Journal of Mechanical Science and Technology 29 (7) (2015) 2975~2986 www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-015-0628-6
The obstacle-negotiation capability of rod-climbing robots and the improved mechanism design† Fengyu Xu1,*, J. L Hu2 and Guoping Jiang1 1
College of Automation, Nanjing University of Posts and Telecommunications, Wenyuan Road 9, Nanjing, China 2 Jiangsu Yangli CNC machine Tools Co., Ltd., Yangzhou, China (Manuscript Received August 14, 2014; Revised January 4, 2015; Accepted March 8, 2015)
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Abstract To detect internal steel wire fractures in the cylindrical cable of cable-stayed or suspension bridges automatically in hazardous environments instead of workers, a trilateral clamping-wheeled, rod-climbing robot is designed in this study. In line with this objective, this study also introduces the climbing principle and mechanical structure of this robot (Model-1) and analyzes the static dynamic characteristics of this mechanism. Furthermore, it establishes the mathematical models of the moving wheels during obstacle negotiation. This study also analyzes the relationships of main driving force and resistance with obstacle height to determine the obstacle-negotiation capability of the robot and the two main parameters that influence its obstacle negotiation performance, namely, wheel radius and positive pressure. The Model-1 structure was updated to a new climbing mechanism (Model-2) based on analysis results. Furthermore, the optimal angles of the upper and lower supporting arms were obtained by building the static model of the new mechanism. Finally, Model-2 is superior to Model-1 in terms of obstacle-negotiation capability and satisfies the requirements for suspended cable detection. Keywords: Rod-climbing robot; Obstacle-negotiation capability; Static dynamic analysis ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction Suspended cables are exposed to air for long periods of time as a main stress component of cable-stayed bridges. The Poly ethylene (PE) protection layer on the cable surface is subjected to various degrees of hardening and damage from wind and rain vibrations. Moreover, the steel wires in the interior are prone to erosion or even breakage [1]. Therefore, the steel wire in the cable must be detected. The outer layer of the finished cable is coated with a 4 mm thick PE protection layer, the surface of which is completely smooth. However, various degrees of pits and bulges form on this surface when it is exposed to air for a long time (The height generally does not exceed 4 mm). To limit the influences of wind and rain vibrations, the surface of a new type of cable is pressed with tiny pits or a spiral line. Thus, the robot must display a certain level of obstacle-negotiation capability and should overcome the effects of self-gravity and resistance completely, thereby complicating the negotiation of obstacles on the cable compared with that on the ground. The existing mechanisms of wheeled obstacle-negotiation are typically designed for ground movement [2], whereas vertical rod-climbing mechanisms are little *
Corresponding author. Tel.: +82 2585866506, Fax.: +82 85866504 E-mail address:
[email protected] † Recommended by Associate Editor Kyoungchul Kong © KSME & Springer 2015
emphasized. Some similar climbing mechanisms have recently been designed for pole-like structures. For instance, Cho [3] proposed the use of a cable-climbing robot to inspect long cables. The robot is composed of three similar modules that are circumferentially arranged 120° apart from one another on a frame around the cable. Each module displays three functional mechanisms, namely, driving, adhesion, and safe landing. Ahmadabadi [4] presented a human-inspired pole climbing robot, and a novel design for a naturally stable climbing robot was simulated, implemented and subject to static analysis based on this mechanism. Researchers [5] also constructed a spiny-based bio-inspired robot called RiSE for scansorial environments using microspines that catch on surface asperities to design a small climbing mechanism. Lam [6] proposed a tree-climbing robot known as Treebot that can climb up tree trunks to branches. The robot follows several design principles that are adapted from arboreal animals, including claw gripping and inchworm locomotion. These principles are artificially optimized to enhance maneuverability on irregularly shaped trees. The tree-climbing robot was built by combining six modules as its legs. However, these robots require numerous driving devices, which complicates the mechanical structures. Lee [7] constructed a pipe-climbing robot to inspect pipe structures. It can move along the outer surfaces of straight
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and bent pipes with various diameters and utilizes independently driven wheels. Other special pole-like climbing robots have also been developed and implemented, including a 4DOF climbing structure known as a pole climbing robot [8], the climbing robot RISE V3 [9], the tree-climbing robot [10], the ExplorerTM family of pipe robots [11], the 3DCLIMBER for 3D tubular structures [12], and the Robot V2, which can climb cylindrical or conical poles [13]. However, these robots mainly perform low-altitude climbing tasks, such as the inspection of highway lampposts, vertical and inclined pipes in nuclear power plants, ground storage tanks, and other tubelike structures. Thus, our group proposed a cable inspection robot to inspect external cracks [14-16], and climbing and landing experiments were performed in the field. Given these circumstances, the present study proposes an improved cable-detecting robot (Model-2) to inspect smooth and straight cables. Moreover, it analyzes the obstaclenegotiation capability of this robot to determine the main parameters that influence this capability. The paper is organized as follows. Structure of the trilateral-wheeled climbing robot is presented in Sec. 2. Analysis of the static features of the robot is carried out in Sec. 3. In Sec. 4, an improved mechanism (Model-2) is proposed to overcome the poor climbing capability of Model-1. In Sec. 5, this study constructs the robot and tests it by simulation and experiments. Finally, conclusions and future work are discussed in Sec. 6.
(a) Moving robot based on squirmy mode
t
(b) Moving robot based on crawler FD
v
N T
a G cos a
2. Structure of the trilateral-wheeled climbing robot
Driving wheel
2.1 Climbing principle of the robot G sin a
To achieve a suitable moving mode in high altitude, we analyzed the motivation methods of various specialized climbing robots including squirmy mode (Fig. 1(a)), crawler mode (Fig. 1(b)), walking mode and wheel-driven mode (Fig. 1(c)). We can conclude if the robot uses the squirmy mode and the walking mode in high altitude, the robot can encounter difficulties to return the ground automatically when something goes wrong with the electrical circuits. The crawler mode mechanism is extremely complicated, and its construction cost is relatively high. Thus, reliable wheel-driven robot mode with high efficiency and reliability is employed. The moving wheel of the cable-climbing robot was attached to the surface of the cable by compaction rather than by magnetic or vacuum adsorption given the particularity of suspended cable. In the proposed climbing mechanism, the moving wheel rolls upward along the cable through the motordriven friction wheel. This friction should exceed the sum of the weight and the loads of the robot. That is, maximum static friction FD should surpass the driving force required by upward climbing ( FD = m N ³ Fz ± G sin a ; Fig. 1(c)). m represents the static friction coefficient; N is the positive pressure applied to the moving wheel; Fz is the sum of the loads on the moving trolley with various resistances; a is the inclination angle of the cable; and G is the equivalent gravity of the robot during travel. The moving mechanism of the detection
a
(c) Climbing principle of the friction wheel
(d) Clamping mechanism Fig. 1. Attachment and climbing principle of the robot.
robot is demonstrated by the even distribution of the clamping of the three trolleys on the circumference of the cable and the rotation of the driven wheel. Thus, the robot can move along the vertical, horizontal, and straight suspension cable structures (Fig. 1(d)). The climbing robot is a special field mobile robot. In the process of design, the designer should consider the following requirements: (1) Climbing capability, which enables the robot surmount
F. Xu et al. / Journal of Mechanical Science and Technology 29 (7) (2015) 2975~2986
2 B
BC
2 C
AC
AB S 1
A
Upper wheel Driving module
Upper limb
Spring
Landing machine Lower limb Lower wheel
Fig. 2. Structure of the trilateral-wheeled, rod-climbing robot.
some surface obstacles, such as ridges on the ship hulls, whose dimension is about 5 mm equal to the thickness of the polyethylene sheathing. (2) High operation efficiency and easy Installation. The climbing robot should possess high efficiency as the length of cable reaches several hundreds meters. (3) Safety landing capability to guarantee the robot return safely to the ground in case of electrical interruption. (4) Complexity of the whole structure. It demands the robot possess small size and light weight, which is followed by low energy consumption, to guarantee the robot be carried and mounted on the cable by only one worker. (5) Other characteristics such as high payload capacity, easy controlling mode, convenience of carrying sensor and whole cost are the other mainly factors. 2.2 Structure of the trilateral-wheeled, rod-climbing robot The overall structure (Fig. 2) of the cable-detection robot consists of a driving trolley (A) and two driven trolleys (B and C). The three trolleys are connected in a barrel shape by connecting plates (AB, BC, and AC) and are evenly distributed around the cable. The robot can adapt to cables in different diameters by adjusting the length of the connecting plates.
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The driving module bears the payload and the lithium battery, and two driven modules generate the clasping force. The upper wheel of the powered module alone is actuated by a direct-current (DC) motor. The other two modules simply enhance the stability of the robot and provide the required supporting force. The adhesive forces between the robot and the climbing surface are produced entirely by mechanical means rather than the usual methods of vacuum suction or magnetic force. As a result, system cost is lowered and the system is easily manipulated. The two driven modules (Fig. 2(b)) are identical, and their rolling wheels are connected by an extension spring to generate the clasp force. The two limbs hinged on the vehicle body can rotate flexibly around the shaft such that the mechanism can crawl over a small obstacle by elongating the spring. The driving module supplies power to the climbing robot and is composed of a sub-driving module and a landing mechanism (Fig. 3(c)). The electric magnetic clutch is locked while the robot moves upward. Meanwhile, the one-way clutch is free and the landing mechanism (Sec. 2.3) is deactivated. In the event of electrical outage, the robot slips down automatically as a result of self-gravity. The safety landing mechanism reduces the slipping velocity of the robot as the one-way clutch is locked and the electric magnetic clutch is freed. Sec. 2.3 details the damping principle. The driving and driven wheels are processed in a “V” shape to increase the contacting area of the moving wheel with the cable, to reduce wear, and to prevent the locking phenomenon induced by the deviation of the robot from the cable. The entire mechanism weighs 5 kg, whereas the weights of the battery, charge-coupled device camera, and additional devices total 2 kg. The climbing force of the robot is generated by the friction between the driving wheel and the cable surface. The entire mechanism consists of a single driving wheel, which is produced by casting hard rubber on an aluminum wheel hub. This processing method increases the coefficient of friction of the wheel with the cable surface. 2.3 Safe recovery mechanism of the robot The proposed climbing robot generally operates at an altitude that is several hundred meters high. Once electrical fault occurred, the robot will slip down along the cable by a constant acceleration from several hundred meters high altitude. This will destroy the mechanism and threaten operators and workers. Therefore, automatic recovery is essential in the event of circuit faults. In line with this need, this study presents two safe recovery mechanisms. When the robot operates normally, we can control the motor to make the robot return to the ground. Once electrical fault occurred, the robot can return by the action of safe recovery mechanism. 2.3.1 Frictional plate-type, speed-limiting mechanism This mechanism limits the descent speed of the mechanism by employing the counter moment between the brake pad
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Brake pad
Friction plate Climbing robot
Flexible docking mechanism
(a) Clamp friction-damping mechanism Piston rod
Seal ring Cylinder Throttle hole Piston
Rescue mechanism
(a) Rescue mechanism of the robot (b) Liquid-damping mechanism
1
2
3
4
Fig. 3. Principle of the safe recovery mechanism.
attached by a spring steel disc and the frictional plate (Fig. 3(a)). The results of the indoor experiment confirm the favorable effect of this mechanism. However, the pre-tightening force should be adjusted according to the pitch of the cable after each installation. Therefore, this mechanism is inconvenient in actual application. 2.3.2 Liquid-damping mechanism This mechanism utilizes a sealed cylinder filled with oil, which is divided into left and right parts. The piston is opened with an orifice (Fig. 3(b)). When the piston moves either leftward or rightward, viscous liquid flows to the other side through this orifice. Viscous frictional resistances are thus generated between the oil and the orifice. Fast pistons (namely, the rapid descent of the robot) increase oil pressure and the viscous damping force. The descent of the robot decelerates as the excess energy produced in the process is converted into heat and dissipated. This resistance is generally known as viscous damping. The liquid-damping mechanism is more complex than that of the frictional mechanism to ensure the reliability and durability and to prevent leakages of each component of the liquid-damping mechanism. Moreover, it is accurate although it is costly to manufacture. Therefore, this study applies the simple frictional plate-type, speed-limiting structure (Fig. 3).
(b) Flexible docking mechanism: 1-spring; 4-armature; 3-yoke iron; 2strong permanent magnet
(c) B-type magnetic circuit absorption unit
2.4 Design of the rescue mechanism of the robot This study presents a rescue mechanism to prevent automatic recovery failure induced by the locking phenomenon when the robot climbs. We designed a flexible mechanism to achieve this rescue function. The rescue mechanism is installed by four pairs of flexible spring mechanisms. The locked robot can be pulled back down to the ground by mag-
(d) Rescue mechanism Fig. 4. Rescue mechanism of the robot.
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netic attraction force. Each pair of spring flexible mechanisms is composed of two groups of flexible units (Spring 1 and armature 4; Fig. 4(b)), and each pair of magnetic adsorption devices consists of a yoke and two strong magnets. Fig. 4 shows the rescue mechanism. The magnetic adsorption system especially the magnet may be cracked during absorption; thus, the magnet and adsorption units are sealed and protected with rubber to avoid magnet damage. If the rubber protection shield is used, as Fig. 4(c) shows, the spring mechanism can be removed. The upper ferror plate (upper yoke) is connected with the climbing robot. The magnet is adsorbed on the upper ferror plate, and the upper ferror plate (lower yoke) is connected with the rescue robot (Fig. 4(d)). Therefore, the rescue robot can climb up to reach the place where the robot is locked. Through the magnetic attraction force produced by B-type magnetic circuit, the rescue robot can drag the robot back to the ground.
x
N12 y
N11
45°
45°
N 21
N 32 N 22
N 31
Fig. 5. Overall model of the climbing mechanism.
z
F f 23, xz
3. Analysis of the static features of the robot 3.1 Force analysis of the robot
N i = N i1 sin
2
+ N i 2 sin
b 2
.
Ff 1
l1
L
·P
Mg
(2)
Ff 4
F f 56, xz
N 56, xz
(1)
The direction is perpendicular to the axes of wheel i. Given the symmetrical characteristic of the rolling wheels and the equal arrangement around the cable when two driven modules are identical, we can conclude that: ìï Ffij = N ij m1 (i ¹ 1) í ïî Ffi = Ffi1 + Ffi 2 = N i1m1 + N i 2 m1 .
O1
γ
Fig. 5 is the overall model of the climbing mechanism. We label the wheels on the driving side as wheels 1, 2, and 3. These wheels move counterclockwise. The comparative lower wheels are wheels 4, 5, and 6. N i1 and N i 2 ( i is the number of the wheel) are the supporting forces by which the cable acts on two planes of wheel i and N i is the resultant force of N i1 and N i 2 : b
t
N1
·
N 23, xz
·×
x
O
N4
Fig. 6. Force diagram in the xoz coordinate plane.
In the coordinate plane of xoz , we can determine the equilibrium equation in x directions:
åX = N
1
+ N 4 - N 23, xz - N 56, xz = 0 .
(3)
Based on Eq. (2), we can rewrite Eq. (3) as: In these equations, Ffi1 and Ffi 2 are the rolling frictional resistances by which the cable acts on two planes of wheel i . Ffi denotes the resultant force of Ffi1 and Ffi 2 , which is vertical. m1 is the coefficient of rolling friction and b is the angle of the running wheel. The components of N i in the xoz and yoz planes are denoted by N i , xz and N i , yz , respectively. Ff 23, xz is the resultant friction of driven wheel 2 and wheel 3 and N 23, xz is the resultant supporting force of wheels 2 and 3. Ff 56, xz and N 56, xz can be determined in the same manner, as depicted in Fig. 6. All external forces are projected to plane xoz as in Fig. 6. The robot is considered an entire body, and these forces generate a counterbalance. A series of equilibrium equations can then be established based on the balance condition.
N1 + N 4 - N 2 - N 5 = 0
(4)
å Z = Ff 1 - Mg - Ff 4 - Ff 23, xz - Ff 56, xz = 0 .
(5)
Thus, we can obtain: Ff 1 = Mg + Ff 4 + Ff 2 + Ff 3 + Ff 5 + Ff 6 .
(6)
According to moment-equilibrium: 6
6
M o1 ( F ) =τ- mgl1 + å M o1 ( N i1 ) + å M o1 ( N i 2 ) i =1
6
6
+ å M o1 ( Ffi1 ) + å M o1 ( Ffi 2 ) = 0 . i =1
i =1
i =1
(7)
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γ
N2
Using Eqs. (1) and (11), we obtain:
F2
N 22 b
mw2 g Ft
N 51 = N 52 =
N 21
Ff 2
Fig. 7(c) shows the force diagram of the driving wheel (Wheel 1), where F1 is the force robot body that acts on the driving wheel and r1 is the diameter of the driving wheel. According to the moment balance:
(a) Force diagram of driven wheel 2
Ft
N 51
N5
τ= Ff 1 × r1 .
γ
mw5 g F 5
(Ft - mw5 g )tgγ . 2(sin b 2 + m1tgγ)
(12)
N 52
Ff 5
From Eq. (6), we derive:
(b) Force diagram of driven wheel 5
2 Ff 11 = Mg + 4 N 21m1 + 4 N 51m1 + 2 N 41m1 .
Ff 1 O2 F1
mw1 g
N1
N12 Based on Eqs. (8), (12) and (13):
b
Ff 2
(13)
N11
N 41 =
Mgl1 + B - C - A - D(r1 + r sin b 2 ) 2( L cos15° + m1r1 )
(14)
(c) Force diagram of the driving wheel Fig. 7. Force analysis of the wheels.
In this study, P is the gravity center of the mechanism and
where A = 2rN 21m1 (cos b 2 + sin 45°) , B = 2 LN 51 (cos b 2 + sin 45°) , C = 2rN 51m1 (cos b 2 + sin 45°) , and D = Mg + 4 N 21m1 + 4 N 51m1 . Using Eq. (14), we establish:
r is cable radius. Eq. (7) can therefore be simplified as Ff 1 = 2 Ff 11 = Mg + 4( N 21 + N 51 + N 41 ) m1 .
(15)
τ= 2 N 51 (cos b 2 L + sin 45° L) - 2 Ff 11r sin b 2 -2 Ff 21r (cos b 2 + sin 45°) + 2 Ff 41r sin b 2 -2 Ff 51r (cos
b 2
+ sin 45°) - 2 N 41 sin
b 2
(8)
L + mgl1
where τ is torque output of the driving electric engine. Fig. 7 a depicts the force diagram of wheel 2. In this figure, γ denotes the angle between the limb and the body; mwi g is the gravity force of wheel i ; Ft is the pulling force of the spring; and Fi ( i = 1, 2, 3, 4, 5, 6) corresponds to the supporting force limbs that act on the driven wheels. According to the equilibrium condition: ìï F2 cosγ= Ft + mw 2 g + Ff 2 í b ïî F2 sinγ= N 2 = 2 N 21 sin 2 .
(9)
From Eqs. (1) and (9), we derive:
N 21 = N 22 =
(Ft + mw 2 g )tgγ . 2(sin b 2 - m1tgγ)
(10)
Fig. 7(b) displays the force diagram of wheel 5: ìï Ft = F5 cosγ+ Ff 5 + mw5 g í b ïî F5 sinγ= N 5 = 2 N 51 sin 2 .
(11)
Therefore, we can conclude that when the robot climbs at a constant speed, the required output torque of the DC motor is: τ= Ff 1r1 = [ Mg + 4( N 21 + N 51 ) m1 + 2 N 41m1 ]r1 .
(16)
Thus, we can select the proper driving motor based on Eq. (16). 3.2 Simulation analysis The driving wheel is fabricated from aluminum-cast hard rubber, and the passive wheels are made of MC nylon. Given φ80 mm cable as an example, the main parameters of the climbing robot are as follows: Gravity of the robot: M 1 = 5 kg ; gravity of the inspection instruments: M 2 = 2 kg ; effective radius of the driving wheel: r1 = 32.77 mm ; distance between the upper and lower wheels: L = 315 mm ; stiffness coefficient of the spring: K t = 3.61N mm ; initial pulling force of the spring: Ft = 321N ; the angle between the limb and the body: γ= 30° ; the angle of the “V” wheels: b = 150° ; the weight of the passive wheels: mwi = 0.138 kg ; deflection of the gravity center: d = 17 mm ; static friction coefficient: m = 0.8 ; coefficient of rolling friction: m1 = 0.05 ; and cable diameter: D = 80 mm . The analytical methods of other wheels are identical to that
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450
400 resisting force driving force
Driving force and resisting force(N)
Driving force and resisting force(N)
400
350
300
250
200
150
300
250
200
resisting force driving force
150
0
0.2
0.4
0.6 0.8 1 1.2 1.4 Height of the obstacle(mm)
1.6
1.8
100
2
(a) Driving wheel surmounting an obstacle 200
250
195
240
190 185 resisting force driving force
180 175 170 165
0.5
1 1.5 Height of the obstacle(mm)
2
2.5
230 220 resisting force driving force
210 200 190 180 170
160 155
0
(b) Passive wheels 2 and 5 surmounting an obstacle
Driving force and resisting force(N)
Driving force and resisting force(N)
350
0
0.2
0.4
0.6 0.8 1 Height of the obstacle(mm)
1.2
1.4
(c) Passive wheel 4 surmounting an obstacle
160
0
0.5
1 1.5 Height of the obstacle(mm)
2
2.5
(d) Passive wheels 3 and 6 surmounting an obstacle
Fig. 8. Effect of obstacles on driving force and total resistance.
of wheel 2, and we can simulate climbing capability according to static features. Fig. 8 shows the simulation results of driving force, total resistance, and obstacle height. Figs. 8(a)-(d) depict the simulation results of the driving wheel, upper passive wheels 2 and 5, lower passive wheel 4, and the obstacleclimbing passive wheels 3 and 6. The torque of the motor cannot generate climbing force although the driving force is greater than total resistance, as indicated in Fig. 8(b). Moreover, low climbing capability is mainly caused by the inflexible structure of wheel 3, as presented in Fig. 8(d). Other significant causes of low climbing capability include: (1) excessively small wheel diameter; (2) the wheel3 isn’t a flexible structure; and (3) the slight output torque of the motor.
4. Improved climbing mechanism and the corresponding obstacle-negotiation performance Moving robots on the rugged ground can choose to either negotiate or avoid obstacles. However, rod climbing robots can only climbing over obstacles along the cable line because their movement route is completely limited by the cable. To improve the climbing ability of the robot, we analyzed the Model 1 and concluded that wheel 4 of the original mechanism displays poor obstacle-negotiation capability, as indicated in Fig. 8(c). Therefore, the original support of wheel 4 is removed from the improved structure such that the original mechanism is altered into a stable, three-point support mecha-
nism (Fig. 9). This section introduces the overall improved structure. In addition, negotiation capability is analyzed and simulated. 4.1 Improved robot structure Fig. 9(a) illustrates the principle of the improved robot (Model-2). The original mechanism is modified into a threepoint clamping mechanism with stable support by removing the fix and support-orientated driven wheel 4. This wheel negotiated obstacles on the original robot with the most difficulty (Model-1). Robot deflection can thereby be avoided given the “V”-shaped wheel by eliminating a driven trolley and widening the moving wheel. In detection, the robot must operate stably and uniformly and must be free of swings. Therefore, the driving wheel is still provided with fixed support during design, whereas obstacles can only be negotiated through the swings of the driven trolley. The mechanism can be simplified as displayed in Fig. 9(b) when wheel 2 crosses the obstacle. It can describe the motion state of the robot as a whole by setting the motion of the obstacle-negotiation wheel as pure rolling and by simplifying wheel 2 into a crank. Furthermore, the motion diagram of the mechanism is obtained by simplifying wheels 1 and 4 into sliding blocks. The motion state of the robot can be analyzed through two multi-bar linkages, namely, BCDA and AEFA . The upper and lower swing arms of the driven trolley swing
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wheel 2
z
N2 l2
Ft
q2
Ff 2
l2 AB1
AB2
q2
T1
wheel1
t
N1 l1
P·
AB5
AB6
Ft
Mg q3
wheel 4
l3
C
x
a1
O1
T1
Ff 3
h y
O
·
N3
(a) Improved robot structure
B
t ·
L4
L1
O1
Ff 1 a1
2
Fig. 10. Stresses on the improved climbing mechanism.
l02 x
· Ft
Ff 1
D
A
1
mechanism can be obtained by simplifying wheel 1 into a crank and wheels 2 and 4 into sliding blocks. The motion state of the robot can then be analyzed through two other multi-bar linkages, namely, OACD and OAEF .
q2
j
4.2 Obstacle-negotiation dynamics of the robot
Ft E
In the improved mechanism, the driving wheel displays the poorest obstacle-negotiation capability among the three moving wheels (labeled as wheels 1, 2, and 3) because the driving force is divided horizontally. Therefore, the obstacle-negotiation capability of Model-2 is analyzed based on the obstaclenegotiation performance of the driving wheel (Fig. 10). Analysis of the obstacle-negotiation capability of driven wheel 2
F
(b) Obstacle negotiation by wheel 2 Ff 2
C
Ft y
D
O
x
t
ìï F2 sin q 2 = T1 + mw 2 g + Ff 2 í ïî F2 cosq 2 = N 2 .
(17)
A
Ft
E
Analysis of the obstacle-negotiation capability of driven wheel 4
F
(c) Obstacle negotiation by wheel 1
ìïT1 = mw3 g + F3 sin q3 + Ff 3 í ïî F3 cos q3 = N 3
(18)
Fig. 9. Improved climbing mechanism.
cooperatively during obstacle negotiation. Therefore, the static characteristics of the moving wheel in plane ABF alone require analysis when the moving wheel meets the obstacle. Fig. 9(c) shows the motion principle of the mechanism during obstacle negotiation by wheel 1. The motion graph of the
where T1 is the tension of the spring and l2 and l3 are the lengths of swing arms 2 and 3 of the driven wheel. The upper and lower swing arms of the driven wheel rotate around the upper supporting point of the trolley as the mechanism acts on the suspended cable. In this case, the spring tension is:
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ìï N 2 + N 4 = N1 cos a1 + Ff 1 sin a1 í D ïît + N 2 L4 + ( Ff 2 + Ff 4 )( D + r1 ) + M 2 g (l1 + 2 + r1 ) = N 4 L4 + 2 Ff 1 r1 .
180
Pressure on the driven wheel(N)
160 140
(20)
120 100
The resistance of the mechanism:
80 60 40
0
0
10
20 30 40 50 60 70 Swing angle range of the supporting arm(deg)
80
90
The restrictions on static frictional force:
Fig. 11. Range of the swing angle of the supporting arm of the driven wheel.
B
A
O2
O q2 1
l
m1
(21)
Fz = N1 sin a1 + M 2 g + Ff 2 + Ff 4 .
20
q 2¢
q3
K
q3¢
F
(22)
b 2 is the vertical projection angle of the positive pressure on the two contact surfaces of the moving wheel with cables (The angle between the two surfaces is b 2 = 150° ); a1 refers to the angle of the supporting force of the obstacle as applied horizontally to wheel 1; and M 2 is the total weight of the improved mechanism at approximately 6.5kg . The relationship of the obstacle height with wheel radius is:
l m2
F
N1m cos a1 ³ ( N1 sin a + M 2 g + Ff 2 + Ff 4 )cos b 2 .
Fig. 12. The swing angle of the supporting arm.
h = r2 × (1 -
50 45
1 (tan a1 ) 2 + 1
(23)
).
Radius of driving wheel(mm)
40
The restrictions on the torque of the motor are:
35 30 25
t³
( N1 sin a1 + M 2 g + Ff 2 + Ff 4 )r1
20
cos a1
.
15 10 5 0
0
1
2
3 4 Height of the obstacle(mm)
5
6
7
Fig. 13. Influences of driving-wheel radius on obstacle-negotiation capability.
T1 = KLt = K ( L1 + l2 sin q 2 + l3 sin q3 - L2 )
(19)
where L1 refers to the distance between the supporting points of the upper and lower swing arms; L2 is the original length of the spring; and K is the stiffness of the spring. Swing angles ( q 2 and q3 ) that satisfy the climbing requirements of the mechanism can vary from 33° - 74° when Eq. (19) is combined with the climbing conditions [Eqs. (17) and (18)] of the robot on the cable in simulation (Fig. 11). As Fig. 12 shows, q 2 and q3 repent the swing angle of the supporting arm of the driven wheel. And q 2¢ , q3¢ is the variation range. When the angle of the swing arm is less than 33° or greater than 74° , the tensile spring cannot place enough positive pressure on the driving wheel (Fig. 13). Thus, the minor differences between q 2 and q 4 are ignored such that the mechanism can climb over large obstacles (pits or convexes). We therefore set q 2 = q 4 = 50° to obtain maximum positive pressure. Analysis of the total external force of the mechanism:
Given adequate motor torque, we can approximately deduce the linear relationship (Fig. 13) between the radius of the driving wheel and the obstacle height obtained using Eqs. (21)(23). The radii of the driving and driven wheels are all set to 35.69 mm to ensure that the mechanism crosses a 4 mm high rectangular obstacle.
5. Experiments and analysis of the obstacle-negotiation Climbing experiments were performed in the lab. In our laboratory, two cables with length of 5.3 and 3.7 m and a diameter of 100 mm were placed and can be adjusted to any slant angles randomly. These smooth cables are the same cables used on the real Cable-Stayed Bridge. There is one tube with a diameter of 139 mm can be adjusted from 30° to be approximately vertical. 5.1 Climbing experiments Fig. 14 shows the climbing state of the trilateral-wheeled rod-climbing robot along the cable in our laboratory. These experiments on the cables with diameters of 100 mm suggest that this robot can steadily climb without deflection. The climbing and landing velocity can satisfy the demands of cable detection. Based on the theoretical analysis and the laboratory experiments, the following conclusions are concluded:
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Fig. 14. Climbing experiments in laboratory.
The robot can be installed on the cable by only one worker. The climbing velocity can be adjusted in the scope of 0 m/s to 0.225 m/s. The climbing ability of the robot almost corresponds to the cables of different diameters. From Fig. 14(b), we can conclude that small changes are observed if the mass of the robot and the cable diameters alters. Lines 1, 2, and 3 represent the climbing speed of the robot with various payloads (rated load 2.5 kg, 2.8 kg and 3.2 kg). The curve 4, curve 5, and curve 6 represent the climbing speed when the robot is climbing over an obstacle. In this condition, the driving wheel does not slip, indicating that the friction coefficient of the driving wheel satisfies the climbing conditions. This finding demonstrates that the height of the obstacles exceed the nominal load-bearing capacity. Furthermore, we also compare the variations in the obstaclenegotiation capabilities of Model-1 and Model-2. Fig. 15 presents the relationships of the main driving force and total resistance of the mechanism with obstacle height during obstacle negotiation by driving wheel 1 and driven wheels 2 and 3. The obstacle-negotiation capabilities of the moving wheels of the original robot are valued at 2 mm (Wheel 1), 2.5 mm (Wheel 2 or Wheel 3), 2.3 mm (Wheel 5 or Wheel 6), and 1.2 mm (Wheel 4), whereas those of the improved mechanism are 5.1 mm (Wheel 1), 5.2 mm (Wheel 2), and 5.6 mm (Wheel 3) at an identical moving-wheel radius. Thus, the improved
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three-wheeled mechanism is superior to the original Model-1 in terms of obstacle negotiation capability. Furthermore, the obstacle-negotiation capability of the improved robot Model-2 meets the detection requirements of suspended cable when the radius of the moving wheel increases to 35.69 mm. 5.2 Influence of the cable curvature The cable in the lab becomes a curve cable at the action of self-weight, as AB in Fig. 16 shows. When the robot climbs, if the elongation of the spring is controlled in a reasonable scope (Elongation is smaller than the elongation of the spring when
F. Xu et al. / Journal of Mechanical Science and Technology 29 (7) (2015) 2975~2986
(a) Climbing experiment on a vertical cable
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torque and excessively small radius of wheel 3 and of the moving wheel. This study improved the reasonability of the original model by adjusting the robot structure, increasing the radius of the moving wheel, and selecting suitable motors based on the three factors stated above. Moreover, the optimal swing angle of the supporting arm of the driven wheel was 50° . The improved climbing robot met the detection requirements for suspended cable according to simulation and experimental data of the original mechanism (Model-1) and of the improved mechanism (Model-2). Meanwhile, the obstaclenegotiation analysis provided a theoretical basis for further optimization. The present study presents an improved cable-detecting robot to inspect smooth and straight cables. To perfect the entire system, the vortex-induced cable vibration should be investigated further and a leakage inspection method should be considered.
Acknowledgement (b) Climbing experiment on a inclined cable
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References
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This project is supported by the National Natural Science Foundation of China (51005046), Natural scientific research fund of Nanjing University of posts and telecommunications (NY213042), and Jiangsu Province Natural Science Fund Project of colleges and Universities (13KJB460013).
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(c) The length of the cable on bridge (L = 300 m) Fig. 16. Influence of the curvature.
adjusted the connecting holes), the curvature had little affect on the climbing ability. The climbing robot is mainly used on the long cables on cable-stayed bridges. Though the curvature exists, the length of these cables reache several hundreds meters (Fig. 16(c)). However, the height of the robot is only 400 mm. If divided the cable into many sub-segments, whose dimension is identical with the height of the robot, the curvature of the sub-segment can be neglected, and we can regard it as a line. Therefore, as far as the long cable is concerned, the curvature has little influence on the climbing ability of the robot.
6. Conclusion and future work This study analyzed the obstacle-negotiation capability of an existing suspended cable-detecting robot (Model-1) for cable-stayed bridges. The climbing mechanical model indicated that this capability was mainly influenced by the driving
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Fengyu Xu received his M.S. degree from Hefei University of Technology in 2005 and the Ph.D. degree from Southeast University in 2009. He was an associate professor of the Automation Engineering of Nanjing University of Posts and Telecommunications. His current research interests include robotics and dynamics. Jinlong Hu recieved his M.S. degree from South East University in 2008. He was a senior engineer of Jiangsu Yangli CNC machine Tools Co., Ltd. His current research interests include R&D of CNC machine Tools and Dynamic analysis of structure using finite element analysis technology. Guoping Jiang received his M.S. degree and the Ph.D. degree from Southeast University, Nanjing, China, in 1994 and 1997, respectively, all in automation school. Dr. Jiang was a professor with the Department of Automation Engineering at Nanjing University of Posts and Telecommunications. His research interests include robotics and Complex network theory and its application.