference temperature of 25 DEG C, and the residual error drift after compensation is less than 0.005% FS / DEG C; The MCU runs the decoupling matrix calculation through the hardware acceleration coprocessor, and outputs Fx / Fy / Fz and Mx / My / Mz in real time, and the calculation results are output through Ethernet (TCP / IP), RS485 (ModbusRTU) or USB-CDC.
[0022] Compared with the prior art, the beneficial effects of the present application are: Significantly reduce the interdimensional coupling degree to meet the high-precision detection requirement: through the topology-optimized flexible mechanism (radial flexibility C_radial≥10 -4 m / N, the axial stiffness and the radial stiffness ratio K_axial / K_radial≥10 4 ), the axial paste of the strain gauge (high sensitivity to axial strain, strain factor GF≈2, and very low response to shear strain), and the symmetrical layout of 12 flexible hinges (8 horizontal + 4 vertical), the force interdimensional coupling degree is less than or equal to 0.8% FS, and the torque interdimensional coupling degree is less than or equal to 1.2% FS, which is significantly lower than the upper limit of 5% specified in ISO9403:2001, and can meet the requirement of detecting less than 0.1N tissue reaction force (coupling degree needs to be less than 0.5%) in minimally invasive surgery robot, and solve the problem that the large coupling error of traditional sensors leads to the failure of precision scene detection.
[0023] Greatly simplify the calibration process, reduce the calibration cost and time consumption: relying on the low coupling characteristics of the physical layer, the calibration method is changed from the traditional full combination calibration (56 =15,625 loading cycles, taking more than 70 hours, and with equipment costs exceeding US$2 million) has been simplified to single-dimensional independent loading. At a single temperature point, only 5 load points (a total of 30 loading cycles) need to be tested in each of the 6 dimensions (Fx / Fy / Fz / Mx / My / Mz), taking less than 2 hours. The theoretical number of tests is reduced by 520 times, the actual calibration efficiency is improved by more than 35 times, and only a unidirectional force source is required. The cost of loading equipment has been reduced to the US$200,000 level, a reduction of 90%, solving the problems of large data volume, low efficiency and high equipment cost of traditional sensor calibration.
[0024] Eliminating sliding friction and assembly errors, improving dynamic response and long-term stability: Employing a one-piece molded elastomer using selective laser melting (SLM) or integral machining avoids the sliding friction wear and assembly errors inherent in assembled structures (such as those in patent CN102323000A); Measured resonant frequency >200Hz (≥80% improvement over assembled structures), step response time <2ms, capable of capturing millisecond-level transient forces such as robot foot impacts; Taking AlSi10Mg aluminum alloy as an example, after solution treatment at 530℃ / 6h + aging at 160℃ / 8h, the yield strength reaches 280MPa, and the fatigue life of the flexible hinge >10... 7 This cycle (compliant with ASTM E466 standard) solves the problems of poor dynamic response and limited lifespan due to wear in traditional assembled sensors.
[0025] Achieving comprehensive overload protection and avoiding plastic deformation and contact jamming: The concentric double-ring structure of the inner and outer rings of the flexible hinge constitutes a limiting overload protection mechanism. The gap size is matched to the material yield limit through finite element simulation to ensure that when Fx / Fy is overloaded to the point where the inner and outer rings contact, the stress is less than 0.8 times the material yield strength, thus avoiding plastic deformation of the flexible mechanism. In addition, the contact surface between the inner and outer rings is a circular surface, reducing jamming caused by sliding friction during contact. The 12 flexible hinges can cover comprehensive overload protection for Fx / Fy / Fz / Mx / My / Mz. Among them, four horizontal flexible hinges in the Fx direction suppress Fy / Fz overload, four horizontal flexible hinges in the Fy direction suppress Fx / Fz overload, and four vertical flexible hinges in the Fz direction suppress Fx / Fy overload, improving the safety of sensor use.
[0026] Excellent temperature stability, suppressing the influence of temperature drift: The signal processing system establishes a temperature-output model through multi-point temperature calibration (-10℃ / 0℃ / 25℃ / 50℃ / 70℃), and achieves temperature compensation based on the formula Vcomp=Vraw*[1+α*(T−T0)] (α is the channel temperature coefficient, T is the real-time temperature, T0=25℃). The zero drift in the range of -10℃~70℃ is <0.02%FS / ℃, and the residual drift after compensation is <0.005%FS / ℃. This solves the problem of repeated calibration and dead zone in low load area caused by temperature drift of traditional sensors, ensuring detection accuracy in a wide temperature environment.
[0027] Reduce the risk and loss of high-end equipment application: with low coupling and high stability characteristics, reduce the attitude misjudgment (risk of losing control) of biped robot caused by coupling error of foot sensor > 3%, reduce the wafer breakage rate of semiconductor wafer handling robot caused by coupling of Z force and Mx, meet the high requirements of force control precision in robot precision operation, aerospace thrust test, industrial automation and other fields, and break through the restriction of existing sensors on the development of high-end equipment.
[0028] Optimize force / torque calculation efficiency and improve real-time performance: 12 rectangular strain beams form 6 full-bridge outputs, combined with the hardware acceleration coprocessor (CORDIC and FMAC units) of STM32G474RET6 MCU to run decoupling matrix calculation, the sampling rate reaches 10kSPS, and Fx / Fy / Fz and Mx / My / Mz can be output in real time; At the same time, 6-channel synchronous sampling (channel skew < 1ns) of 24-bit sigma-delta ADC (ADS131A06) eliminates inter-axis phase shift, solves the problem of complex traditional decoupling algorithm and poor real-time performance (delay > 1ms).
[0029] Adapt to the installation and material requirements of multiple scenes: The top of the force input platform is provided with 8 screw holes, which can be rigidly connected to the external force applying component through bolts, and is suitable for the installation requirements of different scenes; The elastomer material can be selected from metal (stainless steel, AlSi10Mg aluminum alloy, etc.) or non-metal (polyether ether ketone PEEK, etc.) according to performance requirements, taking into account the strength and weight requirements of different application scenarios, and improving the universality of the sensor. BRIEF DESCRIPTION OF DRAWINGS
[0030] Figure 1 It is a flexible hinge front view of the one-piece six-dimensional force sensor based on low-coupling flexible hinge of the application; Figure 2 It is a flexible hinge rear view of the one-piece six-dimensional force sensor based on low-coupling flexible hinge of the application; Figure 3 It is a flexible hinge front planar view of the one-piece six-dimensional force sensor based on low-coupling flexible hinge of the application; Figure 4 It is a flexible hinge rear planar view of the one-piece six-dimensional force sensor based on low-coupling flexible hinge of the application; Figure 5 It is an explosion view of the six-dimensional force sensor based on low-coupling flexible hinge of the one-piece six-dimensional force sensor of the application; Figure 6 It is a base schematic diagram of the one-piece six-dimensional force sensor based on low-coupling flexible hinge of the application; Figure 7This is a bottom view of the force input platform of the integrally molded six-dimensional force sensor based on a low-coupling flexible hinge according to the present invention. Figure 8 This is a side view of the six-dimensional force sensor of the present invention, which is a one-piece molded six-dimensional force sensor based on a low-coupling flexible hinge. Figure 9 This is a diagram illustrating the force / torque measurement of the six-dimensional force sensor based on a low-coupling flexible hinge, as described in this invention. Detailed Implementation
[0031] 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, and 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.
[0032] Please see Figures 1-9 The present invention provides a technical solution: See Figures 1-9 As shown, an embodiment of a one-piece molded six-dimensional force sensor based on a low-coupling flexible hinge is presented: I. Flexible hinge structure: 1.1 Structure of a flexible hinge: See Figures 1-4 As shown, where Figure 1 It includes a force isolation sleeve, an outer ring, and a guide rod. Figure 2 The system includes an isolation sleeve, a flexible mechanism, and a force-guiding rod. In this embodiment, the flexible hinge is the core component for the sensor's low-coupling output. Its structure consists of a central force-guiding rod (a thin, solid cylinder), an outer force-isolation sleeve (a thick, hollow cylinder), a flexible mechanism rigidly connected to the force-guiding rod and the force-isolation sleeve, an inner ring rigidly connected to the force-guiding rod, and an outer ring rigidly connected to the force-isolation sleeve. The force-guiding rod and the force-isolation sleeve have high stiffness, and the flexible mechanism has high radial flexibility and high axial stiffness. The inner diameter of the outer ring is larger than the outer diameter of the inner ring, and a gap exists between them.
[0033] This rigid connection of the integral structure solves the existing publication number CN102323000A patent "elastic body independent processing after assembly" caused by the assembly error amplification stress deviation, sliding friction wear caused by measurement drift (such as spherical contact wear caused by Fx measurement deviation, linear contact wear caused by Fy / Fz coupling error), coulomb friction consumes mechanical energy to reduce the resonant frequency (unable to capture transient forces above 200Hz), static and dynamic friction conversion produces dead zone (low load area micro force detection failure) and other problems, while avoiding CN107131983A patent "double structure sensitive beam fixed on the center hub" caused by the wheel hub micro deflection amplification false strain (such as Fx caused by My drift), Z force Fz produces parasitic bending moment Mx / My coupling problems.
[0034] 1.2 Flexible mechanism topology optimization design: Flexible mechanism can adopt cross S-shaped elastic arm, honeycomb, spider web, multi-layer concentric ring and other styles, and the topology optimization objective function is: maximize the radial flexibility (C_radial≥10 -4 m / N) and axial stiffness ratio (K_axial / K_radial≥10 4 ), the constraint condition is that the maximum stress is less than 0.2σ_yield (σ_yield is the yield strength of the material).
[0035] The optimization design solves the core problems of traditional six-dimensional force sensor, such as low calibration efficiency caused by "dimensional force coupling effect" (such as ±500N range sensor needs full combination calibration 5^6=15625 times, time-consuming more than 70 hours), complex decoupling algorithm (dependent on 6*6 high-dimensional matrix compensation, delay more than 1ms and needs repeated calibration), by improving the radial and axial stiffness ratio at the physical layer, reducing the inter-dimensional coupling from the source.
[0036] 1.3 Working principle of flexible hinge: When the external force Fx / Fy / Fz (relative to the circular cross-section of the guide rod input end, the direction of Fx / Fy is radial and perpendicular to each other, and the direction of Fz is axial) is applied on the circular cross-section of the guide rod input end, and the force isolation sleeve is in a fixed state, the radial external force Fx / Fy will cause the flexible mechanism to deform elastically, and then generate the reaction force F'x / F'y acting on the guide rod; F'x / F'y and Fx / Fy are equal in size and opposite in direction, and the residual coupling degree of the guide rod in the radial direction is <1% FS, and finally only Fz (Fx / Fy output is minimal) is obtained at the output end of the guide rod, realizing low coupling output of Fx / Fy and high coupling output of Fz.
[0037] This principle directly addresses the force control precision pain points in high-end equipment fields: such as the risk of losing control in biped robot walking due to "insole sensor coupling error > 3% leading to attitude misjudgment", the yield problem of semiconductor wafer handling robots "Z force coupling with Mx leading to a 0.15% increase in fragment rate (industry annual loss over 200 million US dollars)", and the failure problem of minimally invasive surgical robots "need to detect <0.1N tissue reaction force with coupling degree <0.5%" in emerging scenarios.
[0038] 1.4 Limiting overload protection mechanism: The inner ring and outer ring of the flexible hinge form a concentric double-ring structure, forming a limiting overload protection mechanism: when Fx / Fy increases to deform the flexible mechanism to the point where the inner ring and outer ring come into contact, the force will be transmitted to the force isolation sleeve through the rigid inner ring and outer ring, and the flexible mechanism will no longer deform, avoiding plastic deformation; at the same time, the gap size between the inner ring and the outer ring is determined through finite element simulation, strictly matching the material yield limit to ensure that the stress is less than 0.8 times the material yield strength when the gap is zero, and the circular contact surface reduces the risk of jamming caused by sliding friction.
[0039] Finite element simulation tool: ANSYS Workbench 2023R1, select "static analysis module", meshing accuracy 0.1mm (hexahedral mesh), ensure stress calculation error <5%; Critical deformation example: taking AlSi10Mg aluminum alloy flexible hinge as an example, when the material yield strength is 280MPa, the critical deformation is 0.3mm through simulation, so the gap between the inner ring and the outer ring is designed as 0.3mm, ensuring that the stress is <224MPa (0.8x280MPa) when the gap is zero, avoiding plastic deformation.
[0040] This protection mechanism solves the problem of traditional sensors "without overload protection or protection structure prone to jamming", especially suitable for dynamic load scenarios such as robot walking and precision assembly, avoiding permanent damage to sensors caused by overload and ensuring long-term stability.
[0041] II. Overall structure of six-axis force sensor: refer to Figures 5-8 as shown: 2.1 Overall structure layout of elastomer: The sensor elastomer adopts an integrated structure, including a base, a flexible hinge layer, and a force input platform from bottom to top, with the specific structure as follows: Base: as the rigid foundation of the sensor, the main plane adopts a disc or other planar shape to provide stable support for the upper structure; Flexible hinge layer: contains 12 flexible hinges, rectangular strain beams, and bosses / pillars for supporting strain beams and force isolation sleeves. Among them, 2 flexible hinges are arranged in the +Fx / -Fx and +Fy / -Fy directions (a total of 8), symmetrically arranged about the x / y axis, the axis is parallel to the x / y axis, close to the periphery of the base, the force input end is towards the center of the circle, and the force output end is rigidly connected to a horizontal thin rectangular strain beam (length-width ratio > 5:1) respectively, and the strain beam is rigidly connected to the base through the pillar; 4 flexible hinges are arranged in the Fz direction at the 45°, 135°, 225°, 315° angles (4 directions of "X" shape) on the base plane, the axis is parallel to the z axis, close to the periphery of the base and on the same central circumference, the force input end is close to the upper force input platform, and the force output end is rigidly connected to a vertical thin rectangular strain beam respectively, and the strain beam is rigidly connected to the base through a small boss; the force isolation sleeves of all flexible hinges are rigidly connected to the base through the pillar; Among them: 8 horizontal flexible hinges: the distance from the edge of the base is 1 / 3~1 / 2 of the radius of the base (for example, the base with a diameter of 100mm, the distance is 16.7~25mm), the distance from the force input end to the center of the circle is 1 / 4 of the radius of the base (i.e. 12.5mm); 4 vertical flexible hinges: the diameter of the central circumference is 2 / 3 of the diameter of the base (i.e. 66.7mm), and the vertical distance between the flexible hinge axis and the upper surface of the base is 5~8mm (adapted according to the overall height of the sensor).
[0042] Force input platform: the main plane is parallel to the main plane of the base, and is arranged above the flexible hinge layer and used for receiving external forces Fx / Fy / Fz (Fx / Fy is radial and vertical to the main plane of the force input platform, and Fz is axial). The lower surface has 2 horizontal force output rods in the +Fx / -Fx and +Fy / -Fy directions and 4 vertical force output rods in the Fz direction, and the ends of the 12 force output rods are rigidly connected to the guide rods of the corresponding flexible hinges below, achieving the transmission of external forces to the input end of the guide rod.
[0043] The spatial layout of the 12 flexible hinges (8 horizontal + 4 vertical) and the rigid connection design of the force output rods solve the problems of "incomplete dimension coverage" and "lack of overload protection" of existing "uncoupled" sensors: the limiting mechanism of the 4 horizontal flexible hinges in the Fx direction can inhibit Fy / Fz overload, the 4 horizontal flexible hinges in the Fy direction can inhibit Fx / Fz overload, and the 4 vertical flexible hinges in the Fz direction can inhibit Fx / Fy overload, while the moment load can be converted into force acting on different position flexible hinges, achieving Fx / Fy / Fz / Mx / My / Mz all-around overload protection, avoiding single direction overload damage to the sensor; in addition, the integral structure completely eliminates the assembly error and sliding friction of the assembled structure, solving the problems of "poor dynamic response (low resonance frequency)" and "low repeatability accuracy (large backlash error and obvious dead zone)" of traditional assembled sensors.
[0044] 2.2 Elastomer processing technology and material: The elastomer is integrally formed by additive manufacturing (selective laser melting SLM technology) or whole machining, and the preferred SLM technology in this embodiment is AlSi10Mg aluminum alloy, and the specific processing and treatment process is as follows: The printing layer thickness is 30 μm; Post-processing: 530℃ / 6h solid solution treatment + 160℃ / 8h aging; Material performance: yield strength up to 280 MPa, elastic modulus 70 GPa, fatigue life >10 7 Secondary cycle (reference standard ASTM E466).
[0045] At the same time, 8 screw holes are arranged at the top of the force input platform, and the external force applying part is rigidly connected with the force input platform through bolts to realize stable input of external forces Fx / Fy / Fz.
[0046] This processing technology and material selection solves the problem of "mismatch between material performance and machining precision" of traditional sensors: CN102323000A patent uses GCr15 bearing steel but has no wear compensation / sealing protection, which limits the service life. The high-precision forming of SLM technology and the high yield strength and long fatigue life of AlSi10Mg ensure the stability of the sensor under long-term dynamic load (such as robot walking), and the integral forming avoids the friction and wear of the assembled structure, thereby improving the service life.
[0047] III. Strain gauge arrangement and signal processing system: 3.1 Strain gauge arrangement and circuit design: The 12 thin rectangular strain beams (8 horizontal and 4 vertical) in the flexible hinge layer are all located at the circumferential periphery. When the low-coupling output radial force and the high-coupling output axial force of the flexible hinge act on the strain beams, a large axial elastic strain and a small shear strain will be generated. The strain gauge arrangement and circuit design are as follows: Each strain beam is symmetrically pasted with 2 foil strain gauges along the axial center line to form a half-bridge circuit; Strain gauge type: metal foil strain gauge (such as BX120-3AA) is used, with a strain factor GF=2.0±0.5%, a working temperature range of -55℃~150℃, and a wide temperature use requirement of the sensor; Pasting process: epoxy resin adhesive (such as 502 instant glue + epoxy resin AB glue) is used, and the surface of the strain beam should be sandblasted (particle size 80 mesh) and alcohol degreased before pasting, and the curing conditions are 25℃ curing for 24h + 80℃ for 2h, to ensure that the strain gauge is tightly attached to the strain beam and reduce the strain transmission error.
[0048] The same direction 2 groups of half-bridge series form full-bridge output; All strain gauge combinations form 6 full-bridge outputs, respectively for testing +Fx / -Fx / +Fy / -Fy / Fz12 / Fz34.
[0049] Since the foil strain gauge is pasted along the axial direction, it has high sensitivity to axial elastic strain (strain factor GF≈2) and very low response to shear strain; by measuring the output voltage signal of the strain gauge (proportional to the axial strain ε) through the Wheatstone bridge, combined with the elastic modulus E and cross-sectional area A of the beam, the tension / compression on the beam can be calculated by the formula F=E*A*ε / k (k is the structural coefficient), and the external force Fx / Fy / Fz is finally decoupled.
[0050] This arrangement solves the problem of traditional strain gauges "pasting direction is not appropriate, resulting in large shear interference and low signal-to-noise ratio", further reduces the inter-dimensional coupling error, and simplifies the decoupling algorithm - without complex high-dimensional matrix compensation, only the voltage signals of the full-bridge outputs can be used to calculate the component force, improving the real-time decoupling.
[0051] 3.2 Working principle of signal processing system: The signal processing system takes MCU (STM32G474RET6) as the core to realize signal acquisition, amplification, filtering, sampling and decoupling calculation, and the specific process is as follows: Multi-temperature point calibration loading: single-dimensional calibration loading is carried out at-10℃ / 0℃ / 25℃ / 50℃ / 70℃ multiple temperature points to provide basic data for temperature compensation and decoupling algorithm; Signal amplification and conditioning: real-time acquisition of strain gauge voltage signal, amplified by built-in PGA (programmable gain amplifier, gain 50-200 times adaptive), to ensure that the output is within 10%-90% of the ADC range; then conditioned by 2-order Butterworth anti-aliasing filter (500Hz cutoff, passband fluctuation <0.1dB) to avoid high-frequency interference; Synchronous sampling: 24-bit Σ-Δ ADC (ADS131A06) is used, which has a built-in 6-channel synchronous sampling mechanism (channel skew <1ns), which can meet the testing needs of 12 strain beams corresponding to 6 full-bridge outputs; the PG1 pin of STM32 is connected to the SYNC pin of ADS131A06, and the 6-channel synchronous sampling is started by triggering the SYNC pulse (pulse width >50ns) through the falling edge, eliminating the inter-dimensional phase shift; Data processing and output: sampled data are read in batches through SPI (SCLK = 10 MHz) at a sampling rate of 10 kSPS; the hardware acceleration coprocessor (CORDIC and FMAC units) of the STM32G4 is used to run decoupling matrix calculation, and real-time output of external forces Fx / Fy / Fz and moments Mx / My / Mz; the calculation results are output through Ethernet (TCP / IP), RS485 (Modbus RTU) or USB-CDC (virtual serial port).
[0052] The system solves the problems of traditional signal processing, such as "different sampling leading to inter-dimensional phase shift, slow processing speed leading to poor real-time performance (delay exceeding 1 ms)", and the hardware acceleration coprocessor and synchronous sampling design ensure fast and accurate decoupling calculation, which is suitable for precise robot operation, aerospace thrust testing and other scenarios with high real-time requirements.
[0053] 3.3 Temperature compensation design: Based on the temperature-output model established by multi-point calibration, the original voltage Vraw is compensated in real time to obtain the voltage Vcomp, and the compensation formula is: Vcomp=Vraw*[1+α*(T−T0)] Where, a is the channel temperature coefficient (pre-stored in Flash after calibration), T is the real-time temperature (monitored by the internal ADC12 of STM32 to monitor the on-chip temperature sensor), T0 is the reference temperature 25℃; the residual drift after compensation is <0.005%FS / ℃.
[0054] This compensation design solves the problems of traditional sensors, such as "temperature drift leading to repeated calibration on site, and precision decline in low load area", especially meets the needs of minimally invasive surgical robots "temperature changes during long-term operation leading to detection errors exceeding the standard", and ensures the stability of the sensor in a wide temperature range of -10℃~70℃.
[0055] Four, six-dimensional force / torque measurement principle: 4.1 Coordinate system establishment and force transmission: Referring to Figure 9 The coordinate system O-XYZ is established on the upper surface of the base, and the origin O coincides with the center of the upper surface of the base; the force output rod below the force input platform is in rigid contact with the input end face of each flexible hinge guide rod, and the external forces Fx / Fy / Fz are transmitted to the 12 flexible hinge guide rods at the same time, and the forces at the output end of the flexible hinge guide rod are recorded as Fxi, Fyi, Fzi (i=1, 2, 3, 4), and the directions of each force are perpendicular or parallel to the upper surface of the base.
[0056] The definition of the force and the common perpendicular distance of the coordinate system axis: the common perpendicular distance of Fxi and OX, OY, OZ axis is Lxxi, Lxyi, Lxzi (i = 1, 2, 3, 4); the common perpendicular distance of Fyi and OX, OY, OZ axis is Lyxi, Lyyi, Lyzi (i = 1, 2, 3, 4); the common perpendicular distance of Fzi and OX, OY, OZ axis is Lzxi, Lzyi, Lzzi (i = 1, 2, 3, 4).
[0057] 4.2 Force and moment calculation: According to the principle of superposition of forces and the definition of moment, the three axial output components of the sensor and the moment calculation formula of the three components are as follows: Axial component: Fx = Fx1 + Fx2 - Fx3 - Fx4; Fy = Fy1 + Fy2 - Fy3 - Fy4; Fz = Fz1 + Fz2 + Fz3 + Fz4; Component moment: Mx = -Fy1*Lyx1 - Fy2*Lyx2 + Fy3*Lyx3 + Fy4*Lyx4 - Fz1*Lzx1 - Fz2*Lzx2 + Fz3*Lzx3 + Fz4*Lzx4; My = Fx1*Lxy1 + Fx2*Lxy2 - Fx3*Lxy3 - Fx4*Lxy4 - Fz1*Lzy1 + Fz2*Lzy2 - Fz3*Lzy3 + Fz4*Lzy4; Mz = Fx1*Lxz1 - Fx2*Lxz2 - Fx3*Lxz3 + Fx4*Lxz4 + Fy1*Lyz1 - Fy2*Lyz2 - Fy3*Lyz3 + Fy4*Lyz4.
[0058] Through the above formula calculation, the six-dimensional force / moment information can be accurately obtained, solving the problem of traditional sensor "moment calculation depends on complex decoupling model, error accumulation is large", combined with the low coupling characteristics of flexible hinge, further improving the moment measurement accuracy, meeting the demand of aerospace thrust test, industrial automation and other scenes for torque detection.
[0059] Five, performance verification: 5.1 Test conditions and methods: According to ISO376:2017 standard, finite element simulation and physical test are carried out, the specific conditions and methods are as follows: Test environment: 23±0.5℃, 50%RH; Loading device: E2 standard weight (relative error ≤0.001%) + 1:20 lever system; Test items and methods: Force coupling: single dimension loading 100% Fx / Fy / Fz, record the output peak of other dimensions; Moment coupling: single dimension loading 100% Mx / My / Mz, record the output peak of other dimensions; Temperature drift: -10℃ / 25℃ / 70℃ three-point constant temperature for 2 hours, measure the zero point change.
[0060] The test is based on 3 machines, each repeated 3 times to ensure the reliability of the results.
[0061] 5.2 Test results: Static performance: Force coupling between dimensions ≤0.8% FS; Moment coupling between dimensions ≤1.2% FS; Temperature characteristics: -10℃~70℃ zero drift <0.02% FS / ℃.
[0062] After compensation by the formula Vcomp=Vraw*[1+α*(T−T0)], the residual drift is <0.005% FS / ℃ (for example, Fx range ±500N, residual drift <0.025N / ℃), which is much better than the temperature drift error caused by no temperature compensation mentioned in the existing CN102323000A patent (usually >0.1% FS / ℃).
[0063] The above indicators are significantly lower than the 5% upper limit specified in ISO9403:2001 (clause 7.3.2), and compared with traditional sensors: Calibration efficiency: this embodiment uses single dimension calibration (six dimensions are loaded independently, and there are 5 load points for each dimension), the total test number is only 6*5=30 times, and the time consumption is <2 hours; traditional full combination calibration needs 15625 times, and the time consumption is >70 hours, the theoretical test number is reduced by 520 times, and the actual test efficiency is increased by more than 35 times; Equipment cost: this embodiment only needs a single force source, and the cost of force loading equipment is reduced from US$2 million to US$200,000, with a reduction of 90%; Dynamic performance: the integrated elastomer eliminates assembly friction and assembly error, and the actual measured resonance frequency is >200Hz (increased by ≥80% compared with the assembled structure), and the step response time is <2ms, meeting the millisecond-level transient force detection requirements such as bottom impact.
[0064] The performance verification results prove that this embodiment completely solves the problems of low calibration efficiency, high equipment cost, poor dynamic response, and excessive coupling of existing six-dimensional force sensors, and can meet the force control requirements of high-end equipment fields such as robot precision operation, aerospace, precision manufacturing, and medical treatment, while meeting the strategic demand of national high-end equipment self-controlling.
Claims
1. An integrally formed six-dimensional force sensor based on low-coupling flexure hinges for simultaneous detection of three-dimensional orthogonal forces Fx / Fy / Fz and three-dimensional moments Mx / My / Mz, characterized in that: The elastic body is sequentially composed of a base, a flexible hinge layer and a force input platform from bottom to top; The base is a rigid base, and the main plane is disc-shaped; The flexible hinge layer comprises 12 flexible hinges, 12 rectangular strain beams and bosses / pillars for supporting the strain beams and the flexible hinges, wherein 8 of the flexible hinges are horizontally arranged, symmetrically arranged along the +Fx / -Fx and +Fy / -Fy directions respectively, 2 in each direction, the axis is parallel to the x / y axis, the position is close to the periphery of the base, and the force input end faces the center of the disc, the force output end of each of the 8 horizontally arranged flexible hinges is rigidly connected with a horizontal rectangular strain beam, and the horizontal rectangular strain beam is rigidly connected with the base through the pillar; 4 of the flexible hinges are vertically arranged, arranged along the 45°, 135°, 225° and 315° directions of the base plane and parallel to the z axis, the position is close to the periphery of the base and located on the same central circle, the force input end is close to the force input platform, and the force output end is rigidly connected with a vertical rectangular strain beam, and the vertical rectangular strain beam is rigidly connected with the base through the boss; Each of the flexible hinges comprises a force guide rod, a force isolation sleeve, a topologically optimized flexible mechanism, an inner ring and an outer ring, the force guide rod is a thin solid cylinder, the force isolation sleeve is a hollow cylinder, the shape of the force isolation sleeve includes but is not limited to a circle and a square, the flexible mechanism is rigidly connected between the force guide rod and the force isolation sleeve, the inner ring is rigidly connected with the force guide rod, the outer ring is rigidly connected with the force isolation sleeve, the outer diameter of the outer ring is larger than the outer diameter of the inner ring, and there is a gap between the outer ring and the inner ring, forming a limit overload protection mechanism, the limit protection mechanism further comprises a structure form of outward protruding mechanism and inward protruding mechanism: composed of the protruding mechanism of the force guide rod facing the outer diameter direction and the protruding mechanism of the force isolation sleeve facing the inner diameter direction; the opposite pre-contact surfaces between the two are concentric curved surfaces with gaps; the radius of the curved surface of the protruding mechanism of the force isolation sleeve is larger than the radius of the curved surface of the protruding mechanism of the force guide rod; The force isolation sleeves of all the flexible hinges are rigidly connected with the base through the pillars; The main plane of the force input platform is parallel to the main plane of the base, and the lower surface of the force input platform is provided with 12 force output rods, wherein 2 horizontal force output rods are arranged along the +Fx / -Fx and +Fy / -Fy directions respectively, and 4 vertical force output rods are arranged along the Fz direction, and the ends of the force output rods are rigidly connected with the force guide rods of the corresponding flexible hinges respectively; Each of the rectangular strain beams is symmetrically pasted with 2 foil strain gauges along the axial center line to form a half-bridge circuit, 2 groups of half-bridges in the same direction are connected in series to form a full-bridge output, and the strain gauges of the 12 strain beams form 6 full-bridge outputs corresponding to the detection of the +Fx / -Fx / +Fy / -Fy / Fz12 / Fz34 dimensions respectively.
2. The low coupling flexure-based, integrally formed six-axis force sensor of claim 1, wherein: The flexible mechanism is a cross-over S-shaped elastic arm, a honeycomb structure, a spiderweb structure or a multi-layer concentric ring structure, and is topologically optimized, with an optimization objective function being to maximize a ratio of radial flexibility to axial stiffness, wherein the radial flexibility C_radial≥10 -4 The ratio of axial stiffness to radial stiffness K_axial / K_radial≥10 4 , and a constraint condition being that a maximum stress of the flexible mechanism when bearing an external force is <0.2σ_yield, and σ_yield is a yield strength of a material of the flexible mechanism.
3. The low coupling flexure based integrally formed six-axis force sensor of claim 1, wherein: 8 of the horizontal arrangement of flexible hinge, + Fx direction of 2 flexible hinge and - Fx direction of 2 flexible hinge about y axis symmetry, + Fy direction of 2 flexible hinge and - Fy direction of 2 flexible hinge about x axis symmetry;4 of the vertical arrangement of flexible hinge axis all through the center of the base and the center of the force input platform connection, and the included angle between adjacent two vertical flexible hinge is 90 DEG.
4. The low coupling flexure based integrally formed six-axis force sensor of claim 1, wherein: The top of the force input platform is provided with 8 screw holes, which are used for rigidly connecting the external force applying component and the force input platform by bolts, and are used for Fx / Fy / Fz external force input;The length-width ratio of the rectangular strain beam is greater than 5:1, and all the strain beams are located outside the circumference of the base.
5. The low coupling flexure based integrally formed six-axis force sensor of claim 1, wherein: The elastomer is integrally formed by selective laser melting additive manufacturing or overall machining, and the material is AlSi10Mg aluminum alloy, stainless steel or polyether ether ketone; when the SLM additive manufacturing is used and the material is AlSi10Mg aluminum alloy, the printing layer thickness is 30 μm, after forming, the material is subjected to solid solution treatment at 530℃ / 6h and aging treatment at 160℃ / 8h, the yield strength of the material is ≥280MPa, the elastic modulus is ≥70GPa, and the fatigue life of the flexible hinge is >10 7 secondary cycles.
6. The low coupling flexure based integrally formed six-axis force sensor of claim 5, wherein: The strain factor GF of the foil strain gauge is approximately 2, which is high in axial elastic strain sensitivity and low in shear strain response;The signals output by the 6 full bridges are conditioned, combined with the elastic modulus E and cross-sectional area A of the rectangular strain beam, and the tension / compression of the beam is calculated by the formula F=E*A*ε / k, wherein ε is the axial strain and k is the structure coefficient, and then the external forces Fx / Fy / Fz are decoupled.
7. The low coupling flexure based integrally formed six-axis force sensor of claim 1, wherein: The gap size between the inner ring and the outer ring is determined by finite element simulation, and the simulation is based on the material yield limit to calculate the critical deformation, so that when Fx / Fy increases to the contact between the inner ring and the outer ring, the contact surface stress is less than 0.8 times the material yield strength;The contact surface between the inner ring and the outer ring is a circular surface to reduce the jam caused by sliding friction when contacting.
8. The low coupling flexure based integrally formed six-axis force sensor of claim 1, wherein: It also includes a signal processing system, which takes STM32G474RET6 MCU as the core, and is equipped with 24-bit sigma-delta type ADC, which has 6-channel synchronous sampling function, channel skew <1ns, sampling rate 10kSPS, and sampling data is read through SPI;The MCU amplifies the strain gauge voltage signal through the built-in PGA, and inputs the ADC after being conditioned by the 2-order Butterworth anti-aliasing filter; The signal processing system also has temperature compensation function, and the compensation formula is: Vcomp=Vraw*[1+α*(T-T0)], Wherein Vcomp is the compensated voltage, Vraw is the original voltage, α is the channel temperature coefficient, T is the real-time temperature, T0 is the 25 DEG C reference temperature, and the residual drift after compensation is less than 0.005% FS / ℃; The MCU runs the decoupling matrix calculation through the hardware acceleration coprocessor, and outputs Fx / Fy / Fz and Mx / My / Mz in real time, and the calculation results are output through Ethernet (TCP / IP), RS485 (ModbusRTU) or USB-CDC.
Citation Information
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