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Abstract

To ensure the perpendicularity of drilling holes in aircraft manufacturing, the attitude of spindle axis must be adjusted to coincide with the normal vector of drilling point before drilling. The double eccentric discs-spherical pair structure was used as attitude adjustment mechanism in drilling end-effector. Therefore, the attitude adjustment algorithm of spindle axis is proposed in this article. There were two attitudes for current and target position, respectively, and the rotation sequence of each eccentric disc would affect the attitude adjustment efficiency. This article presents the path planning and optimal solution choosing from multiple solutions. Finally, the effectiveness and accuracy of the algorithm are verified in simulation and drilling experiment, resulting in a normality tolerance of ±0.5° and precision of H9.

Keywords

Drilling end-effector attitude adjustment perpendicularity path planning drilling experiment

Introduction

The automotive industry extensively uses robots to efficiently manufacture automobiles with high quality and low defect rates.¹ With the increasing demand for aircrafts, it is essential to apply the robot technology to the aerospace industry. The robot drilling system has been widely applied in the aviation industry.² However, the strength of joints greatly affects the service life of aircrafts. It is reported that 70% fatigue failure of airplane body is due to joint problems and 80% fatigue crack occurs in the connecting holes.^3,4

One of the important indicators to evaluate the quality of holes is perpendicular precision. Low perpendicular precision of drilling holes will make stress concentration and fatigue crack, resulting in poor hole quality.^5,6 So, it is necessary to adjust attitude of spindle axis before drilling holes. At present, only a few companies, such as Electroimpact, Boeing, Airbus and Fatronic Tecnalia company, have matured application of attitude adjustment in robot drilling system.^7

–10

Electroimpact added two rotational axes to provide the capability to normalize the spindle axis relative to the workpiece surface. The pivot points for these axes were offset from the workpiece surface.¹¹ The second generation of Electroimpact’s ONCE (ONe-sided Cell End effector) robotic drilling system used three unique nose pieces to realize auto-normalization. The robot was controlled closed loop around the sensors to normalize the end-effector when deviation beyond a specified threshold from normal exists.¹² But this article does not tell the principle in detail and cannot obtain the key technology.

YC Shan et al.¹³ designed a 2R1T three parallel mechanism to adjust the spindle axis. An attitude adjustment mechanism with 2 degrees of freedom of rotary motion was designed by L Zhang and X Wang,^14,15 and the 2 degrees of freedom were perpendicular to each other. It can adjust the spindle axis parallel to the normal of drilling point. R Zhang et al.¹⁶ also proposed a method to adjust spindle axis with 2 degrees of freedom. However, all the parallel mechanisms for attitude adjusting are confronted with a same problem. The drill point needs to be removed again after adjusting the drill attitude.

In our drilling system, the end-effector is mounted on KUKA industrial robot. Double eccentric discs normal adjustment mechanism is designed to adjust attitude.¹⁷ In order to ensure the perpendicularity of holes in aircraft manufacturing, the attitude of spindle axis must be adjusted to coincide with the normal vector of drilling point before drilling. The centre of spherical bearing pair is the centre of pressure head, so the drill point remains the same after adjusting attitude and the drill axis avoids repeating adjustment. And improving the drilling efficiency is critical for aircraft manufacturing. Therefore, how to accurately and efficiently send spindle to target position is a research emphasis in our automatic drilling system.

C Wang and P Yuan⁵ proposed the movement planning and algorithm simulation of attitude adjustment. In order to be more energy-efficient, this article aims at the path planning and optimal solution choosing from multiple solutions to send spindle to target position quickly and accurately. The effectiveness of the path planning is verified through simulation. Finally, the verification experiment of attitude adjustment and drilling experiments certifies the accuracy of algorithm.

The attitude adjustment algorithm

In the drilling process, the spindle attitude must be adjusted when spindle axis deviates from the normal vector of the drilling point more than $0.5 \circ$ . The double eccentric discs-spherical pair structure is used to adjust attitude of spindle axis. The schematic diagram is shown in Figure 1.

Figure 1.

Schematic diagram of double eccentric discs mechanism.

The geometric centreline of macro-eccentric disc is line O. Line $O_{2}$ is the eccentric line of the micro-eccentric disc and the position of spherical plain bearing is point $O_{2}$ . The eccentric radius of two eccentric discs is r. The geometric centreline of the micro-eccentric disc coincides with the eccentric line of the macro-eccentric disc, which is the line $O_{1}$ . The distance between centre of the spherical plain bearing and the geometric centreline of the micro-eccentric disc is eccentric distance r.

The spherical plain bearing is embedded in micro-eccentric disc, and the micro-eccentric disc is embedded in macro one. With respective rotation of the two eccentric discs, the tail shaft swings discretionarily in spherical plain bearing to drive spatial attitude adjustment of the spindle axis.

The drill vertex coincides with the spherical centre $O_{sp}$ of the spherical pair. It can make the drill axis adjust in a cone range without changing the drill vertex position, and the angle is $φ$ . As shown in Figure 2, the maximum range of $O_{2}$ is a circle of $2 r$ , which is the maximum angle of attitude adjustment.

\tan φ = \frac{2 r}{d}

(1)

\tan θ = \frac{\sqrt{x_{2}^{2} + y_{2}^{2}}}{d}

(2)

Figure 2.

Region of attitude adjustment.

where $r = 25 mm$ , $x_{2} and y_{2}$ are the coordinates of the target point $O_{2}$ and $θ$ is the angle between spindle axis and origin axis at any time. d is the vertical distance between the centre of the spherical plain bearing and double eccentric discs plane, so the maximum angle $θ$ is $5 \circ$ and the adjusting angle scope is $[0, 5 \circ]$ . According to the normal vector of the drilling point, the intersection of normal vector and double eccentric discs plane can be attained, which is the target position and point $O_{2}$ needs to reach it.

The essence of attitude adjustment is making the spindle axis coincide with the normal vector of the drilling point. First, the normal vector is obtained to calculate the angle between spindle axis and vertical direction. If the angle is more than $0.5 \circ$ , the spindle axis needs to be adjusted. And the target point can be obtained according to the intersection of the normal vector and eccentric plane. Then, the calculated angles of double eccentric discs need rotation. After attitude adjustment, the drill axis coincides with the normal vector. Two absolute encoders are added to form a closed loop of attitude adjustment. It can precisely control the actual rotary angles of double eccentric discs.

Double eccentric discs mechanism can be simplified as two-link model, as shown in Figure 3. The length of rods is eccentricity $r = 25 mm$ , $O O_{1} = O_{1} O_{2} = r$ , which is the eccentric radius of two eccentric discs.

Figure 3.

Two-link model.

The double eccentric discs coordinate system is $x_{0} O y_{0}$ . Where $α$ is the rotation angle of axis $x_{0}$ relative to macro-eccentric disc, and $β$ is the angle between extension cord of line $O O_{1}$ and micro-eccentric disc. The full rotation locus of $O_{1}$ around the point O is shown as the dotted line 1. When the motor rotates angle $α$ ( $O O_{1}$ rotates $α$ ), the full rotation locus of $O_{2}$ around the point is shown as the dotted line 2. When $O_{1} O_{2}$ rotates $β$ relative to $O O_{1}$ , the coordinate value of $O_{2}$ is $(a, b)$ . When $β = 0$ , $O O_{1}$ and $O_{1} O_{2}$ are in a straight line, and the locus of the $O_{2}$ is shown as the dotted line 3.

When $α$ ranges from $0 \circ$ to $360 \circ$ , the movement of $O_{2}$ rotating around O is the maximum. When $O O_{1}$ and $O_{1} O_{2}$ rotate different angles $α$ and $β$ , respectively, the target point $O_{2}$ can move to any position in dotted line 3. Therefore, the purpose of attitude adjustment is achieved. The initial position is the centre of spherical plain bearing at the origin, $O O'_{1} - O'_{1} O'_{2}$ , and the coordinate origin coincides with $O'_{2}$ , $α = 0 \circ$ and $β = 180 \circ$ . According to mathematical calculation, the relationship between $O_{2} (a, b)$ and the rotation angles $α$ and $β$ can be calculated

{\begin{matrix} x_{2} = r (\cos α + \cos (α + β)) \\ y_{2} = r (\sin α + \sin (α + β)) \end{matrix}

(3)

For current position $O_{2} (x_{2}, y_{2})$ , there are two attitudes $O O_{1} - O_{1} O_{2}$ and $O O_{"}^{1} - O_{"}^{1} O_{2}$ . So, there are two solutions $α_{1}, β_{1}$ and $α_{2}, β_{2}$ . To calculate the angles of double eccentric discs rotate to any target position, the coordinate system $x_{0} O y_{0}$ is set up in Figure 4.

Figure 4.

Coordinate system of double eccentric discs plane.

The target position is $O'_{2}$ , and the target attitude is $O O'_{1} - O'_{1} O'_{2}$ . The current attitude is $O O_{1} - O_{1} O_{2}$ . Where $α$ is the rotation angle of $O O_{1}$ relative to axis $x_{0}$ , $β$ is the rotational angle of $O_{1} O_{2}$ relative to axis $x_{1}$ . The coordinate system $x_{1} O y_{1}$ is set up at current attitude $O O_{1} - O_{1} O_{2}$ and $x_{1}$ direction along the direction of $O O_{1}$ . $α', β'$ is the rotational angle of $O O'_{1} - O'_{1} O'_{2}$ relative to $O O_{1} - O_{1} O_{2}$ , which is the rotational angle of macro- and micro-eccentric discs, respectively.

Suppose $(^{0} x'_{2},^{0} y'_{2})$ is the target point $O'_{2}$ in $x_{0} O y_{0}$ , and $(^{1} x'_{2},^{1} y'_{2})$ is the target point $O'_{2}$ in $x_{1} O y_{1}$

(\begin{matrix} ^{1} {x'}_{2} \\ ^{1} {y'}_{2} \\ 0 \end{matrix}) =_{0}^{1} R \cdot (\begin{matrix} ^{0} {x'}_{2} \\ ^{0} {y'}_{2} \\ 0 \end{matrix})

(4)

where $_{0}^{1} R = (\begin{matrix} \cos α \sin α 0 \\ - \sin α \cos α 0 \\ 0 0 1 \end{matrix})$ , $_{0}^{1} R$ is the rotational transformation matrix.

In $x_{1} O y_{1}$ , equation (5) can be obtained according to equation (3)

{\begin{matrix} ^{1} {x'}_{2} = r (\cos α' + \cos (α' + β + β')) \\ ^{1} {y'}_{2} = r (\sin α' + \sin (α' + β + β')) \end{matrix}

(5)

If $^{1} x'_{2}^{2} +^{1} y'_{2}^{2} \neq 0$ , there are four solutions $α'_{1}, α'_{2}, α'_{3}, α'_{4}$

{\begin{matrix} {α'}_{1} = A - B \\ {α'}_{2} = A + B - π \\ {α'}_{3} = π - A - B \\ {α'}_{4} = B - A \end{matrix}

(6)

where

$A = \arcsin \frac{\sqrt{^{1} x'_{2}^{2} +^{1} y'_{2}^{2}}}{2 r}$

$B = \arcsin \frac{^{1} {x'}_{2}}{\sqrt{^{1} x'_{2}^{2} +^{1} y'_{2}^{2}}}$

For every $α', β'$ , there are two solutions $β'_{1}, β'_{2}$

{\begin{matrix} {β'}_{1} = M - α' - β \\ {β'}_{2} = π - M - α' - β \end{matrix}

(7)

where

$M = \arcsin (\frac{^{1} {y'}_{2}}{r} - \sin α')$

According to geometric position, the target position $O'_{2} (^{0} x'_{2},^{0} y'_{2})$ is

{\begin{matrix} ^{0} {x'}_{2} = r (\cos (α + α') + \cos (α + α' + β + β')) \\ ^{0} {y'}_{2} = r (\sin (α + α') + \sin (α + α' + β + β')) \end{matrix}

(8)

When the spindle axis needs to adjust attitude again, the system will regard the current attitude as the former attitude and repeats to calculate the above equations to get new rotary angles. Then, two motors control two eccentric discs to make the spindle axis coincide with the target attitude.

Path planning

Both the macro- and micro-eccentric discs are driven by high-precision DC servo motors through gears. Double eccentric discs rotate different angles and make spindle axis coincide with normal vector. According to measure unit, robot system can transform it to the corresponding angle $α$ and $β$ of double eccentric discs. With the limit of spherical pair, drill axis can be adjusted to any spatial location in the cone range whose vertex is drill vertex.

The current attitude of spindle is not always the origin position. It returns to the initial position and then begins to adjust every time, which will greatly reduce the efficiency. In order to be efficient and energy saving, it is necessary to adjust spindle attitude with the shortest path. The drilling system needs continuous attitude adjustment in actual adjustment process. The algorithm of attitude adjustment regards the current attitude as the start of next attitude. So, the path planning is how to adjust the spindle from current position to target position quickly.

There are two attitudes of macro- and micro-eccentric disc in current position. Similarly, in target position, there are two attitudes of spherical plain bearing centre moving to the target point. So, four solutions can be obtained after combination. However, there are two directions (clockwise and counterclockwise) that macro-eccentric disc can rotate, so the mechanism can move from $O_{2} (x_{2}, y_{2})$ to $O'_{2} (x'_{2}, y'_{2})$ in two ways, directions 1 and 2, which is shown in Figure 5. In summary, there are eight solutions in total. $O_{2}$ is the current location of spherical plain bearing, and $O'_{2}$ is the location of the target point. According to equations (6) and (7), the eight solutions are as follows

\begin{matrix} {\begin{matrix} {α'}_{1} = A - B \\ {β'}_{1} = M - {α'}_{1} - β \end{matrix} \\ {\begin{matrix} {α'}_{2} = A - B \\ {β'}_{2} = π - M - {α'}_{2} - β \end{matrix} \end{matrix}

\begin{matrix} {\begin{matrix} {α'}_{3} = A + B - π \\ {β'}_{3} = M - {α'}_{3} - β \end{matrix} \\ {\begin{matrix} {α'}_{4} = A + B - π \\ {β'}_{4} = π - M - {α'}_{4} - β \end{matrix} \end{matrix}

\begin{matrix} {\begin{matrix} {α'}_{5} = π - A - B \\ {β'}_{5} = M - {α'}_{5} - β \end{matrix} \\ {\begin{matrix} {α'}_{6} = π - A - B \\ {β'}_{6} = π - M - {α'}_{6} - β \end{matrix} \end{matrix}

\begin{matrix} {\begin{matrix} {α'}_{7} = B - A \\ {β'}_{7} = M - {α'}_{7} - β \end{matrix} \\ {\begin{matrix} {α'}_{8} = B - A \\ {β'}_{8} = π - M - {α'}_{8} - β \end{matrix} \end{matrix}

How to plan the rotational paths of macro- and micro-eccentric disc? And how to find out the optimal solution to target position from eight solutions and move the spindle axis to normal vector with high efficiency? The problem is how to choose the optimal solutions of $α$ and $β$ .

Figure 5.

Two attitudes in same point.

In order to reduce time, $α', β'$ should be as small as possible. Macro-eccentric disc should choose the rotational direction of $| α' | \leq π$ . According to the shortest path and effective solution of the rotation angles, the minimum sum of rotational angles of macro- and micro-eccentric disc is the optimal solution ${(| α' | + | β' |)}_{min}$ .

$β'$ is the rational angle of current attitude $O_{1} O_{2}$ relative to axis $x_{1}$ , $- π \leq α' \leq π, - π \leq β' \leq π$ . Due to the inverse trigonometric function of evaluation, there are two redundant solutions $α'$ . Put all the solutions $α, β, α', β'$ into equation (6), and the equation is only true for efficient solutions. Then, choose minimum of $| α' | + | β' |$ as optimal solutions from efficient solutions.

The motion simulation of double eccentric discs was done in Adams according to the attitude adjustment algorithm. From origin position to target position, the mechanism of double eccentric discs is simplified to reduce calculation, which is shown in Figure 6. The green solid line is the trajectory of spherical plain bearing. The red eccentric disc is macro and yellow is micro.

Figure 6.

Motion simulation in Adams.

There are four ways to adjust attitude according to rotary speed of motor and rotational order of macro- and micro-eccentric disc. Four groups of trajectory are obtained by simulations in Adams, as shown in Figure 7.

Figure 7.

Four groups of simulations.

Keep the macro-eccentric disc immobile, and micro-eccentric disc rotates $β$ by servo motor. The macro-eccentric disc rotates $α$ after micro finishes. The trajectory is shown in Figure 7(1).

Keep the micro-eccentric disc immobile, and macro-eccentric disc rotates $α$ by servo motor. The micro-eccentric disc rotates $β$ after macro finishes. The trajectory is shown in Figure 7(2).

Macro- and micro-eccentric discs rotate $α, β$ at the same time by servo motors at same speed. In the process of simulation, the macro stops first, then micro stops. The trajectory is shown in Figure 7(3).

Macro- and micro-eccentric discs rotate $α, β$ at the same time by servo motors at different speed. Then two eccentric discs stop at the same time. The trajectory is shown in Figure 7(4).

Export the data of four groups of trajectory and draw curves in MATLAB, as shown in Figure 8. The blue dotted line is the trajectory of centre $O_{1}$ of micro-eccentric disc, and it is the same as shown in four figures. The red solid line is the trajectory of centre $O_{2}$ of spherical plain bearing.

Figure 8.

Four groups of trajectory.

According to the trajectory and the length of the curve, the red solid line is repeated by rotating eccentric discs separately as shown in Figure 7(1) and (2). Obviously, it is not desirable to improve the efficiency of the system. In Figure 7(3) and (4), the two eccentric discs rotate together and the fourth curve is shorter and smoother than the third one. So, the fourth group of trajectory is more stable and shorter path in comparison with four different trajectories. So, we choose the fourth group as the best path.

The verification experiment of attitude adjustment

Before drilling experiments, the attitude of spindle axis should be adjusted to coincide with normal vector by the rotation of motors. In order to ensure perpendicularity of holes, this article designs verification experiments of attitude adjustment.

First, adjust the plane of pressure head at random, and three laser sensors measure the distance to the plane. The normal vector of drilling point can be calculated based on the principle of non-collinear three points define a plane, as shown in Figure 9.

Figure 9.

Normal vector measured by laser sensors.

In Figure 9, $\vec{n}$ is the normal vector of drilling point. So, the rotational angles of double eccentric discs and rotational cycles of two motors are obtained by algorithm of attitude adjustment. In the process of attitude adjustment, two absolute encoders measure the actual rotational angles of macro- and micro-eccentric disc, respectively.

From a large number of trials, eight experiments are selected, and the target point, actual position, the value of laser sensor and rotational angles are recorded in each experiment. Then, the theoretical angle, the actual angle between spindle axis and origin axis, is calculated by equation (2), as shown in Tables 1 and 2.

Table 1.

Data of location.

No.	Laser sensor (mm)			Target point (mm)		Actual point (mm)		Difference (mm)
No.	1	2	3	X	Y	x	y	X–x	Y–y
1	27.70471	26.93536	30.55924	−20.3884	−5.55371	−20.480	−5.7420	0.0916	0.18829
2	29.93950	29.12995	28.33094	4.49532	−5.84390	4.48870	−5.8914	0.00662	0.0475
3	27.19497	25.56180	31.11438	−31.2394	−11.7894	−31.2268	−11.7503	−0.0126	−0.0391
4	26.40897	28.45938	31.66562	−18.0387	14.8013	−18.0218	14.8549	−0.0169	−0.0536
5	25.64891	31.56838	32.43865	−4.89624	42.7309	−4.87610	42.7332	−0.02014	−0.0023
6	28.28838	29.74734	30.06896	−1.80947	10.5318	−1.8069	10.5087	−0.00257	0.0231
7	27.01858	28.51256	31.34006	−15.9078	10.7846	−15.9166	10.7857	0.0088	−0.0011
8	28.27281	30.90819	30.03005	4.94051	19.0240	4.89340	18.9658	0.04711	0.0582

Table 2.

Data of angle.

No.	Angle of macro-eccentric disc (°)		Angle of micro-eccentric disc (°)		Angle between spindle axis and origin axis (°)
No.	Theoretical $α'$	Actual $α'_{a}$	Theoretical $β'$	Actual $β'_{a}$	Theoretical $θ$	Actual $θ'$	Difference $θ - θ'$
1	−99.7629	−99.5137	50.0008	50.3512	2.1242	2.1381	−0.0139
2	29.0891	28.7851	16.9592	17.0373	0.7415	0.7449	−0.0034
3	−82.4365	−82.4522	100.832	100.7531	3.3543	3.3517	0.0026
4	−4.00324	−4.104	45.1153	45.0608	2.3454	2.3475	−0.0021
5	61.7728	61.7459	−73.6195	−73.6195	4.3175	4.3175	0
6	83.8352	83.8154	−98.2895	−98.2347	1.0746	1.0723	0.0023
7	−62.9248	−62.9225	−53.0244	−53.0048	1.9321	1.9329	−0.0008
8	−54.3329	−54.3272	−99.3001	−99.1305	1.976	1.9691	0.0069

The theoretical rotational angle of macro-eccentric disc is $α'$ , and the micro is $β'$ . $α'_{a}$ and $β'_{a}$ are the actual rotational angle of macro and micro, respectively. The theoretical angle between spindle axis and origin axis is $θ$ , which is the angle between normal vector $\vec{n}$ and z axis. The difference angle between spindle axis and origin axis is $θ - θ'$ .

As shown in Table 2, the angle between theoretical normal vector and actual attitude of spindle axis is $< \pm 0.014 \circ$ , meeting a normality tolerance of $\pm 0.5 \circ$ .

The drilling experiments

The feasibility and correctness of the algorithm of attitude adjustment have been verified in simulation and verification experiment. This article also designs the drilling experiments to test the quality of holes. The carbide drill is used in drilling experiments because it performed well during the drill.¹⁸ The material of test specimen (thickness = 6 mm, flat plate) is aluminium alloy 2024, and the drill diameter is 6 mm. Experimental conditions include spindle speed of 500 r/min, feed 0.1 mm/s and pressure 0.3 MPa. In order to test the influence of attitude adjustment on actual drilling, there are two groups of drilling experiments, no attitude adjustment and attitude adjustment. The drilling experiments were carried out, and the effect of the hole is shown in Figure 10.

Figure 10.

Effect of drilling: (a) with no attitude adjustment and (b) with attitude adjustment.

The inside micrometer was used to measure the diameter of four holes along the circumferential direction every $30 \circ$ . The results are shown in Table 3 and Figure 11.

Table 3.

Diameter of holes.

No.	0°	30°	60°	90°	120°	150°
1	6.178	6.186	6.102	6.079	6.062	6.139
2	6.123	6.196	6.107	6.079	6.178	6.113
3	6.015	6.019	6.029	6.025	6.019	6.020
4	6.028	6.017	6.021	6.020	6.013	6.019

Figure 11.

Tolerance of drilling holes.

Results

Holes 1 and 2 are the holes with no attitude adjustment and holes 3 and 4 with attitude adjustment. In Figure 10, the shape of holes 1 and 2 is oval and more burr. The main reason is that the angle between normal vector and spindle axis is too large without attitude adjustment before drilling. So, the drill is tilted, causing oval holes. At the same time, the surface of aluminium alloy has a lot of burr.

The tolerance of four holes’ diameter is shown in Figure 11. The fluctuation of holes 1 and 2 is large without attitude adjustment of spindle axis. However, the data of holes 3 and 4 are stable, and the hole is circular.

As shown in Table 3, the tolerance of hole 1 is 124 µm and hole 2 is 117 µm. With the attitude adjustment of spindle axis, the tolerance of holes 3 and 4 is 29 and 28 µm, respectively. The accuracy of holes satisfies the requirement and reaches H9. (According to the national standard of mechanical design, H9 refers to the tolerance grade 9, and the tolerance zone of hole is 30 µm for diameter 6 mm.)

Conclusion

In order to ensure the perpendicularity of drilling holes, spindle axis must be adjusted to coincide with the normal vector of drilling point automatically and efficiently before drilling. The double eccentric discs-spherical pair structure was used as attitude adjustment mechanism in drilling end-effector. So, the attitude adjustment algorithm of spindle axis was based on this mechanism.

The uncertain attitudes of current and target positions, and the rotation sequence of each eccentric disc, would affect the attitude adjustment efficiency. In summary, there were eight solutions in total. This article presented the path planning and optimal solution choosing from multiple solutions. Finally, the effectiveness and accuracy of the algorithm were verified in simulation and drilling experiment.

From the results of simulation and experiments, the conclusions are as follows:

The minimum sum of rotational angles of macro- and micro-eccentric disc is the optimal solution.

The best path is that macro- and micro-eccentric discs rotate $α, β$ at the same time at different speed and stop at the same time.

The angle between normal vector and actual direction of spindle axis meets the tolerance of ±0.5°.

The precision of holes satisfies the tolerance requirement and reaches H9.

Footnotes

Academic Editor: Zhijun Li

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 study was supported by the National Natural Science Foundation of China (no. 61375085).

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The attitude adjustment algorithm in drilling end-effector for aviation

Abstract

Keywords

Introduction

The attitude adjustment algorithm

Path planning

The verification experiment of attitude adjustment

The drilling experiments

Results

Conclusion

Footnotes

Declaration of conflicting interests

Funding

References