Introduction

With the rapid economic development and the accelerated urbanization process, the urban population continues to increase, which brings a large amount of domestic garbage while promoting the prosperity of the city. At present, in view of the garbage collection, high labor intensity, mechanization, automation and low level of intelligence, for the existing garbage collection mode, garbage collection and transportation facilities and technologies have been unable to quickly and timely meet the increasing demand for garbage, and it is urgent to improve the mechanization, automation, intelligence and networking level of assembly in the garbage collection and transportation links.

The United States and Germany were the first countries to use robotic arms on garbage trucks1. There are many types of robotic arms currently in use, including rail type robotic arms, articulated link type robotic arms, and combination type robotic arms2,3,4. Andryukhov et al.5 generates a structure that minimizes stress. The main body of the rocker arm model is determined using the Equivalent Static Load Method (ESL). Based on simulation, the design of the rocker arm was developed. The improved rocker arm has reduced its weight by 10.8 kg while maintaining the stress level generated by the load. The design of the rocker arm is not suitable for heavy garbage bins such as kitchen and bathroom waste, and has limitations in its application. Zheng et al.6 takes the loading mechanism of a loading garbage truck as the research object. A three-dimensional model of the mechanism was established through software and force analysis was conducted under operating conditions. Using MATLAB software to draw a curve to display the relationship between the compression filling force FL and the pusher stroke x and installation angle α. When selecting the optimal installation angle, the maximum compression filling force FL is 188.29. This study provides a good research idea, but lacks specific experimental evidence and only stays in theoretical research. Zheng et al.7 established a topology optimization model for the overweight problem of the entire working condition, taking the rocker arm of the compressed garbage truck tipping system as the research object. This model is constrained by stress and optimized with the objective of minimizing mass. In the optimization process, a multi-body dynamics rigid flexible coupling model was established using the equivalent static load method. Topology optimization was carried out on the rocker arm, and the structural design of the rocker arm was improved. At the same stress level, the improved rocker arm reduced its weight by 10.8 kg, a decrease of 44%. Lina et al.8 takes the lifting condition of the garbage truck manipulator as the main research object, and uses virtual prototyping method to simulate the dynamics of the manipulator, providing a basis for the design and selection of manipulator components. However, this design is not suitable for situations where the garbage can is heavy. Tao et al.9 used finite element method to simulate and optimize the structure of the robotic arm, but this design only exists for theoretical verification and simulation, lacking specific experiments and prototype construction.

From the above, it can be seen that the mechanical arms of the garbage trucks currently used have problems such as lack of accuracy, garbage leakage, and damage to garbage bins; However, scholars’ research mainly focuses on theoretical verification and simulation of different robotic arms, with less emphasis on overall physical verification. Based on this, it is of great significance to improve the accuracy of the garbage truck manipulator and control the gripping force of the manipulator, and to conduct physical experiments to demonstrate it. This study designed a garbage truck robotic arm with clamping force feedback and a lifting structure, which has good motion performance. The design scheme was theoretically verified and experimentally demonstrated. The results showed that this machine can accurately clamp and transport garbage cans by setting different clamping forces according to their weight.

Scheme design and working principle

Design criteria

Due to different road conditions and environmental conditions, it is necessary to develop a gripper mechanism that can carry different weights of garbage. The goal of this paper is to achieve fast, accurate and efficient garbage collection and transportation, positioning the garbage cans from both sides of the road, moving them accurately to the garbage can position, thereby shrinking to the position of the side-mounted garbage truck, in order to achieve the best collection effect, and accurately recycling the garbage in the garbage can to the garbage car. When designing a garbage truck manipulator, it must be ensured that it can meet the following requirements:

  1. 1.

    It has a certain degree of freedom. In order to operate more conveniently and improve work efficiency, it is necessary to design a manipulator to make up for this deficiency, so the manipulator needs to have three basic spatial degrees of freedom, that is, accurate operation on the X axis, Y axis and Z axis.

  2. 2.

    Enough grab power. Grasping force refers to the maximum load that the manipulator can bear when extracting the trash can, reflecting its grasping ability of the total weight of the entire trash can. Therefore, having enough grasping power is essential, which is the basic requirement. When the conditions are met, the robot claw can grasp the garbage can to be collected by the roadside firmly and accurately.

  3. 3.

    Faster reaction time. The response speed of the manipulator can significantly improve the efficiency of its overall stroke, thus effectively improving the efficiency and quality of garbage collection. Improve efficiency, save time and reduce costs.

  4. 4.

    Plenty of work space. Having sufficient working space is a key factor in ensuring that the robotic arm and the end gripper can perform the task of garbage collection and disposal efficiently and accurately. In order to ensure that the robot can complete the assigned work, it is necessary to ensure that the space is sufficient and the necessary safety guarantees are provided.

  5. 5.

    Bear a certain load. By increasing the strength and stiffness of the manipulator, it can be ensured that there will be no serious deformation or damage during movement. In order to ensure the efficient completion of the task, the manipulator must have sufficient strength and rigidity to resist the impact of external forces.

Design index

According to the working characteristics and design requirements of the manipulator of the garbage collection truck, the design indicators of the manipulator are determined as shown in Table 1 below.

Table 1 Technical index of manipulator.
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Design scheme and working principle

This project selects the most used garbage cans in today’s society as the research object. The existing garbage cans are mainly divided into two types, 120 L and 240 L respectively, and the density of urban kitchen waste is generally 0.2–0.4 tons/cubic meter. In order to ensure that the designed garbage can has a high enough carrying capacity, Here, the average value is 488.85 kg/m310, the total weight of 120 L garbage can and 240 L garbage can is between 77 and 155 kg, and the weight of 120 L garbage can is 100 kg as the design weight for specific analysis.

Based on the shape and force characteristics of the garbage can, a side-mounted garbage truck automatic grasping manipulator is designed. The manipulator mainly consists of claw mechanism, telescopic mechanism, distance compensation mechanism, clean and jerk mechanism, and the hydraulic system is designed for experimental verification. The three-dimensional structure is shown in Fig. 1.

Fig. 1
figure 1

3D modeling of the mechanical arm of the hydraulic garbage truck.

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The work flow of the device is mainly divided into the following stages, and the flow diagram is shown in Fig. 2.

  1. 1.

    Back extension: According to Figure a, the telescopic square tube of the mechanical arm extends along the Y-axis and finally reaches the position of the trash can. This process is achieved through the use of hydraulic cylinders.

  2. 2.

    Positioning: According to Figure b, the infrared sensor placed in the middle position of the claw is used to locate and align the center of the trash can, and the feedback is sent to the control system. The control system fine-adjusts the claw by adjusting the X-direction distance compensation mechanism, so that the claw and the trash can are in the same horizontal line.

  3. 3.

    Grasping: According to Figure b, the grasping mechanism completes the grasping of the trash can and lifts the trash can off the ground. The process is driven by the hydraulic cylinder in the claw mechanism and the clean and jerk cylinder in the reverse clean and jerk mechanism.

  4. 4.

    Recovery: According to Figure c, the manipulator shrinks vertically along the Y-axis and finally returns to its original position, a process controlled by a hydraulic cylinder.

  5. 5.

    Lifting: According to Figure d, the clean and jerk mechanism starts to work so that the whole holding mechanism turns and rises along the Z axis to realize the lifting of the trash can. The process is driven by the clean and jerk oil cylinder in the clean and jerk mechanism.

  6. 6.

    Dumping: According to Figure e, the garbage in the trash can be effectively dumped through the coordination of the holding mechanism and the lifting mechanism, and this process is driven by the thrust cylinder of the clean and jerk mechanism and the clamping hydraulic cylinder.

  7. 7.

    Empty bucket reset: According to Figure f, after completing the dumping of garbage, the robot will first turn the garbage cans and adjust them well, then extend them out, and finally lower them to a suitable height and put them on the ground. During this process, the claw mechanism helps them unload so that they can return to their original state.

  8. 8.

    Garbage truck manipulator reset: After the re-positioning of the empty drum is completed, the entire component of the holding mechanism will shrink along the Y axis to achieve the reset of the manipulator.

Fig. 2
figure 2

Schematic diagram of the working process of the mechanical arm.

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In this process, the sensor plays the role of information feedback. When the robot arm reaches the position of the garbage can, the position sensor on the clamp baffle determines the distance between the hand claw and the garbage can and feeds back to the control system, so that the control system can give instructions to remind the driver whether the vehicle position needs to be readjusted or take the next step. The infrared sensor located in the center of the hand claw determines the position of the center line of the trash can and feedbacks to the control center of the robot arm, and then the X-direction distance compensation mechanism moves to the designated position to complete the accurate intelligent clamping of the trash can.

Materials and methods

Design of key components

Telescopic mechanism

In this study, the maximum working length of the telescopic mechanism is 600 mm, the mass of the 240 L garbage can has been calculated as 150 kg above, and the weight of the mechanical arm itself is 130 kg. Considering the influence of working conditions, the total weight is 300 kg. And the Y direction is the direction of the car width, the length of the installation is longer, and the straight-arm sleeve can be telescoped. Since the maximum working length is 600 mm, the first-level expansion mechanism can be used. When calculating the length of the basic arm and the telescopic arm, the section type and section number of the sleeve should be considered first, and the section size and material of the sleeve should be determined according to the maximum bearing weight.

(1) Section size calculation

By analyzing the section size of the sleeve, it can be determined whether its bending performance meets the requirements under the maximum weight. Because the bending modulus of the telescopic arm is much lower than that of the basic arm, it is only necessary to check and calculate its bending performance in detail. According to the maximum load of 300 kg, the bending force of the maximum section is calculated.

$$M_{{{\text{max}}}} = FL/2$$
(1)

In the formula, Mmax represents the maximum bending strength, F is the applied force, and L is the total length of the moment arm.

The minimum bending section modulus can be calculated from formula 211.

$$W = M/\sigma$$
(2)

where W represents the minimum bending section modulus, M represents the maximum bending moment, and σ represents the maximum section pressure.

From these parameters, the length and width of the section of the basic arm and the fillet size can be preliminarily determined to ensure that the bending section coefficient obtained after design should be at least greater than the minimum bending section modulus.

(2) Length determination and verification

In this project, the length design of the mechanical arm should take into account the maximum working interval, which is 600 mm. Therefore, the basic arm length of the mechanical arm should not exceed the length of the vehicle width. However, the telescopic arm can extend a certain distance in the direction of the trash can, so in order to ensure the safety of the robot arm, the non-overlapping part and the overlapping part of the entire sleeve need to be checked and calculated to ensure the correct installation of the robot arm. First, look at the normal stress of the section of the non-overlapping part12, as shown in Formula 3 below.

$$\sigma_{{\text{x}}} { = }\frac{N}{A} + \frac{{M_{{\text{y}}} }}{{W_{{\text{y}}} \left( {1 - \frac{N}{{0.9N_{{{\text{cry}}}} }}} \right)}} \le \left[ \sigma \right]$$
(3)

In the formula, N represents the axial pressure borne by the telescopic arm; My represents the cross-section bending moment generated by the lateral load on the amplitude changing plane, which can be calculated; Ncry is a kind of critical force, which can affect the movement of the telescopic arm on the amplitude plane. A is the cross-sectional area of the telescopic arm. Wy is a parameter of the flexural performance of the telescopic arm section on the y and z axes.

According to the above formula, the normal stress σx of the section of the overlapping part can still be calculated, but the stress of the local bending part needs to be calculated according to the characteristics of the support point of the telescopic arm, which is generally calculated by multiplying the analytical solution of the bending of the steel plate by the correction factor, as shown in Fig. 3, which is a schematic diagram of the force on the overlapping part of the telescopic arm, and the calculation formula can be referred to formula 4.

$$\sigma = \frac{{N_{{\text{h}}} }}{{24\pi \delta^{2} }}\left( {1 + \mu } \right)$$
(4)

where δ is the thickness of the steel. Nh is the branch reaction in the overlapping cutoff region calculated by formula 513.

Fig. 3
figure 3

Schematic diagram of cross-sectional force of telescopic mechanism.

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$${N}_{h}=\frac{T\left(H+L\right)+M}{L}$$
(5)

In the formula, each letter represents the meaning in the schematic diagram of the telescopic arm structure in Fig. 4.

Fig. 4
figure 4

Schematic diagram of the force on the overlapping section of the telescopic mechanism.

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After calculation and substitution, it is known that σ = 143 MPa, the strength of 45# steel [σ] = 355 MPa, σ < [σ], and the empirical calculation meets the requirements of the safety factor specification.

Clean and jerk mechanism

This project adopts a clean and jerk turning mechanism with two hydraulic rods placed symmetrically, as shown in Fig. 7. In this mechanism, two parallel hydraulic rods fixed in the chassis are articulated and driven in series to achieve the clean and jerk work, the process is firm and reliable, and the turnover process is smooth. The advantage of this mechanism is that the parallel double hydraulic rods provide protection for the safety of heavy machinery, and the strength and stiffness of the garbage truck manipulator are significantly improved, reducing the generation of partial load.

Figure 5 is the physical diagram of the flip jerk mechanism. In the double hydraulic rod flip jerk mechanism, the hydraulic cylinder mounting base and the hydraulic rod are hinged, and the hydraulic cylinder has a certain activity space in the Y direction, which provides a buffer effect for the side pressure of the hydraulic cylinder in the work. The two parallel hydraulic rods are connected together by 4 connecting shafts to ensure that the hydraulic rods rise and fall synchronously during the clean and jerk. In the clean and jerk mechanism, a triangle-like mechanism with 6 supporting lower arms and 7 clamping jaw mounting arms and 8 supporting upper arms at a fixed Angle14 is shown in Fig. 6.

Fig. 5
figure 5

Physical picture of the reverse jerk mechanism.

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Fig. 6
figure 6

Schematic diagram of a triangle-like mechanism.

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During the movement of the reverse clean and jerk mechanism, the main component that changes relative Angle (see Fig. 7) is the Angle between the 5 connecting rod and the 6 supporting lower arm, and the initial Angle is 124.40°. At this time, the manipulator of the garbage truck is in a state of natural droop, and the force of the 5 connecting rod is the least at this time, and the load is mainly borne by the hydraulic rod from the weight of the manipulator itself. After the manipulator is righted, see Fig. 10a. The supporting arm is under the gravity of its own gravity and the gravity of the gripper mechanism. The Angle between the supporting arm and the connecting rod is enlarged to drive the mounting arm of the 7 grippers to lift up. The Angle between the connecting rod and the supporting arm reaches a maximum of 138.35°. After that, the hydraulic rod is extended to the maximum distance to flip the supporting arm, the Angle between the connecting rod and the supporting arm is gradually reduced to 108.61°, and all the garbage in the trash can is dumped. The Angle change between the supporting arm and the connecting rod reflects the movement process of the clean and jerk mechanism. The Angle change in the process is relatively gentle, indicating that the process is smooth and smooth in the process of tipping the garbage.

Fig. 7
figure 7

Diagram of relative Angle change during flipping.

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Claw mechanism

Two different forms of opening and closing are used in the end-effector, one is the translational type as shown in Fig. 8a, and the other is the back transition15 as shown in Fig. 8b. Due to its mechanical properties, the stress distribution of the horizontal gripper is more uneven than that of the curved gripper when it is subjected to external force, so that their destructive force on the surface of the trash can is greatly enhanced. Since the power of the rotary gripper comes from the center, it can be clearly observed from Fig. 8b that its power is transmitted to the various components, and its power source is usually a micro motor, its main use is to grab fruits, vegetables and other plants, but due to the large volume of the trash can, it cannot be used for grabbing when the trash can is full of garbage.

Fig. 8
figure 8

Schematic diagram of jaw opening and closing form.

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Based on the above analysis, this topic combined the advantages of both and comprehensively considered the two gripper configurations to design a gripper with two sides of the manipulator capable of mutual motion and controllable clamping force monitoring. The three-dimensional model is shown in Fig. 9.

Fig. 9
figure 9

Force mechanism diagram of the gripper.

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In the force analysis of the clamp, F represents the force exerted by the push rod on the piston cylinder, Fm is the force exerted on the connecting rod when the hydraulic cylinder is moving, and F1 and F2 are the branch force exerted on the clamp, which can be expressed as F1 = F2 = F/(2cosθ). According to the data in the figure, it can be clearly seen that the distance between a and b has an effect on the clamping force. Therefore, through comparative analysis, the best force effect can be obtained, so as to improve the design effect of the clamping claw.

(1) Structural design of the claw

Through the analysis of the gripper, this topic designs the gripper structure as shown in Fig. 10. It is composed of 1 end clip, 2 clamp transmission box, 3 positioning pin, 4 clamp hydraulic cylinder, 5 connecting rod and 6–8 fixing pin. By pushing out and retracting the piston rod, the hydraulic cylinder drives the connecting rod to move in the X direction, so that the two jaw transmission boxes can move relative to each other and realize the clamping and relaxing of the chuck.

Fig. 10
figure 10

Claw structure.

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Selection and design of pressure sensor

When the claw grabs the trash can, if the clamping force is too large, it may damage the trash can; If the clamping force is too small, it is difficult to grasp it firmly, resulting in the fall of the trash can. In order to better grasp and control the clamping force, the pressure sensor can be used to accurately measure the shrinkage of the clamp hydraulic rod. When their shrinkage exceeds the set range, the PLC will send the corresponding electrical signal, and the PLC will control the work of the hydraulic cylinder according to this information to achieve the best clamping effect.

With the development of science and technology, the types of pressure sensors are becoming more and more abundant, but due to the needs of garbage collection and the design structure of the mechanical clamp of garbage trucks, the space for installing pressure sensors is limited. In order to meet these requirements, it is necessary to select a pressure sensor with small size, fast response, oil resistance, easy maintenance and affordable price16. The use of the BCBU-1 type spoke pressure sensor, with extremely high measurement accuracy, up to 0–2400 N.

In the installation position, because the force boss of the sensor is located in the central position of the sensor, if the sensor is placed in the middle position of the claw when the garbage can is picked up by the claw, the garbage can will be broken, because the middle position of the claw corresponds to the middle position of the garbage can, the middle position of the garbage can is the lowest thickness of the garbage can material, so the sensor is placed in the position of the garbage can reinforcement. Figure 11 shows the dimensions and positions of the sensors placed horizontally.

Fig. 11
figure 11

Sensor size and position diagram.

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Static finite element analysis

Static modeling

ANSYS Workbech finite element analysis can carry out pre-processing and mesh division, in order to meet the function and strength requirements of the manipulator under the working state, in the early development and design of the whole machine need to select the material and grade of each component. In this study, Q345 material was selected to make the gripping mechanism and lifting arm, and 45 steel was used to make the base and hydraulic system, while the slide dovetail groove was made of cast iron. The mechanical properties of these three materials are shown in Table 2: In the early stage of part design, the system can utilize limited data to generate more comprehensive design solutions, improve the efficiency of small batch and multi change production design, and reduce the error rate of manual operation17.

Table 2 Material properties table.
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The robot part is divided by a hexahedral mesh18,19, the mesh size is set to 10 mm, and the mesh size of the remaining parts is set to 20 mm, and the tetrahedral mesh is divided. At the same time, the fine features of each part, such as small faces, small circular holes and split edges, are processed, and some rounded corners are removed. The smaller faces can be simplified by merging with other faces. The existence of split edges will also affect the distribution of mesh seeds, thus affecting the mesh quality20. Smooth transition is selected at the transition point of the grid. Meanwhile, the grid quality of each component is observed, and the grid encryption process is carried out at parts with poor grid quality. The final grid division results of the model are shown in Fig. 12.

Fig. 12
figure 12

Grid division results.

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The load received by the manipulator under working conditions is the total weight of the trash can full of garbage. Here, the total mass of the trash can is equivalent to the force exerted on the contact surface. The total weight of the trash can full of garbage is 150 kg, that is, 1500 N, and the force direction is the gravity direction. The contact area of the contact surface of the manipulator is cut out with a plane, and a remote point is set to connect the two contact surfaces through a rigid connection. Under the conditions of lifting, lifting and tipping of the manipulator, the center axis of the turning arm remains static, and the hydraulic cylinder system is used to drive it under each working condition. Therefore, fixed constraints are applied at the axis of the rotating arm, and fixed constraints are added at the bottom of the guide rail.

Finite element analysis results under different working conditions

(1) Grasping conditions

The cloud image of maximum deformation under the grasping state is shown in Fig. 13a. As can be seen from the figure, the largest deformation position of the manipulator appears at the most front position of the right clamp claw, with a size of 4.3 mm, and the deformation of the component is smaller the closer it is to the fixed position of the manipulator. It can be seen from Fig. 13b that the maximum stress of the manipulator in the grasping state is 103.36 MPa, and the maximum position where the stress value appears is the contact position between the corner of the lifting arm and the cylinder piston as shown in Fig. 13c. The reason for the above results is that under the working condition of the manipulator grabbing the barrel, the barrel is lifted by pushing the connecting shaft of the manipulator lifting arm forward through the piston, so the phenomenon of maximum stress will appear at the connecting shaft of the lifting arm.

Fig. 13
figure 13

Deformation nephogram and stress nephogram under grasping state.

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Because the manipulator and the connecting shaft of the lifting arm made of No. 45 steel are used, the pressure under is extremely low, only 103.36 MPa, which is obviously lower than its yield strength of 355 MPa. It can be concluded that the overall structure of the manipulator is reliable and stable under grasping conditions, and the cost of the whole machine can be reduced by replacing cheaper materials or reducing the diameter of the connecting shaft.

(2) Clean and jerk conditions

As can be seen from Fig. 14a, the maximum deformation of the left gripper is 9.52 mm when the manipulator is in lifting condition, and the deformation is smaller when the distance from the fixed position of the manipulator is closer. According to the analysis of the above results, under the working condition of the manipulator lifting the barrel, the main body bearing the barrel load is still the left and right gripper, and the large deformation is also because one end of the gripper is the farthest from the turning center of the rotating arm, and the value of the moment arm is the largest, thus bearing the maximum torque value. According to the stress cloud diagram analysis in Fig. 14b, the position where the greatest stress occurs is still the connecting shaft of the lifting arm connected to the piston, and the stress value is 123.52 MPa. The reason is that the barrel is still lifted by the piston pushing the connecting shaft of the lifting arm, so the stress point appears at the connecting shaft, and the maximum stress occurs21. The stress value in the lifting state is 123.52 MPa, and the yield strength of the selected material 45# steel is 355 MPa, indicating that the manipulator structure in the lifting state has reliability.

Fig. 14
figure 14

Deformation nephogram and stress nephogram under clean and jerk.

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(3) Distance compensation condition

As can be seen from the analysis of Fig. 15a, the maximum deformation still appears at the left grasping front end of the barrel, and the deformation of 5.53 mm is slightly larger than the deformation of the barrel under normal condition. The reason for this result is that when the slide rail is extended forward, the overall force of the manipulator is less concentrated than that under normal condition, and the overall carrying capacity decreases. Therefore, when lifting the same weight of the barrel, there will be a larger deformation phenomenon. Meanwhile, by analyzing the stress cloud diagram in Fig. 15b, it can be seen that stress concentration occurs at the connection between the square tube of the mechanical arm and the base, not at the connection axis of the mechanical arm, and the maximum stress is 81.26 MPa. It can be seen from the analysis that because the slide rail extends in the X direction, the farther the mechanical arm is from the fixed position of the base, The application point of the lever appears at the connection between the square tube of the manipulator and the base, but the reliability cannot be determined by comparing the maximum stress value with the yield value of the material at this time, because the square tube and the base are fixed through an L-shaped connection, so the connection strength between them needs to be considered here. The connection strength between the two can be strengthened by adding multiple solder joints22, etc., so as to effectively prevent failure in this case.

Fig. 15
figure 15

Deformation nephogram and stress nephogram under the maximum X displacement state.

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Kinematics simulation analysis

Modeling based on Adams platform

In order to introduce the model better, the relevant parameters of the working environment need to be adjusted first. Due to the large number of models and huge amount of data, before introducing a new model, the parts that will not affect the core movement of the device should be eliminated, so as to simplify the robot model23,24. Through the introduction of constraints, activation mechanisms and the application of loads, a complex mechanical system can be built to achieve effective motion simulation analysis.

After the manipulator geometry model is imported successfully, in order to ensure the interaction between each component, a series of constraint measures must be taken to ensure that the contact between them is formed into a motion system. The types of motion constraints are shown in Table 3.

Table 3 Indicates the types of motion pairs added in the manipulator model.
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Add all constraints in Adams and set the quality attributes of each part, as shown in Fig. 16 below.

Fig. 16
figure 16

Adding motion pairs and drivers to the 3D model in Adams.

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As shown in Fig. 16, the simulation model of the robot arm of the garbage truck is reversed, and the trash can is added on the right side to simulate the force during grabbing. In addition, the motion and force of the model can be simulated by adding constraints and loads.

The collection and transportation process of the garbage truck manipulator in this project is distributed successively, so the STEP function24 can be used to control its movement.

Format expression of STEP function:

$$F = STEP\left( {x,x_{0} ,h_{0} ,x_{1} ,h_{1} } \right)$$
(6)

In formula (6), x is a variable independent variable, which can represent time, Angle or other variables, while x0 and x1 represent the starting point and end point of these two variables respectively, and their variation ranges can be used to describe the relationship between variables. In addition, h0 and h1 are function values of these two variables, which can be a constant, such as displacement, speed, Angle, torque, etc. The function F = STEP(x,x0,h0,x1,h1)means that the function can be implemented through these steps.

h represents the result of the calculation of the STEP function, which is used to describe the process.

$$F = \left\{ {\begin{array}{*{20}l} {h_{0} } \hfill & {(x \le x_{0} )} \hfill \\ h \hfill & {(x_{0} \le x \le x_{1} )} \hfill \\ {h_{1} } \hfill & {(x \ge x_{1} )} \hfill \\ \end{array} } \right.$$
(7)

In the formula (7), h is the value automatically modeled by the STEP function in the analysis of the dynamic motion process.

Based on the function expression, you can observe the corresponding function curve, as shown in Fig. 17.

Fig. 17
figure 17

F = STEP(x,x0,h0,x1,h1)function curve.

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The device completes the automatic dumping of garbage can under the action of driving function and force. Its movement process is relatively complex, and in the whole process of garbage collection, the motion control of each mechanism is completely determined by the motion stroke of each hydraulic rod, so it is necessary to formulate and control each movement. The entire control process is divided into the following processes:

The first step is the horizontal alignment of the device, because when the claw grabs the trash can, it needs to maintain the horizontal position of the claw and the trash can, and the device is in a natural drooping state under the initial condition, here it needs to drive the jerk hydraulic rod, and turn the jerk mechanism back to maintain the horizontal position, the stroke is 70 mm, the time of each step is set to be 5 s, and the time of the following steps is the same.

The second step is to drive the XY hydraulic rod, positioning the device near the trash can, so that the claw can grab the trash can within a limited range, its total stroke is 500 mm, at the same time, the claw hydraulic rod is driven at the same time, so that the open claw can grab the trash can later; Travel is 40 mm;

The third step is the contraction of the claw, the trash can grab, the stroke is between 35 and 45 mm, the specific value depends on the strength of the sensor, when the measurement strength reaches the set size, that is, stop the drive, that is, to achieve the accurate grasp of the trash can, and not too much strength and damage the trash can;

The fourth step is to lift the trash can. In order to avoid the collision between the trash can and the ground or the bottom of the device, the clean and jerk mechanism is driven to lift the trash can a certain distance to make it suspended, and the stroke is 100 mm.

The fifth step is the return of the telescopic direction, the distance auxiliary hydraulic rod and the Y-telescopic hydraulic rod will be driven at the same time, and the device will be brought back to the starting position with a stroke of 500 mm;

The sixth step is to drive the clean and jerk mechanism, turn the garbage can to the top of the garbage can, and all the garbage will be poured into the garbage truck, and the travel time is 140 mm;

The seventh step is the straightening of the clean and jerk mechanism, the trash can is returned to the original position, and the stroke is 140 mm. Finally, the work flow of this device is 35 s, and different step functions are used to control each stage. The following are the driving functions of each driving hydraulic rod:

Moving hydraulic rod in XY direction:step(time,5,0,10,-500) + step(time,20,0,25,500)Clean and jerk mechanism hydraulic rod:step(time,0,0,5,70) + step(time,15,0,20,100) + step(time,25,0,30,120) + step(time,30,0,35,-220)Clamp hydraulic rod:step(time,0,0,5,40) + step(time,10,0,15,-40).

When the garbage can is filled with garbage, it weighs 80-150 kg, and for the convenience of calculation, the total weight is 100 kg, which means that its external load is 980 N. Refer to Table 4 for specific values.

Table 4 Types of garbage cans and related standards.
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Device kinematics simulation analysis

(1) Kinematics of the claw

Through simulation, changes in displacement, velocity and acceleration of the claw in the Y-axis direction can be obtained, as shown in Fig. 18. In the process of dumping garbage in the device, the function step(time,0,0,5,40) + step(time,10,0,15,-40) and other hydraulic drive functions of the mechanism show a negative speed within 20–30 s, which means that the Y direction moves in the opposite direction during this period. That is, the mechanical arm completes the process of tipping and resetting. The acceleration image shows that the maximum acceleration in the Y direction of the centroid of the gripper is 1500 mm/s2, and the acceleration image well verifies the motion characteristics of the gripper in the process of expansion and contraction.

Fig. 18
figure 18

Displacement,velocity and acceleration curves of the geometric center of the claw in the Y direction.

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The displacement, velocity and acceleration images of the gripper’s centroid in the Z direction are shown in Fig. 19. It can be seen that the movement in the Z direction is relatively stable compared with the movement in the Y direction, and the number of jumps and fluctuations is less. In terms of displacement, it increases slightly within 0–5 s, with a relative value of about 200 mm, and is basically stable within the interval 5–15 s, indicating that the height of the centroid of the claw in the x direction remains unchanged and maintains the horizontal direction. At the same time, combined with the velocity and acceleration images, it can be seen that the velocity is zero, further indicating that there is no movement in the Z direction in this interval.

Fig. 19
figure 19

Displacement, velocity and acceleration curves of the geometric center of the clamp in the Z direction.

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Similarly, the displacement, velocity and acceleration images of the claw in the X direction of the centroid are shown in Fig. 20 above. It can be seen that its movement is more stable than that in the YZ direction. Combined with the drive function step(time,0,0,5,40) + step(time,10,0,15,-40), it can be seen that the drive function mainly controls the movement in the X direction, and the first acceleration and then deceleration within 0–5 s conform to the setting of the drive function step. At the same time, the displacement has a relative change of 40 mm. Combined with the simulation animation, it can be seen that the two movements here are exactly the movements of the claw when it opens to grab the trash can and when it pulls back after grabbing the trash can.

Fig. 20
figure 20

Displacement, velocity and acceleration curves of the geometric center of the claw in the X direction.

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As can be seen from the above image, in the motion of the gripper, the driving function realizes its function by directly controlling its movement in the Z direction, while the movement in the YZ direction is mainly driven by other mechanisms, such as moving and flipping mechanisms. By controlling the movement in the X direction, the claw can be controlled directly, and the opening and closing of the claw can be controlled quantitatively and accurately.

(2) Kinematics of clean and jerk mechanism

The clean and jerk mechanism controls the dumping process of the garbage can in this device. How to control and optimize the flipping process is the core problem to realize the normal movement of the whole device. Because the clean and jerk mechanism involves connecting rod mechanism and many parts, it is difficult to observe its kinematic phenomenon. The hydraulic rod piston of the clean and jerk mechanism is measured below, and its movement process is analyzed through the piston movement.

In combination with Fig. 21, it can be seen that within 0–5 s, its displacement increases by 70 mm, which corresponds to the process of the device returning to the horizontal position from natural sag after operation. In the time 5–15 s, the displacement and speed are zero, indicating that there is no movement, the main movement in this stage is the implementation of the telescopic device and the claw, the flipping mechanism is at rest; In the last 30–35 s, the reversing mechanism is righted, the device and the trash can return to the horizontal initial position, and the acceleration of the reversing mechanism changes abruptly, which is related to the motion function setting.

Fig. 21
figure 21

Displacement, speed and acceleration of the hydraulic rod of the turning mechanism.

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Through the above kinematic analysis of the flipping mechanism, claw mechanism and telescopic mechanism, including the simulation results of displacement, speed and acceleration, it is shown that their motion characteristics in different time stages can effectively control the motion and effectively prevent the equipment damage caused by excessive load impact. According to the simulation results, the existing oscillation is a normal phenomenon. The experimental verification was carried out in the following garbage dumping experiment.

Mechanical dynamics simulation analysis

By adding slip pair between hydraulic cylinder and hydraulic piston, and connecting two grippers by multi-rod mechanism, the opening and closing function of gripper can be realized. In order to better observe the displacement change, it is combined with the force curve, and the graph 22 is drawn to represent the change of the driving function step(time,0,0,5,40) + step(time,10,0,15,-40). The speci- fic changes are shown in Fig. 22.

Fig. 22
figure 22

Clamp clamp hydraulic rod force.

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Continues to drop to zero, as shown by the continuous dumping of the garbage can, in the time of 30–35 s, the garbage can is completely dumped, and to a certain extent out of the claw, but due to the structural restrictions at the bottom of the garbage can, the garbage can will not fall completely, and then the flipping mechanism returns to the right, the garbage can continues to return to the claw, and the force suddenly increases, because the self-weight of the garbage can impacts the claw. Its value appeared a larger value, reaching 1300 N, with the trash can stabilized in the claw, the force returned to about 200 N, and maintained. In order to check whether the impact force generated by the dynamic load in the opening and closing process of the clamp exceeds the allowable stress value of the material, the impact force load of the clamp is calculated by formula (8).

$$\sigma = \frac{W}{A}\left( {1 + \sqrt {1 + \frac{2EAh}{{Wl}}} } \right)$$
(8)

In the formula (8): σ is the stress generated by the impact load (MPa);W stands for impact force (N); A represents the area of operation (mm2); E stands for elastic modulus (MPa); h stands for impact distance (mm); l stands for object length (mm). The maximum peak value of the impact force W is 1300 N. A is the outside diameter of the clamp hydraulic rod 20 mm; The elastic modulus of Q345 is 210 MPa, and the maximum impact distance, that is, the stroke h of the claw hydraulic rod, is 100 mm. l means that the length of the hydraulic rod is 400 mm, which is calculated as σ = 170.12 MPa, and the yield strength of Q345 in Chapter 4 is [σ] = 345 MPa; σ < [σ], so the designed mechanism meets the requirements of dynamic load use.

Experimental results and discussion

Experiments under different trash can weights

In order to verify whether the clamping action of the manipulator can accurately grasp according to the predetermined action setting, this topic conducts experiments on the mechanical feedback of the clamping claw, verifying that the clamping claw takes different trash can weights for on-site clamping experiments under the clamping force of 600 N, 1000 N, 1800 N, 1960 N and 2100 N respectively. The specific operation mode is to set the maximum clamping force to 600 N, 1000 N, 1800 N, 1960 N, 2100 N through the control interface, and then carry out the garbage can grabbing experiment according to the no-load–full load weight of the garbage can, and carry out the complete dumping action, record the completion time, and confirm the preliminary experiment. The process time from the initial state of the garbage truck to the completion of the garbage truck dumping and reset is set to 35 s, and the time is taken as a parameter. If the fixed completion time is exceeded or the garbage can falls off or is damaged, the scheduled action cannot be completed. The experimental process is shown in Fig. 23.

Fig. 23
figure 23

Experimental process.

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Firstly, the pressure is set to 600 N, 1000 N, 1800 N, 1960 N and 2100 N by the PLC integrated machine of model MK070E-33DT. Then, the trash can weight is loaded and weighed successively under each pressure, and the garbage can grab and dump experiment with different weight is carried out several times respectively.

Under different pressure Settings, the movement completion time of each weight of the trash can is recorded. Garbage collection and transportation failure means that the completion time is less than 30 s and the garbage collection and transportation process cannot be completed completely. The following data are obtained through experiments, as shown in Table 5.

Table 5 Completion time of the experimental process of picking up, receiving and transporting garbage cans with different weights under different clamping forces.
Full size table

From the above experimental data, it can be seen that the garbage truck manipulator can carry out the clamping action between the designed clamping force of 1568 N and 2100 N, and the clamping success rate increases with the increase of the clamping force of the clamping claw. When the clamping force is insufficient, the main reason for the clamping failure is that the friction between the garbage can and the clamping claw is less than the gravity of the garbage itself, resulting in the sliding of the garbage can. When the clamping force is within the range of the design clamping force, it can meet the clamping work requirements, but when the clamping force is too large, it will cause deformation of the garbage can and thus cannot complete the clamping and dumping action of the garbage can.

When the weight of the garbage can is in the range of 0–100 kg, the time to complete the garbage can collection and transportation is about 35 s under different clamping forces, indicating that under the garbage can of ordinary weight, no matter how much the setting value of the clamping force of the claw is, the designed mechanism can complete the predetermined action.

When the weight of the trash can is about 100 kg, in the initial movement stage of 25 s clean and jerk, due to the moment when the hydraulic cylinder enters the start of the clean and jerk, slight tremor occurs in the clean and jerk part of the manipulator, and 25–30 s during the dumping process. Due to the inertia force generated by the garbage falling off the garbage bin and the elastic deformation caused by the garbage, the fit degree between the clamp and the garbage bin becomes worse. Similarly, at the end of the dumping stage, the moment of the jerk hydraulic cylinder retracting movement causes the mechanism to vibrate; This is consistent with the sudden change of the acceleration value in the kinematics and dynamics analysis of the jerk mechanism and the stress value of the hydraulic rod. However, due to the addition of solder joints and reinforcement in the L-shaped support main arm after the static analysis, the design mechanism fully takes into account the situation of heavy-duty machines. The shock caused by the start or stop of the hydraulic rod or the oscillation caused by the existence of inertial force during the tipping process does not affect the garbage collection and transportation movement of the manipulator itself.

Fixed time clamp experiment

Within 30 min, the clamping force was set to be between 1800 and 2200 N and multiple equalization clamping forces were taken, and different garbage cans were tested. A total of 72 clamping and transportation experiments were carried out within 30 min (only working time was calculated, and the experimental preparation time was not included). The experimental results of centralized grabbing under different working conditions are shown in Table 6 below. 1 in the table means that the total time of garbage collection and transportation process 34 s ≤ t ≤ 36 s is successfully completed, 0 means that the problem of garbage can falling off or pinching occurs during the working process of the manipulator, or the working time t ≤ 34 s means that dumping and collection and transportation fails.

Table 6 Experimental results of dumping and transportation under different clamping forces in the concentrated time.
Full size table

According to the experimental results, when the clamping force reaches 2200 N, the clamping force of the claw is too large, resulting in the stress deformation of the trash can, resulting in the failure of the collection and transportation experiment. However, in actual work, the clamping force of the claw can be artificially set to not exceed 2100 N, so the number of experiments conducted when the clamping force is 2200 N should be excluded in the calculation of success rate. In practical application, the clamping force range is selected according to the type of garbage collected. Therefore, according to the experimental results, there are 60 successful collection and transportation experiments and 3 failed collection and transportation experiments among the 63 capture experiments in the concentrated time. It can be calculated that the success rate of the garbage truck manipulator’s collection, transportation and dumpster dumping in this project reaches 95.24%, and the collection and transportation time is t ≤ 36 s.

Conclusion

This article studies and designs a side mounted garbage truck robotic arm that can automatically locate and recognize garbage bins, and perform operations such as picking, handling, lifting, dumping, and resetting of garbage bins. This article designs and verifies key components based on the size structure of existing universal garbage trucks and the size of garbage bins, and develops a multifunctional robotic arm with automatic grasping function, distance compensation function, and lifting and flipping function, providing a solution for garbage collection devices. The structural rationality and functional feasibility of the robotic arm are verified through experiments, solving the problem of easy detachment or collapse of garbage bins during the picking and dumping process.

  1. 1.

    Conduct design and selection analysis on key components such as telescopic mechanism, flipping and lifting mechanism, gripper mechanism, distance compensation mechanism, etc. Use SolidWorks to model and design the components, and calculate the gripper gripping force, length calculation and strength verification of telescopic mechanism, and design and motion angle analysis of lifting and flipping mechanism based on the weight of the garbage bin and the weight of the robotic arm itself. The robotic arm designed in this article is more reliable than traditional garbage collection robotic arms, capable of achieving greater distance gripping, and solves the problem of garbage bins easily falling off or collapsing during the gripping and dumping process. The dual hydraulic rod lifting mechanism and distance compensation mechanism are used to achieve multifunctional collection and dumping of garbage bins, solving the problem of traditional garbage trucks relying on manual pulling or human eye positioning of the distance between the vehicle and the bin for lifting and dumping, and the easy occurrence of slipping during the dumping process, thus improving the efficiency and automation level of garbage collection and dumping.

  2. 2.

    In ANSYS Workbench finite element software, conduct stress analysis on four working conditions of the garbage truck robotic arm: gripper grasping condition, lifting condition, dumping condition, and X maximum displacement condition. According to the analysis results, it can be concluded that the stress concentration generated at the contact position between the gripper lifting arm corner and the cylinder piston does not exceed the yield limit of 45 # steel. The overall structure of the robotic arm is reliable and stable under grasping conditions; Under the condition of clean and jerk, stress concentration still occurs at the connecting shaft but is still far below the yield limit of the material; The maximum stress occurs at the connection of the base under the tilting condition, which serves as the basis for strengthening the structural reliability and reinforcing the reinforcement bars.

  3. 3.

    Using a design based on dynamics, statics analysis, and control system, the prototype was assembled and improved, and a complete machine assembly dumping experiment was conducted. The results of the dynamic analysis were verified by performing different clamping and dumping experiments on garbage bins of different weights with different clamping forces. The experimental results showed that the impact and oscillation generated by the garbage truck robotic arm during operation were within the normal range. When the weight of the garbage bin was between 15-150 kg, the completion time was around 35 s, indicating that within this weight range, the robotic arm studied in this project can complete the predetermined collection process with a clamping force of 1800–2100 N, and the success rate of collection reached 95.24%, with a collection time t ≤ 36 s. The experimental results show that the recycling time of the entire process meets the market’s requirements for garbage recycling robotic arms, and the success rate of collection far exceeds that of currently applied robotic arms.

In addition, the robotic arm studied in this article can also be combined with intelligent car chassis in terms of control, making garbage recycling more intelligent and improving recycling efficiency.