CN102928137A - Four-interdigital-electrode type three-dimensional force contact sensor for artificial skin - Google Patents

Abstract

The invention discloses a four-finger electrode type three-dimensional force tactile sensor for artificial skin. The finger electrodes are covered with a pressure-sensitive material layer to form resistors R ₁ , R ₂ , R ₃ and R ₄ respectively, and the upper surface of the pressure-sensitive material layer is covered with hemispherical contacts to form a three-dimensional force tactile sensor set on the surface of the detected area. unit.

Description

Four-digit electrode-type three-dimensional force tactile sensor for artificial skin

technical field

The invention belongs to the field of sensor technology, in particular to a three-dimensional force touch sensor applied to robots.

Background technique

With the development of robotics, research on tactile sensors has received more and more attention. At present, the research on single-dimensional force sensors is relatively mature, but as a robot's smart skin, not only the sensor is required to detect the vertical pressure on the surface, but also the sensor is required to detect the shear force in the horizontal direction. For example, when a robot holds an object, it needs to sense tangential force and sense positive pressure at the same time. When the robot touches some objects with irregular surfaces, it is necessary to realize the detection of three-dimensional or even multi-dimensional force. The development of three-dimensional force tactile sensor has become an important research field of intelligent robot technology.

At present, a variety of three-dimensional force sensors have been developed at home and abroad for use in robot skin. Japan's Van A H et al. used MEMS technology to paste piezo-sensitive thin film resistors on the cross beam structure to make a three-dimensional force tactile sensor for robot fingers; Huang et al. at National Cheng Kung University in Taiwan used curved platinum/titanium film, fixed a section of it and arranged it into a cross-beam structure, and made a tactile sensor for detecting vertical force and shear force; Su et al. at National Tsing Hua University in Taiwan generated anisotropic carbon nanotubes on a silicon substrate, And transfer it and spin it to PDMS to make a flexible tactile sensor that can detect vertical force and shear force; these sensors for measuring three-dimensional force information mainly use metal or metal oxide cross beams or semiconductor materials, etc., these The materials are all rigid materials, not flexible.

Chen et al. used PDMS and PET as matrix materials, and ITO as electrodes to make a flexible capacitive tactile sensor that can detect vertical and shear forces; Xu Fei et al. from Hefei Institute of Intelligent Machinery, University of Science and Technology of China, used carbon black/silicone rubber as the matrix material, and the upper and lower layers inside the material are wired into a cross structure to form a three-dimensional force flexible tactile sensor, which realizes the detection of three-dimensional force. Although the three-dimensional force sensor made of conductive rubber has a certain degree of flexibility, the double-sided contact between the electrode and the force-sensitive material makes the sensor manufacturing process very difficult, and it is not reliable in terms of stability and sensitivity.

Contents of the invention

The invention provides a flexible four-finger electrode type three-dimensional force tactile sensor for the artificial sensitive skin of an intelligent robot with good flexibility, high precision and stable performance.

The present invention adopts following technical scheme for solving technical problems:

The structural characteristics of the four-finger electrode type three-dimensional force tactile sensor for artificial skin of the present invention are: on the flexible circuit board, four identical fork-finger electrodes are arranged symmetrically at 90° on the same plane; The finger electrode is covered with a pressure-sensitive material layer to form resistance R ₁ , resistance R ₂ , resistance R ₃ and resistance R ₄ , and the upper surface of the pressure-sensitive material layer is covered with a hemispherical contact to form a sensor set on the surface of the detected area. Three-dimensional force tactile sensing unit.

The structural features of the four-finger electrode type three-dimensional force tactile sensor for the artificial skin of the present invention also lie in:

The three-dimensional force tactile sensing units are arranged in an array on the surface of the detected area to form a three-dimensional force tactile sensor.

The pressure-sensitive material layer is made of flexible pressure-sensitive conductive rubber, and the flexible pressure-sensitive conductive rubber is filled with carbon black in silicon rubber.

The hemispherical contact is made of polyethylene.

In the three-dimensional force touch sensing unit, the pressure-sensitive material layer is independently covered on each single interdigital electrode, and silicon rubber is used between the pressure-sensitive material layers covered on the interdigital electrodes. connected as one structure.

The three-dimensional force in the three-dimensional force tactile sensing unit is analyzed and obtained according to the following formula:

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="2"\; label="R"\; filenames="HDA00002401182500011.png,HDA00002401182500013.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="1"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="1"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="2"\; label="R"\; filenames="HDA00002401182500011.png,HDA00002401182500013.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="R"\; filenames="HDA00002401182500011.png,HDA00002401182500013.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}$

In the formula:

F _x , F _y , F _z are the forces on the hemispherical contact in the directions x, y and z respectively;

k _x , _ky and k _z are the resistance coefficients of the three-dimensional force sensing unit for the acting forces F _x , F _y and F _z respectively, and the k _x , ky _and k _z are obtained through experimental calibration;

R ₁ , R ₂ , R ₃ and R ₄ are the initial resistance value of the three-dimensional force tactile sensing unit in the positive direction of the y-axis, the initial resistance value of the resistance in the positive direction of the x-axis, and the negative direction of the y-axis of the three-dimensional force tactile sensing unit, respectively. The initial resistance value of the resistance on , the initial resistance value of the resistance in the negative direction of the x-axis;

ΔR ₁ , ΔR ₂ , ΔR ₃ and ΔR ₄ are respectively the variation of R ₂ , R ₂ , R ₃ and R ₄ after the three-dimensional force tactile sensing unit receives force.

Compared with the prior art, the beneficial effects of the present invention are reflected in:

1. All the production materials of the four-digit electrode type three-dimensional force tactile sensor for artificial skin of the present invention include interdigital electrodes, force-sensitive materials, and contacts are all flexible materials, which meet the flexibility requirements of artificial skin.

2. The four-fingered electrode structure on the flexible circuit board of the present invention fully considers the coupling relationship between different directions, and can effectively improve the stability and sensitivity of the sensor.

2. The three-dimensional force sensor of the present invention uses pressure-sensitive conductive rubber to contact the flexible circuit board on one side, which has a simpler contact structure and simpler manufacturing process than electrodes arranged on both sides.

3. In the present invention, the pressure-sensitive conductive rubber and the interdigitated electrodes are all elastic materials, which allow the three-dimensional force sensor to realize bending deformation, so that the entire tactile sensor can be reliably adhered to various curved surfaces, realize the detection of three-dimensional force, and improve its flexibility and surface adaptability.

4. The measuring range and sensitivity of the three-dimensional force of the present invention can be controlled by the component ratio of carbon black contained in the pressure-sensitive material and the electrode finger width and size, and the adjustment range is wide.

Description of drawings

Fig. 1 is the cross-sectional structure schematic diagram of the tactile sensor based on flexible conductive rubber of the present invention;

Figure 2a is a schematic structural view of the flexible circuit board unit in the present invention;

Fig. 2b is a schematic diagram of the position distribution of four equivalent resistances of the three-dimensional force sensor in the present invention;

Labels in the figure: 1 hemispherical contact; 2 pressure-sensitive material layer; 3 flexible circuit board; 4 interdigitated electrodes.

Detailed ways

Referring to Fig. 1, Fig. 2 and Fig. 3, the structural form of the four-digital electrode type three-dimensional force tactile sensor for artificial skin in this embodiment is: on the flexible circuit board 3, four identical interdigital electrodes 4 are on the same plane arranged symmetrically at 90° above each other; each interdigital electrode 4 is covered with a pressure-sensitive material layer 2 to form a resistance R ₁ , a resistance R ₂ , a resistance R ₃ and a resistance R ₄ respectively, and the upper surface of the pressure-sensitive material layer 2 is covered The hemispherical contact 1 constitutes a three-dimensional force tactile sensing unit arranged on the surface of the detected area.

In the specific implementation, the three-dimensional force tactile sensing units are arranged in an array on the surface of the detected area to form a three-dimensional force tactile sensor; the pressure-sensitive material layer 2 is made of flexible pressure-sensitive conductive rubber, and the flexible pressure-sensitive conductive rubber is made of silicone rubber. Carbon black is filled in the middle; the hemispherical contact 1 is made of polyethylene;

The pressure-sensitive material layer is independently covered on each single interdigital electrode, and the pressure-sensitive material layers covered on each interdigital electrode are connected by silicon rubber as an integral structure.

The three-dimensional force in the three-dimensional force tactile sensing unit is obtained by analysis according to the following formula:

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="2"\; label="R"\; filenames="HDA00002401182500011.png,HDA00002401182500013.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="1"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$

${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="1"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="1"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="2"\; label="R"\; filenames="HDA00002401182500011.png,HDA00002401182500013.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="R"\; filenames="HDA00002401182500011.png,HDA00002401182500013.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;<figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="R"\; filenames="HDA00002401182500011.png"\; state="\{\{state\}\}">R</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}$

In the formula:

F _x , F _y , F _z are the forces on the hemispherical contact in the directions x, y and z respectively;

k _x , _ky and k _z are the resistance coefficients of the three-dimensional force sensing unit for the acting forces F _x , F _y , and F respectively, and k _x , ky _and k _z are obtained through experimental calibration;

R ₁ , R ₂ , R ₃ and R ₄ are the initial resistance value of the three-dimensional force tactile sensing unit in the positive direction of the y-axis, the initial resistance value of the resistance in the positive direction of the x-axis, and the negative direction of the y-axis of the three-dimensional force tactile sensing unit, respectively. The initial resistance value of the resistance on , the initial resistance value of the resistance in the negative direction of the x-axis;

ΔR ₁ , ΔR ₂ , ΔR ₃ and ΔR ₄ are respectively the variation of R ₁ , R ₂ , R ₃ and R ₄ after the three-dimensional force tactile sensing unit receives force.

In FIG. 1 : the tactile sensor based on flexible pressure-sensitive conductive rubber is composed of a hemispherical contact 1 , a pressure-sensitive material layer 2 and a flexible circuit board 3 with interdigital electrodes 4 to form a compact whole from top to bottom.

In Fig. 2a and Fig. 2b, the four interdigital electrodes 4 are electrically connected with the pressure-sensitive material layer 2 to form four equivalent resistances to realize three-dimensional force detection.

The mechanism of detecting the three-dimensional force information is as follows: the three-dimensional force acts on the pressure-sensitive material layer 2 through the hemispherical contact 1, the pressure-sensitive material layer is in contact with the four interdigital electrodes, and the equivalent resistances R ₁ , R ₂ , R ₃ and _R4 will change resistance when subjected to strain. The detection of the three-dimensional forces F _x , F _y , and F _z can be realized by measuring the changes of the four resistances.

According to the existing research, the size of the electrodes of the flexible circuit board and the distance between the electrodes have an impact on the strain output.

When _Fx acts, the resistance of R ₁ is reduced by the pressure strain, the resistance of R ₃ is increased by the strain of tension, and the strains on both ends of R ₂ and R ₄ cancel each other out, and the resistance change is negligible.

When F _y acts, the resistance of R ₂ is reduced by the pressure strain, and the resistance of R ₄ is increased by the tension strain, while the strains on both ends of R ₁ and R ₃ cancel each other out, and the resistance change is negligible.

When F _z acts, R ₁ , R ₂ , R ₃ , and R ₄ are subjected to the same degree of compressive strain, and the four resistances decrease equally.

The output voltage signal of the sensor is input to the computer through the switch gating circuit, the voltage comparison amplifier circuit, and the data acquisition conversion, and then processed by matrix operation to obtain the values of F _x , F _y , and F _z .

The tactile sensor based on the flexible pressure-sensitive conductive rubber of the present invention can be produced by the following process:

Firstly, the flexible circuit board 3 is produced by using the standard flexible circuit board production technology; the interdigitated electrodes 4 are produced on the flexible circuit board 3 by the screen printing technology, and the pressure-sensitive material layer 2 is produced by the room temperature synthesis process; The pressure-sensitive material of material layer 2 has been publicly reported in "Research on Conductive Composite Materials for Composite Flexible Tactile Sensors" published by Zhao Xing, Huang Ying, etc. in the second issue of "Functional Materials" in 2010; The shape contact 1 is made of resin material, and the hemispherical contact 1 is glued on the pressure-sensitive material layer 2 .

After that, calibrate the tactile sensor based on flexible pressure-sensitive conductive rubber, apply different pressures to the sensor repeatedly, and detect the relationship between the resistance value of the sensor and the applied pressure under different pressures, so as to calibrate the sensor , by extracting and processing the three voltage signals output by each three-dimensional force sensitive unit in the three-dimensional force sensitive array under the action of three-dimensional contact force, the linear coupling relationship between the force in each direction and the three voltage signals is obtained through linear decoupling, and then The coupling relationship between each sensitive unit is obtained through neural network decoupling.

Claims (6)

1. The four-finger electrode type three-dimensional force tactile sensor for artificial skin is characterized in that: on the flexible circuit board (3), four identical interdigital electrodes (4) are arranged symmetrically at 90° on the same plane ; Covering the pressure-sensitive material layer (2) on each interdigital electrode (4) to form resistance R ₁ , resistance R ₂ , resistance R ₃ and resistance R ₄ respectively, on the pressure-sensitive material layer (2) The surface is covered with hemispherical contacts (1) to form a three-dimensional force touch sensing unit arranged on the surface of the detected area. 2. The four-digit electrode type three-dimensional force touch sensor for artificial skin according to claim 1, characterized in that: the three-dimensional force touch sensing units are arranged in an array on the surface of the detected area to form a three-dimensional force touch sensor. 3. The four-digit electrode type three-dimensional force tactile sensor for artificial skin according to claim 1, characterized in that: the pressure-sensitive material layer (2) is made of flexible pressure-sensitive conductive rubber, and the flexible pressure-sensitive Conductive rubber is filled with carbon black in silicone rubber. 4. The four-digit electrode type three-dimensional force tactile sensor for artificial skin according to claim 1, characterized in that: the hemispherical contact (1) is made of polyethylene. 5. The four-digit electrode type three-dimensional force touch sensor for artificial skin according to claim 1, characterized in that: in the three-dimensional force touch sensing unit, the pressure-sensitive material layer is independently covered on each single On the interdigital electrodes, the pressure-sensitive material layers covered on the interdigital electrodes are connected by silicon rubber as an integral structure. 6. The four-digit electrode type three-dimensional force tactile sensor for artificial skin according to claim 1 is characterized in that: the three-dimensional force in the three-dimensional force tactile sensing unit is obtained by analyzing according to the following formula: ${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$ ${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}}$ ${\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&Delta;R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}}{\mathrm{<span\; class="notranslate">\; 4</span>}}$ In the formula: F _x , F _y , F _z are the forces on the hemispherical contact in the directions x, y and z respectively; k _x , _ky and k _z are the resistance coefficients of the three-dimensional force sensing unit for the acting forces F _x , F _y and F _z respectively, and the k _x , _ky and k _z are obtained through experimental calibration; R ₁ , R ₂ , R ₃ and R ₄ are the initial resistance value of the three-dimensional force tactile sensing unit in the positive direction of the y-axis, the initial resistance value of the resistance in the positive direction of the x-axis, and the negative direction of the y-axis of the three-dimensional force tactile sensing unit, respectively. The initial resistance value of the resistance on , the initial resistance value of the resistance in the negative direction of the x-axis; ΔR ₁ , ΔR ₂ , ΔR ₃ and ΔR ₄ are respectively the variation of R ₁ , R ₂ , R ₃ and R ₄ after the three-dimensional force tactile sensing unit receives force.

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