Structural synthesis for broken strands repair operation metamorphic mechanism of EHV transmission lines

3.1. Operational requirements

According to the operating requirements, the reposition mechanism must be designed with 2 DOFs. One DoF is the motion of making two cut-open nuts clamp EHV power lines, the other is the motion of locking the two cut-open nuts into a united one through pins. Because of the special operation condition, it is required to reduce the weight of repair mobile robot, to simplify the control system, and to save the carrying energy (usually lithium battery). Therefore, 2-DOF constrained metamorphic mechanism is designed as the reposition mechanism which completes the two motions above with only one driver.

3.2. The design of source metamorphic mechanism

In accordance with the kinematic requirements and operating condition, the metamorphic mechanism is designed with 2 DOFs and two rotational constrained metamorphic joints. Metamorphic processes are achieved during the configuration transforming. The working statuses of constrained metamorphic joints will transfer between moving and static depended on the changing of constrained forces to form the corresponding working stages, while the diver joint and general joints keep working. The displacement (turning angle or moving distance) $\theta$ of the driver is shown in horizontal axis, and the working conditions of joints $J$ ($J=R$ for revolute joint, $J=P$ for prismatic joint etc.) in corresponding working stages (or metamorphic configurations) is shown in vertical axis. The working configuration transferring and the working statuses of metamorphic joints can be described in metamorphic cyclogram as shown in Fig. 3 [16], which shows the working statuses of all the joints with the movement of driver in the corresponding working stages. Finally, the metamorphic cyclogram of 2-DOF reposition metamorphic mechanism is obtained as shown in Fig. 3. Configuration I and Configuration II denote two working configurations of the metamorphic mechanism. Suppose the driving link obtains translational motion of screw driven by a motor, a kind of corresponding planar 5-bar mechanism, i.e. source metamorphic mechanism is designed as shown in Fig. 4.

Fig. 3Metamorphic cyclogram of the metamorphic mechanism

Fig. 4The source metamorphic mechanism of broken strands reposition

4.1. Equivalent resistance gradient sketch of metamorphic joints

Fig. 5Equivalent resistance gradient sketch

Based on Fig. 3 and equivalent resistance gradient model proposed in reference [16], the equivalent resistance gradient sketch of constrained metamorphic mechanism (Fig. 4) is obtained as shown in Fig. 5, in which $f_e$ denotes equivalent resistance coefficient and $\theta$ denotes the displacement of the driver.

The equivalent resistance gradient sketch of metamorphic joints can be described as matrix, i.e. the equivalent resistance matrix:

where, working configurations are shown in columns of the matrix, constrained status of metamorphic joints with different working configurations are shown in rows, and $f_{ij}$ denotes that metamorphic joint $R_{ij}$ keeps constrained, 0 means $R_{ij}$ keeps working.

4.2. The structural topology matrix of constrained metamorphic mechanism

4.2.1. Constrained metamorphic joints

Typical constrained structures and constrained matrixes of metamorphic joints are shown in Fig. 6. Fig. 6(a) shows the turning joint and prismatic joint with geometric constraint which overlaps two links into one and provides infinite constraint force at the point. Fig. 6(b) shows the turning joint and prismatic joint with spring force constraint. Fig. 6(c) shows the turning joint and prismatic joint with geometric constraint controlled by spring which provides limited constraint force at the point. Fig. 6(d) shows the turning and prismatic joints with geometric constraint and spring force constraint respectively. Fig. 6(e) shows the turning and prismatic joints with geometric constraint and geometric constraint controlled by spring respectively. In constrained matrixes, 0 denotes that metamorphic joint $R_{ij}$ keeps moving and 1 denotes that $R_{ij}$ keeps static. Suppose $g=r\text{,}$$p$ which denotes revolving or prismatic metamorphic joints with geometric constraints. $s=rk\text{,}rt\text{,}pk\text{,}pt$, where $rk$, $rt$ denote revolving metamorphic joints with spring force constraint and geometric constraint controlled by spring respectively, and $pk$, $pt$ denote prismatic metamorphic joints with spring force constraint and geometric constraint controlled by spring respectively. $sg=rkg\text{,}rtg\text{,}pkg\text{,}ptg$, which denotes metamorphic joints (revolving or prismatic) with spring force constraint and geometric constraint, and with geometric constraint and geometric constraint controlled by spring.

Fig. 6Typical constrained structures of metamorphic joints

a)$g=r$, $p$

b)$s=rk$, $pk$

c)$s=rt$, $pt$

d)$sg=rkg$, $pkg$

e)$sg=rtg$, $ptg$

4.3. Structural diagram of constrained metamorphic mechanism

According to the structural topology matrix ${\mathbf{C}}_i$($i=$ 1, 2,…, 8), the eight structural diagrams of reposition metamorphic mechanisms are illustrated in Fig. 7.

5.1. Design of the practical reposition metamorphic mechanisms and its topological transformations

The selection of the structural form is based on the reliable working configuration transforming ability and the structure simplicity. In this point of view, the mechanisms of Fig. 7(c) and Fig. 7(d) can both achieve reliable metamorphic process in metamorphic joint C. Fig. 7(c) mechanism is selected as the practical broken strands reposition metamorphic mechanism because the structure of joint C is simpler than that of Fig. 7(d). The mechanisms of Fig. 7(e)-(h) are ignored, because the form combinations of metamorphic joints with spring force constraint and geometric constraint controlled by spring are less reliable in the configuration transforming than that of Fig. 7(c). The joints C in mechanisms of Fig. 7(a) and Fig. 7(b) only have spring force constrains (no geometric constrains), which make them deselected. The mechanism in Fig. 7(c) is selected as the practical broken strands reposition metamorphic mechanism. Metamorphic joint C is spring force constraint and geometric constraint, and D is geometric constraint. Considering the symmetrical operation of practical mechanism, the practical broken strands reposition metamorphic mechanism is finally designed (Fig. 8).

Fig. 7Structural diagrams of reposition metamorphic mechanisms

a)

b)

c)

d)

e)

f)

g)

h)

Fig. 8The proposed broken strands reposition metamorphic mechanism

a) The main 2-mobility clamping metamorphic mechanism

b) The locking mechanism

This mechanism mainly consists of 2 parts, a main clamping metamorphic mechanism and a locking mechanism. The main clamping mechanism is a 5-bar metamorphic mechanism, which is comprised of screw nut 1, link 2, link 3, clamp 4 and the frame 0 in $x$-$y$ plane (Fig. 8(a)). Cut-open nut 11 is embedded in clamp 4, and spring 10 and a geometric structure constrains joint C, and the geometric limitation (strand 12) constrains pair D. This mechanism can provide 2 motions, one for carrying two cut-open nuts clamping EHV power lines, and the other for providing driving motion (link 3) for the locking mechanism below.

The locking mechanism is made up of crank 6, link 7, slider 8 and the frame 0 in $x$-$z$ plane, which actually is a crank-slider mechanism, as is shown in Fig. 8(b). It can provide the motion of locking the two half cut-open nuts into a united one through pins. The main clamping mechanism and locking mechanism are connected through a pair of bevel gears 3’ and 6’, which are rigidly connected to link 3 and crank 6 respectively. Pin 9 is a joining pin used to lock the two half cut-open nuts, while the pin on the other side is just part of slider 8’ used to disassemble the united nut after the repairing operation.

5.2. The working configurations analysis of metamorphic process

The reposition metamorphic mechanism proposed will be carried by a mobile robot and mounted onto the EHV power line. In its initial working configuration (Fig. 9), link 3 and clamp 4 are fixed together by spring 10 and a special geometrical constraint.

When operation starts, screw 5 rotates driven by a motor, and screw nut 1 moves towards the symmetrical centre, which drives clamp 4 to swing around D to carry the cut-open nut 11 to clamp and tighten the EHV power line 12, as shown in Fig. 9.

Fig. 9The configuration of changing work stage

Fig. 10The locking configuration of the main clamping metamorphic mechanism

When clamping operation is finished, clamp 4 will be fixed as a part of the frame. Along with the motion of screw nut 1, link 3 begins to rotate around joint C after overcoming the spring resistance to provide a driving motion for the locking mechanism as shown in Fig. 10.

Beginning to rotate around joint C, link 3 drives bevel gear 3’ (Fi. 8(b)) to rotate relative to clamp 4 in $x$-$z$ plane. Through the bevel gears 3’ and 6’ (Fig. 8(b)), movement and power are transferred to the locking mechanism which moves along with crank 6, and makes slider 8 move toward the cut-open nuts. Pin 9 connects the two cut-open nuts into a united one. The motor rotates inversely, so slider 8 moves toward the opposite direction, and joining pin 9 will remain in the pin hole. While on the right side, pin 9’ will move with slider 8’ retreating from the corresponding hole, and then the locking operation is finished. After moving back to the initial configuration, the united cut-open nut meshes with the strands to perform the reposition operation. The disassemble operation of the united cut-open nut will be done by the mechanism when the mobile robot pushes the nut to a position where the nut’s phase angle is 180°relative to the initial orientation.

6.1. Main kinematic structure size

Table 1 shows the designed key structural parameters of the broken strands reposition metamorphic mechanism.

6.2. Position analysis of the mechanism

6.2.2. Position analysis of locking mechanism

Fig. 12 shows the vector diagram of the locking mechanism, which is a crank-slider mechanism in $x$-$z$ plane. A closed loop vector can be calculated as:

8

$L_6+L_7=S_8.$

Eqs. (9) and (10) are deduced according to the geometrical relationship:

9

$S_8=L_6\mathrm{c}\mathrm{o}\mathrm{s}{\theta }_6+\sqrt{L_7^2-L_6^2\mathrm{s}\mathrm{i}{\mathrm{n}}^2{\theta }_6},$

10

${\theta }_6={\theta }_{60}+\frac{{\theta }_3-180^{\circ }}{i_{3\mathrm{\text{'}}6\mathrm{\text{'}}}},$

where, ${\theta }_{60}=\mathrm{}$40.5358° which is the initial location angle of the crank, as is shown in Fig. 12. $i_{3\mathrm{\text{'}}6\mathrm{\text{'}}}=\text{0.7}$, which is the transmission ratio of the bevel gear pair. According to the Eqs. (5) to (10), the relationship between ${\mathbf{S}}_1$ and ${\mathbf{S}}_8$ can be obtained, as well as functional relationships of angle ${\theta }_3$, ${\theta }_4$ and position of the slider ${\mathbf{S}}_8$ against ${\mathbf{S}}_1$, as shown in Fig. 13. The values in key points are listed in Table 2.

Fig. 11The vector diagram of the metamorphic mechanism

Fig. 12The vector diagram of the locking crank-slider mechanism

Fig. 13Relations of θ3, θ4 and S8 against S1

Table 2The key kinematic parameters transforming from Configuration I to Configuration II

	$S_1$ (mm)	${\theta }_4$ (°)	${\theta }_3$ (°)	${\theta }_6$ (°)	$S_8$ (mm)
Configuration I	155.50-122.42	240-255	165-180	40.5358	50
Transforming	122.42	255	180	40.5358	50
Configuration II	122.42-109.27	255	180-200	40.5358-69.0752	50-34.98

6.3. Simulation

Practical metamorphic process (1 to 4) is simulated with a 3D modelling software package (Solidworks 2010).

1) The initial configuration of the mechanism which is carried by a mobile robot and mounted onto EHV power line is shown in Fig. 14.

2) The configuration of clamp 4 (two clamps) which carries the cut-open nuts clamping the EHV power line is shown in Fig. 15.

3) During the working Configuration II, link 3 drives bevel gears and locking mechanism to insert the pins into the holes of cut-open nuts for connecting the two cut-open nuts as a united one, as is shown in Fig. 16.

4) Slide 1 moves back and joining pins remains in the pin holes of the cut-open nuts to keep two cut-open nuts as a united one, as shown in Fig. 17. The mechanism moves back to the initial configuration, and the mobile robot can push the united nut to mesh with power transmission lines for the broken strands reposition operation, as shown in Fig. 18.

Fig. 14The initial configuration of the mechanism

Fig. 15The cut-open nuts clamping the EHV line

Fig. 16The locking mechanism inserts pins into cut-open nuts

a)

b)

Fig. 17The phase of finishing inserting the pins

Fig. 18The configuration describing the starting of the broken strands reposition operation