Design and implementation of the wheel-clamping stay cable inspection robot

A new wheel-clamping type inspection robot for bridge stay cables was designed. Its clamping mechanism adopts a four-auxiliary-two-drive wheel clamping scheme, and the driving unit utilizes a single motor with double output shaft. A simple automatic control system of the robot was designed based on Arduino. Then, the diameter range of the stay cable that the robot can hold was calculated. The mechanical model of the robot under clamping condition was established. The curves for the minimum thrust Fe and driving force F required by the robot under different stay cable diameters Φ and inclined angles γ were obtained through Matlab data processing. Based on Adams dynamic simulation, the appropriate shape and material of the wheel, the optimal position of the centroid distribution and how to improve the wind resistance of the wheel were determined. Finally, a prototype robot was developed and a climbing experiment was carried out. The results show that the inspection robot is easy to clamp, simple to operate and control, and the detection speed is 0–5 m/min. The robot can grab stay cables with diameters ranging from 70 to 245 mm and can be used for stay cables with angles ranging from 0° to 90°.


Introduction
As the main load-bearing component of cable-stayed bridge, stay cable plays a crucial role in the service life and structural safety of cable-stayed bridge, and the cost of stay cable is expensive, accounting for 25%-30% of the cost of the whole bridge on average. Due to long-term exposure to the natural environment, the outer protective layer of the stay cable will be damaged to varying degrees. If these damage are not dealt with in time, corrosion damage will occur inside the cable of the bridge, which will affect the fatigue life, 1 main girder alignment, 2 and pneumatic stability of the cable, 3,4 and may even lead to cable breakage. Therefore, regular inspection on the surface of the bridge stay cable is an essential and crucial part of the safety maintenance of the stay cable. At present, it is a feasible research scheme to improve personnel safety through robot technology. 5 Robot inspection is one of the most convenient, efficient, and economical methods for cable-stayed bridge inspection, and relevant scholars have carried out a lot of research. For example, a stay cable snow removal robot developed by the Institute of Civil Engineering and Construction Technology in Korea. It adopts a symmetrical mechanical clamping mechanism, and the robot clamps the stay cable by adjusting the screws on both sides. 6 The clamping mechanism of the pipe climbing robot designed by Sungkyunkwan University is composed of worm drive and ball screw mechanism. 7 Li et al. 8 designed a tracked rod climbing robot that squeezes the compression block to clamp the inclined ties by manually tightening the knob. Chen et al. 9 designed a tracked rod climbing robot with a multi-joint linkage structure clamping structure. Wang et al. 10 designed a cablestayed robot that tightens the diagonal cable by manually tightening four joint tie-rod screws. Some pole climbing robots were designed based on bionic principles, such as snake robot designed by Sun et al., 11 mimic looper robot designed by Li et al. [12][13][14] To sum up the above literature, scholars have done a lot of research on the clamping mechanism of related inspection robots. On the one hand, most of these mechanical structures adopt closed-loop clamping mechanisms. When using these type of inspection robots, it is usually necessary to manually tighten the screws and bolts, lead screws or tie rod screws to tighten the stay cables, as shown in Figure 1. The installation and adjustment procedures are cumbersome and require employees to be highly skilled to make each tightening torque similar to avoid affecting the climbing stability of the robot. There are also some inspection robots are designed based on bionic, but their inspection speed is very slow, and it is difficult to meet the actual detection efficiency requirements.
On the other hand, most of these robot-driven controls still require human remote control, as shown in Figure 2.
In view of the above problems, a new type of wheelclamping stay cable inspection robot was developed. The robot adopts an open-loop clamping mechanism, and only needs to remotely control the electric push rod to achieve tight clamp. No need for additional auxiliary fixing devices and control of tightening torque. Its control system is designed based on Arduino, and it can realize automatic inspection without manual remote control, which can meet the engineering application requirements of rapid inspection of robots.

Design scheme
The mechanical principle The stay cable inspection robot adopts the combination of four auxiliary wheels and two drive wheels for clamping and driving, and its mechanical principle is shown in Figure 3. The driving unit consists of a twoaxis motor that drives two driving wheels via two toothed belts. The clamping device consists of rod 1, rod 2, and rod 3, of which rod 1 can extend or contract, and control the magnitude of force. One end of rod 2 is fixed on the robot body, and the other end of rod 2 is   (1) Auxiliary wheel; (2) timing belt; (3) drive motor; (4) robot body; (5) rod 2; (6) rod 1; (7) stay cable; (8) rod 3; (9) drive wheel. hinged on rod 3. One end of rod 3 is hinged with rod 1, and the other end of rod 3 is installed with auxiliary wheels. The rubber drive wheel and auxiliary wheel are designed with a curved structure to better fit the surface of the stay cable. The clamping principle is as follows: rod 1 extends and drives rod 3 to rotate around rod 2, which in turn drives the auxiliary wheel and driving wheel to clamp the cable.

Clamping device design
An important performance of the stay cable inspection robot is that it can hold the cable with different diameters and clamp them quickly. This paper proposes a new four-auxiliary and two-drive wheel-clamping scheme, which can enable the robot to clamp different diameters of stay cables and achieve fast clamping capability, and its mechanism principle is shown in Figure 4.
The four auxiliary wheels have the freedom of rotation on the X-axis, and their wheel bodies are designed with a curved structure, so they have a certain selfadjusting ability when clamping the cable, which allows the auxiliary wheels to better grip onto the cable. The clamping principle is that the electric push rods on both sides of the robot body push the left and right clamping arms to rotate around the bracket until the auxiliary wheels and driving wheels are pressed on the cable surface, thus realizing the clamping of cables with different diameters.

Driving unit design
In order to drive synchronously, save space and reduce cost, the driving unit of the robot adopts the design scheme of single motor and two driving wheels, as shown in Figure 5. The two output axes of the dual-axis motor share a common spindle, which can synchronize the output of both ends of the dual-axis motor and its control is simpler, compared to the single-motor, singledrive-wheel design. The two output shafts of the dualaxis motor are respectively connected to a driving wheel, and the driving wheel is connected to the driven wheel by a trapezoidal synchronous belt, which in turn drives the driven wheel for synchronous rotation.

Control system design
The ability of the inspection robot to operate stably on the cable requires not only a reasonable structural design, but also a stable control system. To reduce manual intervention and simplify the control logic, an overall framework of the control system based on Arduino Mega development board is designed, as shown in Figure 6.
After the overall framework of the control system is designed, the control program is designed in the Arduino IDE. The main control code of the motion control system is shown in Figure 7. Among them,     checkdistance_2_3( ) is the front-end ultrasonic sensor control code, used to detect the distance between the robot and the bridge top, checkdistance_4_5( ) is the back-end ultrasonic sensor control code, used to detect the distance between the robot and the bridge bottom, and 9 is the PWM wave of the control board Interface, PWM wave can be used for robot speed regulation. go( ) is the part of the climbing code that controls the robot to climb, stop( ) is the part of the hovering code that controls the robot to hover, back( ) is the part of the return code that controls the return of the robot. Due to space limitations, the detailed codes of these parts have been omitted.
The principle of its motion control system is as follows: turn on the switch on the control board and adjust the speed, and the robot climbs, emitting a prompt beep every 1 s to disperse the possible birds. If the distance detected by the front-end ultrasonic rangefinder is less than 25 cm, the robot hovers for 2 s and starts to return with a prompt beep every 1 s. When the distance detected by the back-end ultrasonic rangefinder is less than 25 cm, the robot stops the operation and makes a prompt beep every 0.1 s to remind the personnel that the inspection is completed. The motion control flowchart is shown in Figure 8.

Kinematic and mechanical analysis
The stay cable diameter that the robot can clamp As shown in Figure 9, the travel range L2[0, 80] of the electric push rod, O(0,0) is the inner tangent point between the arc of the driving wheel and the circle of   the stay cable section, A (120, 33) is the hinge point of the clamping arm and the bracket, B (B x , B y ) is the center of the auxiliary wheel, the dashed circle centered at point B is the rotatable trajectory of the auxiliary wheel, the radius of the auxiliary wheel is 24 mm, L ab = 130 mm is the distance from point A to point B, a2[80°, 155°] is the angle between L ab and the positive direction of X-axis, C (C x , C y ) is the center of the circle of the stay cable section, D (D x , D y ) is the hinge point of the electric actuator and the clamping arm, D 1 (165, 219) is the initial coordinate when the electric actuator pushes L = 0 mm, L ad = 68 mm is the distance from point A to point D, E (119, 2202) is the hinge point of the electric actuator and the frame.
Based on the geometric relations in Figure 9, the coordinate point B (B x , B y ) can be expressed as: The relationship between the dashed circle of the auxiliary wheel and the circle of the stay cable section is: According to (1) and (2), the diameter F of the stay cable that the robot can hold tightly can be expressed as: The coordinate point D (D x , D y ) can be expressed as: The travel range L of the electric push rod can be expressed as: After inputting the above relationship into Matlab software, and then analyze the relationship between the travel range L of the electric push rod and the diameter F of the stay cable that the robot can clamp, as shown in Figure 10.

Required electric actuator thrust
Because the left and right clamping arms are symmetrically arranged, the force analysis principle of the left and right clamping arms is the same, so one of the clamping arms can be selected for analysis. The right clamping arm is selected for mechanical analysis. When the robot clamps the stay cable with a inclined angle of g, the circular plane of the section of the stay cable is selected for mechanical analysis, and its force diagram is shown in Figure 11. F p is the reaction force of the stay cable on the clamping arm, F e is the thrust of the electric push rod on the clamping arm, and F d is the reaction force of the stay cable on the drive gear train.
The cosine values of some of the angles in Figure 11 can be expressed by the following equation.
The moment balance for point A is as follows: Figure 10. The relationship between L and F during clamping.
Where, M A (F e ) and M A (F p ) are the torque of F e and F p to point A.
During the hovering process of the robot, the driving wheel group and the auxiliary wheel group jointly provide static friction to balance the component force of its gravity along the direction of the stay cable. The force analysis is as follows: The thrust F e can be expressed as: The preselected material of the driving wheel is nylon or rubber, and the surface material of the stay cable is set to nylon. According to the mechanical design manual, set the static friction coefficient of the driving wheel m 1 = 0.5, set the static friction coefficient of the auxiliary wheel m 2 = 0.01, and set the robot gravity G = 100 N. And then, the curve of the minimum thrust F e of the electric push rod required under different stay cable diameter F and its inclined angle g can be obtained, as shown in Figure 12. It can be seen from Figure 12 that the minimum thrust value of the required electric push rod is 73.9 N and the maximum is 244.9 N.

Required driving force
In order to calculate the driving force required under different cable diameters and different inclined angles, the force analysis of the upper drive wheel and the lower drive wheel was established as shown in Figure  13. Point M is the center of gravity of the robot. The force of the upper and lower drive wheels is mainly affected by the contact reaction force of the cable, the driving force of the motor, gravity, and rolling resistance.
On the coordinate system, there are: Where, F p1 , F p2 , F p3 , and F p4 are the reaction forces of the stay cable on each auxiliary wheel, and F N1 and F N2 are the reaction forces of the stay cable on the upper and lower driving wheels.   According to the layout of the robot transmission part, it can be seen that the driving torque of the upper driving wheel and the lower driving wheel are equal, and the torque balance of the upper and lower driving wheel centers is as follows: Where, T t1 and T t2 are the driving torque of the upper and lower driving wheels respectively, T is the total driving torque required, r = 25 mm is the radius of the driving wheel, m is the rolling friction coefficient. According to the mechanical design manual, considering the static friction coefficient of the bearing and the elastic deformation of the wheel, the rolling friction coefficient of the wheel train is 0.01. According to formula (8) to (11), the following formula can be obtained.
Where, F is the driving force required by the robot. After inputting the above relationship into Matlab software, the driving force F required by the robot under different stay cable diameters F and its inclined angle g is obtained, as shown in Figure 14. It can be seen from Figure 14 that the minimum driving force required for the robot is 38.4 N and the maximum is 286.5 N.

Simulation analysis
In order to simulate the climbing stability when the thrust of the electric push rod is the maximum, the diameter of the stay cable F = 120 mm is selected as the simulation condition. According to the relationship between the minimum thrust F e of the electric push rod required under the different diameter F of the stay cable and its inclined angle g in Figure 12, the relationship curve between g and F e was obtained by making F = 120 mm, as shown in Figure 15. It can be seen that when the inclined angle of the stay cable is about 63.9°, the maximum thrust of the electric push rod is about 184.3 N. The simulation parameters are set in Adams software as follows: the diameter of the stay cable is 120 mm, the total length of the stay cable model is 3000 mm, the total mass of the robot is 10 kg, the inclination of the stay cable is 63.9°, the thrust is 184.3 N, the rotational speed of the drive wheel is 210°/s, and the simulation time is 40 s. The climbing stability of the robot is mainly measured by the deflection angle of the center of mass (the deflection angle of the robot's center of mass relative to the center of the circle of the cable section) and the speed of the center of mass.

Influence of wheel shape and material on climbing stability
The wheel shape can be roughly divided into two types: the one type is a commonly used ordinary wheel body, the other type is the curved wheel body. The common wheel body experimental results are shown in Figure  16(a). When the simulation experiment lasts for 20 s, the right clamping arm will contact the stay cable, as shown in Figure 16(b). However, because the curved design of the auxiliary wheel can provide the constraint effect of moving along the direction of the stay cable, the robot can still climb, but it will scratch the surface of the stay cable. Therefore, the ordinary wheel body is not suitable for the design of this robot.
The common wheel body material is nylon or rubber. The difference in Adams software is mainly reflected in the setting of contact force parameters. The Figure 14. The relationship between F, g, and F in a tight state. Figure 15. The relationship between g and F e when F = 120 mm.
contact force parameters of the two materials acting on nylon stay cables are shown in Table 1, and the simulation results of the curved wheel body are shown in Figure 17. It can be seen from Figure 17 that the deflection angle of the overall centroid of the robot equipped with the curved rubber wheel does not exceed 3.5°in the simulation time of 40 s, and the curve is relatively smooth, while the deflection angle of the overall centroid of the robot equipped with the curved nylon wheel is close to 4°, and the curve fluctuates greatly. According to the above simulation experiments, the curved wheel body is more suitable for the design of this robot than the ordinary wheel body and the curved rubber wheel is more suitable for the design of this robot than the curved nylon wheel.

Influence of centroid position on climbing stability
When the wheeled robot climbs the cylinder, it is easy to spiral climb, which has a great influence on the climbing stability. To study the climbing stability of the robot, the robot battery is installed in different positions during the simulation, and then the centroid position of the robot is changed. The climbing stability of the robot under different centroid positions can be studied, and the optimal position of the battery can be obtained. Several different battery placement positions were set up in Adams, as shown in the rectangular box in Figure 18. The battery measures 77 mm in length, 66 mm in width, and 55 mm in height, with a total mass of 1 kg.    The deflection angle curve of the robot's centroid, as measured under different conditions of battery placement, is depicted in Figure 19. As can be seen from the simulation results in Figure  19, the anti-deflection effect is the best when the batteries are distributed in the lower right position of the robot. At this time, the centroid deflection angle measures of the robot is 1.5°. Compared with the centroid deflection angle of 4°when the battery is distributed in the lower left position of the robot, the optimization effect reaches 62%. It can be concluded that battery and other components should be installed in the lower right position of the robot as far as possible, so that the center of gravity of the robot is offset to the lower right, which can play a good anti-deviation effect.

Influence of wind on climbing stability
The cable inspection robot is classified as an aerial work robot, and as such, its climbing stability must take into account the effects of lateral wind forces. A wind load calculation formula can be used for this purpose: As specified in the Crane Design Manual, the wind force coefficient C for a planar object is selected as 1.2, and the wind height variation coefficient K h is selected as 1.86 according to the conditions such as the height above the ground on the land is greater than 80 m. For wind speed v of 20 m/s as measured by the anemometer and force eight gale selected, the calculated wind pressure q is taken as 1000 N/m 2 . The maximum projected area of the robot, as measured by SolidWorks, is 0.038 m 2 , giving a windward area A of 0.038 m 2 . An approximation of P W = 85 N can be obtained.
To simulate the effects of lateral winds and their varying wind speeds on the robot's crawling motion, a force function STEP (time, 0, 0, 10, 85) + STEP (time, 15, 0, 30, 2170) is applied to the robot's centroid during the simulation. The applied force function and the robot's climbing speed can be seen in Figure 20.
As shown in Figure 20, when the wind force reaches 85 N, the reaction force of the stay cable on the driving wheel set becomes insufficient, causing the robot to slip and reducing its speed to nearly 0, resulting in unstable climbing.
To address the adverse effects of wind on the robot's climbing stability, the thrust of the left and right electric push rods can be increased. Three different thrust levels of F = 185 N, F = 225 N, and F = 265 N were used for simulation and comparison experiments. The simulation results, presented in Figure 21, show that increasing the thrust F reduces the centroid deflection angle of the robot. When F = 225 N, the robot's measured speed returned to the normal value of 85 mm/s. Thus, during patrol missions in windy conditions, increasing the thrust of the electric push rod can help maintain the climbing stability of the robot.

Prototype test
When the robot clamps the vertical pipe with a diameter of 120 mm, front, back, left, and right views of the robot are provided in Figure 22. As shown in    Figure 22, the robot clamps the pipe effectively. Among them, the rectangular frame in Figure 22(a) is the first camera position, the left rectangular frame in Figure  22(b) is the second camera position, and the right rectangular frame is the third camera position.
The control module of the robot prototype is shown in Figure 23.
The experimental study was conducted with a pipe diameter of 120 mm, inclination of 63.9°, and a speed adjusted to 5 m/min. After placing the robot on the pipe, adjust the push distance of the electric push rod by remote control so that the robot holds the pipe tightly and does not slide down, then turn on the drive switch, the robot climbs up the pipe emitting a beep with a time interval of 1 s, as shown in Figure 24(a) and (b). When the robot reaches the top of the pipeline, it hovers for 2 s while the ultrasonic distance finder at the front-end measures a distance of 25 mm from the obstacles in front, as shown in Figure 24(c). The robot then reverses its motor and starts to descend while emitting a beep with a time interval of 1 s. When the ultrasonic range finder at the back-end detects that the   robot is 25 mm above the ground, it stops moving, as shown in Figure 24(d), and emits a sharp beep with a time interval of 0.1 s to indicate that the pipeline inspection task is complete. Throughout the experiment, the robot travels approximately 3 m and takes about 40 s to complete the inspection.
The inspection robot's camera unit is composed of three cameras. The first camera position is the camera on the robot body frame, the second camera position is the camera on the left clamping arm, and the third camera position is the camera on the right clamping arm. The camera is hard wired and its angle can be manually adjusted and fixed to ensure a clearly capture of the pipe surface. The inspection camera effect is shown in Figure 25.
The experimental results of the robot prototype show that the clamping device of the robot can continuously clamp the pipeline during both ascending and descending movements, while maintaining stable and normal speed, good posture, and clear camera images. The automatic control system operates logically. The relevant performance parameters of the inspection robot are shown in Table 2.

Conclusion
(1) A new type of inspection robot for bridge stay cable was proposed, which uses wheels to clamp the stay cable. The clamping mechanism is based on a four-auxiliary two-drive wheelclamping scheme, and the driving mode adopts the single-motor double-drive scheme. The robot is equipped with a simple automatic control system based on Arduino. (2) The geometric relationship of the robot was analyzed based on its structural design, and it was determined that the robot can theoretically clamp stay cables with a diameter range of 70 to 245 mm. Additionally, a mechanical model of the robot in its clamping state was established based on the force situation of the robot on the stay cable. Through Matlab data processing, the relationship curve between the minimum required thrust F e and the driving force F required by the electric push rod under different stay cable diameters F and inclined angles g were obtained.
(3) Adams dynamics simulation was performed to investigate the effects of various factors on the motion stability of the robot. The simulation results show that the appropriate wheel shape and body material is curved rubber wheel. The installation position of the battery has an impact on the motion stability of the robot, as the center of gravity of the robot is shifted to the lower right, which can play a good antideviation effect. When the wind speed in the inspection environment is relatively high, the way of increasing the thrust of the electric push rod can effectively maintain the climbing stability of the robot. (4) A prototype of the inspection robot was developed, and climbing experiments were carried out. The results show that the robot is convenient to clamp, simple to operate and control, the detection speed range is 0-5 m/min, the diameter range of the clamped stay cable is 70-245 mm, and the inclination of the applicable stay cable is 0°-90°. The prototype experiment shows that its climbing and control system has good stability and the camera is clear, which provides a new design idea and theoretical basis for the stay cable inspection robot.  ministry of education of higher school science and technology innovation engineering projects and state key laboratory of robotics fund projects, Chinese academy of sciences robotics opening laboratory fund projects, etc.

Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This project was funded by National Natural