A controllable bending stacked chain structure

Abstract

The present invention discloses a controllable bending stacked chain structure, which includes a series of similar link units based on a planar four-bar linkage structure. Each link unit includes a compression bar, a lifting bar, a compression bar link, and a lifting bar link; the lifting bar is hinged to one end through-hole of the compression bar and one end through-hole of the compression bar of the next unit through through-holes at both ends, and the three bars are folded into a Z shape; by arranging and stacking one compression bar and one lifting bar alternately, a stacked chain structure arranged in a zigzag shape is formed. As the moving body of a robotic arm, the present invention can realize multi-curvature bending operations in narrow spaces, and has the characteristics of small footprint, large rotation angle, high load, light weight, rear drive, and internal wire routing, so as to meet the miniaturization, simplification, and high-performance operation requirements of robots, especially minimally invasive surgical robots, in narrow space operations.

Description

Technical Field

[0001] The present invention relates to a mechanical transmission structure, and particularly to an overlapping chain structure with controllable bending. Background Art

[0002] For fine and dexterous operations in narrow spaces, the robotic arm needs to reduce its size, streamline its volume, and reduce its mass, while maintaining a large number of degrees of freedom, a high load capacity, and a large movement range. These requirements are mutually contradictory and often lead to a situation where one aspect is sacrificed for another. The current solutions mainly include rigid joint arms and flexible continua. For rigid joint arms, a micro motor can be built into the joint, sacrificing the advantage of rear drive. However, the micro motor cannot provide a large load capacity. Alternatively, a cable drive combined with pulleys at the joints can be used, where a rear motor pulls a steel wire rope to drive the pulleys to rotate the joints. However, the rotation range is limited, and a large pre-tightening force is required to prevent the pulleys from slipping. These solutions all have extremely high difficulties in internal wiring, requiring a large amount of movement space for transmission cables and also considering communication lines and power supply lines. Flexible continua use elastic tubes, which are naturally suitable for hollow wiring, and the deformation of the elastic body can achieve flexible bending motion forms. However, their deformation is easily affected by external environmental forces, making it difficult to achieve precise positioning and the load is also very low. Summary of the Invention

[0003] In order to meet the requirements of robotic arm operations in narrow spaces, while taking into account the excellent characteristics of small footprint, large turning angle, high load, lightweight, rear drive, and internal wiring, the present invention realizes the curvature bending motion form unique to flexible continua based on a rigid link structure, and provides an overlapping chain structure with controllable bending.

[0004] The technical solution adopted by the present invention to address the deficiencies of the prior art is: an overlapping chain structure with controllable bending, which is composed of any number of link units connected in series. Each link unit includes a pressure rod, a lifting rod, a pressure rod link, and a lifting rod link;

[0005] The pressure rod and the lifting rod have through holes at both ends and a through hole in the middle, and the axes of the three holes are parallel to each other; the pressure rod link and the lifting rod link have through holes at both ends, and the axes of the two holes are parallel to each other;

[0006] The lifting rod of this unit is hinged to the through hole at one end of the pressure rod of this unit and the through hole at one end of the pressure rod of the next unit through the through holes at both ends, and the three rods are folded into a Z shape; by arranging one pressure rod and one lifting rod alternately and stacking and shrinking, an overlapping chain structure arranged in a zigzag shape is formed;

[0007] The lifting rod link of this unit is hinged and constrained to the through hole in the middle of the lifting rod of this unit and the through hole in the middle of the lifting rod of the next unit through the through holes at both ends; the pressure rod link of this unit is hinged and constrained to the through hole in the middle of the pressure rod of this unit and the through hole in the middle of the pressure rod of the next unit through the through holes at both ends.

[0008] Further, the strut, the lifting rod, and the strut connecting rod of this unit and the strut of the next unit form a reverse four-bar linkage structure, such that the strut connecting rod of this unit crosses the lifting rod, presenting an 8-shaped structure; the lifting rod, the lifting rod connecting rod of this unit and the strut, the lifting rod of the next unit form a reverse four-bar linkage structure, such that the lifting rod connecting rod of this unit crosses the strut of the next unit, presenting an 8-shaped structure;

[0009] Both of the two 8-shaped structures include the lifting rod of this unit and the strut of the next unit, thus sharing an angle with each other, enabling the two reverse four-bar linkage structures to be coupled in pairs to form a dual reverse four-bar linkage structure.

[0010] Further, the strut and the lifting rod of this unit adopt the same design parameters, and the strut connecting rod and the lifting rod connecting rod adopt the same design parameters, then the two 8-shaped structures are mirror images of each other, and the alternate interior angles unique to each of the two structures corresponding to the shared angle are equal, forming a conjugate reverse four-bar linkage structure.

[0011] Further, the angle θ between the lifting rod and the strut of this unit k and the angle between the lifting rod of this unit and the strut of the next unit satisfy the functional relationship between the alternate interior angles of the reverse four-bar linkage structure; through the paired arrangement of the reverse four-bar linkage structures, the angle between the lifting rod of this unit and the strut of the next unit k+1 and the angle θ between the strut of the next unit and the lifting rod

[0012] satisfy another functional relationship between the alternate interior angles of the reverse four-bar linkage structure; 1 Let the center distance between the through holes at both ends of the strut be m. The strut is divided into two sections by the middle through hole. The length of the section connected to the lifting rod of this unit is m 2 , and the length of the section connected to the lifting rod of the previous unit is m 1 +m 2 =m; the center distance between the through holes at both ends of the lifting rod is n. The lifting rod is divided into two sections by the middle through hole. The length of the section connected to the strut of this unit is n 1 , and the length of the section connected to the strut of the next unit is n 2 , n 1 +n 2 =n; the length of the strut connecting rod is d 1 , and the length of the lifting rod connecting rod is d 2 ;

[0013] When n 1 =m 1 , n 2 =m 2 , d 1 =d 2 at this time, there is θ k+1 =θ k and At this time, the movement form of the stacked link structure is shown as arc bending, which is called meeting the equal curvature bending condition.

[0014] Furthermore, if the ratio of m 1 to m 2 is changed, the stacked link structure still meets the equal curvature bending condition, but the bending strokes on both sides are different;

[0015] When d 1 ≠d 2 or m≠n, the equal curvature bending condition is violated, and the trend of the bending curvature will produce a positive feedback regulation effect according to linear transmission, and the bending curvature will become larger or smaller, thus generating variable curvature bending.

[0016] Furthermore, in the dual anti-four-bar link structure, the middle through hole of the pressure bar is split into two, and the pressure bar link of this unit and the pressure bar link of the next unit respectively occupy one of them; and / or the middle through hole of the lifting bar is split into two, and the lifting bar link of this unit and the lifting bar link of the next unit respectively occupy one of them.

[0017] Furthermore, the two middle through holes split from the pressure bar / lifting bar are both designed on the connection line of the through holes at both ends of the pressure bar / lifting bar, or the two split middle through holes are distributed on both sides of the connection line of the through holes at both ends of the pressure bar / lifting bar.

[0018] Furthermore, the stacked link structure can break the articulated relationship between the lifting bar of this unit and the pressure bar of the next unit at any place, flip the next unit, so that the two rods originally forming an angle are placed in parallel, the connection method of the pressure bar link and the lifting bar link remains unchanged, and two supplementary rods are added. The lifting bar of this unit, the pressure bar of the next unit and the two supplementary rods form a parallelogram structure, so that the two anti-four-bar link structures no longer share an angle, but each has an inner diagonal of the parallelogram structure, and the movement directions of the two anti-four-bar link structures are opposite. The dual anti-four-bar link structure becomes an S-shaped dual anti-four-bar link structure.

[0019] Furthermore, the stacked link structure is applied to a robotic arm. The robotic arm is composed of several units connected in series. The pressure bar and the lifting bar are designed as square frames to ensure that the inside is hollow for wire routing; the robotic arm can be used as a module, and multiple modules are assembled. The cables are laid to the base through the hollow wire routing design, and the joint motion can be decoupled, and each module can be independently controlled to move, realizing the movement of a multi-degree-of-freedom robotic arm.

[0020] Furthermore, the driving end is set to control the dual four-bar link unit in various forms, including changing the angle between the pressure bar link and the pressure bar, changing the relative distance between the lifting bar link and the pressure bar link, and can also be set to control the whole linear robotic arm, including eccentrically arranging the cables to pass through all the pressure bars in series from the fixed end to the base, and realizing the overall bending by pulling the cables.

[0021] The beneficial effects of the present invention are as follows:

[0022] In the stacked link structure of the present invention, the included angle θ between the starting rod and the pressing rod of this unit k and the included angle between the pressing rod of this unit and the starting rod of the next unit satisfy the functional relationship between the alternate interior angles of the anti-four-bar linkage. Through the mirror-arranged anti-four-bar structure, the included angle and the included angle θ of the next unit k+1 satisfy another functional relationship between the alternate interior angles of the new anti-four-bar linkage. Therefore, by simply changing the included angle θ k the entire stacked link structure can be driven. Under specific design parameters, if the two functional relationships are the same, the included angles θ k on one side of the stacked link structure are all equal, and the included angles on the other side are also all equal, and several units form an arc-shaped structure with an equal curvature. Further, by changing the design parameters, the movement of each unit can be realized according to different rotation angles, generating a linear structure with a variable curvature. The linear arrangement of the stacked link structure has good passability, resulting in the characteristic of small footprints; through the combination of N units, the bending of one unit can be amplified by N times, generating the characteristic of large rotation angles; the link structure itself can transmit motion, and the drive can be placed on any unit, and the motion form will be linearly transmitted, having the characteristic of rear drive; the structure similar to a truss formed by the link structure reflects good stability and stiffness, having the ability to bear high loads; the link structure can be made into a hollow structure, and the movement range of a single module is small, and there is enough space to accommodate various other cables to pass through, having the characteristic of internal wiring. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is the mechanical schematic diagram of the dual anti-four-bar structure;

[0024] Figure 2 is the parameter annotation diagram of the dual anti-four-bar structure;

[0025] Figure 3 is the analysis diagram of the planar anti-four-bar structure;

[0026] Figure 4 is the example diagram of the stacked link structure based on the conjugate anti-four-bar structure;

[0027] Figure 5 is the design of different bending strokes of the conjugate anti-four-bar structure;

[0028] Figure 6 is the example diagram of the stacked link structure based on the dual anti-four-bar structure;

[0029] Figure 7 is the misaligned hole design of the generalized conjugate anti-four-bar structure;

[0030] Figure 8 Structural analysis diagram for the misaligned hole design of the dual anti - four - link structure;

[0031] Figure 9 Example diagram of the stacked chain structure with hollow wire routing;

[0032] Figure 10 Example diagram of the stacked chain structure with rear drive;

[0033] Figure 11 Example diagram of the modular assembly structure;

[0034] Figure 12 Misaligned hole design of the conjugate anti - four - link structure;

[0035] Figure 13 Mechanical schematic diagram of the S - type dual anti - four - link structure. Specific implementation manners

[0036] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0037] As Figure 1 shown, the present invention provides a controllable bending stacked chain structure, which is composed of any number of link units connected in series. Each link unit includes a pressure rod, a lifting rod, a pressure rod link, and a lifting rod link. The pressure rod, lifting rod, pressure rod link, and lifting rod link of the k - th link unit are respectively denoted as k.1, k.2, k.3, and k.4.

[0038] The pressure rod k.1 and the lifting rod k.2 have, but are not limited to, a long - rod structure. There are two through - holes at both ends of the rod and another small through - hole in the middle. The axes of the three holes are parallel to each other; the pressure rod link k.3 and the lifting rod link k.4 have, but are not limited to, a long - rod structure. There are two through - holes at both ends of the rod, and the axes are parallel to each other.

[0039] Further, the lifting rod k.2 is respectively hinged to one - end through - hole of the pressure rod k.1 and one - end through - hole of the pressure rod (k + 1).1 of the next unit through the through - holes at both ends, and the three rods are folded into a Z - shape. By staggering and stacking one pressure rod k.1 and one lifting rod k.2, a stacked chain structure arranged in a zigzag shape is formed.

[0040] Further, the lifting rod link k.4 is respectively hinged and constrained to the middle through - hole of the lifting rod k.2 of this unit and the middle through - hole of the lifting rod (k + 1).2 of the next unit through the through - holes at both ends; correspondingly, the pressure rod link k.3 is respectively hinged and constrained to the middle through - hole of the pressure rod k.1 of this unit and the middle through - hole of the pressure rod (k + 1).1 of the next unit through the through - holes at both ends.

[0041] Furthermore, the pressure rod k.1, the lifting rod k.2, and the pressure rod link k.3 in this unit and the pressure rod (k + 1).1 of the next unit form an inverted four-bar linkage structure, such that the pressure rod link k.3 intersects with the lifting rod k.2, presenting an 8-shaped structure; and the lifting rod k.2, the lifting rod link k.4 in this unit and the pressure rod (k + 1).1, the lifting rod (k + 1).2 of the next unit form an inverted four-bar linkage structure, such that the lifting rod link k.4 intersects with the pressure rod (k + 1).1 of the next unit, presenting the same 8-shaped structure; and both 8-shaped structures have the lifting rod k.2 and the pressure rod (k + 1).1 of the next unit, thus sharing an angle with each other, enabling the two inverted four-bar linkage structures to be coupled in pairs to form a dual inverted four-bar linkage structure.

[0042] Furthermore, the pressure rod k.1 and the lifting rod k.2 adopt the same design parameters, and the pressure rod link k.3 and the lifting rod link k.4 adopt the same design parameters, then the two 8-shaped structures are mirror images of each other, and the alternate interior angles unique to each of the two structures corresponding to the shared angle are equal, forming a conjugate inverted four-bar linkage structure.

[0043] Specifically, the angle θ between the lifting rod k.2 and the pressure rod k.1 in this unit k and the angle between the lifting rod k.2 in this unit and the pressure rod (k + 1).1 of the next unit satisfy the functional relationship between the alternate interior angles of the inverted four-bar linkage structure. Let the center distance between the through holes at both ends of the pressure rod be m. The pressure rod is divided into two sections by the middle through hole. The length of the section connected to the lifting rod in this unit is m 1 , and the length of the section connected to the lifting rod of the previous unit is m 2 , m 1 + m 2 = m; the center distance between the through holes at both ends of the lifting rod is n. The lifting rod is divided into two sections by the middle through hole. The length of the section connected to the pressure rod in this unit is n 1 , and the length of the section connected to the pressure rod of the next unit is n 2 , n 1 + n 2 = n. From Figure 2 , Figure 3 as shown, considering the length d k C k+1 of the pressure rod link c 1 , there is:

[0044]

[0045] After arrangement, Equation 1 is obtained:

[0046]

[0047] This equation describes the angle θ k and the angle The functional relationship between them. Considering that neither of the two included angles is negative in the normal working state, the above formula passes through the limit coordinate point 1:

[0048]

[0049] Limit coordinate point 2:

[0050]

[0051] The working ranges of the two included angles can be analyzed.

[0052] Through the paired anti-four-bar linkage structure, the included angle and the included angle θ with the next unit k+1 satisfy another functional relationship between the alternate interior angles of the new anti-four-bar linkage structure. Considering the length d of the starting rod linkage D k D k+1 corresponding to Equation 1, there is Equation 2: 2

[0053]

[0054] It can be found that when n 1 = m 1 , n 2 = m 2 , d 1 = d 2 , the two equations are exactly the same, then θ k+1 = θ k . Similarly At this time, the movement form of the stacked chain structure is the simplest, showing an arc bend, as Figure 4 shown. The above formula is called the equal curvature condition.

[0055] If the ratio of m 1 to m 2 is changed, the stacked chain structure still satisfies the equal curvature bend, but the bending strokes on both sides are different, depending on the solution results of the limit coordinate point 1 and the limit coordinate point 2, as Figure 5 shown, with different left and right bending strokes.

[0056] Changing other conditions, such as d 1 ≠ d 2 , or m ≠ n, then the equal curvature bend condition is violated, and the trend of the bending curvature can be imagined to produce a positive feedback regulation effect according to linear transmission, as Figure 6 shown, with the bending curvature becoming larger or smaller, thus generating a variable curvature bend, and the result needs to be solved by combining Equation 1 and Equation 2.

[0057] Furthermore, for the dual anti-four-bar linkage structure, the compression bar link k.3 of all units does not have to be connected end to end and share a hinge hole in the middle of the compression bar k.1. Instead, the through hole in the middle of the compression bar k.1 is split into two, and the compression bar link k.3 of this unit and the compression bar link (k + 1).3 of the next unit each occupy one of them. The lifting bar k.2 can also be treated in the same way. For the sake of simplicity, the two split through holes are both designed on the line connecting the through holes at both ends of the link, as Figure 7 shown. The splitting of the symmetric middle through hole will not destroy the characteristics of the dual anti-four-bar linkage, so that the positions of the compression bar link k.3 and the lifting bar link k.4 can be arranged more flexibly. Without loss of generality, it can be considered that the middle through holes are distributed on both sides of the line connecting the two ends of the link, as Figure 8 shown. At this time, only a part of an angle originally shared by the dual anti-four-bar linkage structure will be shared. For θ, each shares Considering making equal to then the θ angle of the dual anti-four-bar linkage structure still satisfies the equal relationship. Similarly, considering making equal to then the angle of the dual anti-four-bar linkage structure still satisfies the equal relationship. Let the center distance between the through holes at both ends of the compression bar be m, and the middle through hole of the compression bar is divided into an upper connection through hole and a lower connection through hole. The length of the connection section between the upper connection through hole and the lifting bar of this unit is m 1 , and the length of the connection section between the lower connection through hole and the lifting bar of the previous unit is m 2 , m 1 +m 2 ≠m; the center distance between the through holes at both ends of the lifting bar is n, and the middle through hole of the lifting bar is divided into an upper connection through hole and a lower connection through hole. The length of the connection section between the lower connection through hole and the compression bar of this unit is n 1 , and the length of the connection section between the upper connection through hole and the compression bar of the next unit is n 2 , n 1 +n 2 ≠n. Therefore, the variant formula 3 of formula 1 can be obtained:

[0058]

[0059] And the variant formula 4 of formula 2:

[0060]

[0061] From formula 3 and formula 4, it can be seen that the equal curvature condition still applies to formula 3 and formula 4. At this time, the conjugate four-bar linkage structure becomes a generalized conjugate four-bar linkage structure, as shown in the mechanical schematic diagram on the right of Figure 7 , which perfectly satisfies the arc-shaped bending of equal curvature.

[0062] Further, the stacked link structure can break the hinged relationship between the starting rod k.2 of this unit and the pressing rod (k+1).1 of the next unit at any point, flip the next unit and subsequent parts, so that the two rods originally forming an angle are placed in parallel. The connection method of the pressing rod link k.3 and the starting rod link k.4 remains unchanged, and a supplementary rod s.1 and a supplementary rod s.2 are added. The supplementary rod s.1 and the supplementary rod s.2 are exactly the same, similar in structure to the starting rod link k.4 and the pressing rod link k.3, and their lengths can be different. The starting rod k.2 of this unit, the pressing rod (k+1).1 of the next unit, and the two supplementary rods s.1, s.2 form a parallelogram structure. So that the two anti-four-bar link structures originally contained in the dual anti-four-bar link structure no longer share an angle, but each has an interior diagonal of the parallelogram structure. Since the interior diagonals of a parallelogram are equal, Equation 1 and Equation 2 are still satisfied. However, after inserting the parallelogram structure, the two anti-four-bar link structures move in opposite directions, as Figure 12 shown, then the dual anti-four-bar link structure becomes an S-shaped dual anti-four-bar link structure, as Figure 13 shown.

[0063]

Example 1

[0064] The stacked link structure is applied to a robotic arm. The entire robotic arm is composed of several units connected in series. Considering the design of equal curvature conditions, the pressing rod k.1 and the starting rod k.2 are designed as square frames to ensure that wires can be routed through the hollow parts, as Figure 9 shown. The fixed end adopts a design similar to that of a bicycle brake wire. Pulling the cable in the wire tube changes the angle between the starting rod and the pressing rod of the first unit, as Figure 10 shown, driving the entire robotic arm to generate an equal bending motion to complete the operation.

[0065]

Example 2

[0066] On the basis of Example 1, considering the design of the generalized conjugate four-bar link structure, as Figure 7 and Figure 9 shown, different misaligned hole designs are adopted, all of which satisfy equal curvature bending.

[0067]

Example 3

[0068] On the basis of Example 2, the entire robotic arm is used as a module, and multiple modules are assembled. The cable is laid to the base through the hollow wire routing design, and the joint motion can be decoupled to independently control the motion of each module, as Figure 9 and Figure 11 shown, realizing the motion of a robotic arm with multiple degrees of freedom.

[0069]

Example 4

[0070] According to actual needs, modify the parameters of the four-bar unit. For example, arrange the compression rod link k.3 on the left and the lifting rod link k.4 on the right. As Figure 6 shown, it can achieve the movement of variable curvature bending. The rotation angle of the unit closer to the distal end will become larger and larger, meeting the needs of the scenario with a large rotation angle at the end.

[0071]

Embodiment 5

[0072] According to actual needs, insert an S-shaped dual anti-four-bar structure into the stacked chain mechanism composed of dual anti-four-bar structures. As Figure 13 shown, it can achieve the movement of S-shaped bending. Inserting it at different positions or modifying different parameters can achieve different bending effects and meet the needs of specific scenarios.

[0073]

Embodiment 6

[0074] From the perspective of transmission, the driving end can be set to control the four-bar unit in various forms. For example, change the angle between the compression rod link k.3 and the compression rod k.1, and change the relative distance between the lifting rod link k.4 and the compression rod link k.3. It can also be set to control the entire linear robotic arm. For example, eccentrically arrange the cable to pass through all the compression rods (through holes are provided on the compression rods along this direction) in sequence from the fixed end to the base of the series-connected units. By pulling the cable, the overall bending can be achieved. Due to the unit replication characteristic of the present invention, each unit will still maintain the same bending curvature.

[0075]

Embodiment 7

[0076] From the perspective of sensing, the sensor can be arranged on any unit, and monitoring the movement of any unit can represent the movement form of the entire robotic arm.

[0077] Those skilled in the art of this technology can easily make various changes and modifications according to the written description, drawings, and claims provided by the present invention without departing from the spirit and scope of the present invention defined by the claims. Any modification and equivalent change made to the above embodiments based on the technical idea and essence of the present invention fall within the protection scope defined by the claims of the present invention.

Claims

1. A controllable bending stacked chain structure, characterized in that, it is composed of any number of connecting rod units connected in series, and each connecting rod unit includes a pressure rod, a lifting rod, a pressure rod connecting rod and a lifting rod connecting rod; the pressure rod and the lifting rod have through holes at both ends and a through hole in the middle, and the axes of the three holes are parallel to each other; the pressure rod connecting rod and the lifting rod connecting rod have through holes at both ends, and the axes of the two holes are parallel to each other; the lifting rod of this unit is hinged to the through hole at one end of the pressure rod of this unit and the through hole at one end of the pressure rod of the next unit through the through holes at both ends, and the three rods are folded into a Z shape; by arranging and stacking one pressure rod and one lifting rod alternately, a stacked chain structure arranged in a zigzag shape is formed; the lifting rod connecting rod of this unit is hinged and constrained to the through hole in the middle of the lifting rod of this unit and the through hole in the middle of the lifting rod of the next unit through the through holes at both ends; the pressure rod connecting rod of this unit is hinged and constrained to the through hole in the middle of the pressure rod of this unit and the through hole in the middle of the pressure rod of the next unit through the through holes at both ends; the pressure rod, the lifting rod and the pressure rod connecting rod of this unit and the pressure rod of the next unit form an anti-four-bar linkage structure, so that the pressure rod connecting rod of this unit intersects with the lifting rod, presenting an 8-shaped structure; the lifting rod, the lifting rod connecting rod of this unit and the pressure rod and the lifting rod of the next unit form an anti-four-bar linkage structure, so that the lifting rod connecting rod of this unit intersects with the pressure rod of the next unit, presenting an 8-shaped structure; both 8-shaped structures have the lifting rod of this unit and the pressure rod of the next unit, so that they share an included angle with each other, and the two anti-four-bar linkage structures are coupled in pairs to form a dual anti-four-bar linkage structure.

2. A controllable bending stacked chain structure according to claim 1, characterized in that, the pressure rod and the lifting rod of this unit adopt the same design parameters, and the pressure rod connecting rod and the lifting rod connecting rod adopt the same design parameters, then the two 8-shaped structures are mirror images of each other, and the alternate interior angles unique to the two structures corresponding to the shared included angle are equal, forming a conjugate anti-four-bar linkage structure.

3. A controllable bending stacked chain structure according to claim 1, characterized in that, The included angle θ between the starting rod and the pressing rod of this unit k and the included angle between the starting rod of this unit and the pressing rod of the next unit satisfies the functional relationship between the alternate interior angles of the anti-four-bar linkage structure; through the paired anti-four-bar linkage structures, the included angle between the starting rod of this unit and the pressing rod of the next unit and the included angle θ k+1 between the pressing rod of the next unit and the starting rod satisfies another functional relationship between the alternate interior angles of the anti-four-bar linkage structure; Let the center distance between the through holes at both ends of the compression bar be m. The compression bar is divided into two sections by the through hole in the middle, and the length of the connecting section with the starting bar of this unit is m 1 and the length of the connecting section with the starting bar of the previous unit is m 2 , m 1 +m 2 = m; Let the center distance between the through holes at both ends of the starting bar be n. The starting bar is divided into two sections by the through hole in the middle, and the length of the connecting section with the compression bar of this unit is n 1 and the length of the connecting section with the compression bar of the next unit is n 2 , n 1 +n 2 = n; The length of the connecting rod of the compression bar is d 1 and the length of the connecting rod of the starting bar is d 2 ; When n 1 = m 1 , n 2 = m 2 , d 1 = d 2 , there is θ k+1 = θ k and At this time, the motion form of the stacked chain structure is shown as arc bending, which is called meeting the equal curvature bending condition.

4. A controllable bending stacked chain structure according to claim 3, characterized in that, If m is changed 1 and the ratio with m 2 is changed, the stacked chain structure still satisfies equi-curvature bending, but the bending strokes on both sides are different; When d 1 ≠ d 2 or m ≠ n, the equal-curvature bending condition is violated, and the trend of the bending curvature will produce a positive feedback regulation effect according to linear transfer, and the bending curvature will become larger or smaller, thus generating variable-curvature bending.

5. A controllable bending stacked chain structure according to claim 1, characterized in that, in the dual anti-four-bar linkage structure, the through hole in the middle of the pressure rod is split into two, and the pressure rod connecting rod of this unit and the pressure rod connecting rod of the next unit respectively occupy one of them; and / or the through hole in the middle of the lifting rod is split into two, and the lifting rod connecting rod of this unit and the lifting rod connecting rod of the next unit respectively occupy one of them.

6. A controllable bending stacked chain structure according to claim 5, characterized in that, both of the two split through holes in the middle of the pressure rod / lifting rod are designed on the connection line of the through holes at both ends of the pressure rod / lifting rod, or the two split through holes are distributed on both sides of the connection line of the through holes at both ends of the pressure rod / lifting rod.

7. A controllable bending stacked chain structure according to claim 1, characterized in that, The overlapping chain structure can break the hinge relationship between the starting rod of the current unit and the pressing rod of the next unit at any point, flip the next unit, so that the two rods that originally form an angle are placed in parallel. The connection method between the pressing rod connecting rod and the starting rod connecting rod remains unchanged, and two supplementary rods are added. The starting rod of the current unit, the pressing rod of the next unit, and the two supplementary rods form a parallelogram structure, so that the two anti-four-bar linkages no longer share an angle, but each has an interior diagonal angle of the parallelogram structure. The two anti-four-bar linkages move in opposite directions, and the dual anti-four-bar linkage structure becomes an S-shaped dual anti-four-bar linkage structure.

8. A controllable bending overlapping chain structure according to any one of claims 1-7, characterized in that the overlapping chain structure is applied to a robotic arm. The robotic arm is formed by connecting several units in series. The pressing rod and the starting rod are designed as square frames to ensure that wires can be routed through the hollow parts. The robotic arm can be used as a module, and multiple modules can be assembled. The cables are laid to the base through the hollow wire routing design, and the joint motion can be decoupled to independently control the movement of each module, realizing the movement of a multi-degree-of-freedom robotic arm.

9. A controllable bending overlapping chain structure according to any one of claims 1-7, characterized in that the driving end is set to control the four-bar unit pair, including changing the angle between the pressing rod connecting rod and the pressing rod, changing the relative distance between the starting rod connecting rod and the pressing rod connecting rod, or setting to control the entire linear robotic arm, including eccentrically arranging the cables to pass through all the pressing rods in sequence from the fixed end to the base along the series-connected units, and realizing the overall bending by pulling the cables.

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