Overall structure of rope-driven flexible mechanical arm joint

Abstract

The invention discloses an overall structure of a rope-driven modularized flexible mechanical arm. The modular flexible mechanical arm comprises modular flexible mechanical arm modules, a power driving module and a multifunctional connecting module, the installation number of the modular flexible mechanical arm modules includes but is not limited to 1, 2, 3, 4, 5 or more modular flexible mechanical arms, and the overall structure of the rope-driven flexible mechanical arm with the length N times that of the single modular flexible mechanical arm is formed; the power driving module comprises a steering engine, a rope winding wheel is fixed to the steering engine through a rope winding wheel fixing screw, a rope is fixed to a fixing hole of the rope winding wheel, stretching and releasing are achieved through rotation of the rope winding wheel, reversing is conducted through a rope winding wheel set, and the power driving module is connected with the modular flexible mechanical arm module at the lower end from a rope passing hole. Deflection of the joint sections can be achieved by stretching or releasing the connecting rope through the steering engine, the response speed is high, the flexibility is high, the collision problem in the operation process can be effectively avoided, and the joint is simple and compact in structure, can be modularly stacked and is convenient to assemble.

Description

Technical Field

[0001] The invention belongs to the field of mechanical arms, and in particular relates to the overall structure of a rope-driven flexible mechanical arm joint. Background Art

[0002] Traditional rigid robotic arms are mainly composed of rigid links and motors or rudders, and their notable features are discrete joints and rigid connections. The movement of this type of robotic arm depends on the joint drive of the servo or motor, resulting in low degrees of freedom and flexibility, limited range of motion, large mass and inertia, and relatively high energy consumption. In contrast, flexible robotic arms are driven by ropes and show greater flexibility than metal transmission mechanisms. This design gives its mechanical structure a certain flexibility, which is suitable for application scenarios with high requirements for interactive safety, and is easier to achieve lightweight and miniaturization. However, existing flexible robotic arms are usually integral structures and cannot be adjusted once the shape is determined. Summary of the invention

[0003] The purpose of the present invention is to provide an overall structure of a rope-driven flexible robotic arm joint, which improves the flexibility of the robotic arm, reduces energy consumption, expands the range of motion, and also has modular characteristics. The number of single-section modules can be increased arbitrarily, thereby constructing an overall robotic arm structure with a length that is N times that of a single-section flexible robotic arm to achieve a larger activity space.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] A rope-driven modular flexible robotic arm overall structure, comprising: a modular flexible robotic arm module, a power drive module, and a multifunctional connection module, wherein the number of modular flexible robotic arm modules installed includes but is not limited to 1, 2, 3, 4, 5 or more modular flexible robotic arms, forming a rope-driven flexible robotic arm overall structure that is N times longer than a single modular flexible robotic arm;

[0006] The power drive module includes a steering gear, which is fixed with a rope wheel through a rope wheel fixing screw, and the rope is fixed on the fixing hole of the rope wheel. The rope is stretched and released by rotating the rope wheel and is reversed through the rope winding pulley group, and is connected to the modular flexible mechanical arm module at the lower end through the rope hole;

[0007] The modular flexible robotic arm includes a spinous process plate, a sleeve, and an elastic diaphragm. The screw heads of two downward joint fixing bolts one are partially hidden in the sleeve screw head floating hole of sleeve two, and the other end is fixed in the sleeve threaded hole of sleeve one. The screw heads of two upward joint fixing bolts two are placed in the spinous process plate screw head floating hole, and the other end is fixed in the sleeve threaded hole of sleeve two.

[0008] Furthermore, the two downward joint fixing bolts 1 of the modular flexible robotic arm pass through the washer, the elastic diaphragm bolt through hole, the washer, the spinous process plate bolt through hole from top to bottom in sequence, and are finally fixed in the threaded hole of the sleeve; the two upward joint fixing bolts 2 pass through the washer, the elastic diaphragm screw through hole, the washer from bottom to top in sequence, and are finally fixed in the threaded hole of the sleeve 2. The above steps are repeated including but not limited to N times to build the joint.

[0009] Furthermore, the two spinous process plate bolt passing holes are arranged in a 180° circle for the joint fixing bolt to pass through, and together with the elastic diaphragm, provide a fulcrum for the bending of the flexible joint;

[0010] The two floating holes of the spinous process plate screw heads are arranged in a 180° circle, and their diameters are larger than the bolts so that they can float in the holes, thus providing bending space for the flexible joint to bend;

[0011] The two threaded holes of the shaft sleeve are arranged in a 180° circle, and are used to fix the joint fixing screws, and together with the elastic diaphragm, provide a fulcrum for the bending of the flexible joint module;

[0012] The two screw head floating holes are arranged in a 180° circle, and their diameters are slightly larger than the joint fixing bolts (26) so that the bolts can float in the holes, thus providing bending space for the flexible joint to bend.

[0013] Furthermore, there are four rope passage holes on the outer side of the spinous process plate, the four rope passage holes are arranged in a 90° circle, and nylon sleeves are installed in the rope passage holes.

[0014] Furthermore, the elastic diaphragm screw holes are arranged in a 90° circle to allow the joint fixing bolts to pass through. The elastic diaphragm screw holes work together with the gasket to provide support and elastic reset, ultimately achieving multi-degree-of-freedom bending of the flexible robotic arm joint.

[0015] Furthermore, the rope winding pulley group of the power driving module is installed on the rope winding pulley group base, and the rope winding pulley group base is installed on the base plate by fixing screws, and its position and corresponding angle meet the requirements that the straight line where the rope is connected from the rope winding wheel is parallel to the upper plane of the base plate, and coincides with the tangent drawn from the characteristic circle corresponding to the rope winding wheel and the rope winding pulley group pulley, and the rope passing hole through which the rope passes vertically after changing direction through the rope winding pulley group.

[0016] Furthermore, the servo is installed on the servo support through the servo fixing screws and is fixed to the base plate through the fixing screws. Each base plate is installed with including but not limited to 1, 2 or 3 servos, and further drives but not limited to 2, 3, 4, 5, 6 ropes. The base plates are all equipped with a group of threaded holes for installing the servo support and cooperating with the servo fixing screws to fix the servo. The base plate has 4 threaded holes for installing fixing screws, 4 rope holes for allowing ropes to pass through the base plate, 2 threaded grooves that can cooperate with joint fixing bolts to realize the connection between the joint module and the transmission module, and 2 screw head floating holes, in which the screw heads of the joint fixing bolts can float, thereby realizing the bending function between the joint module and the transmission module.

[0017] Furthermore, the servo is a 360° servo. After installation, the servo shaft and the rope pulley are in a neutral position. The servo drives the rope pulley to rotate forward or reverse according to the control signal of the single-chip microcomputer. The rotation angle is determined according to the number of superimposed joints, thereby realizing the extension or shortening of the rope on the rope pulley. The movement of a single servo can realize the contraction of two ropes to make the modular single robotic arm module produce a unidirectional bending of 5.5° to +5.5°. The cooperation of multiple servos can further realize the free bending of a single structure of the modular flexible robotic arm.

[0018] Furthermore, the multifunctional connection module includes support columns, which are evenly distributed and installed at openings on the base plate through threads. The support column fixing screws cooperate with the support columns to be fixed on the top plate. A top shaft sleeve is installed on the top plate to support and fix the top plate to leave a fixed space for the installation of the rope pulley group and provide a connection for the next group of modular flexible robotic arms.

[0019] Furthermore, the top sleeve has a group of evenly arranged threaded through holes, which are used to fix the joint fixing bolts, provide a fulcrum for the bending of the elastic diaphragm, and provide a connection point for the next modular flexible robotic arm; the screw head floating holes on the top sleeve are arranged in a 180° circle, and their diameter is larger than the screw head so that the bolts can float in the holes, thereby providing bending space for the bending of the flexible joint.

[0020] The beneficial effects of the present invention are:

[0021] The rope of the present invention can be extended or contracted by the steering gear driving the rope wheel to rotate clockwise or counterclockwise. The rope extension and contraction can drive each joint module to bend to a specified corresponding angle.

[0022] The elastic diaphragm of the present invention can be bent under force and can also support each joint module. Each rope drive of a single modular flexible manipulator can achieve a maximum bending of 5° in one direction of the manipulator. The coordinated drive of multiple servos can give the manipulator great flexibility and room for movement.

[0023] Each module of the present invention is relatively independent and can be replaced at will. A plurality of modularized flexible mechanical arms can be stacked together through fixed connection to form an overall mechanical arm structure that is N times longer than a single flexible mechanical arm.

[0024] The modular flexible joints of the present invention can be connected to each other through the top sleeve and the sleeve to form an overall mechanical arm structure that is N times longer than a single modular flexible mechanical joint, and the module type can be replaced, so that the mechanical arm has stronger flexibility and achieves the purpose of freely increasing or decreasing the activity space. The multi-degree-of-freedom modular flexible mechanical arm structure of the present invention can realize the deflection of the joint segment by stretching or releasing the connecting rope, has a fast response speed, high flexibility, and can effectively avoid collision problems during operation. The joint structure is simple and compact, can be modularly stacked, and is easy to assemble. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Attached Figure 1 It is a structural schematic diagram of the present invention.

[0026] Attached Figure 2 It is a detailed schematic diagram of the present invention.

[0027] Attached Figure 3 It is an exploded view of the modular flexible robotic arm of the present invention.

[0028] In the attached figure: 1: multi-functional connection module, 2: power drive module, 3: modular flexible robotic arm module, 4: top sleeve, 5: top plate, 6: support column, 7: bottom plate, 8: servo support, 9: servo, 10: servo fixing screw, 11: rope wheel, 12: rope, 13: rope wheel fixing screw, 14: rope through hole, 15: rope winding pulley group, 16: rope winding pulley group base, 17: spinous process plate, 18: sleeve two, 19: washer, 20: nylon sleeve, 21: sleeve threaded hole, 22: sleeve screw head floating hole, 23: elastic diaphragm screw through hole, 24: spinous process plate screw through hole, 25: spinous process plate screw head floating hole, 26: joint fixing bolt one, 27: elastic diaphragm, 28: washer, 29: sleeve one, 30: joint fixing bolt two, 31: nut floating hole, 32: support column fixing screw. DETAILED DESCRIPTION

[0029] The present invention is further described below in conjunction with the accompanying drawings.

[0030] Embodiment 1:

[0031] The present invention discloses a general structure of a rope-driven flexible mechanical arm joint, as shown in the attached Figure 1As shown, the composition includes: a modular flexible mechanical arm module 1, a power drive module 2, and a multifunctional connection module 3. The number of modular flexible mechanical arm modules 1 installed includes but is not limited to 1, 2, 3, 4, 5 or more modular flexible mechanical arms, forming a rope-driven flexible mechanical arm overall structure that is N times the length of a single modular flexible mechanical arm;

[0032] As attached Figure 2 As shown, a single modular flexible mechanical arm includes a steering gear 9 on a base plate 7 and a rope reel 11 mounted on the steering gear. The steering gear 9 is fixed to the steering gear support 8 using a steering gear fixing screw 10. The steering gear support 8 is fixedly connected to the base plate 7. The rope reel 11 is fixed to the steering gear 9 by a rope reel fixing screw 13 so as to achieve synchronous rotation with the steering gear. The rope 12 is fixedly connected to the rope reel 11. The steering gear 9 rotates clockwise or counterclockwise to drive the rope reel 11 to wind the rope to achieve its extension or contraction. The clockwise or counterclockwise rotation of the steering gear drives the rope reel to rotate, thereby controlling the rope to move in the forward and reverse directions of its rotation direction, respectively. This process adjusts the stretching or release of the rope in the flexible joint module, thereby driving the rotation of the joint.

[0033] Furthermore, the top end of the rope 12 connected to the servo 9 is fixed in the opening on the rope winding wheel 11. After the rope 12 penetrates into the hole, it enters the spinous process sleeve at the tail end of the joint. After the rope passes through the rope winding pulley group to change direction and passes through the rope hole of the bottom plate, it passes through the nylon sleeve on the spinous process plate 17 corresponding to each joint module, and the tail end is knotted and fixed in the rope hole 14 of the spinous process sleeve of the last section of the modular flexible robotic arm of the joint.

[0034] Furthermore, in each joint module, the bushing and the spinous process plate are supported by a gasket and an elastic diaphragm. When the servo drives the rope to bend the robotic arm, the servo fixing screw will move in the screw head floating hole, allowing the joint to bend, and the elastic diaphragm will also be forced to bend synchronously, and at the same time can play a supporting and rebounding role.

[0035] Furthermore, the modular flexible robotic arms can be stacked together and fixedly connected in multiples to form an overall robotic arm structure that is N times longer than a single-section flexible robotic arm. At the same time, each module is relatively independent and can be replaced.

[0036] As attached Figure 2 As shown, the modular flexible robotic arm includes a spinous process plate 17, a sleeve 18, and an elastic diaphragm 27. The screw heads of two downward joint fixing bolts 26 are partially hidden in the sleeve screw head floating hole 22 of the sleeve 18, and the other end is fixed in the sleeve threaded hole of the sleeve 29. The screw heads of two upward joint fixing bolts 30 are placed in the spinous process plate screw head floating hole 25, and the other end is fixed in the sleeve threaded hole 21 of the sleeve 18.

[0037] The two downward joint fixing bolts 26 of the modular flexible robotic arm pass through the washer 19, the elastic diaphragm bolt through hole 23, the washer 28, the spinous process plate bolt through hole 24 from top to bottom, and are finally fixed in the sleeve threaded hole 21; the two upward joint fixing bolts 30 pass through the washer, the elastic diaphragm screw through hole, the washer from bottom to top, and are finally fixed in the threaded hole of the sleeve 18. Repeat the above steps including but not limited to N times to build the joint.

[0038] The two spinous process plate bolt holes 24 are arranged in a 180° circle for the joint fixing bolt 26 to pass through, and together with the elastic diaphragm 27, provide a fulcrum for the bending of the flexible joint.

[0039] The two spinous process plate screw head floating holes 25 are arranged in a 180° circle, and their diameters are larger than the bolts so that they can float in the holes, thereby providing bending space for the flexible joint bending.

[0040] The two sleeve threaded holes 21 are arranged in a 180° circle and are used to fix the joint fixing screws, and together with the elastic diaphragm 27, provide a fulcrum for the bending of the flexible joint module;

[0041] The two screw head floating holes are arranged in a 180° circle, and their diameters are slightly larger than the joint fixing bolts 26 so that the bolts can float in the holes, thus providing bending space for the flexible joint to bend;

[0042] The spinous process plate 17 of this embodiment has four rope passage holes on the outside, and the four rope passage holes are arranged in a 90° circle, and nylon sleeves 20 are installed in the rope passage holes.

[0043] The elastic diaphragm screw holes 23 described in this embodiment are arranged in a 90° circle to allow the joint fixing bolts 26 to pass through. The elastic diaphragm screw holes 23 work together with the gasket to provide support and elastic reset, ultimately achieving multi-degree-of-freedom bending of the flexible robotic arm joint.

[0044] The installation method of a single modular flexible mechanical arm structure of this embodiment is as follows: a steering gear support 8 is installed on the bottom plate 7, a steering gear 9 is installed on the steering gear support through a steering gear fixing screw 10, and another steering gear is installed in the same way. Each steering gear 9 is fixed with a rope reel 11 through a rope reel fixing screw 13. The rope 12 is fixed on the rope reel 11 and can be extended or shortened by rotating around the rope reel. The flexible joint is installed in the order of a joint sleeve 18, a washer 19, an elastic diaphragm 27, a washer 19, and a sleeve 18. The bottom plate is provided with a rope hole 14, which allows 2, 3, 4, 5, and 6 ropes 12 to pass through. It also has a support column, a steering gear base installation hole, a sleeve fixing threaded hole, and a screw head floating hole.

[0045] The working method of this embodiment is as follows: the servo 9 fixed on the servo support 8 rotates counterclockwise, driving the rope winding wheel 11 fixed on the servo rotating shaft to rotate counterclockwise, and the rope winding wheel rotates to wind the rope around the wheel to achieve the contraction of the rope 12. The contraction of the rope pulls the spinous process plate 17 to drive it to bend obliquely to one side. The elastic diaphragm 27 is subjected to force to achieve bending and play a supporting role at the same time, and finally realizes the bending of a single modular robotic arm; at the same time, the cooperation of multiple servos can realize multi-degree-of-freedom bending of the robotic arm, which has a larger activity space and is more flexible.

[0046] The present invention effectively solves the problems of insufficient degrees of freedom and narrow activity space of traditional robotic arms, and at the same time, the replacement of modules becomes more convenient, thereby improving the flexibility of the robotic arm.

[0047] Embodiment 2:

[0048] According to the overall structure of the rope-driven flexible mechanical arm joint described in Example 1, as shown in the attached Figure 2-3 As shown, specifically, it includes but is not limited to three modular robotic arms connected, combined and stacked together by a top sleeve 4 and a sleeve 18 to form a structural whole that is N times larger than a single robotic arm, so that the overall structure of the robotic arm has a larger activity space.

[0049] The working method of this embodiment is as follows: the modular flexible robotic arms are fixedly connected using the top sleeve 4 and the sleeve 18, and the length of the overall structure of the robotic arm is adjusted by adjusting the number of modular robotic arms, thereby controlling the range of the activity space of the overall robotic arm structure.

[0050] The modular flexible mechanical arm of the present invention can be connected to each other through the top sleeve 4 and the sleeve 18 to realize an overall mechanical arm structure that is N times longer than a single modular flexible mechanical joint, and the module type can be replaced, so that the mechanical arm has stronger flexibility and achieves the purpose of freely increasing or decreasing the activity space. The multi-degree-of-freedom modular flexible mechanical arm structure of the present invention can realize the deflection of the joint segment by stretching or releasing the connecting rope, has a fast response speed, high flexibility, and can effectively avoid collision problems during operation, and the structure of the joint is simple and compact, can be modularly stacked, and is easy to assemble.

[0051] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A rope-driven modular flexible manipulator overall structure, characterized in that: include: A modular flexible robotic arm module (1), a power drive module (2), and a multifunctional connection module (3), wherein the number of modular flexible robotic arm modules (1) installed includes, but is not limited to, 1, 2, 3, 4, 5 or more modular flexible robotic arms, forming an overall rope-driven flexible robotic arm structure that is N times longer than a single modular flexible robotic arm; The power drive module comprises a steering gear (9), wherein the steering gear (9) is fixed with a rope winding wheel (11) via a rope winding wheel fixing screw (13), a rope (12) is fixed on a fixing hole of the rope winding wheel (11), stretching and releasing are achieved by rotating the rope winding wheel (1) and reversing is achieved via a rope winding pulley group (15), and the modular flexible mechanical arm module (1) at the lower end is connected via a rope passing hole (14); The modular flexible robotic arm comprises a spinous process plate (17), a sleeve (18), and an elastic diaphragm (27). The screw heads of two downward joint fixing bolts (26) are partially hidden in the sleeve screw head floating hole (22) of the sleeve (18), and the other end is fixed in the sleeve threaded hole of the sleeve (29). The screw heads of two upward joint fixing bolts (30) are placed in the spinous process plate screw head floating hole (25), and the other end is fixed in the sleeve threaded hole (21) of the sleeve (18).

2. The overall structure of the rope-driven modular flexible manipulator according to claim 1 is characterized in that: The two downward joint fixing bolts (26) of the modular flexible robotic arm pass through the washer (19), the elastic diaphragm bolt through hole (23), the washer (28), the spinous process plate bolt through hole (24) from top to bottom, and are finally fixed in the threaded hole of the sleeve (21); the two upward joint fixing bolts (30) pass through the washer, the elastic diaphragm screw through hole, the washer from bottom to top, and are finally fixed in the threaded hole of the sleeve (18). The above steps are repeated, including but not limited to N times, to build the joint.

3. The overall structure of the rope-driven modular flexible manipulator according to claim 2 is characterized in that: The two spinous process plate bolt holes (24) are arranged in a 180° circle for the joint fixing bolt (26) to pass through, and together with the elastic diaphragm (27) provide a fulcrum for the bending of the flexible joint; The two spinous process plate screw head floating holes (25) are arranged in a 180° circle, and their diameters are larger than the bolts so that they can float in the holes, thus providing bending space for the flexible joint to bend; The two sleeve threaded holes (21) are arranged in a 180° circle and are used to fix the joint fixing screws, and together with the elastic diaphragm (27) provide a fulcrum for the bending of the flexible joint module; The two screw head floating holes are arranged in a 180° circle, and their diameters are slightly larger than the joint fixing bolts (26) so that the bolts can float in the holes, thus providing bending space for the flexible joint to bend.

4. The overall structure of the rope-driven modular flexible manipulator according to claim 2 is characterized in that: The spinous process plate (17) has four rope passage holes on the outside thereof, the four rope passage holes are arranged in a 90° circle, and a nylon sleeve (20) is installed in the rope passage hole.

5. The overall structure of the rope-driven modular flexible manipulator according to claim 2 is characterized in that: The elastic diaphragm screw holes (23) are arranged in a 90° circle to allow the joint fixing bolt (26) to pass through. The elastic diaphragm screw holes (23) work together with the gasket to play a supporting and elastic reset role, ultimately achieving multi-degree-of-freedom bending of the flexible mechanical arm joint.

6. The overall structure of the rope-driven modular flexible manipulator according to claim 1 is characterized in that: The rope winding pulley block (15) of the power drive module is mounted on a rope winding pulley block base (16), and the rope winding pulley block base (16) is mounted on the bottom plate (7) by fixing screws, and its position and corresponding angle meet the requirements that the straight line where the rope (12) is connected from the rope winding wheel (11) is parallel to the upper plane of the bottom plate (7), and coincides with the tangent drawn from the characteristic circle corresponding to the rope winding wheel (11) and the rope winding pulley block pulley, and the rope passing hole through which the rope (12) passes vertically after changing direction through the rope winding pulley block (15).

7. The overall structure of the rope-driven modular flexible manipulator according to claim 1 is characterized in that: The servo (9) is mounted on the servo support (8) via a servo fixing screw (10) and is fixed to the base plate (7) via a fixing screw. Each base plate (7) is mounted with, but not limited to, 1, 2 or 3 servos, and further drives, but not limited to, 2, 3, 4, 5 or 6 ropes. The base plate (7) is provided with a set of threaded holes for mounting the servo support (8) and cooperating with the servo fixing screw (10) to fix the servo (9). The base plate (7) has 4 threaded holes for mounting the fixing screws, 4 rope holes (14) for allowing the ropes to pass through the base plate (7), 2 threaded grooves for cooperating with the joint fixing bolts to realize the connection between the joint module (3) and the transmission module (2), and 2 screw head floating holes (31) for allowing the screw heads of the joint fixing bolts to float therein, thereby realizing the bending function between the joint module (3) and the transmission module (2).

8. The overall structure of the rope-driven modular flexible manipulator according to claim 7 is characterized in that: The steering gear (9) is a 360° steering gear. After installation, the steering gear shaft and the rope winding wheel (5) are in a neutral position. According to the control signal of the single-chip microcomputer, the steering gear drives the rope winding wheel (5) to rotate forward or reverse. The rotation angle is determined according to the number of superimposed joints, thereby realizing the extension or shortening of the rope (12) on the rope winding wheel. The movement of a single steering gear (9) can realize the contraction of two ropes so that a modular single mechanical arm module generates a unidirectional bending of -5.5° to +5.5°. The cooperation of multiple steering gears (9) further realizes the free bending of a single structure of a modular flexible mechanical arm.

9. The overall structure of the rope-driven modular flexible manipulator according to claim 1, characterized in that: The multifunctional connection module (3) comprises a support column (6), wherein the support column (6) is evenly distributed and installed at the opening on the bottom plate (7) through threads, and the support column fixing screws (32) cooperate with the support column (6) to be fixed on the top plate (5), and a top shaft sleeve (4) is installed on the top plate (5), which plays the role of supporting and fixing the top plate (5) to leave a fixed space for the installation of the rope pulley group (15) and provide a connection for the next group of modular flexible mechanical arms.

10. The overall structure of the rope-driven modular flexible mechanical arm according to claim 8, characterized in that: The top sleeve (4) has a group of evenly arranged threaded through holes for fixing a joint fixing bolt (26), providing a fulcrum for the bending of the elastic diaphragm (27), and providing a connection point for the next modular flexible robotic arm; the screw head floating holes on the top sleeve (4) are arranged in a 180° circle, and their diameter is larger than the screw head so that the bolt can float in the hole, thereby providing a bending space for the bending of the flexible joint.

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