Research on compliant configuration of hydraulic manipulator with passive following characteristic

To decrease the injury caused by an accidental collision between the hydraulic manipulator and human, a hydraulic rotating angle self-servo compliant robot driver joint is designed. Based on this joint, a variable stiffness passive servo-hydraulic rotary joint is improved. The passive follow-up characteristics of the improved servo-hydraulic rotary joint enable it to enter the low stiffness mode by itself when it encounters collisions beyond the force limit. Combining this characteristic, the research method of the hydraulic mechanical arm flexible configuration is proposed. Firstly, the joint motion mode is defined by the Euler angle, and a variety of configurations conforming to the motion characteristics of the manipulator are determined. Then, the virtual prototype and collision environment are built, and the dynamic characteristics of the end effector of the arm under high and low stiffness are measured. The results show that the flexible configurations with passive follow-up characteristics can significantly suppress the collision force. Finally, the visual method is employed to solve, draw, and compare the workspace of the selected compliant configuration, to obtain the optimal compliant configuration with both flexibility and motion, which provides theoretical guidance for the subsequent design of the compliant manipulator.


Introduction
Nowadays, the demand for production efficiency is getting higher and higher, and the mode of working with robots and people has been widely used in people's production activities. As the distance between human and robot approaches, there is a potential risk of injury caused by a robot in a collision. Before designing a robot arm, this kind of accident should be evaluated [1] Therefore, a large number of research works have been carried out to reduce the risk of collision between humans and robots. The human-machine cooperation robot should have the response performance that is mainly based on the collision crisis, i.e. the flexibility of the robot arm. Flexibility is an important indicator to evaluate the operational performance of robots, including the number of states, operability, and operability direction [2].
To improve the flexibility of the arm, it is usually to reduce the impact force by adding a compliant joint to the robot. Zhang et al. [3] designed a soft arm based on a series of elastic actuators (SEAs), Soft Arm IIY, to deal with the dynamic changes of the working environment and the safety of human-computer interaction. To improve the head collision safety of the flexible joint manipulator, Meng et al. [4] proposed a flexible joint manipulator configuration optimisation method based on the mechanical arm safety index and gradient projection method and gave the safe collision direction and the method of determining the safety configuration. Zhao and Zhang [5] presented a three-degrees of freedom (3-DOF) lightweight compliant mechanical arm that used carbon fiber material to achieve lightweight and designed a SEA to achieve the flexibility of the mechanical arm structure. Shi et al. [6] designed a composite flexible joint with both primary and passive variable stiffness characteristics. Choi et al. [7] proposed a robot manipulator variable stiffness joint (VSJ), and a control scheme to control the stiffness and position of the VSJ. Leaf spring generates flexibility, and two actuators control the position and stiffness of the joint through a four-bar mechanism. Hyun et al. [8] presented a variable stiffness mechanism (VSM) for humanfriendly robots to simultaneously meet safety and performance needs. The VSM has high stiffness in normal operation mode and has low stiffness in collision mode when the load applied to the joint exceeds a critical load. Mathijssen et al. [9] designed a new design of modular redundant drive units. Compliant mechanisms called designer muscles can be created by connecting these units in series and parallel. The strain rate is 21.1% and the maximum stress is 1.55 Pa. Yoo et al. [10] designed a manipulator VSJ with terminal support of 1 kg payload. On this basis, a model of a threering permanent magnet mechanism was proposed to meet the requirements of rotational stiffness after optimisation. In [11], a cable-driven manipulator, which can significantly adjust the stiffness of the manipulator through the tension resolution, is proposed. The stiffness matrix with high accuracy and isotropy is obtained by the tension decomposition method. Xiang et al. [12] proposed a method to quickly switch between pneumatic and hydraulic working modes without removing all the hydraulic fluid from the actuator. A compatible and potentially safe pneumatic mode is demonstrated and compared with the more rigorous hydraulic mode. Fu et al. [13] proposed a new joint actuator with variable stiffness based on the plate spring as an elastic element and the spiral disc as a stiffness regulating mechanism, and discussed the stiffness regulating characteristics of the joint actuator, providing a theoretical basis for improving the dynamic characteristics of the interaction between robots and humans. Ryusuke et al. [14] proposed a new rotational flexibility mechanism that allows strong forces and flexibility to coexist, with flexibility in both active rotation directions and orthogonal directions. To do this, they developed a hydraulic artificial muscle that is very light and can produce great power.
At present, most of the research studies on the compliant mechanical arm is focused on the flexible joint. Integrating the configuration of the flexible joint with the mechanical arm to study its passive compliance is not considered, especially in the field of outputting a large torque hydraulic mechanical arm. Aiming at this problem, a hydraulic angle self-servo compliant drive joint was designed, and a variable stiffness passive follower hydraulic swivel joint was improved based on the compliant drive mechanism. Combining the characteristics of the two, the 5-DOF series hydraulic manipulator is taken as the research object. Many common configurations and compliant configurations of the manipulator are derived and the corresponding three-dimensional (3D) models are established and imported into ADAMS for J. Eng collision simulation experiments. A standard D-H parameter table for the compliant configuration was created, and the workspace cloud map was drawn using the MATLAB robot toolbox. After a comparative analysis, the compliant configuration with both compliant performance and athletic performance is obtained, which provides important theoretical guidance for the subsequent structural design and optimisation of the compliant mechanical arm.

Design of hydraulic rotating angle self-servo compliant robot driver joint
The joint is shown in Figs. 1 and 2. It mainly includes low-pressure nozzle 1, left end cover 2, cylinder 3, low-pressure oil passage 4, valve sleeve 5, valve core 6, valve body 7, right end cover 8, bearing of valve body 9, high-pressure oil passage 10, vane seal 11, valve body vane 12, spool bearing 13, high-pressure grease nipple 14, cover 15, steering gear 16, and fixed block 17.
Working principle: High-pressure oil enters high-pressure oil passage through the high-pressure oil nozzle, and return oil nozzle enters low-pressure oil. When the actuator stops, the spool is in the middle, i.e. the rectangular groove on the spool is closed with the convex platform on the valve sleeve, and the high-and lowpressure oil cannot enter the A and B working chambers through the valve spool and the valve sleeve. When the steering gear rotates in a certain opening clockwise, the high-pressure oil flows from the radial direction of the valve blade to the P port through the highpressure channel, and into the A cavity through the distributor port and the rectangular hole A of the valve body. Then, under the pressure difference between the two working chambers, the valve blade rotates clockwise, as shown in Fig. 2a, and outputs the torque through the output shaft of the valve body. At this point, the volume of the B cavity begins to compress, and the low-pressure oil in the B cavity enters the low-pressure oil passage through the rectangular hole B of the valve body, as shown in Fig. 2b. When the spool rotates counter-clockwise, its working condition is contrary to that of the spool, and the principle is the same. The hydraulic angle self-servo compliant driving joint has the advantages of small size, smooth movement, and large output moment when the working pressure is above 3 MPa, and its output moment is not <50 N m and diameter is <130 mm.

Structural design of hydraulic passive follower joints with variable stiffness
The joint is composed of hydraulic rotating self-servo compliant following mechanism and torque transfer mechanism and spring mechanism, as shown in Fig. 3. Among them, the first part is improved from the hydraulic rotating angle self-servo compliant robot driver joint, which is shown in the left half of Fig. 4. The difference is that the spool 21 is fixed through the valve body 20 and the load plate 23 of the torque transmitting mechanism, and the valve body 20 and the separating disc 24 fixed. The corner from the servo principle is the same as the previous improvement, and will not be described again. The torque transmitting mechanism is composed of a load plate 23, a spring actuator 22, a separation disc 24, and a sweep arm disc 25. The joint is multi-staged by the load plate, the separation disc, and the sweep arm.
Working principle: The load disc in the passive servo rotary joint is connected by a spring mechanism and a sweeping arm disc, the sweeping arm disc is fixed with the valve core, and the separation disc is fixed with the valve body. When the force at the end of the passive servo rotary joint is transmitted to the separation disc and exceeds the safety value, the sweeping arm disc connecting the valve core is separated from the output shaft connecting the valve body. The disc mechanism is separated and the sweeping arm disc drives the spool to rotate. Since the output shaft of the valve body is also driven to follow the motion of the self-servo mechanism, the mechanism moves in the direction of reducing the contact force and improving collision safety. When the impact force disappears, the mechanism restores to a relatively stable state.

Derivation of general configuration
Generally, the higher the degree of freedom of the manipulator is, the better the flexibility is. However, in the actual design and manufacture of the manipulator, every additional degree of freedom will multiply the complexity and cost of the mechanism [15]. At present, industrial robots with three axes, four axes, five axes, and six axes are mostly used in industrial applications. The choice of axle number usually depends on the specific application. This paper takes the series 5-DOF hydraulic manipulator as the research object.
To clearly express the motion state of each joint of the manipulator, the joint motion can be defined by referring to the Euler angle (RPY angle) [16]: the motion properties can be expressed in capital letters, such as R for rotation, P for movement, H for spiral motion, S for spherical motion. The letters R, P, and Y are used as subscripts to indicate orientation, such as R R , R P , and R Y to indicate the rotation of roll, pitch, and yaw, respectively, and '−' and '+' to indicate the serial and parallel relationship between pairs of motion.
The configuration of the tandem hydraulic mechanical arm is determined by the joints that provide power through different combinations. A joint can be represented by a motion pair. According to the Euler angle (RPY angle) shown in Fig. 5, there are three kinds of motion states of the revolute joints, namely R Y , R P , and R R , respectively, as shown in Fig. 6.
With the straight bar as the connecting rod and considering the connecting sequence, there are altogether nine combinations of two adjacent joints, as shown in Fig. 7. Considering the actual working conditions, it can be found that combination b rotates 90° around the x-axis, which is the same as combination c. Combination d is rotated 90° around the y-axis, which is the same as combination f, and the combination f is retained. The combination g rotates 90°a bout the z-axis, i.e. the same as the combination h, and the combination h is also retained. The axis of rotation of the two joints of combination a and combination I coincide, so that only one of the joints acts as a linkage, so the unreasonable layout should be ruled out. In conclusion, b, d, e, and h are the reasonable layout of adjacent joints.
A joint of a common industrial mechanical arm has 1-DOF, therefore, n-DOF hydraulic mechanical arm is composed of n joints. To have a larger working space, the first joint should obviously rotate around the z-axis. The only reasonable way to fit adjacent to the first joint is h, and then the second joint rotates about the y-axis. There are two adjacent combinations suitable for the second joint: d and e, i.e. the third joint rotates around the xaxis or y-axis. When the third joint rotates about the x-axis, the adjacent combination with the third joint is b, and the fourth joint should rotate about the y-axis. When the third joint rotates around the y-axis, the appropriate adjacent combinations include d and e, and then the fourth joint should rotate around the x-axis or y-axis. When the fourth joint rotates about the x-axis, the adjacent combination to be considered is b, and then the fifth joint rotates about the y-axis. When the fourth joint rotates around the y-axis, the appropriate adjacent combinations include d and e, and then the fifth joint rotates around the xor y-axis. Thus, when the n − 1 joint rotates around the x-axis, the adjacent combination mode that can be considered is b, and the n − 1 joint rotates around the y-axis. When the n − 1 joint rotates around the y-axis, the suitable adjacent combinations are d and e, and the n − 1 joint rotates around the xaxis or y-axis. There are five reasonable configurations with 5-DOF, as shown in Fig. 8.
The simplified configuration corresponding to Fig. 8 is shown in Fig. 9. Configurations a, b, c, d, and e are reasonable common configurations, which are briefly described as GX1, GX2, GX3, GX4, and GX5, respectively.

Derivation of flexible configuration
After the common configuration is determined, the passive followup joint is continued to be distributed on the rotary joint (R_R, R_Y) of the common configuration. GX1 contains three rotary joints, so three cases are derived. GX2, GX3, and GX4 contain two rotary joints, so there are two cases, respectively; GX5 contains one rotary joint, so there is only one case. Thus, there are ten reasonable flexibility configurations, as shown in Fig. 10, which the passive follow-up joint is simplified in red.

Setting of experimental environment
ADAMS has a powerful simulation function. It is widely used as a design simulation experiment platform. It can add constraints, driving, and special forces, and then set the control parameters to complete the solution and post-processing. In ADAMS, there are two ways to define the collision force: one is the compensation method (restitution) and the other is impact. The parameters of the former are more difficult to set accurately, so this paper chooses the latter to calculate the collision force [17]. The experiment is composed of three groups of comparative simulations. The first group is the high-stiffness collision of ordinary configurations without passive follow-up characteristics; the second group is the collision of compliant configurations with higher stiffness when passive follow-up joints do not exceed the force limit; the third group is the collision simulation of compliant configurations with lower stiffness when passive follow-up joints exceeded the force limit. Owing to the same environment of the three groups of simulation experiments, the simulation process of the flexible configuration is only described here. The simulation process of flexible configuration is as follows: (i) Use SOLIDWORKS to carry out 3D model of all flexible configurations, and then simplify it into ADAMS. Create a spring slider with a volume of 100 mm × 200 mm × 100 mm below the side of the end-effector as the impact object. The slider material is steel and the spring stiffness is 25 N/mm. (ii) The connection is added for each joint of the robotic arm, and corresponding motion is added. The impact function method is used to create contact between the end-effector and the slider. A rotation speed is set at the input end of the first rotary joint connected with the base to drive the output connecting rod, passive follower joint, and other joints to rotate. The robot arm will collide with the actuator after turning a certain angle, and then continue to rotate until the end of simulation.
(iii) The displacement, velocity, and collision force changes of the three-group experimental manipulators in the whole time period from the collision to the end of the collision were analysed and compared.
Also, the simulation parameters are set as follows: the corresponding parameters are set for each group of models, and the collision point is set at the lower end of the end-effector. The distance between the spring slider and the actuator is 150 mm. The hydraulic force between the valve core and the valve body of the passive servo joint at the corresponding position is equivalently replaced by the torsion spring. Its stiffness coefficient is set to 5000 N/mm and the damping coefficient is 0.

Analysis of experimental results
After the simulation, the displacement and velocity curves of the actuator can be measured. The simulation results are shown in Figs. 11 and 12. Among them, the characteristics of displacement, velocity, and collision force of the five common configuration actuators are very close, therefore, only the characteristic curve of one of them is used for comparison. All the configurations are divided into two categories according to the collision results, and their respective characteristic curves are also very close, so a representative set of characteristic curves is selected for comparison. The first kind of flexible configuration can be defined as those configurations which add passive servo joints to the first rotating joint, namely GX1A, GX2A, GX3A, GX4A, and GX5A.
In this case, it can be seen from the response curves of Fig. 8 that the actuator collides with the spring slider at 0.13 s in the general configuration state. The position error of the motion response of the manipulator is the smallest compared with the other two cases, and the reaction speed is obviously the fastest, with the maximum speed of 3600 mm/s. However, its collision force is the largest and the maximum collision force is about 4200 N.
In the higher stiffness state, this state simulates the reaction state of the manipulator when the force limit is not exceeded. The actuator collides with the spring slider at 0.3 s. The collision time is delayed and there is a certain position error. The maximum velocity is 2100 mm/s and the maximum collision force is about 300 N.
Under the condition of low stiffness collision, this state simulates the reaction state of the manipulator in excess of the force limit. The actuator collides with the spring slider at 0.4 s. The collision time is delayed and the position error is large. The maximum velocity is 1450 mm/s and the maximum collision force is about 70 N.
Based on the above comparative analysis, it can be concluded that under the same collision environment, the collision force of the first type of compliant configuration is significantly better than that of ordinary configurations without passive follow-up joints, which indicates that the flexibility performance of this configuration is outstanding.
The second type can be defined as configurations of passive follower joints added to the rest of the revolute joints, i.e. GX1B, GX1C, GX2B, GX3B, and GX4B. As can be seen from the response curves in Fig. 12, the second type of compliant configuration is similar to the collision process of ordinary configuration in both cases where the force limit is exceeded and the force limit is not exceeded, but the collision force decreases to some extent. Generally, the position error is small, the speed is fast, but the collision force is large. By comparing Figs. 11 and 12, it can be found that the first type of compliant configuration has a significantly better ability to suppress collision force than the second type, but the precision is not perfect in the process of movement. Therefore, from the point of view of safety, the performance of the first type of flexible configuration is more prominent.

Establishment of denavit hartenberg (DH) parameters
From the previous section, we can know that GX1A, GX2A, GX3A, GX4A, and GX5A have the best compliance performance, besides this, the workspace capability of the manipulator is also a very important index of the manipulator [18], which has profound significance for the optimisation of structural parameters of the manipulator, so it is necessary to discuss its flexibility in the derivation of configuration theory.
To intuitively show the performance of the above five configurations, the DH parameter table of each configuration is obtained after establishing its linkage coordinate system, as shown in Tables 1-5.

Result analysis
To determine the precise workspace boundary, the Monte Carlo method is used to simulate the workspace of each configuration of the manipulator [19]. Five arbitrary joint angle values obtained The working cloud diagram of the manipulator actuator drawn by MATLAB robot toolbox is shown in Fig. 13. The cloud diagram of each configuration represents its 3D view, XZ direction view, XY direction view, and YZ direction view, respectively, from left to right and from top to bottom. According to the shape of cloud pattern, it can be divided into two categories: the first is GX1A and GX2A. The cloud images show that this kind of configuration has poor accessibility under the base of the manipulator and distributes uniformly in other directions. Comparing the two, it is found that the interior of GX1A is relatively empty and sparse, which indicates that the accessibility of this configuration is better only in the periphery. In addition to poor accessibility at the bottom, GX2A has a uniform distribution of location points and a relatively dense distribution, indicating a larger accessible range. The second category is GX3A, GX4A, and GX5A, which are lack of accessibility on the left side of the base of the robot arm. Among them, the cloud images of GX5A are very sparse, indicating that the overall accessibility of the configuration is poor. However, the workspace visualisation of GX3A and GX4A is almost identical,     which indicates that the accessibility of the two configurations is slightly different, but in the YZ direction, GX3A is denser than the point inside the cloud image of GX4A, which indicates that GX3A's accessibility is better than GX4A's on the whole. In summary, GX2A and GX3A are the optimal configurations for flexibility and accessibility, respectively, and they can be applied to different work scenarios. Their corresponding two models are shown in Figs. 14 and 15.

Conclusion
(i) Based on the safety concept of man-machine integration, a hydraulic rotating angle self-servo compliant robot driver joint with large output torque and smooth operation is designed. Based on this joint, a variable stiffness passive servo-hydraulic rotary joint with the multi-stage compliant mode is improved. Combining the characteristics of the two joints, the compliant series hydraulic manipulator is proposed. (ii) Various compliant configurations of the hydraulic manipulator are derived. The 3D model of each configuration of the manipulator is established by using SOLIDWORKS. Under the same posture, the simplified model is imported into ADAMS to carry out collision simulation experiments. (iii) Compared with the experimental results, five configurations with outstanding flexibility are obtained. Furthermore, the connecting rod coordinate system is established for the obtained configurations, and the D-H parameter tables of each configuration are obtained. The working space of each configuration is solved by the Monte Carlo method, and the working clouds of the end effectors of each configuration are drawn with the help of MATLAB, which intuitively shows the working ability of each configuration. (iv) A reasonable configuration with both flexibility and motion performance is obtained, which can be used as an important theoretical guidance for the follow-up structural design and optimisation of the manipulator.