# Optimization and Experimental Study of an Intelligent Bamboo-Splitting Machine Charging Manipulator

Authors: Tian-Hu Liu; Yong-Lu Wen; Gui-Qi Li; Xiang-Ning Nie
Journal: Journal of Robotics
 (2020)

---

## Abstract

A nonautomatic bamboo-splitting machine must charge with material and change tools manually. However, manual charging is very dangerous. An intelligent bamboo-splitting machine can feed automatically and change tools intelligently and has broad application prospects. A charging manipulator is an important part of an intelligent bamboo-splitting machine. The size of the manipulator was optimized here using a genetic algorithm. The capture rate, centering rate, and dynamic characteristics of an intelligent bamboo-splitting machine charging manipulator, in which key factors were considered, were experimentally studied. First, three different manipulators, with arm lengths at 210, 220, and 230 mm, were developed. Then, the bamboo materials were divided into three gradients (60–85, 85–110, and 110–135 mm) according to diameter ranges. Accelerators were used to measure the manipulator arm dynamic characteristics, and a high-speed charge-coupled device was used to record the grasping process. Experimental results showed that the manipulator capture rate with an arm length of = 220 mm was as high as 100%, but that of manipulators with arm lengths of = 210 and 230 mm was 96 and 98.67%, respectively. Thus, the manipulator with a 220 mm arm length showed better performance than the other two manipulators. Trend curves of the influence of material diameter on capture time were similar to an exponential function.


---

## Body

## 1. Introduction

Asia Pacific, America, and Africa are the main distribution areas of bamboo in the world [1]. In Asia, bamboo plants are mainly distributed in China, India, and other developing countries. Bamboo grows rapidly and has good mechanical properties, such that it can be processed into many kinds of daily necessities. The production process of bamboo products is shown in Figure 1. Bamboo material is split into pieces by a bamboo-splitting machine. Then, it is drawn into a silk from by a wire-drawing machine, dried, and finally processed into products, such as toothpicks and chopsticks. Thus, a bamboo-splitting machine plays an important role in bamboo processing. A nonautomatic bamboo-splitting machine must charge with material and change tools manually. However, manual charging is very dangerous. An intelligent bamboo-splitting machine can feed and charge automatically and can change tools reliably and therefore has broad application prospects. A charging manipulator is an important part of an intelligent bamboo-splitting machine.Figure 1
The production process for bamboo products.As an important part in many kinds of intelligent machinery, many studies have been conducted regarding various manipulators, such as a flexible manipulator [2, 3]. Peng et al. have studied an apple internal-quality-grading manipulator [4]. Li et al. have designed a kind of transplanting manipulator [5]. Wan et al. have carried out dimensional synthesis of a parallel manipulator using a particle swarm optimization algorithm [6]. A reconfigurable 6-degree-of-freedom (DOF) manipulator has been optimized [7], in which three performance criteria have been combined using the weighted-sum approach and optimization was carried out using the sequential simplex method. Mandur and Budman have discussed a method for updating mechanism model parameters using state measurements [8, 9]. Okazaki et al. have developed a 6-DOF manipulator driven by McKibben artificial muscles [10]. A P-4R (prismatic-four-rotational-joint) has been proposed to measure a high-temperature steel cylinder robotic system [11]. Abe has built a dynamic model for a planar flexible-rigid manipulator by assumed mode method (AMM) [12]. Abe defined trajectories as cubic splines and used particle swarm optimization (PSO) to optimize the spline control points. Trajectory functions have been defined as high order polynomials for planar flexible manipulators [13]. A 7-DOF manipulator has been designed, actuated entirely by antagonistic McKibben artificial muscle pairs [14]. Ahmad et al. have proposed a PD-type fuzzy logic controller for tip angular position control in a flexible joint manipulator [15]. Nikdel et al. have also developed a fuzzy approach based on the parallel distributed compensation technique in controlling a flexible joint robot [16].A genetic algorithm, analytical approach, and linear-least-square (LLS) method are widely used in mechanism design. For example, Li and Xu have used a genetic algorithm to optimize a planar 3-DOF parallel manipulator [17]. Gao et al. have applied a genetic algorithm based on the Pareto front approach to synthetize a 6-DOF parallel manipulator [18]. A genetic algorithm has also been adopted to optimize the parameters of cubic polynomials, in which four cubic polynomials are used to describe angular velocities of a flexible manipulator’s two joints [19]. Chen et al. have proposed an analytical approach to determine the redundant parameters for the calibration of serial manipulators [20]. A manipulator has been studied using an electrostatic model [21]. An approach to consider the bearing’s contribution to the manipulator dynamics has been introduced [22]. Liu et al. studied an elliptical boundary model method detecting object for intelligent machinery [23, 24]. Bucolo et al. studied control methods of imperfect dynamical systems [25, 26].The complex characteristics of bamboo-splitting processes make it expensive to devise an accurate mechanism. An empirical model in which a certain degree of expertise is required is somewhat easier and more suitable for mechanism design. In this paper, the charging manipulator of an intelligent bamboo-splitting machine was optimized using a genetic algorithm, and a series of experiments was conducted to study key performance characteristics, such as capture rate, centering rate, and dynamic characteristics.


## 2. Design and Optimization of Manipulator

### 2.1. Composition of an Intelligent Bamboo-Splitting Machine

In general, an intelligent bamboo-splitting machine includes a feeding mechanism, charging manipulator, tool changer, and control mechanism (Figure2). A local structure of an intelligent bamboo-splitting machine was developed for this study, where (1) is the charging manipulator, (2) represents the feeding mechanism, (3) represents the frame, (4) represents the pushing mechanism, and (5) represents the automatic tool changer (Figure 3). The feeding mechanism (2) fed bamboo materials and concurrently measured diameters automatically and continuously, the charging manipulator (1) grasped material accurately, the pushing mechanism (5) pushed materials continuously to the tool, and the automatic tool changer (5) changed tools automatically according to material diameter.Figure 2
Overall structure of intelligent bamboo-splitting machine.Figure 3
(a) The virtual model and (b) the image of developed bamboo-splitting machine.
(a)
(b)The workflow chart of this intelligent bamboo-splitting machine is shown in Figure4. During operation, the tool was first reset. During feeding, the bamboo diameter was measured using a laser beam sensor. The machine then selected the tool automatically according to the measured diameter. At the end of the feeding process, the bamboo arrived at the tray and was picked up by the charging manipulator, grasped, and centered. Then, it was pushed into the tool by the pushing mechanism.Figure 4
Workflow chart of intelligent bamboo-splitting machine.


### 2.2. Manipulator Design and Optimization

The manipulator structure has a great influence on its stability and motion performance, and thus it was necessary to obtain the ideal motion performance through optimization. In the process of optimization, the working space of the manipulator needed to be maximized, but its flexibility and stability needed to satisfy the working requirements.Two optional structures of the manipulator are shown in Figures5(a) and 5(b). As the sizes of big and small arms are the same, the workspace of these two manipulators is drawn together with the solid lines in Figure 5(c) representing the manipulator of Figure 5(a), and the dotted line represents that of Figure 5(b) after movement. It was obvious that, under the condition of the arm and joints sizes being the same, the target trajectory of the mechanism shown in Figure 5(a) was larger than that in Figure 5(b). Therefore, the charging manipulator in Figure 5(a) was adopted.Figure 5
Manipulator configuration.
(a)
(b)
(c)The manipulator in the configuration grasped the target object through an up and down movement of a pneumatic cylinder and rotations of the shoulder, elbow, and wrist joints. Due to the limitation of the overall size of the intelligent bamboo-splitting machine, the working path of the manipulator fingers must meet formula (1) to grasp the target object.(1)fx1min=a+bsinθ1+dsinθ2>600,where a, b, c, θ1, and θ2 are shown in Figure 6.Figure 6
Manipulator parameters.To make the manipulator reach the maximum target trajectory with minimized size, the objective function is written as(2)Minimizefx2=a+b+c+d.The optimization function must be subject to formula (1) to reduce the manipulator weight and ensure that the manipulator is lighter and more flexible. The ranges of a, b, c, d, θ1, and θ2 were from 0 to 300 mm, 0 to 400 mm, 0 to 500 mm, 0 to 300 mm, 0 to π/2, and 0 to 3π/4, respectively. This size optimization problem was solved using a multivariable genetic algorithm, and the algorithm flow is shown in Figure 7. A set of initial values satisfying the conditions was selected to start the optimization process. The initial population number was set as 50, the maximum evolution generation was set as 100, the crossover probability was set at 0.7, the mutation probability was set at 0.01, and the termination condition was set such that the average changes of fitness function were less than 10−2.Figure 7
Flowchart of the genetic algorithm.The algorithm actually evolved 97 generations, with the optimized result of these parameters fora, b, and d equal to 190, 220, and 220 mm, respectively (Figure 8). The total length of rods c and d needed to meet c+dsinθ2≥600 because 0°≤θ2≤3π/4, 0°sinθ2≤1. Therefore, c+d≥600, when c+d=600, such that the object function was minimized, and the length of rod c was 380 mm.Figure 8
Iteration diagram of genetic algorithm.


### 2.3. Optimized Charging Manipulator

The structure of the optimized charging manipulator is shown in Figure9. It mainly included a cylinder (1), five hinges (10), two big arms (6), two small arms (7), two wrist joints (8), a V-shaped finger (11), and two U-shaped fingers (9). It had four columns (3), two upper beams (2), and two bottom beams (4). The cylinder (1) was mounted on upper beam (2) using bolts. Component (10) acted as a shoulder, which was mounted at the end of cylinder piston. One end of big arm (6) was connected with component (10) and another end connected with small arm (7) a through hinge. The upper end of small arm (7) was mounted on a hinge, which was also mounted on a rotation axis. V-shaped fingers (11) and U-shaped fingers (9) were mounted on the bottom end of small arm (7). In the process of charging, bamboo was picked up by U-shaped fingers (9). Next, the sample was urged to the front of the pushing mechanism before touching V-shaped fingers (11). Then, it was caught and tightly fastened between the U-shaped (9) and V-shaped fingers (11).Figure 9
Manipulator structure.


## 2.1. Composition of an Intelligent Bamboo-Splitting Machine

In general, an intelligent bamboo-splitting machine includes a feeding mechanism, charging manipulator, tool changer, and control mechanism (Figure2). A local structure of an intelligent bamboo-splitting machine was developed for this study, where (1) is the charging manipulator, (2) represents the feeding mechanism, (3) represents the frame, (4) represents the pushing mechanism, and (5) represents the automatic tool changer (Figure 3). The feeding mechanism (2) fed bamboo materials and concurrently measured diameters automatically and continuously, the charging manipulator (1) grasped material accurately, the pushing mechanism (5) pushed materials continuously to the tool, and the automatic tool changer (5) changed tools automatically according to material diameter.Figure 2
Overall structure of intelligent bamboo-splitting machine.Figure 3
(a) The virtual model and (b) the image of developed bamboo-splitting machine.
(a)
(b)The workflow chart of this intelligent bamboo-splitting machine is shown in Figure4. During operation, the tool was first reset. During feeding, the bamboo diameter was measured using a laser beam sensor. The machine then selected the tool automatically according to the measured diameter. At the end of the feeding process, the bamboo arrived at the tray and was picked up by the charging manipulator, grasped, and centered. Then, it was pushed into the tool by the pushing mechanism.Figure 4
Workflow chart of intelligent bamboo-splitting machine.


## 2.2. Manipulator Design and Optimization

The manipulator structure has a great influence on its stability and motion performance, and thus it was necessary to obtain the ideal motion performance through optimization. In the process of optimization, the working space of the manipulator needed to be maximized, but its flexibility and stability needed to satisfy the working requirements.Two optional structures of the manipulator are shown in Figures5(a) and 5(b). As the sizes of big and small arms are the same, the workspace of these two manipulators is drawn together with the solid lines in Figure 5(c) representing the manipulator of Figure 5(a), and the dotted line represents that of Figure 5(b) after movement. It was obvious that, under the condition of the arm and joints sizes being the same, the target trajectory of the mechanism shown in Figure 5(a) was larger than that in Figure 5(b). Therefore, the charging manipulator in Figure 5(a) was adopted.Figure 5
Manipulator configuration.
(a)
(b)
(c)The manipulator in the configuration grasped the target object through an up and down movement of a pneumatic cylinder and rotations of the shoulder, elbow, and wrist joints. Due to the limitation of the overall size of the intelligent bamboo-splitting machine, the working path of the manipulator fingers must meet formula (1) to grasp the target object.(1)fx1min=a+bsinθ1+dsinθ2>600,where a, b, c, θ1, and θ2 are shown in Figure 6.Figure 6
Manipulator parameters.To make the manipulator reach the maximum target trajectory with minimized size, the objective function is written as(2)Minimizefx2=a+b+c+d.The optimization function must be subject to formula (1) to reduce the manipulator weight and ensure that the manipulator is lighter and more flexible. The ranges of a, b, c, d, θ1, and θ2 were from 0 to 300 mm, 0 to 400 mm, 0 to 500 mm, 0 to 300 mm, 0 to π/2, and 0 to 3π/4, respectively. This size optimization problem was solved using a multivariable genetic algorithm, and the algorithm flow is shown in Figure 7. A set of initial values satisfying the conditions was selected to start the optimization process. The initial population number was set as 50, the maximum evolution generation was set as 100, the crossover probability was set at 0.7, the mutation probability was set at 0.01, and the termination condition was set such that the average changes of fitness function were less than 10−2.Figure 7
Flowchart of the genetic algorithm.The algorithm actually evolved 97 generations, with the optimized result of these parameters fora, b, and d equal to 190, 220, and 220 mm, respectively (Figure 8). The total length of rods c and d needed to meet c+dsinθ2≥600 because 0°≤θ2≤3π/4, 0°sinθ2≤1. Therefore, c+d≥600, when c+d=600, such that the object function was minimized, and the length of rod c was 380 mm.Figure 8
Iteration diagram of genetic algorithm.


## 2.3. Optimized Charging Manipulator

The structure of the optimized charging manipulator is shown in Figure9. It mainly included a cylinder (1), five hinges (10), two big arms (6), two small arms (7), two wrist joints (8), a V-shaped finger (11), and two U-shaped fingers (9). It had four columns (3), two upper beams (2), and two bottom beams (4). The cylinder (1) was mounted on upper beam (2) using bolts. Component (10) acted as a shoulder, which was mounted at the end of cylinder piston. One end of big arm (6) was connected with component (10) and another end connected with small arm (7) a through hinge. The upper end of small arm (7) was mounted on a hinge, which was also mounted on a rotation axis. V-shaped fingers (11) and U-shaped fingers (9) were mounted on the bottom end of small arm (7). In the process of charging, bamboo was picked up by U-shaped fingers (9). Next, the sample was urged to the front of the pushing mechanism before touching V-shaped fingers (11). Then, it was caught and tightly fastened between the U-shaped (9) and V-shaped fingers (11).Figure 9
Manipulator structure.


## 3. Materials and Methods

### 3.1. Materials

The test samples were bamboo of different diameters felled at the end of September 2019 at Nankun Mountain, Longmen County, Huizhou, Guangdong, China. All samples were placed at the laboratory of South China Agricultural University in Guangzhou, China, and few samples are shown in Figure10. The sample diameters were a key parameter in this study and equal to the average of the diagonal outer diameters of both sample ends, measured using a caliper.Figure 10
Experimental materials.


### 3.2. Methods

A previous study has demonstrated that when the length of big arm was between 200 and 240 mm, the manipulator could grasp bamboo materials of common diameters. Therefore, three manipulators, with big arm lengths of 210, 220, and 230 mm, were developed for this trial and comparison. Hereinafter, those three manipulators were referred to as manipulators A, B, and C, respectively.


#### 3.2.1. Grasp Reliability and Accuracy Test

The rate and centering rates were two parameters used to determine the grasping reliability and accuracy. Samples were divided into three gradients: 60–85, 85–110, and 110–135 mm according to diameter differences. If a sample was tightly captured between V-shaped and U-shaped fingers, the grasp was successful. Therefore, the capture rate was calculated by the number of successfully grasped samples divided by the total number of grasped samples.If the distance between tool and sample centerlines was less than or equal to 5 mm, the charging was accurate enough for useful production. Otherwise, the charging failed. Thus, the centering rate was computed by the number of successfully charged samples divided by the number of total charged samples. To estimate whether the charging was successful or not, a laser pointer was installed at the tool head center. At the end of every charging test, the distance between the laser light point and the center of the bamboo sample was measured using a caliper.


#### 3.2.2. Dynamic Characteristic Test

To analyze the instantaneous movement of samples, a mercury series mer–030–120gx–pdes Poe Ethernet interface CCD was used to capture images of the grasping process. Its acquisition frequency was at 20 frames per second. Four images are shown in Figure11, including before grasping (Figure 11(a)), a manipulator touching a sample (Figure 11(b)), a manipulator grasping a sample (Figure 11(c)), and after grasping was finished (Figure 11(d)).Figure 11
Four captured images in the grasping process.
(a)
(b)
(c)
(d)A piezoelectric accelerometer (Chengke CT1010SLFP) was installed on manipulator wrist joint to detect its acceleration. The sampling frequency of the accelerometer was set as 1 kHz, and the measured voltages of acceleration signals, termedVx, Vy, and Vz, were converted into X, Y, and Z axis accelerations, termed ax, ay, and az, through a USB-6001 acquisition card, and input into a computer using USB 2.0 port (Figure 12).Figure 12
Accelerometer and signal conditioning system.An expression used to calculate the magnitude of the acceleration vectorar was obtained using (3), which was obtained in terms of its components ax, ay, and az, using the Pythagorean theorem.(3)ar=ax2+ay2+az2,where ar is an absolute value or ar≥0.The average of the median of the resultant acceleration peaks and their standard deviation, which reflected the overall trend of acceleration more clearly, were used in result analyses and calculated using the following equation:(4)Medar¯=1n∑i=1nMedari,where Medari represents the median of the resultant acceleration peaks for grasping the i sample and n represents the quantity of data in a group.An example ofX, Y, and Z axis accelerations detected by the accelerometer is shown in Figure 13. The magnitude of acceleration vectors calculated from the accelerations in Figure 13 is shown in Figure 14. By analyzing the acceleration curve, the start and end time points of the grasp were found. Furthermore, the total period of grasp process was calculated using the following equation:(5)t=nf,where n is the sampled acceleration signal number from being a sample picked up to grasped firmly and f is the sampling frequency of the accelerometer.Figure 13
X axis acceleration (a), Y axis acceleration (b), and Z axis acceleration (c).
(a)
(b)
(c)Figure 14
Magnitude of acceleration.


## 3.1. Materials

The test samples were bamboo of different diameters felled at the end of September 2019 at Nankun Mountain, Longmen County, Huizhou, Guangdong, China. All samples were placed at the laboratory of South China Agricultural University in Guangzhou, China, and few samples are shown in Figure10. The sample diameters were a key parameter in this study and equal to the average of the diagonal outer diameters of both sample ends, measured using a caliper.Figure 10
Experimental materials.


## 3.2. Methods

A previous study has demonstrated that when the length of big arm was between 200 and 240 mm, the manipulator could grasp bamboo materials of common diameters. Therefore, three manipulators, with big arm lengths of 210, 220, and 230 mm, were developed for this trial and comparison. Hereinafter, those three manipulators were referred to as manipulators A, B, and C, respectively.


### 3.2.1. Grasp Reliability and Accuracy Test

The rate and centering rates were two parameters used to determine the grasping reliability and accuracy. Samples were divided into three gradients: 60–85, 85–110, and 110–135 mm according to diameter differences. If a sample was tightly captured between V-shaped and U-shaped fingers, the grasp was successful. Therefore, the capture rate was calculated by the number of successfully grasped samples divided by the total number of grasped samples.If the distance between tool and sample centerlines was less than or equal to 5 mm, the charging was accurate enough for useful production. Otherwise, the charging failed. Thus, the centering rate was computed by the number of successfully charged samples divided by the number of total charged samples. To estimate whether the charging was successful or not, a laser pointer was installed at the tool head center. At the end of every charging test, the distance between the laser light point and the center of the bamboo sample was measured using a caliper.


### 3.2.2. Dynamic Characteristic Test

To analyze the instantaneous movement of samples, a mercury series mer–030–120gx–pdes Poe Ethernet interface CCD was used to capture images of the grasping process. Its acquisition frequency was at 20 frames per second. Four images are shown in Figure11, including before grasping (Figure 11(a)), a manipulator touching a sample (Figure 11(b)), a manipulator grasping a sample (Figure 11(c)), and after grasping was finished (Figure 11(d)).Figure 11
Four captured images in the grasping process.
(a)
(b)
(c)
(d)A piezoelectric accelerometer (Chengke CT1010SLFP) was installed on manipulator wrist joint to detect its acceleration. The sampling frequency of the accelerometer was set as 1 kHz, and the measured voltages of acceleration signals, termedVx, Vy, and Vz, were converted into X, Y, and Z axis accelerations, termed ax, ay, and az, through a USB-6001 acquisition card, and input into a computer using USB 2.0 port (Figure 12).Figure 12
Accelerometer and signal conditioning system.An expression used to calculate the magnitude of the acceleration vectorar was obtained using (3), which was obtained in terms of its components ax, ay, and az, using the Pythagorean theorem.(3)ar=ax2+ay2+az2,where ar is an absolute value or ar≥0.The average of the median of the resultant acceleration peaks and their standard deviation, which reflected the overall trend of acceleration more clearly, were used in result analyses and calculated using the following equation:(4)Medar¯=1n∑i=1nMedari,where Medari represents the median of the resultant acceleration peaks for grasping the i sample and n represents the quantity of data in a group.An example ofX, Y, and Z axis accelerations detected by the accelerometer is shown in Figure 13. The magnitude of acceleration vectors calculated from the accelerations in Figure 13 is shown in Figure 14. By analyzing the acceleration curve, the start and end time points of the grasp were found. Furthermore, the total period of grasp process was calculated using the following equation:(5)t=nf,where n is the sampled acceleration signal number from being a sample picked up to grasped firmly and f is the sampling frequency of the accelerometer.Figure 13
X axis acceleration (a), Y axis acceleration (b), and Z axis acceleration (c).
(a)
(b)
(c)Figure 14
Magnitude of acceleration.


## 3.2.1. Grasp Reliability and Accuracy Test

The rate and centering rates were two parameters used to determine the grasping reliability and accuracy. Samples were divided into three gradients: 60–85, 85–110, and 110–135 mm according to diameter differences. If a sample was tightly captured between V-shaped and U-shaped fingers, the grasp was successful. Therefore, the capture rate was calculated by the number of successfully grasped samples divided by the total number of grasped samples.If the distance between tool and sample centerlines was less than or equal to 5 mm, the charging was accurate enough for useful production. Otherwise, the charging failed. Thus, the centering rate was computed by the number of successfully charged samples divided by the number of total charged samples. To estimate whether the charging was successful or not, a laser pointer was installed at the tool head center. At the end of every charging test, the distance between the laser light point and the center of the bamboo sample was measured using a caliper.


## 3.2.2. Dynamic Characteristic Test

To analyze the instantaneous movement of samples, a mercury series mer–030–120gx–pdes Poe Ethernet interface CCD was used to capture images of the grasping process. Its acquisition frequency was at 20 frames per second. Four images are shown in Figure11, including before grasping (Figure 11(a)), a manipulator touching a sample (Figure 11(b)), a manipulator grasping a sample (Figure 11(c)), and after grasping was finished (Figure 11(d)).Figure 11
Four captured images in the grasping process.
(a)
(b)
(c)
(d)A piezoelectric accelerometer (Chengke CT1010SLFP) was installed on manipulator wrist joint to detect its acceleration. The sampling frequency of the accelerometer was set as 1 kHz, and the measured voltages of acceleration signals, termedVx, Vy, and Vz, were converted into X, Y, and Z axis accelerations, termed ax, ay, and az, through a USB-6001 acquisition card, and input into a computer using USB 2.0 port (Figure 12).Figure 12
Accelerometer and signal conditioning system.An expression used to calculate the magnitude of the acceleration vectorar was obtained using (3), which was obtained in terms of its components ax, ay, and az, using the Pythagorean theorem.(3)ar=ax2+ay2+az2,where ar is an absolute value or ar≥0.The average of the median of the resultant acceleration peaks and their standard deviation, which reflected the overall trend of acceleration more clearly, were used in result analyses and calculated using the following equation:(4)Medar¯=1n∑i=1nMedari,where Medari represents the median of the resultant acceleration peaks for grasping the i sample and n represents the quantity of data in a group.An example ofX, Y, and Z axis accelerations detected by the accelerometer is shown in Figure 13. The magnitude of acceleration vectors calculated from the accelerations in Figure 13 is shown in Figure 14. By analyzing the acceleration curve, the start and end time points of the grasp were found. Furthermore, the total period of grasp process was calculated using the following equation:(5)t=nf,where n is the sampled acceleration signal number from being a sample picked up to grasped firmly and f is the sampling frequency of the accelerometer.Figure 13
X axis acceleration (a), Y axis acceleration (b), and Z axis acceleration (c).
(a)
(b)
(c)Figure 14
Magnitude of acceleration.


## 4. Results and Discussion

### 4.1. Results

#### 4.1.1. Grasp Reliability and Accuracy Test

Experimental results for the capture and centering rates of manipulatorsA, B, and C are shown in Table 1. The average capture rate of manipulators A, B, and C were 96, 100, and 98.67%, and their centering rates were at 87.52, 90.45, and 88.35%, respectively. In general, the average capture rate for grasping samples of 85–110 mm diameter was the highest and that for grasping samples of 60–85 mm diameter was the lowest. There results also demonstrated that the capture rate of manipulator B was as high as 100%, and therefore manipulator B was the most suitable for this intelligent bamboo-splitting machine. The average centering rate of this experiment was <91%. The captured images showed that the cause of the centering error was that some sample sections were not circular.Table 1
Test results.
Manipulator
Diameter (mm)
Centering rate (%)
Capture rate (%)
A
60–85
87.50
92
85–110
85.43
100
110–135
89.64
96
Average
87.52
96
B
60–85
91.01
100
85–110
87.76
100
110–135
92.59
100
Average
90.45
100
C
60–85
90.00
96
85–110
86.34
100
110–135
88.72
100
Average
88.35
98.67


#### 4.1.2. Dynamic Characteristic Test

Capture time curves of manipulatorsA, B, and C are in shown in Figure 15, which demonstrated that capture time decreased with sample diameter. No significant capture time differences were observed among these three manipulators in grasping samples with diameters between 105.1 and 114.4 mm. The trend curves of the influence of sample diameter on average capture time were similar to exponential curves; the fitted curve expressions are listed in Table 2.Figure 15
Capture time of grasping diameter.Table 2
Capture time formula.
Manipulator
Capture time formula
R
2
A
t = 2.8144e−0.033d
0.8284
B
t = 2.8384e−0.038d
0.9665
C
t = 2.6327e−0.033d
0.9535No matter which manipulator was used for grasping, the average acceleration decreased with decreased sample diameter (Figure16). The longer the big arm was, the greater the average acceleration became. The trend curves of the influence of the sample diameter on the average acceleration were also similar to exponential curves; the fitted curve expressions are listed in Table 3.Figure 16
Average acceleration of grasping.Table 3
Average acceleration formula of grasping.
Manipulator
Average acceleration formula
R
2
A
a = 18.65d−0.044
0.8491
B
a = 24.472d−0.17
0.8549
C
a = 31.05d−0.239
0.8676


### 4.2. Discussion

The longer the big arm was, the larger the grasping force of the manipulator was, and the faster the grasping speed was. Captured images showed that in grasping with manipulatorC, small samples always slipped in the groove of U-shaped fingers acting at high speed, and some samples stuck between U and V-shaped fingers at wrong positions. Thus, the capture rate of manipulator C grasping samples of diameters between 60 and 85 mm was only 96%. If the big arm was too short, the grasping force became too small to grasp small materials, which also explained why the average centering rate of manipulator A was the lowest.When picked up by U-shaped fingers, big samples can barely slide, being captured firmly and quickly. Therefore, the required time for grasping big samples was shorter. If the big arm was too short, the grasping force became insufficient and materials vibrated in U-shaped fingers with a large amplitude. This explained why the required time for manipulator A for capturing samples was the longest.The captured images showed that small samples vibrated violently in U-shaped fingers. Due to the size limitation of U-shaped fingers, the vibration space of large samples was limited. As the big arm became longer, the grasping force became larger and the instantaneous grasping acceleration became larger. This explained why the detected average acceleration of manipulatorC was the highest.


## 4.1. Results

### 4.1.1. Grasp Reliability and Accuracy Test

Experimental results for the capture and centering rates of manipulatorsA, B, and C are shown in Table 1. The average capture rate of manipulators A, B, and C were 96, 100, and 98.67%, and their centering rates were at 87.52, 90.45, and 88.35%, respectively. In general, the average capture rate for grasping samples of 85–110 mm diameter was the highest and that for grasping samples of 60–85 mm diameter was the lowest. There results also demonstrated that the capture rate of manipulator B was as high as 100%, and therefore manipulator B was the most suitable for this intelligent bamboo-splitting machine. The average centering rate of this experiment was <91%. The captured images showed that the cause of the centering error was that some sample sections were not circular.Table 1
Test results.
Manipulator
Diameter (mm)
Centering rate (%)
Capture rate (%)
A
60–85
87.50
92
85–110
85.43
100
110–135
89.64
96
Average
87.52
96
B
60–85
91.01
100
85–110
87.76
100
110–135
92.59
100
Average
90.45
100
C
60–85
90.00
96
85–110
86.34
100
110–135
88.72
100
Average
88.35
98.67


### 4.1.2. Dynamic Characteristic Test

Capture time curves of manipulatorsA, B, and C are in shown in Figure 15, which demonstrated that capture time decreased with sample diameter. No significant capture time differences were observed among these three manipulators in grasping samples with diameters between 105.1 and 114.4 mm. The trend curves of the influence of sample diameter on average capture time were similar to exponential curves; the fitted curve expressions are listed in Table 2.Figure 15
Capture time of grasping diameter.Table 2
Capture time formula.
Manipulator
Capture time formula
R
2
A
t = 2.8144e−0.033d
0.8284
B
t = 2.8384e−0.038d
0.9665
C
t = 2.6327e−0.033d
0.9535No matter which manipulator was used for grasping, the average acceleration decreased with decreased sample diameter (Figure16). The longer the big arm was, the greater the average acceleration became. The trend curves of the influence of the sample diameter on the average acceleration were also similar to exponential curves; the fitted curve expressions are listed in Table 3.Figure 16
Average acceleration of grasping.Table 3
Average acceleration formula of grasping.
Manipulator
Average acceleration formula
R
2
A
a = 18.65d−0.044
0.8491
B
a = 24.472d−0.17
0.8549
C
a = 31.05d−0.239
0.8676


## 4.1.1. Grasp Reliability and Accuracy Test

Experimental results for the capture and centering rates of manipulatorsA, B, and C are shown in Table 1. The average capture rate of manipulators A, B, and C were 96, 100, and 98.67%, and their centering rates were at 87.52, 90.45, and 88.35%, respectively. In general, the average capture rate for grasping samples of 85–110 mm diameter was the highest and that for grasping samples of 60–85 mm diameter was the lowest. There results also demonstrated that the capture rate of manipulator B was as high as 100%, and therefore manipulator B was the most suitable for this intelligent bamboo-splitting machine. The average centering rate of this experiment was <91%. The captured images showed that the cause of the centering error was that some sample sections were not circular.Table 1
Test results.
Manipulator
Diameter (mm)
Centering rate (%)
Capture rate (%)
A
60–85
87.50
92
85–110
85.43
100
110–135
89.64
96
Average
87.52
96
B
60–85
91.01
100
85–110
87.76
100
110–135
92.59
100
Average
90.45
100
C
60–85
90.00
96
85–110
86.34
100
110–135
88.72
100
Average
88.35
98.67


## 4.1.2. Dynamic Characteristic Test

Capture time curves of manipulatorsA, B, and C are in shown in Figure 15, which demonstrated that capture time decreased with sample diameter. No significant capture time differences were observed among these three manipulators in grasping samples with diameters between 105.1 and 114.4 mm. The trend curves of the influence of sample diameter on average capture time were similar to exponential curves; the fitted curve expressions are listed in Table 2.Figure 15
Capture time of grasping diameter.Table 2
Capture time formula.
Manipulator
Capture time formula
R
2
A
t = 2.8144e−0.033d
0.8284
B
t = 2.8384e−0.038d
0.9665
C
t = 2.6327e−0.033d
0.9535No matter which manipulator was used for grasping, the average acceleration decreased with decreased sample diameter (Figure16). The longer the big arm was, the greater the average acceleration became. The trend curves of the influence of the sample diameter on the average acceleration were also similar to exponential curves; the fitted curve expressions are listed in Table 3.Figure 16
Average acceleration of grasping.Table 3
Average acceleration formula of grasping.
Manipulator
Average acceleration formula
R
2
A
a = 18.65d−0.044
0.8491
B
a = 24.472d−0.17
0.8549
C
a = 31.05d−0.239
0.8676


## 4.2. Discussion

The longer the big arm was, the larger the grasping force of the manipulator was, and the faster the grasping speed was. Captured images showed that in grasping with manipulatorC, small samples always slipped in the groove of U-shaped fingers acting at high speed, and some samples stuck between U and V-shaped fingers at wrong positions. Thus, the capture rate of manipulator C grasping samples of diameters between 60 and 85 mm was only 96%. If the big arm was too short, the grasping force became too small to grasp small materials, which also explained why the average centering rate of manipulator A was the lowest.When picked up by U-shaped fingers, big samples can barely slide, being captured firmly and quickly. Therefore, the required time for grasping big samples was shorter. If the big arm was too short, the grasping force became insufficient and materials vibrated in U-shaped fingers with a large amplitude. This explained why the required time for manipulator A for capturing samples was the longest.The captured images showed that small samples vibrated violently in U-shaped fingers. Due to the size limitation of U-shaped fingers, the vibration space of large samples was limited. As the big arm became longer, the grasping force became larger and the instantaneous grasping acceleration became larger. This explained why the detected average acceleration of manipulatorC was the highest.


## 5. Conclusions

Experiment results showed that the average capture rate of manipulatorB was 100%, and its average centering rate was 90.45%. Therefore, it grasped samples with different diameters successfully. The size of manipulator B was also equal to our calculated optimal size. These experiments partly validated the present optimization strategy.The required time for grasping larger samples was shorter than that of grasping smaller samples. The trend curves of the influence of sample diameter on average grasping time were similar to exponential curves, and the fitted curve expression of manipulatorB was t = 2.8384e−0.038d. The trend curves of sample diameter influence on the average acceleration were also similar to exponential curves, and the fitted curve expression of manipulator B was a = 24.472d−0.17.



---

*Source: 4675301-2020-03-17.xml*