Single-degree-of-freedom multi-joint mechanism with controllable deformation on two sides

Abstract

The invention discloses a double-side controllable deformation single-degree-of-freedom multi-joint mechanism, and belongs to the technical field of underwater detection equipment, the double-side controllable deformation single-degree-of-freedom multi-joint mechanism comprises N joint units connected in sequence, and a degree-of-freedom adjusting rod is connected between the adjacent joint units; the joint unit comprises a swing rod, a frame rod, a crank connecting rod and a sliding block and forms a plane connecting rod mechanism. The swing rod is connected with the front end of the frame rod through a first pin shaft, the other end of the frame rod is connected with one end of the crank connecting rod through a second pin shaft, the sliding block is assembled on the swing rod and forms a linear moving pair moving along the swing rod, and the other end of the crank connecting rod is connected with the sliding block through a third pin shaft. The rear end of the swing rod is fixedly connected with the front end of the swing rod in the rear adjacent joint unit; the two ends of the freedom degree adjusting rod are connected with the third pin shafts in the two joint units correspondingly. The multi-joint mechanism has the advantages that the number of driving units is small, control is easy, the track is accurate, the structure is light, reliability is high, bearing capacity is high, motion characteristics are adjustable, and the position of a driving link is flexibly selected.

Description

Technical Field

[0001] The invention belongs to the technical field of underwater detection equipment, and in particular relates to a single-degree-of-freedom multi-joint mechanism with controllable deformation on both sides. Background Art

[0002] The design of the bionic flexible flapping wing system is inspired by flying animals in nature and imitates their efficient and flexible movement. In recent years, bionic theory and bionic mechanism design have received widespread attention, especially in the development of bionic underwater robots. Improving the robot's movement ability and efficiency by simulating the movement of natural organisms has become an important research direction. The bionic flexible flapping wing system, especially the design of its spanwise deformation mechanism, can achieve bilateral deformation through a multi-joint structure, thereby meeting the needs of underwater robots in posture adjustment, bionic fishtail swing, etc. Due to their special application scenarios, this type of system requires a compact mechanism layout, strong waterproofness, high reliability and precise motion control. Based on these characteristics, the bionic flexible flapping wing can not only be used to improve the posture adjustment ability of underwater robots, but also provide important technical support for the design of other underwater robots that require precise operation in a small space.

[0003] Driven by multiple motors, multi-degree-of-freedom and multi-joint mechanisms have greater flexibility and fine motion control capabilities, and can achieve complex spatial postures and motion trajectories, which are particularly suitable for the field of bionic robots. In bionic underwater robots, such mechanisms can imitate the various motion modes of natural organisms, achieve complex movements such as bionic flapping wings, tail swinging, and swinging, and significantly improve the robot's maneuverability and stability underwater.

[0004] Although motor-driven multi-degree-of-freedom multi-joint mechanisms have significant advantages in flexibility and control accuracy, they also have some shortcomings in certain application scenarios. First, such systems usually take up a large space. Since each degree of freedom requires a separate motor drive and transmission mechanism, the system structure is relatively complex and bulky. This space requirement is particularly evident in compact devices. For example, underwater robots need to be designed as small as possible to improve operational flexibility and adapt to small spaces. However, motor-driven multi-degree-of-freedom systems often find it difficult to achieve such a highly integrated and compact layout.

[0005] Secondly, dynamic seal design is difficult. In special environments such as underwater, the motor drive system needs to have a strict dynamic seal design to ensure that the motor and drive components are not invaded by water and other media. With the increase of joints and degrees of freedom, the number of sealing points also increases accordingly, making the difficulty of seal design multiplied. Reliable dynamic seals not only increase the complexity of the design, but also increase the risk of failure and the difficulty of maintenance to a certain extent.

[0006] In addition, such systems have high energy consumption. Multi-motor drive requires a separate motor for each degree of freedom and consumes corresponding energy to maintain precise posture and motion control. Therefore, the increase in the number of motors directly leads to an increase in the overall energy consumption of the system. For equipment with high endurance requirements, such as underwater drones and robots that operate for long periods of time, high energy consumption will significantly shorten the use time of the equipment and affect the efficiency of task execution.

[0007] The heavy weight is also a disadvantage that cannot be ignored. Each motor and its corresponding transmission mechanism will increase the overall weight of the system, resulting in multi-degree-of-freedom mechanisms being generally bulky. This is a significant disadvantage for many scenarios, such as aerial or underwater operations. In underwater robots, excessive weight will affect buoyancy and motion performance, making the device inflexible in water and difficult to achieve the desired motion effect.

[0008] Overall, the motor-driven multi-degree-of-freedom, multi-joint mechanism has shortcomings in terms of occupied space, dynamic sealing difficulty, energy consumption and weight, which makes it have certain limitations in scenarios with high requirements for space, endurance and flexibility. Summary of the invention

[0009] In response to the problems existing in the prior art, the present invention provides a double-sided controllable deformation single-degree-of-freedom multi-joint mechanism that solves the problems of accuracy and flexibility of motion control that are currently driven by motors, but which still has limitations in terms of large occupied space, complex dynamic sealing design, high energy consumption, and large overall weight.

[0010] The present invention is achieved as follows: a single-degree-of-freedom multi-joint mechanism with controllable deformation on both sides, characterized in that: it includes N joint units connected in sequence, and a freedom adjustment rod is connected between adjacent joint units; the joint unit includes a rocker rod, a frame rod, a crank connecting rod and a slider to form a planar connecting rod mechanism; the front ends of the rocker rod and the frame rod are connected by a first pin, the other end of the frame rod is connected to one end of the crank connecting rod by a second pin, the slider is mounted on the rocker rod and constitutes a linear moving pair that moves along the rocker rod, the other end of the crank connecting rod is connected to the slider by a third pin, and the rear end of the rocker rod is fixedly connected to the front end of the rocker rod in the joint unit adjacent to the rear; the two ends of the freedom adjustment rod are respectively connected to the third pins in two joint units.

[0011] In the above technical solution, preferably, the slider is provided with a guide hole, and the slider is mounted on the rocker arm through the guide hole and forms a linear motion pair with the rocker arm as a guide rod.

[0012] In the above technical scheme, preferably, it includes three joint units, and the three joint units are connected in series to form a span arrangement from the inside to the outside. In the span direction from the inside to the outside, the rocker arm of the joint unit at the first position is installed on the support rod and the angle between it and the support rod is 20°, the angle between the frame rod of the joint unit at the second position and the rocker arm at the first position is 25°, and the angle between the frame rod of the joint unit at the third position and the rocker arm at the second position is 23°.

[0013] In the above technical scheme, preferably, it includes three joint units, and the three joint units are connected in series to form a span arrangement from the inside to the outside. In the span direction from the inside to the outside, the rocker arm of the joint unit at the first position is installed on the support rod and is located in the same straight line with the support rod, the frame rod of the joint unit at the second position is located in the same straight line with the rocker arm at the first position, and the frame rod of the joint unit at the third position is located in the same straight line with the rocker arm at the second position.

[0014] In the above technical solution, preferably, the rod length conditions of the three joint units meet:

[0015] c1+a1+d1=b1+c2+a2

[0016] c2+a2+d2=b3+c3+a3

[0017] In the formula, a1, a2, a3 are the lengths of the crank connecting rods of each joint unit, b1, b2, b3 are the lengths of the rocker arms of each joint unit, c1, c2, c3 are the lengths of the frame arms of each joint unit, d1 and d2 are the lengths of the degree-adjusting rods between the first joint unit and the second joint unit and between the second joint unit and the third joint unit.

[0018] In the above technical solution, preferably, the rod length conditions of the three joint units meet:

[0019]

[0020] In the formula, a1, a2, and a3 are the lengths of the crank connecting rods of each joint unit, b1, b2, and b3 are the lengths of the rocker rods of each joint unit, c1, c2, and c3 are the lengths of the frame rods of each joint unit, d1 and d2 are the lengths of the degree-of-freedom adjustment rods between the first joint unit and the second joint unit, and the lengths of the degree-of-freedom adjustment rods between the second joint unit and the third joint unit; x1, x2, and x3 are the distances from the slider to the revolute pair at the end of the rocker rod, α1, α2, and α3 are the joint angles at the left extreme position of the multi-joint mechanism, θ1, θ2, and θ3 are the angles between the frame rod of the joint unit and the rocker rod of the adjacent joint unit, δ1, δ2, and δ3 are the angles between the crank connecting rod and the rocker rod of the joint unit at the left extreme position of the multi-joint mechanism, and in the span direction, β2 is the angle between the degree-of-freedom adjustment rod and the rocker rod of the first joint unit, and β3 is the angle between the degree-of-freedom adjustment rod and the rocker rod of the second joint unit.

[0021] The bilaterally controllable deformation single-degree-of-freedom multi-joint mechanism proposed in this application has a series of significant advantages and excellent use effects, making it very suitable for use in complex and harsh underwater environments. The advantages of this mechanism are described in detail below in terms of structural characteristics, performance advantages and adaptability:

[0022] 1. Fewer drive units and simplified system control:

[0023] The mechanism can achieve overall motion control through a single motor, significantly reducing the number of drive units. This simplified drive solution not only reduces the complexity of the control system, but also reduces the power consumption of the motor and the weight of the overall mechanism, which helps to achieve longer endurance and more compact structural layout in underwater environments. At the same time, simplified control also makes the system more reliable and reduces the risk of failure caused by multiple drive units.

[0024] 2. Precise and controllable motion trajectory:

[0025] The design of this mechanism can achieve precise motion control, ensuring that the action can be completed according to the preset trajectory under various working conditions. Especially in applications such as bionic fish tail propulsion, bionic head and tail deflection, and bionic flapping wing flexible deformation, precise trajectory control is crucial to simulate the motion characteristics of organisms and helps to achieve natural and smooth bionic motion effects. This precise and controllable trajectory enables it to flexibly adapt to various task requirements and achieve high-precision posture adjustment and stable movement.

[0026] 3. Lightweight structure, suitable for underwater applications:

[0027] With fewer drive units and no need for a complex multi-motor system, the overall structure can be lightweight. Compared with traditional multi-degree-of-freedom motor drive mechanisms, this design is lighter, which is particularly important in terms of buoyancy and energy consumption control, making it more efficient in underwater environments. The lightweight design reduces the tendency of the device to sink in the water, which is conducive to improving movement performance and control flexibility.

[0028] 4. High reliability and good carrying capacity:

[0029] The mechanism is based on the traditional mechanical rod group structure design, with high reliability and excellent load-bearing capacity, and can adapt to the high pressure and complex environment of underwater operations. Compared with smart materials, mechanical structures have significant advantages in durability and load capacity, reducing the risk of failure due to material fatigue or unstable deformation. Therefore, this mechanism is more suitable for underwater robot application scenarios with high requirements for load-bearing capacity.

[0030] 5. The spanwise deformation range is large and has multifunctional application:

[0031] The mechanism can achieve a large spanwise deformation stroke on both sides, which provides good support for bionic flexible deformation and enables it to perform well in bionic flapping, fishtail swinging, and target grasping. Its large spanwise deformation can not only effectively simulate the streamlined motion of organisms, but can also be flexibly applied to grasping tasks, providing more functions and operational flexibility for underwater operations.

[0032] 6. Adjustability of motion characteristics:

[0033] The mechanism has good adjustability, and different motion characteristics can be achieved by adjusting the design parameters, such as bilateral symmetrical synchronous motion, or bilateral asymmetric motion, or even setting an extreme position on one side. This diverse motion mode adaptability allows users to optimize the configuration according to different mission requirements, and can achieve efficient and flexible response in complex underwater missions.

[0034] 7. The length of the rod and the number of joints can be flexibly adjusted:

[0035] The design supports obtaining the length and parameters of each rod under the target working condition by solving the rod length condition, so as to flexibly adjust the length of the rod and the number of joints according to the actual application, and further optimize the motion characteristics of the system. The adjustability of rod and joint parameters facilitates customized design to meet the special needs of different tasks, making the mechanism have good adaptability.

[0036] 8. Flexible selection of the position of the prime mover:

[0037] This mechanism allows the user to set the driving source (i.e., the prime mover) to any rod according to application requirements without affecting the trend and trajectory of the overall movement. This feature of freely selecting the position of the prime mover provides great convenience for the design in special scenarios, allowing the mechanism to better adapt to special operating environments and space restrictions.

[0038] In summary, the bilaterally controllable single-degree-of-freedom multi-joint mechanism has many advantages such as few drive units, simple control, precise trajectory, lightweight structure, high reliability and strong adaptability, providing an ideal solution for the application of underwater robots in bionic motion, precise control and special tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a schematic structural diagram of Embodiment 1 of the present invention;

[0040] Figure 2 It is a structural schematic diagram of the joint unit in the present invention;

[0041] Figure 3 It is a schematic diagram of the structure of changing the number of rod groups in the present invention;

[0042] Figure 4 It is a structural schematic diagram of Embodiment 2 of the present invention;

[0043] Figure 5 is a schematic diagram of dynamic changes of the first embodiment of the present invention;

[0044] Figure 6 It is a schematic diagram of dynamic changes of the second embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0046] In order to solve the problem of accuracy and flexibility of motion control, but there are still limitations in terms of large occupied space, complex dynamic seal design, high energy consumption, and large overall weight, the present invention provides a single-degree-of-freedom multi-joint mechanism with controllable deformation on both sides. The single-degree-of-freedom multi-joint mechanism with controllable deformation on both sides has the advantages of few drive units, simple control, precise trajectory, lightweight structure, high reliability, strong bearing capacity, adjustable motion characteristics, and flexible selection of the position of the prime mover, which can meet the high stability and versatility requirements of complex underwater operations. In order to further illustrate the structure of the present invention, the detailed description is as follows in conjunction with the accompanying drawings:

[0047] Embodiment 1

[0048] A bilaterally controllable deformable single-degree-of-freedom multi-joint mechanism comprises N joint units connected in sequence, with freedom adjustment rods connected between adjacent joint units.

[0049] See also Figure 1 and Figure 2 The joint unit includes a rocker rod 2-1, a frame rod 2-2, a crank connecting rod 2-3 and a slider 2-4 to form a planar connecting rod mechanism.

[0050] The front ends of the rocker arm and the frame arm are connected by a first pin, the other end of the frame arm is connected to one end of the crank connecting rod by a second pin, the slider is mounted on the rocker arm and forms a linear moving pair moving along the rocker arm, the other end of the crank connecting rod is connected to the slider by a third pin, and the rear end of the rocker arm is fixedly connected to the front end of the rocker arm in the joint unit adjacent to the rear. Specifically, the slider is provided with a guide hole, the slider is mounted on the rocker arm through the guide hole and forms a linear moving pair with the rocker arm as a guide rod. Alternatively, a long hole is designed on the rocker arm as a slideway, and the slider is a slider component installed on the rocker arm by a pin mounted in the long hole and sliding in the long hole. In the prior art, there are many optional ways to form a moving pair in this guide rod and slider manner, which are not limited here.

[0051] Two ends of the freedom adjustment rod 5 are respectively connected to the third pins in the two joint units.

[0052] This embodiment includes three joint units, namely the first joint unit 2, the second joint unit 3 and the third joint unit 4. The three joint units are connected in series to form a spanwise arrangement from the inside to the outside. The spanwise direction refers to the extension direction of the multi-joint structure from the mounting contact to the outside. In this embodiment, in the spanwise direction from the inside to the outside, the swing rod of the joint unit at the first position is installed on the support rod 1 and the angle with the support rod is 20°, the angle between the frame rod of the joint unit at the second position and the swing rod at the first position is 25°, and the angle between the frame rod of the joint unit at the third position and the swing rod at the second position is 23°. The support rod is the basic rod of the multi-joint mechanism, which is arranged at the innermost side, and the direction from it to the outside is the spanwise direction.

[0053] In this embodiment, the three joint units are constructed in the same way, all of which are plane connecting rod type crank rotating guide rod mechanisms, with the crank connecting rod as the active part driving the rocker rod to produce reciprocating swing, the two ends of the frame rod respectively form a rotation pair with the crank connecting rod and the rocker rod, the other end of the crank connecting rod forms a rotation pair with the center hole of the slider, and the slider slides on the rocker rod to form a moving pair. The degree of freedom of each mechanism unit is 1 (F = 3*3-2*4 = 1). The degree of freedom adjustment rod forms a rotation pair with the two sliders of the adjacent joint unit to constrain the movement of the mechanism and limit the distance between the two sliders to its rod length. The support rod serves as the frame of the entire mechanism.

[0054] In this embodiment, in order to imitate the four-bone and three-joint structure of the human hand, the three joint units are arranged in series along the span direction. The frame rod and the support rod of the first joint unit are clamped at 20° and fixedly connected, and no relative movement occurs between the two rods. The frame rod of the second joint unit and the rocker rod of the first joint unit have an angle of 25°, and are fixedly connected, and no relative movement occurs between the two rods. The frame rod of the third joint unit and the rocker rod of the second joint unit have an angle of 23° and are fixedly connected, and no relative movement occurs between the two rods. After fixed connection, a series relationship of three joint units is formed. At this time, the degree of freedom of the mechanism is 3 (F=3*9-2*12=3). The two degree of freedom adjustment rods introduce four low pairs to limit the movement of the slider. At this time, the overall degree of freedom of the mechanism is 1 (F=3*11-2*16=1). At this time, the mechanism can swing from the extreme position on one side to the other side, and the movement characteristics are as follows. Figure 2 shown.

[0055] Specifically, Figure 3 Shown is a schematic diagram of the structure in this embodiment. In this embodiment, the mechanism can adjust the number of joints by increasing or decreasing the number of basic rod groups of the joint without changing the assembly relationship, and its degree of freedom remains 1.

[0056] The basic joint rod group is composed of a frame rod, a rocker rod, a crank, a slider, and a freedom adjustment rod. While introducing five movable components, seven low pairs (F=3*5-2*7=1) are introduced. For a mechanism with n joints, under this condition, the degree of freedom is always 1.

[0057] The rod length condition can be obtained by analyzing the characteristics of the mechanism and the special geometric relationship of the initial position. The initial position is defined as the collinear position of the pendulum rod and the frame rod, such as Figure 5 Second from left Figure 6 As shown in the third figure from the left. In the formula, a1, a2, a3 are the lengths of the crank connecting rods of each joint unit, b1, b2, b3 are the lengths of the swing rods of each joint unit, c1, c2, c3 are the lengths of the frame rods of each joint unit, d1, d2 are the lengths of the adjustment rods of each degree of freedom, x1, x2, x3 are the distances from the slider to the revolute pair at the end of the swing rod, α1, α2, α3 are the joint angles of 18.81°, 28.92°, 16.69° at the left extreme position of this example, θ1, θ2, θ3 are the angles between the frame rod of the joint unit and the swing rod of the adjacent joint unit, δ1, δ2, δ3 are the angles between the crank connecting rod and the swing rod of the joint unit at the left extreme position, in the span direction, β2 is the angle between the degree of freedom adjustment rod and the swing rod of the first joint unit, and β3 is the angle between the degree of freedom adjustment rod and the swing rod of the second joint unit.

[0058] The rod length condition for the collinearity of the rods in the initial position is:

[0059]

[0060] When the rod length condition is met, the components of the mechanism are collinear at the initial position, such as Figure 5 shown.

[0061] Rod length conditions at the left extreme position:

[0062]

[0063]

[0064] When the above rod length conditions are met, the left limit position of the mechanism is Figure 5 As shown, at this time, the joint angles are α1, α2, and α3, and all design parameters of the target joint angle can also be calculated through the rod length condition.

[0065] Embodiment 2

[0066] In this embodiment, three joint units are included, and the three joint units are connected in series to form a span arrangement from the inside to the outside. In the span direction from the inside to the outside, the frame rod of the joint unit at the second position and the rocker arm at the first position are located on the same straight line, and the frame rod of the joint unit at the third position and the rocker arm at the second position are located on the same straight line.

[0067] In this embodiment, Figure 4 , shown is a schematic diagram of the mechanism when the unit frame and the rocker are fixedly connected in a collinear manner. In the figure, the frame rod of the first joint unit is fixedly connected in a collinear manner with the rocker of the second joint unit, and no relative motion occurs between the two rods. The frame rod of the second joint unit is fixedly connected in a collinear manner with the rocker of the first joint unit, and no relative motion occurs between the two rods. The frame rod of the third joint unit is fixedly connected in a collinear manner with the rocker of the second joint unit, and no relative motion occurs between the two rods. The rest of the assembly relationship is the same as that of the first embodiment. At this time, the mechanism can produce a completely symmetrical motion about the initial position, and the motion characteristics are as follows Figure 3 shown.

[0068] The schematic diagram of the mechanism motion when the frame rod and the swing rod of each joint unit of the mechanism are co-linearly integrated. By analyzing the mechanism characteristics and the special geometric relationship of the initial position, the rod length condition can be obtained:

[0069] c1+a1+d1=b1+c2+a2

[0070] c2+a2+d2=b3+c3+a3

[0071] To meet this rod length condition, all the rods of the mechanism are collinear in the initial position and have symmetrical motion on both sides, such as Figure 6 shown.

[0072] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A single-degree-of-freedom multi-joint mechanism with controllable deformation on both sides, characterized in that: It comprises N joint units connected in sequence, and freedom adjustment rods are connected between adjacent joint units; The joint unit includes a rocker rod, a frame rod, a crank connecting rod and a slider to form a planar connecting rod mechanism; The front ends of the swing rod and the frame rod are connected by a first pin shaft, the other end of the frame rod is connected to one end of the crank connecting rod by a second pin shaft, the slider is mounted on the swing rod and forms a linear moving pair moving along the swing rod, the other end of the crank connecting rod is connected to the slider by a third pin shaft, and the rear end of the swing rod is fixedly connected to the front end of the swing rod in the adjacent joint unit at the rear; Two ends of the freedom adjustment rod are respectively connected to the third pins in the two joint units.

2. The bilaterally controllable deformation single-degree-of-freedom multi-joint mechanism according to claim 1, characterized in that: The slider is provided with a guide hole, and the slider is fitted to the rocker arm through the guide hole and forms a linear motion pair with the rocker arm as a guide rod.

3. The bilaterally controllable deformation single-degree-of-freedom multi-joint mechanism according to claim 2, characterized in that: The invention comprises three joint units, which are connected in series to form a span arrangement from the inside to the outside. In the span direction from the inside to the outside, the rocker arm of the joint unit at the first position is installed on the support rod and the angle between the rocker arm and the support rod is 20°, the angle between the frame rod of the joint unit at the second position and the rocker arm at the first position is 25°, and the angle between the frame rod of the joint unit at the third position and the rocker arm at the second position is 23°.

4. The bilaterally controllable deformation single-degree-of-freedom multi-joint mechanism according to claim 2, characterized in that: The invention comprises three joint units, which are connected in series to form a span arrangement from the inside to the outside. In the span direction from the inside to the outside, the rocker arm of the joint unit at the first position is installed on the support rod and is located in the same straight line with the support rod, the frame rod of the joint unit at the second position is located in the same straight line with the rocker arm at the first position, and the frame rod of the joint unit at the third position is located in the same straight line with the rocker arm at the second position.

5. The bilaterally controllable deformation single-degree-of-freedom multi-joint mechanism according to claim 4, characterized in that: The rod length conditions of the three joint units meet: c1+a1+d1=b1+c2+a2 c2+a2+d2=b3+c3+a3 In the formula, a1, a2, a3 are the lengths of the crank connecting rods of each joint unit, b1, b2, b3 are the lengths of the rocker arms of each joint unit, c1, c2, c3 are the lengths of the frame arms of each joint unit, d1 and d2 are the lengths of the degree-adjusting rods between the first joint unit and the second joint unit and between the second joint unit and the third joint unit.

6. The bilaterally controllable deformation single-degree-of-freedom multi-joint mechanism according to claim 3, characterized in that: The rod length conditions of the three joint units meet: In the formula, a1, a2, and a3 are the lengths of the crank connecting rods of each joint unit, b1, b2, and b3 are the lengths of the rocker rods of each joint unit, c1, c2, and c3 are the lengths of the frame rods of each joint unit, d1 and d2 are the lengths of the degree-of-freedom adjustment rods between the first joint unit and the second joint unit, and the lengths of the degree-of-freedom adjustment rods between the second joint unit and the third joint unit; x1, x2, and x3 are the distances from the slider to the revolute pair at the end of the rocker rod, α1, α2, and α3 are the joint angles at the left extreme position of the multi-joint mechanism, θ1, θ2, and θ3 are the angles between the frame rod of the joint unit and the rocker rod of the adjacent joint unit, δ1, δ2, and δ3 are the angles between the crank connecting rod and the rocker rod of the joint unit at the left extreme position of the multi-joint mechanism, and in the span direction, β2 is the angle between the degree-of-freedom adjustment rod and the rocker rod of the first joint unit, and β3 is the angle between the degree-of-freedom adjustment rod and the rocker rod of the second joint unit.

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