WO2023155504A1 - 一种自锁式欠驱动夹持器及其结构优化方法 - Google Patents

一种自锁式欠驱动夹持器及其结构优化方法 Download PDF

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Publication number
WO2023155504A1
WO2023155504A1 PCT/CN2022/131817 CN2022131817W WO2023155504A1 WO 2023155504 A1 WO2023155504 A1 WO 2023155504A1 CN 2022131817 W CN2022131817 W CN 2022131817W WO 2023155504 A1 WO2023155504 A1 WO 2023155504A1
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Prior art keywords
knuckle
bar
immune
phalanx
last
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Ceased
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PCT/CN2022/131817
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English (en)
French (fr)
Inventor
申燚
何淑婷
戴现令
袁明新
缪海鹏
邱贝贝
陶丽佳
印刚
潘先锋
褚兴安
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Jiangsu University of Science and Technology
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Jiangsu University of Science and Technology
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Publication of WO2023155504A1 publication Critical patent/WO2023155504A1/zh
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J15/00—Gripping heads and other end effectors
    • B25J15/08—Gripping heads and other end effectors having finger members
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J15/00—Gripping heads and other end effectors
    • B25J15/0009—Gripping heads and other end effectors comprising multi-articulated fingers, e.g. resembling a human hand
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J15/00—Gripping heads and other end effectors
    • B25J15/02—Gripping heads and other end effectors servo-actuated
    • B25J15/0206—Gripping heads and other end effectors servo-actuated comprising articulated grippers
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B25J19/007—Means or methods for designing or fabricating manipulators
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Definitions

  • the invention belongs to the technical field of industrial robots, and in particular relates to a gripper of a robot and a structure optimization method thereof.
  • underactuated mechanism based on the underrank principle has begun to emerge. Because the underactuated mechanism has the advantage of adaptive envelope and can meet the "one-to-many" clamping method on the production line, it has attracted the attention of domestic and foreign scholars and has become a research topic. hotspot. Therefore, designing a new type of gripper based on the principle of under-rank mechanism is helpful to solve the robot's clamping requirements for multi-shape and multi-size workpieces in the process of workpiece handling.
  • underactuated mechanisms often use multi-joint finger mechanisms, and the current design is mostly based on engineering experience. Therefore, the stability and accuracy of the mechanism are often reduced due to the lack of force balance of each finger joint during envelope clamping. In addition, most of the existing underactuated mechanisms do not have a self-locking function, and may fall off when grasping a slightly heavy workpiece, resulting in a dangerous working condition.
  • the invention patent with the application number "202011408245.X” discloses a robot end picker and its structure optimization method.
  • This patent designs a new type of end picker with adaptive envelope grabbing based on the principle of underrank mechanism.
  • this end picker mainly relies on the tension of the spring itself to clamp the workpiece. It has no self-locking ability and is only suitable for light workpieces. There is a risk of slipping for slightly heavy workpieces, resulting in safety accidents.
  • the workpiece may shake and vibrate, the reliability, stability and positioning accuracy are poor, and even affect the normal operation of the equipment.
  • the object of the present invention is to address the problems and deficiencies in the above-mentioned prior art, and combine the technology of grasping multi-shaped objects with the self-adaptive envelope of the principle of lack of rank mechanism on the robot gripper, to provide a kind of gripping firm, stable, Self-locking underactuated gripper with precise positioning and self-locking capability.
  • a self-locking underactuated clamper comprising a driving mechanism 1, the upper end surface of the driving mechanism 1 is equipped with a clamping mechanism that is mirror-symmetrically arranged, and the clamping mechanism is formed from the bottom to the top by the first knuckle assembly 2, The middle knuckle assembly 3 and the last knuckle assembly 4 are connected to form.
  • the driving mechanism 1 includes a cylinder block 5, and the left and right sides of the upper end of the cylinder block 5 are separately installed with a mirror-symmetrical pneumatic slider 6, and the pneumatic slider 6 is fixedly connected with a transmission slider 7 by bolts.
  • the top of the slider 7 is rotatably connected to the lower end of the drive link 8, the upper end of the drive link 8 is rotatably connected to the lower end of the knuckle drive link 9, and the rear end of the cylinder block 5 corresponds to the drive slider (7)
  • a support arm 10 with mirror image symmetry is fixedly arranged, and the upper end of the knuckle transmission link 9 is rotationally connected with the rotating shaft at the upper end of the support arm 10;
  • the first knuckle assembly 2 includes a first knuckle frame 11, the left and right vertical frames of the first knuckle frame 11 respectively adopt two rod structures with the same front and rear symmetry, and the middle of the lower frame of the first knuckle frame 11 rotates Connected to the rotating shaft at the upper end of the support arm 10, the knuckle frame 11 clamps and fixes the lower knuckle guide 12, the upper knuckle guide 13 and the L-shaped bar 14 of the first knuckle through bolts from bottom to top in sequence , the upper end of the L-shaped bar 14 of the first knuckle is rotatably connected to the left end of the arc of the middle knuckle tripod 15, and the lower guide 12 of the first knuckle includes a first I-shaped piece 16 and a second I-shaped piece parallel to each other.
  • the first I-shaped part 16 and the second I-shaped part 17 are respectively fixed between the left frame and the right frame of the first knuckle frame 11, the first I-shaped part 16 and the second I-shaped part 17
  • the first guide tube 18 with the left port closed and the right port connected is clamped and fixed between them.
  • the first guide tube 18 is equipped with a first spring 19, and the right end of the first spring 19 is supported on the spring bar under the first knuckle.
  • 20 left end, the first pin shaft 21 perpendicular to its axis is also fixed on the left end of the first knuckle lower pressure spring lever 20, and the first pin shaft 21 can be slotted in the first guide tube 18 in the axial direction.
  • the right end of the first knuckle lower pressure spring rod 20 is fixed on the left lower part of the first knuckle clamping block 22, and the first knuckle upper guide 13 includes a third I-shaped piece 23 and a first knuckle parallel to each other.
  • the third I-shaped piece 23 and the fourth I-shaped piece 24 are also respectively fixed between the left frame and the right frame of the first knuckle frame 11, the third I-shaped piece 23 and the fourth I-shaped piece
  • the second guide tube 25 with the left port closed and the right port connected is clamped and fixed between the I-shaped pieces 24.
  • the second guide tube 25 is equipped with a second spring 26, and the right end of the second spring 26 is supported on the first knuckle.
  • Upper compression spring bar 27 left end, the right end of described first knuckle upper compression spring bar 27 is fixed on the upper left part of first knuckle clamping block 22, described first knuckle lower compression spring bar 20 and first knuckle upper compression spring
  • the rods 27 jointly support the clamping block 22 of the first knuckle, the middle bar of the first knuckle frame 11 is rotationally connected with the turning point of the first knuckle curved rod 28, and the lower end of the first knuckle curved rod 28 is embedded in the notch
  • the upper end of the first knuckle crank rod 28 is connected to the lower end of the middle knuckle transmission link 29 so as to convert the left and right movement of the first knuckle clamping block 22 into the first pin shaft 21 that can slide along the groove.
  • the middle knuckle assembly 3 includes a middle knuckle frame 30, and the left and right vertical frames of the middle knuckle frame 30 also adopt the same two rod structures with front and rear symmetry, and the middle knuckle frame 30 is sequentially clamped by bolts from bottom to top
  • the middle knuckle tripod 15, the middle knuckle lower guide 31, the middle knuckle upper guide 32 and the middle knuckle T-shaped bar 33 are fixedly installed, and the right end of the middle knuckle tripod 15 arc is connected with the middle knuckle transmission link 29,
  • the lower middle phalanx guide 31 has the same structure as the first phalanx lower guide 12, including the fifth I-shaped piece 34, the sixth I-shaped piece 35, the third guide tube 36, the third spring 37, the middle finger Joint lower compression spring lever 38 and second pin shaft 39, the right end of the middle knuckle lower compression spring lever 38 is fixed on the left lower part of the middle knuckle clamping block
  • the last knuckle assembly 4 includes a last knuckle clamping block 48, the lower left end of the last knuckle clamping block 48 is rotatably connected to the upper end of the middle phalanx T-bar 33, and the last knuckle clamping block 48
  • the lower right end of the knuckle is connected to the upper end of the last knuckle transmission link 47, and the power of the middle knuckle assembly 3 is transmitted to the last knuckle clamping block 48 through the last knuckle transmission link 47, so that the last knuckle clamping block 48 Rotate around the upper end of the middle knuckle T-bar 33;
  • first phalanx clamping block 22 is a concave structural member including a mounting surface and a clamping surface, and the inner side of the concave part is arc-shaped.
  • the middle knuckle clamping block 40 is a concave structural member including a mounting surface and a clamping surface, and the inner side of the concave part is arc-shaped.
  • the clamping block 48 of the last knuckle is a knife-shaped structural member including an installation end and a clamping end, and the handle of the knife for installation is provided with two connecting holes, and the blade portion for clamping is a concave structure, And the inner side of the recess is arc-shaped.
  • the clamping surfaces of the first knuckle clamping block 22 , the middle knuckle clamping block 40 and the last knuckle clamping block 48 are all provided with anti-shock and anti-skid layers.
  • a structural optimization method for a self-locking underactuated gripper including the establishment of a gripping contact force model of the gripper, a method for optimizing the structural parameters of the gripper, and an optimization process for the structural parameters of the gripper;
  • the model establishment and structure optimization are carried out by taking the three knuckles on the left as an example.
  • the establishment of the geometric model is equivalent to the drive link 8 in the drive mechanism 1 as the AB bar
  • the first knuckle transmission link 9 is equivalent to the BC 2 bar
  • the first knuckle frame 11 is equivalent to a C 1 C 3 C 4 E 1 quadrilateral
  • the first knuckle curved bar 28 is equivalent to a QD 2 D 3 folding bar
  • the left end of the middle cross bar of the first knuckle frame 11 is connected to the first knuckle
  • the part at the turning point of the curved rod 28 is equivalent to a D 1 D 2 rod
  • the middle knuckle transmission link 29 is equivalent to a QP rod
  • the middle knuckle frame 30 is equivalent to an E 1 E 2 E 5 G 1 quadrilateral
  • the middle knuckle curved rod 46 is equivalent to
  • the establishment of the static model is to define the torque of the driving mechanism 1 as T1 , define the driving forces of the springs s1 and s2 as T2 and T3 respectively; define the first knuckle assembly 2, the middle knuckle
  • the contact force of the object clamped by component 3 and last knuckle component 4 is F 1 , F 2 and F 3 respectively; define the distance between point C 1 and force F 1 as h 1 , and define the distance between point E 1 and force F 2 as h 2 , define the distance between G 1 point and F 3 force as h 3 ; define the included angle between bar E 2 P and bar QP, the included angle between bar PQ and bar D 2 Q, and the included angle between bar G 2 U and bar RU , the angle between rod UR and rod E 4 R, the angle between rod C 4 E 1 and rod C 1 E 1 are ⁇ 1 , ⁇ 2 , ⁇ 3 , ⁇ 4 , ⁇ 5 ; define rod E 1 C 1 and The angle between the horizontal
  • v s1 and v s2 are the imaginary velocities on the springs s 1 and s 2 respectively;
  • v F1 , v F2 , and v F3 are the contact forces F 1 , F 2 , F 3 Imaginary velocity at the point of contact.
  • ⁇ ⁇ 1 , ⁇ ⁇ 2 , ⁇ ⁇ 3 are the angular velocities of the rotation angles ⁇ 1 , ⁇ 2 and ⁇ 3 respectively.
  • V F J v [ ⁇ ⁇ 1 ⁇ ⁇ 2 ⁇ ⁇ 3 ] T .
  • the clamper structural parameter optimization method including the immune optimization algorithm based on the group effect
  • the immune evolution algorithm based on the group effect is the operator of the basic immune optimization algorithm (including the immune selection operator O s , the immune crossover operator On the basis of O c and immune mutation operator O m )
  • a new immune aggregation operator O g and immune diffusion operator O d are designed according to the group effect to optimize and improve the algorithm.
  • the immune crossover operator O c can be described as:
  • the immune mutation operator O m can be described as:
  • the immune agglomeration operator O g mainly allows the dominant individuals in the population to form an agglomeration population to form an appeal to the disadvantaged individuals with poor fitness, thereby improving the performance of the disadvantaged individuals.
  • the procedure of immune aggregation operator is:
  • the immune aggregation operator Og can be described as:
  • the immune diffusion operator O d mainly allows individuals with a high concentration in the population to diffuse to prevent individuals from falling into a local minimum.
  • the immune diffusion operator O d can be described as:
  • X is the structure parameter variable set of the gripper
  • the new gripper designed based on the under-rank principle of the present invention can realize the adaptive envelope gripping of disc workpieces with different diameters, greatly improving the efficiency of workpieces caused by workpieces.
  • the replacement of special fixtures due to size changes will cause a large amount of labor and low production efficiency.
  • the gripper can limit the degree of freedom of the workpiece from bottom to top, the clamping force is large, and it has self-locking ability, which effectively avoids the risk of slipping due to the weight of the workpiece itself, and greatly improves the stability of the clamping , reliability and positioning accuracy, effectively reducing the occurrence of safety accidents.
  • the gripper is designed based on the principle of underactuation, and there is only one power source, which greatly reduces the difficulty of control tasks and shortens the entire design cycle of the product.
  • a new immune optimization algorithm based on group effect is proposed. Based on the agglomeration behavior in the group effect, the immune aggregation operator is designed, and the local search ability of the algorithm is improved through the call of the outstanding individuals of the group to the disadvantaged individuals; the immune diffusion operator is designed based on the diffusion behavior in the group effect, and the diffusion of high-concentration individuals To effectively avoid the algorithm from falling into a local minimum.
  • the workpiece clamping stability of the self-locking underactuated gripper depends on the structural parameters of the gripper itself, but it is a multi-parameter structure with multiple constraints on the parameters. If the trial and error design is based on human experience, it will not only take time and effort but also fail to obtain the best structural parameters. Based on the establishment of the contact force model of the gripper, the global optimization of the gripper parameters can be realized by using the immune optimization algorithm based on the group effect, which improves the optimization efficiency and optimization accuracy.
  • Fig. 1 the overall structural diagram of the clamper in the embodiment of the present invention
  • Figure 2 Structural diagram of the driving mechanism of the gripper in the embodiment of the present invention
  • Figure 3 The overall structure diagram of the first knuckle assembly of the gripper in the embodiment of the present invention.
  • Figure 4 A partial structural diagram of the first knuckle assembly of the gripper in the embodiment of the present invention.
  • Fig. 5 Structural diagram of the first knuckle guide and the clamping block assembly of the clamper in the embodiment of the present invention
  • Figure 6 L-shaped bar of the first knuckle of the holder in the embodiment of the present invention.
  • Figure 7 The first phalangeal flexure of the gripper in the embodiment of the present invention.
  • Figure 8 The middle knuckle tripod of the holder in the embodiment of the present invention.
  • Figure 9 Structural diagram of the middle knuckle assembly and the last knuckle assembly of the holder in the embodiment of the present invention.
  • Figure 10 Structural diagram of the combination of the middle knuckle guide and the clamping block of the clamper in the embodiment of the present invention
  • Figure 11 Structural diagram of the last knuckle clamping block of the clamper in the embodiment of the present invention
  • Figure 12 Schematic diagram of the clamper before grabbing the disc workpiece in the embodiment of the present invention.
  • Figure 13 Schematic diagram of the clamper enveloping the disc workpiece in the embodiment of the present invention.
  • Figure 14 A geometric model diagram of the self-locking underactuated gripper in the embodiment of the present invention.
  • Figure 15 Static model diagram of the self-locking underactuated gripper in the embodiment of the present invention.
  • the reference signs in the figure are: 1. drive mechanism; 2. first knuckle assembly; 3. middle knuckle assembly; 4. last knuckle assembly; 5. cylinder block; 6. pneumatic slider; 7. transmission slider; 8. Drive link; 9. First knuckle drive link; 10. Support arm; 11. First knuckle frame; 12. First knuckle lower guide; 13. First knuckle upper guide; 14. First knuckle L-shaped bar; 15. middle knuckle tripod; 16. the first I-shaped part; 17. the second I-shaped part; 18. the first guide tube; 19. the first spring; 21. The first pin shaft; 22. The clamping block of the first knuckle; 23. The third I-shaped piece; 24. The fourth I-shaped piece; 25.
  • the disc workpiece The third guide tube; 37. The third spring; Clamping block; 41. The seventh I-shaped part; 42. The eighth I-shaped part; 43. The fourth guide tube; 44. The fourth spring; .The transmission link of the last knuck
  • front and back in the present invention refers to that when the reader is facing the drawings, the front of the reader is pointed from the paper of the view, and the back is pointed to the inside of the paper, rather than the clamper device of the present invention. Specific restrictions.
  • a self-locking underactuated gripper of the present invention includes a driving mechanism 1, and the upper part of the driving mechanism 1 is connected with left and right symmetrical first knuckle assemblies 2 with the same structure, and the first finger
  • the upper part of the knuckle assembly 2 is connected with a left-right symmetrical middle knuckle assembly 3 with the same structure, and the upper part of the middle knuckle assembly 3 is connected with a left-right symmetrical last knuckle assembly 4 with the same structure.
  • a driving mechanism 1 of a self-locking underactuated gripper of the present invention includes a cylinder block 5, and a left-right symmetrical pneumatic slider 6 with the same structure is installed on the upper end of the cylinder block 5.
  • the upper end of the pneumatic slider 6 is fixedly connected to the transmission slider 7 by bolts, the transmission slider 7 is rotatably connected to the lower end of the drive link 8, and the upper end of the drive link 8 is rotatably connected to the first knuckle
  • the lower end of the transmission connecting rod 9, the rear end of the cylinder block 5 is fixedly provided with a left-right symmetrical support arm 10 corresponding to the transmission slider 7, and the structure is identical, and the upper end of the first knuckle transmission connection rod 9 is connected to the support arm The rotating shaft of 10 upper ends.
  • a first knuckle assembly 2 of a self-locking underactuated gripper of the present invention includes a first knuckle frame 11, and the first knuckle frame 11
  • Each of the left and right vertical frames adopts the same two rod structures with front and rear symmetry, and the middle of the lower frame of the first knuckle frame 11 is connected to the rotating shaft at the upper end of the support arm 10, and the first knuckle frame 11 is connected from bottom to top by bolts.
  • the first phalanx lower guide 12, the upper first phalanx guide 13, and the first phalanx L-shaped bar 14 are clamped and fixed in sequence.
  • the upper end of the first phalanx L-shaped bar 14 is rotatably connected to the middle phalanx tripod 15 arc
  • the left end of the first knuckle guide 12 includes a first I-shaped piece 16 and a second I-shaped piece 17 parallel to each other, and the first I-shaped piece 16 and the second I-shaped piece 17 are respectively fixed on the first Between the left frame and the right frame of the knuckle frame 11, the first I-shaped piece 16 and the second I-shaped piece 17 clamp and fix the first guide tube 18 with the left port closed and the right port connected.
  • a first spring 19 is housed in a guide tube 18, and the right end of the first spring 19 is supported on the left end of the first knuckle lower compression spring rod 20, and the left end of the first knuckle lower compression spring rod 20 is also fixed with its axis Vertical first pin shaft 21, the first pin shaft 21 can move left and right in the first guide tube 18 along the axial direction, the right end of the first knuckle lower pressure spring rod 20 is fixed on the first knuckle clamp
  • the lower left part of the holding block 22, the first knuckle upper guide 13 includes a third I-shaped piece 23 and a fourth I-shaped piece 24 parallel to each other, and the third I-shaped piece 23 and the fourth I-shaped piece 24 are also They are respectively fixed between the left frame and the right frame of the first knuckle frame 11.
  • the third I-shaped piece 23 and the fourth I-shaped piece 24 clamp and fix the second guide tube 25 with the left port closed and the right port connected.
  • the second guide tube 25 is equipped with a second spring 26, the right end of the second spring 26 is supported on the left end of the spring bar 27 on the first knuckle, and the right end of the spring bar 27 on the first knuckle is fixed on the
  • the left upper part of the first knuckle clamping block 22, the first knuckle lower compression spring lever 20 and the first knuckle upper compression spring lever 27 jointly support the first knuckle clamping block 22, and the first knuckle clamping block 22
  • It is a concave structural member including a mounting surface and a clamping surface, and the inner side of the concave part is arc-shaped so as to better fit the contour of the workpiece.
  • the turning point is rotationally connected, the first pin shaft 21 is embedded in the notch at the lower end of the first knuckle bar 28 and can slide along the slot, and the upper end of the first knuckle bar 28 is rotatably connected to the middle knuckle transmission link 29
  • the lower end of the first phalanx clamping block 22 is converted into the rotation of the first phalanx bending rod 28, which provides power for the middle phalanx assembly 3 of the next stage.
  • the clamping block 22 of the first knuckle is pushed to move to the right; Drive the first pin shaft 21 to the right to move to the right, and then promote the first knuckle bar 28 to rotate counterclockwise around the middle turning point, and the middle knuckle transmission link 29 that is connected with the upper end of the first knuckle bar 28 to rotate The power is transmitted to the middle knuckle assembly 3.
  • the first knuckle clamping block 22 When starting to clamp the workpiece, along with the contact with the workpiece, the first knuckle clamping block 22 is pressed, thereby pushing the first knuckle lower compression spring lever 20 and the first knuckle upper compression spring lever 27 to move to the left, while the first knuckle flexes
  • the rod 28 rotates clockwise around the turning point driven by the leftward movement of the first pin shaft 21 , and drives the middle knuckle assembly 3 to rotate through the middle knuckle transmission link 29 .
  • the middle knuckle assembly 3 of a self-locking underactuated gripper of the present invention includes a middle knuckle frame 30, and the left and right vertical sides of the middle knuckle frame 30 are
  • the frame also adopts two rod structures with the same front and rear symmetry.
  • the middle knuckle frame 30 is sequentially clamped and fixed by bolts from bottom to top, and is equipped with a middle knuckle tripod 15, a lower middle knuckle guide 31, and an upper middle knuckle guide 32.
  • the right end of the middle phalanx is fixed on the lower left part of the middle phalanx clamping block 40.
  • the guide 32 on the middle phalanx has the same structure as the upper guide 13 on the first phalanx, including the seventh I-shaped piece 41, the eighth I-shaped piece 42, the fourth I-shaped piece Guide pipe 43, the 4th spring 44 and middle phalanx upper compression spring bar 45, the right end of described middle phalanx upper compression spring bar 45 is fixed on the left upper part of middle phalanx clamp block 40, described middle phalanx lower compression spring bar 38 and The middle phalanx clamping block 40 is jointly supported by the pressure spring bar 45 on the middle phalanx.
  • the middle phalanx clamping block 40 is a concave structural member including a mounting surface and a clamping surface, and the inner side of the recess is arc-shaped, so as to better Fitting the contour of the workpiece, the middle cross bar of the middle knuckle frame 30 is rotationally connected with the turning point of the middle knuckle bar 46, and the second pin that can slide along the slot is embedded in the lower end of the middle knuckle bar 46 Shaft 39, the upper end of the middle knuckle crank 46 is connected to the lower end of the last knuckle transmission link 47, so that the left and right movement of the middle knuckle clamping block 40 is converted into the rotation of the middle knuckle crank 46, which is the next stage
  • the last knuckle assembly 4 provides power.
  • the middle knuckle clamping block 40 is pushed to move to the right, on the other hand the middle knuckle
  • the bent bar 46 is driven by the second pin shaft 39 on the middle phalanx spring bar 38 to rotate counterclockwise around its middle turning point, and the last phalanx transmission link 47 connected to the upper end of the middle phalanx bent bar 46 is rotated The power is transmitted to the last knuckle assembly 4.
  • the middle phalanx clamp block 40 When starting to clamp the workpiece, along with the contact with the workpiece, the middle phalanx clamp block 40 is pressed, thereby promoting the lower pressure spring lever 38 of the middle phalanx and the upper pressure spring lever 45 of the middle phalanx to move to the left, while the middle phalanx curved lever 46 is at the first position
  • the two pin shafts 39 are moved to the left and driven to rotate clockwise around the turning point, and drive the last knuckle assembly 4 to rotate through the last knuckle transmission link 47 .
  • the last knuckle assembly 4 of a self-locking underactuated clamper of the present invention includes a last knuckle clamping block 48, and the lower left end of the last knuckle clamping block 48 is rotatably connected to the T-shaped bar 33 of the middle knuckle The upper end of the upper end of the last knuckle clamping block 48 is rotatably connected to the upper end of the last knuckle transmission link 47, and the power of the middle knuckle assembly 3 is transmitted to the last knuckle clamping through the last knuckle transmission link 47.
  • the clamping block 48 of the last knuckle is rotated around the upper end of the T-bar 33 of the middle knuckle. Before clamping the workpiece, turn counterclockwise away from the workpiece, and when clamping the workpiece, turn clockwise to approach the workpiece.
  • the clamping block 48 of the last knuckle is a knife-shaped structure comprising an installation end and a clamping end, and the handle of a knife for installation is provided with two connecting holes, and the blade portion for clamping is a concave structure, and the recess
  • the inner side is arc-shaped to better fit the contour of the workpiece.
  • the last knuckle assembly 4 of a self-locking underactuated clamper of the present invention includes a last knuckle clamping block 48, and the lower right end of the last knuckle clamping block 48 is rotatably connected to the last knuckle transmission link 47, the lower left end of the last knuckle clamping block 48 is rotatably connected to the upper end of the middle knuckle T-shaped bar 33, and the power of the middle knuckle assembly 3 is transmitted to the last knuckle clamping through the last knuckle transmission link 47.
  • the last knuckle clamping block 48 is rotated around the upper end of the middle knuckle T-bar 33.
  • the last knuckle clamping block 48 rotates counterclockwise away from the workpiece.
  • Block 48 rotates clockwise close to the workpiece, and the last knuckle clamping block 48 is a knife-shaped structural member including an installation end and a clamping end.
  • the handle of a knife for installation is provided with two connecting holes, and the blade for clamping
  • the part is a concave structure, and the inside of the concave part is arc-shaped, so as to better fit the contour of the workpiece.
  • first phalanx clamping block 22, the middle phalanx clamping block 40 and the last phalanx clamping block 48 are in close contact with the disc workpiece 49, so that the first spring 19, the second spring 26, the third spring 37 and the second The four springs 44 stop being compressed by external force, and the elongation is hindered by the workpiece without further deformation, thereby realizing the self-locking of the clamp.
  • the first phalanx assembly 2 , the middle phalanx assembly 3 and the last phalanx assembly 4 are driven by a power source pneumatic slider 6 , realizing underactuation based on the principle of an underrank mechanism. Fig.
  • FIG. 12 shows the state that the first phalanx assembly 2, the middle phalanx assembly 3 and the last phalanx assembly 4 are fully opened when the pneumatic slider 6 is located outside the cylinder.
  • Fig. 13 shows that when the pneumatic slide block 6 is located inside the cylinder, the first phalanx assembly 2, the middle phalanx assembly 3 and the last phalanx assembly 4 completely self-adaptively envelop and grasp the state of the disc workpiece 49.
  • FIG. 14 and Figure 15 it is a structural optimization method of a self-locking underactuated gripper of the present invention, including the establishment of the gripper contact force model, the optimization method of the gripper structural parameters and the gripper Structural parameter optimization process;
  • the model establishment and structure optimization are carried out by taking the three knuckles on the left as an example.
  • the geometric model is mainly that the drive link 8 in the drive mechanism 1 is equivalent to the AB bar, the first knuckle transmission link 9 is equivalent to the BC 2 bar, and the first knuckle frame is 11 is equivalent to a C 1 C 3 C 4 E 1 quadrilateral, the first knuckle curved bar 28 is equivalent to a QD 2 D 3 folding bar, and the left end of the middle cross bar of the first knuckle frame 11 is connected to the first knuckle
  • the part at the turning point of the curved rod 28 is equivalent to a D 1 D 2 rod
  • the middle knuckle transmission link 29 is equivalent to a QP rod
  • the middle knuckle frame 30 is equivalent to an E 1 E 2 E 5 G 1 quadrilateral
  • the middle knuckle curved rod 46 is equivalent
  • the statics model mainly defines the torque of the driving mechanism 1 as T1 , defines the driving forces of the springs s1 and s2 as T2 and T3 respectively; defines the first knuckle assembly 2, the middle knuckle
  • the contact force of the object clamped by component 3 and last knuckle component 4 is F 1 , F 2 and F 3 respectively; define the distance between point C 1 and force F 1 as h 1 , and define the distance between point E 1 and force F 2 as h 2 , define the distance between G 1 point and F 3 force as h 3 ; define the included angle between bar E 2 P and bar QP, the included angle between bar PQ and bar D 2 Q, and the included angle between bar G 2 U and bar RU , the angle between rod UR and rod E 4 R, the angle between rod C 4 E 1 and rod C 1 E 1 are ⁇ 1 , ⁇ 2 , ⁇ 3 , ⁇ 4 , ⁇ 5 ; define rod E 1 C 1 and The angle between the horizontal reverse line
  • v s1 and v s2 are the imaginary velocities on the springs s 1 and s 2 respectively;
  • v F1 , v F2 , and v F3 are the contact forces F 1 , F 2 , F 3 Imaginary velocity at the point of contact.
  • ⁇ ⁇ 1 , ⁇ ⁇ 2 , ⁇ ⁇ 3 are the angular velocities of the rotation angles ⁇ 1 , ⁇ 2 and ⁇ 3 respectively.
  • V F J v [ ⁇ ⁇ 1 ⁇ ⁇ 2 ⁇ ⁇ 3 ] T .
  • the clamper structural parameter optimization method including the immune optimization algorithm based on the group effect
  • the immune evolution algorithm based on the group effect is the operator of the basic immune optimization algorithm (including the immune selection operator O s , the immune crossover operator On the basis of O c and immune mutation operator O m )
  • a new immune aggregation operator O g and immune diffusion operator O d are designed according to the group effect to optimize and improve the algorithm.
  • the basic immune algorithm has distributed and global optimization capabilities, it also has the shortcomings of effective local search capabilities and easy to fall into local problems when facing multivariate optimization. It can be seen from the contact force model of the above-mentioned gripper that there are about 10 variables to be optimized in this structure, so higher requirements are put forward for the optimization ability of the algorithm. For this reason, the present invention draws on the group effect in social development, that is, when an individual faces a group, his behavior will change under the influence of the group, such as agglomeration behavior based on centripetal force and diffusion behavior based on competition.
  • the immune crossover operator O c can be described as:
  • the immune mutation operator O m can be described as:
  • the immune agglomeration operator O g mainly allows the dominant individuals in the population to form an agglomeration population to form an appeal to the disadvantaged individuals with poor fitness, thereby improving the performance of the disadvantaged individuals.
  • the procedure of immune aggregation operator is:
  • the immune aggregation operator Og can be described as:
  • the immune diffusion operator O d mainly allows individuals with a high concentration in the population to diffuse to prevent individuals from falling into a local minimum.
  • the immune diffusion operator O d can be described as:
  • minf(X) min((F 1 ⁇ F 2 ) 2 +(F 1 ⁇ F 3 ) 2 +(F 2 ⁇ F 3 ) 2 ).
  • X is the structure parameter variable set of the gripper
  • GA and IOABOPE which have distributed and global optimization capabilities, are superior to Fmincon in terms of the objective function value and the difference of contact force. This is mainly because Fmincon is a local optimization method for multivariable Optimization has no advantage.
  • the IOABOPE of the present invention is undoubtedly the best, not only the objective function value is the smallest, but also the three contact forces are relatively close, which is mainly due to the immune aggregation operator improving the local optimization ability of the algorithm, while the immune diffusion algorithm The method prevents the algorithm from falling into the local minimum prematurely, effectively improves the optimization effect of the algorithm, and thus also verifies the validity and superiority of the optimization method proposed by the present invention.

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Abstract

一种自锁式欠驱动夹持器及其结构优化方法，自锁式欠驱动夹持器包括驱动机构（1），驱动机构（1）的上部安装着左右对称且结构相同的首指节组件（2），首指节组件（2）上部安装着中指节组件（3），中指节组件（3）上部安装着末指节组件（4）。

Description

一种自锁式欠驱动夹持器及其结构优化方法 技术领域
本发明属于工业机器人技术领域，尤其涉及到机器人的夹持器及其结构优化方法。
背景技术
随着市场产品的配套类型增加，多品种、小批量工件在自动化生产线上不断涌现。工业机器人已经成为自动化生产线上的主角。为了应付生产中的工件搬运，机器人通常需要频繁更换夹具，降低了生产线效率。
近年来一种基于欠秩原理的欠驱动机构开始兴起，因欠驱动机构具有自适应包络的优点，能满足生产线上“一对多”的夹持方式，得到了国内外学者关注并成为研究热点。因此基于欠秩机构原理设计新型夹持器有助于解决工件搬运过程中机器人对多外形、多尺寸工件的夹持需求。但由于欠驱动机构往往采用多关节指形机构，目前设计时多基于工程经验，因此机构在包络夹持时常会因各指节达不到力平衡而降低稳定性和精确性。此外，现有欠驱动机构大多不具有自锁功能，在抓取稍重型工件时会出现脱落导致发生危险工况。
申请号为“202011408245.X”的发明专利，公开了一种机器人端拾器及其结构优化方法。该专利基于欠秩机构原理设计了具有自适应包络抓取的新型端拾器。但该端拾器主要依靠弹簧自身拉力来夹取工件，不具备自锁能力，只适用于轻型类工件，对于稍重型工件会存在有滑落的风险，导致安全事故发生。此外，由于夹紧力较小，工件可能出现摇晃、抖动的情况，牢靠性、稳定性和定位精度较差，甚者影响设备正常运行。
因此在基于欠秩机构原理设计新型夹持器并完成自锁功能的基础上，针对其开展相应结构优化方法设计，有助于提高机器人夹持工件的有效性和稳定性。
发明内容
本发明的目的是针对上述现有技术存在的问题和不足，将欠秩机构原理的自适应包络抓取多形状物件的技术结合到机器人夹持器上，提供一种夹持牢靠、稳定、定位精确且具备自锁能力的自锁式欠驱动夹持器。
为了达到上述目的，本发明采取如下的技术方案予以实现：
一种自锁式欠驱动夹持器，包括驱动机构1，所述驱动机构1的上端面安装着镜像对称设置的夹持机构，所述夹持机构自下而上由首指节组件2、中指节组件3和末指节组件4相连构成。
所述的驱动机构1包括气缸体5，所述气缸体5上端面左右隔离安装有镜像对称的气动滑块6，所述气动滑块6上通过螺栓固定连接有传动滑块7，所述传动滑块7上方转动连接着驱动连杆8的下端，所述驱动连杆8的上端转动连接着首指节传动连杆9的下端，所述气缸体5的后端对应传动滑块(7)固定设置有镜像对称的支撑臂10，所述首指节传动连杆9的上端与支撑臂10上端的转轴转动连接；
所述首指节组件2，包括首指节框架11，所述首指节框架11的左右竖边框各采用前 后对称相同的两根杆结构，所述首指节框架11的下边框的中间转动连接着支撑臂10上端的转轴，所述首指节框架11通过螺栓从下到上依次夹持固定着首指节下导向件12、首指节上导向件13和首指节L型杆14，所述首指节L型杆14的上端旋转连接在中指节三角架15弧形处的左端，所述首指节下导向件12包括相互平行的第一工字件16和第二工字件17，所述第一工字件16和第二工字件17分别固定在首指节框架11的左边框间和右边框间，所述第一工字件16和第二工字件17间夹持固定着左端口封闭右端口导通的第一导向管18，所述第一导向管18内装有第一弹簧19，所述第一弹簧19的右端支撑在首指节下压簧杆20左端部，所述首指节下压簧杆20的左端上还固定着与其轴线垂直的第一销轴21，所述第一销轴21可以在第一导向管18沿轴向所开槽内左右移动，所述首指节下压簧杆20的右端固定在首指节夹持块22的左下部，所述首指节上导向件13包括相互平行的第三工字件23和第四工字件24，所述第三工字件23和第四工字件24同样分别固定在首指节框架11的左边框间和右边框间，所述第三工字件23和第四工字件24间夹持固定着左端口封闭右端口导通的第二导向管25，所述第二导向管25内装有第二弹簧26，所述第二弹簧26的右端支撑在首指节上压簧杆27左端部，所述首指节上压簧杆27的右端固定在首指节夹持块22的左上部，所述首指节下压簧杆20和首指节上压簧杆27共同支撑着首指节夹持块22，所述首指节框架11中间横杆上与首指节曲杆28的转折处转动连接，所述首指节曲杆28下端槽口内嵌着且能沿槽滑动的第一销轴21，所述首指节曲杆28的上端转动连接着中指节传动连杆29的下端，从而将首指节夹持块22的左右移动转化成首指节曲杆28的转动，为下一级中指节组件3提供动力；
所述中指节组件3，包括中指节框架30，所述中指节框架30的左右竖边框同样各采用前后对称相同的两根杆结构，所述中指节框架30通过螺栓从下到上依次夹持固定装有中指节三角架15、中指节下导向件31、中指节上导向件32和中指节T型杆33，所述中指节三角架15弧形处的右端转动连接着中指节传动连杆29的上端，所述中指节下导向件31和首指节下导向件12结构一样，包括第五工字件34、第六工字件35、第三导向管36、第三弹簧37、中指节下压簧杆38和第二销轴39，所述中指节下压簧杆38的右端固定在中指节夹持块40的左下部，所述中指节上导向件32和首指节上导向件13结构一样，包括第七工字件41、第八工字件42、第四导向管43、第四弹簧44和中指节上压簧杆45，所述中指节上压簧杆45的右端固定在中指节夹持块40的左上部，所述中指节下压簧杆38和中指节上压簧杆45共同支撑着中指节夹持块40，所述中指节框架30中间横杆上与中指节曲杆46的转折处转动连接，所述中指节曲杆46下端槽口内嵌着且能沿槽滑动的第二销轴39，所述中指节曲杆46的上端转动连接着末指节传动连杆47的下端，从而将中指节夹持块40的左右移动转化成中指节曲杆46的转动，为下一级末指节组件4提供动力；
所述末指节组件4，包括末指节夹持块48，所述末指节夹持块48的左下端转动连接着中指节T型杆33的上端，所述末指节夹持块48的右下端转动连接着末指节传动连杆47的上端，通过末指节传动连杆47将中指节组件3的动力传递到末指节夹持块48上，使得末指节夹持块48绕中指节T型杆33上端转动；
进一步，所述首指节夹持块22为包括安装面和夹持面的凹形结构件，且凹部内侧为弧形状。
进一步，所述中指节夹持块40为包括安装面和夹持面的凹形结构件，且凹部内侧为弧形状。
进一步，所述末指节夹持块48为包括安装端和夹持端的刀形结构件，用于安装的刀柄部设有两个连接孔，用于夹持的刀片部为凹形结构，且凹部内侧为弧形状。
进一步，所述首指节夹持块22，所述中指节夹持块40和所述末指节夹持块48的夹持面上均设置有防冲击、防滑层。
为了达到上述目的，本发明采取的另一个技术方案如下：
一种自锁式欠驱动夹持器的结构优化方法，包括夹持器夹持接触力模型建立、夹持器结构参数优化方法和夹持器结构参数优化流程；
一、夹持器夹持接触力模型建立，包括如下内容和步骤：
(1)根据夹持器结构建立几何模型和静力学模型；
鉴于自锁式欠驱动夹持器呈左右对称结构，以左边三指节为例进行模型建立和结构优化。所述建立几何模型是将所述驱动机构1中的所述驱动连杆8等效为AB杆，将所述首指节传动连杆9等效为BC 2杆，将所述首指节框架11等效为C 1C 3C 4E 1四边形,将所述首指节曲杆28等效为QD 2D 3折杆，将所述首指节框架11中间横杆的左端到首指节曲杆28转折处的部分等效为D 1D 2杆，将所述中指节传动连杆29等效为QP杆，将所述中指节框架30等效为E 1E 2E 5G 1四边形，将所述中指节曲杆46等效为RE 4E 3折杆，将所述中指节框架30中间横杆的左端到中指节曲杆46转折处的部分等效为E 6E 4杆，将所述末指节传动连杆47等效为RU，将所述末指节夹持块48等效为G 1G 2G 3G 4四边形，由于第一弹簧19和第二弹簧26同步拉伸和压缩，且变形量一样，在模型计算时将两者受力等效到弹簧D 4D 3上，且用s 1表示弹簧D 4D 3；同理将第三弹簧37和第四弹簧44受力等效到弹簧E 7E 3上，且用s 2表示弹簧E 7E 3；定义杆C 1C 3、D 1D 2、E 1E 2、G 1U和E 6E 4的长度分别为a 1、a 2、a 3、a 4和a 5；定义杆E 1B、G 1E 1、G 1G 4、D 1B和E 1E 6的长度为d 1、d 2、d 3、d 4和d 5；定义杆D 2D 3、D 2Q、PQ、E 3E 4、E 4R和RU的长度为l 1、l 2、l 3、l 4、l 5和l 6；
所述建立静力学模型是定义所述驱动机构1的力矩为T 1，定义所述弹簧s 1和s 2的驱动力分别为T 2和T 3；定义所述首指节组件2、中指节组件3和末指节组件4夹持物体的接触力分别为F 1、F 2和F 3；定义C 1点距F 1力的距离为h 1，定义E 1点距F 2力的距离为h 2，定义G 1点距F 3力的距离为h 3；定义杆E 2P与杆QP的夹角，杆PQ与杆D 2Q的夹角，杆G 2U与杆RU的夹角，杆UR与杆E 4R的夹角，杆C 4E 1与杆C 1E 1的夹角分别为α 1、α 2、α 3、α 4、α 5；定义杆E 1C 1与水平反向线的夹角，杆G 1E 1与杆C 1E 1反向延长线的夹角，杆G 4G 1与杆E 1G 1反向延长线的夹角分别为β 1、β 2、β 3；定义杆C 3C 1与水平线的夹角，杆PE 1与水平线的夹角，杆UG 1与水平线的夹角分别为
Figure PCTCN2022131817-appb-000001
(2)基于虚功原理建立夹持器各指节虚功方程：
Figure PCTCN2022131817-appb-000002
式中，
Figure PCTCN2022131817-appb-000003
为力矩T 1作用于首指节上的虚角速度，v s1、v s2分别为弹簧s 1和s 2上的虚速度；v F1、v F2、v F3分别为接触力F 1、F 2、F 3在接触点处的虚速度。
令T＝[T 1 F 1+T 2 F 2+T 3] T，F＝[F 1 F 2 F 3] T，
Figure PCTCN2022131817-appb-000004
V F＝[v F1 v F2 v F3] T，虚功方程可以简化为：F TV F＝T TW。
(3)基于刚体速度公式建立夹持器各指节虚速度V F＝[v F1 v F2 v F3] T为：
Figure PCTCN2022131817-appb-000005
式中，
Figure PCTCN2022131817-appb-000006
δ β1、δ β2、δ β3分别为转角β 1、β 2和β 3的角速度。
将虚速度V F写成矩阵形式：V F＝J v[δ β1 δ β2 δ β3] T。
式中，
Figure PCTCN2022131817-appb-000007
(4)由于所述中指节传动连杆29(PQ)和末指节传动连杆47(UR)都对所在指节组件有直接作用力，计算两杆的虚速度v PQ、v UR：
Figure PCTCN2022131817-appb-000008
因为，
Figure PCTCN2022131817-appb-000009
Figure PCTCN2022131817-appb-000010
Figure PCTCN2022131817-appb-000011
Figure PCTCN2022131817-appb-000012
所以，所述中指节传动连杆29(PQ)和末指节传动连杆47(UR)的虚速度v PQ、v UR为：
Figure PCTCN2022131817-appb-000013
针对五连杆机构E 1PQD 2D 1，以E 1 D 1为x轴正方向，指向圆盘工件方向为y轴正方向，列出其矢量封闭方程：
Figure PCTCN2022131817-appb-000014
将其分解为x、y方向：
Figure PCTCN2022131817-appb-000015
对α 6+β 2、
Figure PCTCN2022131817-appb-000016
求导：
Figure PCTCN2022131817-appb-000017
因为α 6为固定角，所以δ α6＝0。根据同一构件角速度关系可得：
Figure PCTCN2022131817-appb-000018
令上式等号右边项为m，则上式整理可得：
Figure PCTCN2022131817-appb-000019
同样针对五连杆机构G 1URE 4E 6，列出其矢量封闭方程：
Figure PCTCN2022131817-appb-000020
即：
Figure PCTCN2022131817-appb-000021
对α 7+β 3、
Figure PCTCN2022131817-appb-000022
求导，并整理可得：
Figure PCTCN2022131817-appb-000023
由于α 7为固定角，则δ α7＝0，根据同一构件角速度关系可得：
Figure PCTCN2022131817-appb-000024
令上式的等号右边项为n，则其可整理得：
Figure PCTCN2022131817-appb-000025
由于
Figure PCTCN2022131817-appb-000026
将
Figure PCTCN2022131817-appb-000027
和
Figure PCTCN2022131817-appb-000028
代入虚速度v PQ、v UR中，并整 理可得：
Figure PCTCN2022131817-appb-000029
式中，
Figure PCTCN2022131817-appb-000030
Figure PCTCN2022131817-appb-000031
Figure PCTCN2022131817-appb-000032
(5)计算弹簧s 1和s 2上的虚速度v s1、v s2。
根据夹持器的所述几何模型和静力学模型中结构件间几何关系，可以得出：
Figure PCTCN2022131817-appb-000033
所以弹簧s 1和s 2上的虚速度：
Figure PCTCN2022131817-appb-000034
式中，
Figure PCTCN2022131817-appb-000035
Figure PCTCN2022131817-appb-000036
计算夹持器接触力F＝[F 1 F 2 F 3] T。
根据同一构件角速度关系可得：
Figure PCTCN2022131817-appb-000037
再结合弹簧s 1和s 2上虚速度v s1和v s2，可以将上面的W写为矩阵相乘形式：W＝J ω[δ β1 δ β2 δ β3] T。
式中，
Figure PCTCN2022131817-appb-000038
将虚速度V F、W代入简化的虚功方程，可得：F TJ v＝T TJ ω。
则接触力为：
Figure PCTCN2022131817-appb-000039
式中，
Figure PCTCN2022131817-appb-000040
且
Figure PCTCN2022131817-appb-000041
Figure PCTCN2022131817-appb-000042
Figure PCTCN2022131817-appb-000043
鉴于弹簧s 1和s 2的驱动力T 2和T 3远小于夹持力F，所以将其忽略并获得夹持力F：
Figure PCTCN2022131817-appb-000044
进一步化简可得F：
Figure PCTCN2022131817-appb-000045
上式给出了接触力F＝[F 1 F 2 F 3] T与T 1之间的关系。由式可以看出，接触力F受β 1～β 3、
Figure PCTCN2022131817-appb-000046
等角度以及手指机构尺寸的影响。
二、夹持器结构参数优化方法，包括基于群体效应的免疫优化算法，所述基于群体效应的免疫进化算法是在基本免疫优化算法的算子(包括免疫选择算子O s、免疫交叉算子O c和免疫变异算子O m)基础上，根据群体效应设计了新的免疫集聚算子O g和免疫扩散算子O d进行算法优化提升。
已知第k代含有n个个体的种群A(k)＝[a 1(k),a 2(k),…,a n(k)]，则免疫选择算子O s可以描述为：
Figure PCTCN2022131817-appb-000047
免疫交叉算子O c可以描述为：
Figure PCTCN2022131817-appb-000048
Figure PCTCN2022131817-appb-000049
免疫变异算子O m可以描述为：
Figure PCTCN2022131817-appb-000050
Figure PCTCN2022131817-appb-000051
所述免疫集聚算子O g，主要是让种群中优势个体组成集聚种群对适应度差的劣势个体形成号召影响，进而提高劣势个体的性能。
设集聚数为m，集聚距离为l(l<n)，适应度差的劣势个体数为n，免疫集聚算子流程为：
(1)从免疫变异后种群A″′(k)中选择适应度最好的个体a*(k)；
(2)根据a*(k)生成与其集聚距离小于l的m个优势个体，并组成集聚种群
Figure PCTCN2022131817-appb-000052
Figure PCTCN2022131817-appb-000053
|a *-g i(k)|≤l，|·|表示汉明距离；
(3)从种群A″′(k)中选择z个适应度最差的个体，并组成劣势种群W(k)＝[w 1(k),w 2(k),…,w z(k)]；
(4)从W(k)中提取个体w i(k)(i∈[1，z])，将其与G(k)中个体分别进行异或操作，并得到G'(k)＝[g' 1(k),g' 2(k),…,g' m(k)]；
(5)提取G'(k)＝[g' 1(k),g' 2(k),…,g' m(k)]中最优个体与w i(k)比较，若前者优于后者则替换后者，否则保留后者；
(6)判断W(k)中所有个体是否都与G(k)中个体完成异或操作？若否，则转步骤(4)，否则退出。
免疫集聚算子O g可以描述为：
Figure PCTCN2022131817-appb-000054
所述免疫扩散算子O d，主要是让种群中高浓度个体进行扩散，以防止个体陷入局 部极小。
设扩散距离为r(r<n)，扩散数为s，免疫扩散算子流程为：
(1)从免疫集聚后种群A IV(k)中选取浓度最高的s个抗体，并组成扩散种群D(k)＝[d 1(k),d 2(k),…,d s(k)]；
(2)随机产生1个初始个体a 0(k)，且其元素为1的数量大于r并小于等于n；
(3)从D(k)中取出个体d i(k)(i∈[1，s])与个体a 0(k)进行异或操作，并得到新个体d i'(k)；
(4)将个体d i(k)与d i'(k)进行对比，若后者优于前者则替换前者，否则保留前者；
(5)判断D(k)中所有抗体是否都与a 0(k)完成异或操作？若否，则转步骤(3)，否则退出。
免疫扩散算子O d可以描述为：
Figure PCTCN2022131817-appb-000055
三、夹持器结构参数优化流程，包括以下内容与步骤：
(1)基于夹持器夹持力F，并以夹持时接触力尽可能分布均匀且相等为目标，建立夹持器稳定夹持状态下参数优化的目标函数：
min f(X)＝min((F 1-F 2) 2+(F 1-F 3) 2+(F 2-F 3) 2)。
式中，X为夹持器结构参数变量集且
Figure PCTCN2022131817-appb-000056
Figure PCTCN2022131817-appb-000057
(2)设定夹持器参数变量集X的约束范围；
(3)初始化基于群体效应的免疫优化算法参数，及初始种群A(k)＝[a 1(k),a 2(k),…,a n(k)]，k←0；
(4)免疫选择：A′(k)←O s(A(k))＝[a′ 1(k),a′ 2(k),…,a′ n(k)]；
(5)免疫交叉：A″(k)←O c(A′(k))＝[a″ 1(k),a″ 2(k),…,a″ n(k)]；
(6)免疫变异：A″′(k)←O m(A″(k))＝[a″′ 1(k),a″′ 2(k),…,a″′ n(k)]；
(7)免疫集聚：
Figure PCTCN2022131817-appb-000058
(8)免疫扩散：
Figure PCTCN2022131817-appb-000059
(9)终止条件判定。进化代数k是否达到最大代数？若是，则算法终止，并输出最优变量X *；否则k←k+1，并返回步骤(4)。
本发明具有以下优点和有益效果：
1.与现有形式单一的机器人专用夹具相比，本发明基于欠秩原理而设计的新型夹持器，能够实现对不同尺径的圆盘工件自适应包络夹持，大大改善了因工件尺寸发生变化而更换专用夹具造成劳动量大、生产效率低的问题。
2.该夹持器能够自下而上地限制工件自由度，夹紧力大，并具备自锁能力，有效避免了因工件自身较重而发生滑落的风险，大大提高了夹持的稳定性、牢靠性和定位精度，有效降低了安全事故的发生。
3、该夹持器是基于欠驱动原理设计的，只存在一个动力源，大大降低了控制任务的难度，缩短了产品的整个设计周期。
4、提出了一种新的基于群体效应的免疫优化算法。基于群体效应中集聚行为设计 了免疫集聚算子，通过群体优秀个体对劣势个体的号召来提高算法的局部搜索能力；基于群体效应中的扩散行为设计了免疫扩散算子，通过对高浓度个体扩散来有效避免算法陷入局部极小。
5、自锁式欠驱动夹持器的工件夹持稳定性取决于夹持器本身的结构参数，但其是一个多参数结构，且参数存在多约束。若基于人工经验进行试凑设计，不仅费时费力而且无法获得最佳结构参数。在建立夹持器接触力模型基础上，利用基于群体效应的免疫优化算法可以实现夹持器参数的全局优化，提高了优化效率和优化精度。
附图说明
图1：本发明实施例中夹持器的总体结构图；
图2：本发明实施例中夹持器的驱动机构结构图；
图3：本发明实施例中夹持器的首指节组件整体结构图；
图4：本发明实施例中夹持器的首指节组件局部结构图；
图5：本发明实施例中夹持器的首指节导向件和夹持块组合体结构图；
图6：本发明实施例中夹持器的首指节L型杆；
图7：本发明实施例中夹持器的首指节曲杆；
图8：本发明实施例中夹持器的中指节三角架；
图9：本发明实施例中夹持器的中指节组件和末指节组件结构图；
图10：本发明实施例中夹持器的中指节导向件和夹持块组合体结构图；
图11：本发明实施例中夹持器的末指节夹持块结构图；
图12：本发明实施例中夹持器抓取圆盘工件前示意图；
图13：本发明实施例中夹持器包络抓取圆盘工件后示意图；
图14：本发明实施例中自锁式欠驱动夹持器的几何模型图；
图15：本发明实施例中自锁式欠驱动夹持器的静力学模型图；
图中的附图标记为：1.驱动机构；2.首指节组件；3.中指节组件；4.末指节组件；5.气缸体；6.气动滑块；7.传动滑块；8.驱动连杆；9.首指节传动连杆；10.支撑臂；11.首指节框架；12.首指节下导向件；13.首指节上导向件；14.首指节L型杆；15.中指节三角架；16.第一工字件；17.第二工字件；18.第一导向管；19.第一弹簧；20.首指节下压簧杆；21.第一销轴；22.首指节夹持块；23.第三工字件；24.第四工字件；25.第二导向管；26.第二弹簧；27.首指节上压簧杆；28.首指节曲杆；29.中指节传动连杆；30.中指节框架；31.中指节下导向件；32.中指节上导向件；33.中指节T型杆；34.第五工字件；35.第六工字件；36.第三导向管；37.第三弹簧；38.中指节下压簧杆；39.第二销轴；40.中指节夹持块；41.第七工字件；42.第八工字件；43.第四导向管；44.第四弹簧；45.中指节上压簧杆；46.中指节曲杆；47.末指节传动连杆；48.末指节夹持块；49.圆盘工件。
具体实施方式
为使本发明的目的和技术方案更加清楚，下面将结合本发明实施例的附图，对本发明实施例的技术方案进行清楚、完整地描述。显然，所描述的实施例是本发明的一部分实施例，而不是全部的实施例。基于所描述的本发明的实施例，本领域普通技术人员在无需创 造性劳动的前提下所获得的所有其他实施例，都属于本发明保护的范围。
本发明所述的“前、后”的含义指的是阅读者正对附图时，由视图纸面指向阅读者为前，指向纸面里为后，而非对本发明的夹持器装置的特定限定。
本发明所述的“左、右”的含义指的是阅读者正对附图时，由视图纸面的左边为左，纸面的右边为右，而非对本发明的夹持器装置的特定限定。
本发明所述的“上、下”的含义指的是阅读者正对附图时，由视图纸面的上边为上，纸面的右边为右，为而非对本发明的夹持器装置的特定限定。
如图1所示，本发明的一种自锁式欠驱动夹持器，包括驱动机构1，所述驱动机构1的上部连接着左右对称且结构相同的首指节组件2，所述首指节组件2上部连接着左右对称且结构相同的中指节组件3，所述中指节组件3上部连接着左右对称且结构相同的末指节组件4。
如图1和2所示，本发明的一种自锁式欠驱动夹持器的驱动机构1，包括气缸体5，所述气缸体5上端安装着左右对称且结构完全相同的气动滑块6，所述气动滑块6上端部通过螺栓固定连接着传动滑块7，所述传动滑块7上转动连接着驱动连杆8的下端，所述驱动连杆8的上端转动连接着首指节传动连杆9的下端，所述气缸体5的后端对应传动滑块7固定设置有左右对称且结构完全相同的支撑臂10，所述首指节传动连杆9的上端转动连接着支撑臂10上端的转轴。通过驱动气动滑块6的左右移动，就可实现首指节传动连杆9绕支撑臂10上端转轴进行逆时针或顺时针转动，从而带动首指节组件2的转动。
如图1，3，4，5，6和7所示，本发明的一种自锁式欠驱动夹持器的首指节组件2，包括首指节框架11，所述首指节框架11的左右竖边框各采用前后对称相同的两根杆结构，所述首指节框架11的下边框的中间转动连接着支撑臂10上端的转轴，所述首指节框架11通过螺栓从下到上依次夹持固定着首指节下导向件12、首指节上导向件13和首指节L型杆14，所述首指节L型杆14的上端旋转连接在中指节三角架15弧形处的左端，所述首指节下导向件12包括相互平行的第一工字件16和第二工字件17，所述第一工字件16和第二工字件17分别固定在首指节框架11的左边框间和右边框间，所述第一工字件16和第二工字件17间夹持固定着左端口封闭右端口导通的第一导向管18，所述第一导向管18内装有第一弹簧19，所述第一弹簧19的右端支撑在首指节下压簧杆20左端部，所述首指节下压簧杆20的左端上还固定着与其轴线垂直的第一销轴21，所述第一销轴21可以在第一导向管18沿轴向所开槽内左右移动，所述首指节下压簧杆20的右端固定在首指节夹持块22的左下部，所述首指节上导向件13包括相互平行的第三工字件23和第四工字件24，所述第三工字件23和第四工字件24同样分别固定在首指节框架11的左边框间和右边框间，所述第三工字件23和第四工字件24间夹持固定着左端口封闭右端口导通的第二导向管25，所述第二导向管25内装有第二弹簧26，所述第二弹簧26的右端支撑在首指节上压簧杆27左端部，所述首指节上压簧杆27的右端固定在首指节夹持块22的左上部，所述首指节下压簧杆20和首指节上压簧杆27共同支撑着首指节夹持块22，所述首指节夹持块22为包括安装面和夹持面的凹形结构件，且凹部内侧为弧形状，以便更好地贴合工件的轮廓，所述首指节框架11中间横杆上与首指节曲杆28的转折处转动连接，所述首指节曲杆28下端槽口内嵌着且能沿槽滑动的第一销轴21，所述首指节曲杆28的上端转动连接着中指节传动连杆29的下端，从而将首指节夹持块22的左右移动转化成首指节曲杆28的转动，为下一级中指节组件3提供动力。在夹持工件前，在第 一弹簧19和第二弹簧26的自身弹力作用下，一方面首指节夹持块22被推动向右移动，另一方面随着首指节下压簧杆20向右带动第一销轴21向右移动，进而推动首指节曲杆28绕着中间转折处逆时针旋转，并通过与首指节曲杆28的上端转动连接的中指节传动连杆29将动力传递给中指节组件3上。当开始夹持工件时，随着与工件接触，首指节夹持块22被压，从而推动首指节下压簧杆20和首指节上压簧杆27左移，同时首指节曲杆28在第一销轴21左移带动下实现绕转折处顺时针转动，并通过中指节传动连杆29带动中指节组件3转动。
如图1，5，8，9，10和11所示，本发明的一种自锁式欠驱动夹持器的中指节组件3，包括中指节框架30，所述中指节框架30的左右竖边框同样各采用前后对称相同的两根杆结构，所述中指节框架30通过螺栓从下到上依次夹持固定装有中指节三角架15、中指节下导向件31、中指节上导向件32和中指节T型杆33，所述中指节三角架15弧形处的右端转动连接着中指节传动连杆29的上端，所述中指节下导向件31和首指节下导向件12结构一样，包括第五工字件34、第六工字件35、第三导向管36、第三弹簧37、中指节下压簧杆38和第二销轴39，所述中指节下压簧杆38的右端固定在中指节夹持块40的左下部，所述中指节上导向件32和首指节上导向件13结构一样，包括第七工字件41、第八工字件42、第四导向管43、第四弹簧44和中指节上压簧杆45，所述中指节上压簧杆45的右端固定在中指节夹持块40的左上部，所述中指节下压簧杆38和中指节上压簧杆45共同支撑着中指节夹持块40，所述中指节夹持块40为包括安装面和夹持面的凹形结构件，且凹部内侧为弧形状，以便更好地贴合工件的轮廓，所述中指节框架30中间横杆上与中指节曲杆46的转折处转动连接，所述中指节曲杆46下端槽口内嵌着且能沿槽滑动的第二销轴39，所述中指节曲杆46的上端转动连接着末指节传动连杆47的下端，从而将中指节夹持块40的左右移动转化成中指节曲杆46的转动，为下一级末指节组件4提供动力。与首指节组件2工作类似，在夹持工件前，在第三弹簧37和第四弹簧44的自身弹力作用下，一方面中指节夹持块40被推动向右移动，另一方面中指节曲杆46被中指节下压簧杆38上的第二销轴39带动而绕其中间转折处逆时针旋转，并通过与中指节曲杆46的上端转动连接的末指节传动连杆47将动力传递给末指节组件4上。当开始夹持工件时，随着与工件接触，中指节夹持块40被压，从而推动中指节下压簧杆38和中指节上压簧杆45左移，同时中指节曲杆46在第二销轴39左移带动下实现绕转折处顺时针转动，并通过末指节传动连杆47带动末指节组件4转动。
本发明的一种自锁式欠驱动夹持器的末指节组件4，包括末指节夹持块48，所述末指节夹持块48的左下端转动连接着中指节T型杆33的上端，所述末指节夹持块48的右下端转动连接着末指节传动连杆47的上端，通过末指节传动连杆47将中指节组件3的动力传递到末指节夹持块48上，使得末指节夹持块48绕中指节T型杆33上端转动。夹持工件前，逆时针转动远离工件，夹持工件时，顺时针转动靠近工件。所述末指节夹持块48为包括安装端和夹持端的刀形结构件，用于安装的刀柄部设有两个连接孔，用于夹持的刀片部为凹形结构，且凹部内侧为弧形状，以便更好的贴合工件的轮廓。
本发明的一种自锁式欠驱动夹持器的末指节组件4，包括末指节夹持块48，所述末指节夹持块48的右下端转动连接着末指节传动连杆47的上端，所述末指节夹持块48的左下端转动连接着中指节T型杆33的上端，通过末指节传动连杆47将中指节组件3的动力传递到末指节夹持块48上，使得末指节夹持块48绕中指节T型杆33上端转动，夹持工件前，末指节夹持块48逆时针转动远离工件，夹持工件时，末指节夹持块48顺时针转动靠近工件，所述末 指节夹持块48为包括安装端和夹持端的刀形结构件，用于安装的刀柄部设有两个连接孔，用于夹持的刀片部为凹形结构，且凹部内侧为弧形状，以便更好地贴合工件的轮廓。
如图1、2、4、5、9、10、12和13所示，夹持圆盘工件49前，依靠首指节组件2中的第一弹簧19和第二弹簧26，以及中指节组件3中的第三弹簧37和第四弹簧44的自身弹力，使得首指节组件2、中指节组件3和末指节组件4处于张开状态；当夹持圆盘工件49时，驱动气动滑块6来带动首指节组件2运动，首指节夹持块22接触圆盘工件49，首指节下压簧杆20向左移动，通过第一销轴21带动首指节曲杆28绕转折处顺时针转动，通过中指节传动连杆29带动中指节组件3绕首指节L型杆14的上端顺时针转动，使得中指节夹持块40接触圆盘工件49，中指节下压簧杆38向左移动，通过第二销轴39带动中指节曲杆46绕转折处顺时针转动，通过末指节传动连杆47带动末指节组件4绕中指节T型杆33上端顺时针转动，使得末指节夹持块48接触圆盘工件49，实现了夹持器的自适应包络抓取工件。而此时首指节夹持块22、中指节夹持块40及末指节夹持块48与圆盘工件49紧密接触，使得第一弹簧19、第二弹簧26、第三弹簧37和第四弹簧44不受外力停止压缩且伸长受工件阻碍不会继续产生形变，实现了夹持器的自锁。通过一个动力源气动滑块6驱动首指节组件2、中指节组件3和末指节组件4的连动，实现了基于欠秩机构原理的欠驱动。图12给出了气动滑块6位于气缸外侧时，首指节组件2、中指节组件3和末指节组件4全张开的状态。图13给出了气动滑块6位于气缸内侧时，首指节组件2、中指节组件3和末指节组件4完全自适应包络抓取圆盘工件49的状态。
如图14和图15所示，为本发明的一种自锁式欠驱动夹持器的结构优化方法，包括夹持器夹持接触力模型建立、夹持器结构参数优化方法和夹持器结构参数优化流程；
一、夹持器夹持接触力模型建立，包括如下内容和步骤：
(1)根据夹持器结构建立几何模型和静力学模型；
鉴于自锁式欠驱动夹持器呈左右对称结构，以左边三指节为例进行模型建立和结构优化。所述几何模型主要是将所述驱动机构1中的所述驱动连杆8等效为AB杆，将所述首指节传动连杆9等效为BC 2杆，将所述首指节框架11等效为C 1C 3C 4E 1四边形,将所述首指节曲杆28等效为QD 2D 3折杆，将所述首指节框架11中间横杆的左端到首指节曲杆28转折处的部分等效为D 1D 2杆，将所述中指节传动连杆29等效为QP杆，将所述中指节框架30等效为E 1E 2E 5G 1四边形，将所述中指节曲杆46等效为RE 4E 3折杆，将所述中指节框架30中间横杆的左端到中指节曲杆46转折处的部分等效为E 6E 4杆，将所述末指节传动连杆47等效为RU，将所述末指节夹持块48等效为G 1G 2G 3G 4四边形，由于第一弹簧19和第二弹簧26同步拉伸和压缩，且变形量一样，在模型计算时将两者受力等效到弹簧D 4D 3上，且用s 1表示弹簧D 4D 3；同理将第三弹簧37和第四弹簧44受力等效到弹簧E 7E 3上，且用s 2表示弹簧E 7E 3；定义杆C 1C 3、D 1D 2、E 1E 2、G 1U和E 6E 4的长度分别为a 1、a 2、a 3、a 4和a 5；定义杆E 1B、G 1E 1、G 1G 4、D 1B和E 1E 6的长度为d 1、d 2、d 3、d 4和d 5；定义杆D 2D 3、D 2Q、PQ、E 3E 4、E 4R和RU的长度为l 1、l 2、l 3、l 4、l 5和l 6；
所述静力学模型主要是定义所述驱动机构1的力矩为T 1，定义所述弹簧s 1和s 2的驱动力分别为T 2和T 3；定义所述首指节组件2、中指节组件3和末指节组件4夹持物体的接触力分别为F 1、F 2和F 3；定义C 1点距F 1力的距离为h 1，定义E 1点距F 2力的距离为h 2，定义G 1点距F 3力的距离为h 3；定义杆E 2P与杆QP的夹角，杆PQ与杆D 2Q的夹角，杆G 2U与杆RU的夹角，杆UR与杆E 4R的夹角，杆C 4E 1与杆C 1E 1的夹角分别为α 1、α 2、α 3、α 4、α 5；定义杆E 1C 1与水平反向线的夹角，杆G 1E 1与杆C 1E 1反向延长线的夹角，杆G 4G 1与杆E 1G 1反向延长线的夹角分别为β 1、β 2、β 3；定义 杆C 3C 1与水平线的夹角，杆PE 1与水平线的夹角，杆UG 1与水平线的夹角分别为
Figure PCTCN2022131817-appb-000060
(2)基于虚功原理建立夹持器各指节虚功方程：
Figure PCTCN2022131817-appb-000061
式中，
Figure PCTCN2022131817-appb-000062
为力矩T 1作用于首指节上的虚角速度，v s1、v s2分别为弹簧s 1和s 2上的虚速度；v F1、v F2、v F3分别为接触力F 1、F 2、F 3在接触点处的虚速度。
令T＝[T 1 F 1+T 2 F 2+T 3] T，F＝[F 1 F 2 F 3] T，
Figure PCTCN2022131817-appb-000063
V F＝[v F1 v F2 v F3] T，虚功方程可以简化为：F TV F＝T TW。
(3)基于刚体速度公式建立夹持器各指节虚速度V F＝[v F1 v F2 v F3] T为：
Figure PCTCN2022131817-appb-000064
式中，
Figure PCTCN2022131817-appb-000065
δ β1、δ β2、δ β3分别为转角β 1、β 2和β 3的角速度。
将虚速度V F写成矩阵形式：V F＝J v[δ β1δ β2δ β3] T。
式中，
Figure PCTCN2022131817-appb-000066
(4)由于所述中指节传动连杆29(PQ)和末指节传动连杆47(UR)都对所在指节组件有直接作用力，计算两杆的虚速度v PQ、v UR：
Figure PCTCN2022131817-appb-000067
因为，
Figure PCTCN2022131817-appb-000068
Figure PCTCN2022131817-appb-000069
Figure PCTCN2022131817-appb-000070
Figure PCTCN2022131817-appb-000071
所以，所述中指节传动连杆29(PQ)和末指节传动连杆47(UR)的虚速度v PQ、v UR为：
Figure PCTCN2022131817-appb-000072
针对五连杆机构E 1PQD 2D 1，以E 1D 1为x轴正方向，指向圆盘工件方向为y轴正方向，列出其矢量封闭方程：
Figure PCTCN2022131817-appb-000073
将其分解为x、y方向：
Figure PCTCN2022131817-appb-000074
对α 6+β 2、
Figure PCTCN2022131817-appb-000075
求导：
Figure PCTCN2022131817-appb-000076
因为α 6为固定角，所以δ α6＝0。根据同一构件角速度关系可得：
Figure PCTCN2022131817-appb-000077
令上式等号右边项为m，则上式整理可得：
Figure PCTCN2022131817-appb-000078
同样针对五连杆机构G 1URE 4E 6，列出其矢量封闭方程：
Figure PCTCN2022131817-appb-000079
即：
Figure PCTCN2022131817-appb-000080
对α 7+β 3、
Figure PCTCN2022131817-appb-000081
求导，并整理可得：
Figure PCTCN2022131817-appb-000082
由于α 7为固定角，则δ α7＝0，根据同一构件角速度关系可得：
Figure PCTCN2022131817-appb-000083
令上式的等号右边项为n，则其可整理得：
Figure PCTCN2022131817-appb-000084
由于
Figure PCTCN2022131817-appb-000085
将
Figure PCTCN2022131817-appb-000086
和
Figure PCTCN2022131817-appb-000087
代入虚速度v PQ、v UR中，并整理可得：
Figure PCTCN2022131817-appb-000088
式中，
Figure PCTCN2022131817-appb-000089
Figure PCTCN2022131817-appb-000090
Figure PCTCN2022131817-appb-000091
(5)计算弹簧s 1和s 2上的虚速度v s1、v s2。
根据夹持器的所述几何模型和静力学模型中结构件间几何关系，可以得出：
Figure PCTCN2022131817-appb-000092
所以弹簧s 1和s 2上的虚速度：
Figure PCTCN2022131817-appb-000093
式中，
Figure PCTCN2022131817-appb-000094
Figure PCTCN2022131817-appb-000095
(6)计算夹持器接触力F＝[F 1F 2F 3] T。
根据同一构件角速度关系可得：
Figure PCTCN2022131817-appb-000096
再结合弹簧s 1和s 2上虚速度v s1和v s2，可以将上面的W写为矩阵相乘形式：W＝J ω[δ β1 δ β2 δ β3] T。
式中，
Figure PCTCN2022131817-appb-000097
将虚速度V F、W代入简化的虚功方程，可得：F TJ v＝T TJ ω。
则接触力为：
Figure PCTCN2022131817-appb-000098
式中，
Figure PCTCN2022131817-appb-000099
且
Figure PCTCN2022131817-appb-000100
Figure PCTCN2022131817-appb-000101
Figure PCTCN2022131817-appb-000102
鉴于弹簧s 1和s 2的驱动力T 2和T 3远小于夹持力F，所以将其忽略并获得夹持力F：
Figure PCTCN2022131817-appb-000103
进一步化简可得F：
Figure PCTCN2022131817-appb-000104
上式给出了接触力F＝[F 1 F 2 F 3] T与T 1之间的关系。由式可以看出，接触力F受β 1～β 3、
Figure PCTCN2022131817-appb-000105
等角度以及手指机构尺寸的影响。
二、夹持器结构参数优化方法，包括基于群体效应的免疫优化算法，所述基于群体效应的免疫进化算法是在基本免疫优化算法的算子(包括免疫选择算子O s、免疫交叉算子O c和免疫变异算子O m)基础上，根据群体效应设计了新的免疫集聚算子O g和免疫扩散算子O d进行算法优化提升。
基本免疫算法虽然具有分布式、全局优化能力，但是在面向多变量优化时也存在局部搜索能力有效，以及容易陷入局部的不足。由上述夹持器的接触力模型可以看出，该结构待优化变量会有10个左右，因此对算法的优化能力提出了更高的要求。为此，本发明借鉴了社会发展中的群体效应，即个体在面向群体时，其行为会在群体影响下发生变化，比如基于向心力的集聚行为和基于竞争的扩散行为。
已知第k代含有n个个体的种群A(k)＝[a 1(k),a 2(k),…,a n(k)]，则免疫选择算子O s可以描述为：
Figure PCTCN2022131817-appb-000106
免疫交叉算子O c可以描述为：
Figure PCTCN2022131817-appb-000107
Figure PCTCN2022131817-appb-000108
免疫变异算子O m可以描述为：
Figure PCTCN2022131817-appb-000109
Figure PCTCN2022131817-appb-000110
所述免疫集聚算子O g，主要是让种群中优势个体组成集聚种群对适应度差的劣势个体形成号召影响，进而提高劣势个体的性能。
设集聚数为m，集聚距离为l(l<n)，适应度差的劣势个体数为n，免疫集聚算子流程为：
(1)从免疫变异后种群A″′(k)中选择适应度最好的个体a*(k)；
(2)根据a*(k)生成与其集聚距离小于l的m个优势个体，并组成集聚种群
Figure PCTCN2022131817-appb-000111
Figure PCTCN2022131817-appb-000112
|a *-g i(k)|≤l，|·|表示汉明距离；
(3)从种群A″′(k)中选择z个适应度最差的个体，并组成劣势种群W(k)＝[w 1(k),w 2(k),…,w z(k)]；
(4)从W(k)中提取个体w i(k)(i∈[1，z])，将其与G(k)中个体分别进行异或操作，并得到G'(k)＝[g' 1(k),g' 2(k),…,g' m(k)]；
(5)提取G'(k)＝[g' 1(k),g' 2(k),…,g' m(k)]中最优个体与w i(k)比较，若前者优于后者则替换后者，否则保留后者；
(6)判断W(k)中所有个体是否都与G(k)中个体完成异或操作？若否，则转步骤(4)，否则退出。
免疫集聚算子O g可以描述为：
Figure PCTCN2022131817-appb-000113
所述免疫扩散算子O d，主要是让种群中高浓度个体进行扩散，以防止个体陷入局部极小。
设扩散距离为r(r<n)，扩散数为s，免疫扩散算子流程为：
(1)从免疫集聚后种群A IV(k)中选取浓度最高的s个抗体，并组成扩散种群D(k)＝[d 1(k),d 2(k),…,d s(k)]；
(2)随机产生1个初始个体a 0(k)，且其元素为1的数量大于r并小于等于n；
(3)从D(k)中取出个体d i(k)(i∈[1，s])与个体a 0(k)进行异或操作，并得到新个体d i'(k)；
(4)将个体d i(k)与d i'(k)进行对比，若后者优于前者则替换前者，否则保留前者；
(5)判断D(k)中所有抗体是否都与a 0(k)完成异或操作？若否，则转步骤(3)，否则退出。
免疫扩散算子O d可以描述为：
Figure PCTCN2022131817-appb-000114
三、夹持器结构参数优化流程，包括以下内容与步骤：
(1)基于夹持器夹持力F，并以夹持时接触力尽可能分布均匀且相等为目标，建立夹持器稳定夹持状态下参数优化的目标函数：
minf(X)＝min((F 1-F 2) 2+(F 1-F 3) 2+(F 2-F 3) 2)。
式中，X为夹持器结构参数变量集且
Figure PCTCN2022131817-appb-000115
Figure PCTCN2022131817-appb-000116
(2)设定夹持器参数变量集X的约束范围；
(3)初始化基于群体效应的免疫优化算法参数，及初始种群A(k)＝[a 1(k),a 2(k),…,a n(k)]，k←0；
(4)免疫选择：A′(k)←O s(A(k))＝[a′ 1(k),a′ 2(k),…,a′ n(k)]；
(5)免疫交叉：A″(k)←O c(A′(k))＝[a″ 1(k),a″ 2(k),…,a″ n(k)]；
(6)免疫变异：A″′(k)←O m(A″(k))＝[a″′ 1(k),a″′ 2(k),…,a″′ n(k)]；
(7)免疫集聚：
Figure PCTCN2022131817-appb-000117
(8)免疫扩散：
Figure PCTCN2022131817-appb-000118
(9)终止条件判定。进化代数k是否达到最大代数？若是，则算法终止，并输出最优变量X *；否则k←k+1，并返回步骤(4)。
以抓取最小直径70mm的圆形工件为例，针对自锁式欠驱动夹持器结构，分别采用经验法、Fmincon法、遗传算法(Genetic Algorithm,GA)和本发明中基于群体效应的免疫优化算法(Immune Optimization Algorithm Based on Population Effect,IOABOPE)进行了设计。表一给出了设计数据，由表可以看出，相比起经验法，三种优化方法(Fmincon、GA和IOABOPE)的目标函数值要远小于经验法，三种算法的各自三个接触力的差异性也比经验法小，体现了优化方法在多变量结构设计中的重要性。在三种优化方法中，具有分布式和全局优化能力的GA和IOABOPE，无论是目标函数值还是接触力的差异性方面都优于Fmincon，这主要是Fmincon是一种局部优化方法，对于多变量优化不具有优势。与GA相比，本发明的IOABOPE无疑是最优的，不仅目标函数值最小，且三个接触力比较接近，这主要得益于免疫集聚算子提高了算法的局部优化能力，而免疫扩散算子避免了算法过早陷入局部极小，切实提高了算法的优化效果，从而也验证了本发明所提出优化方法的有效性和优越性。
表一：
Figure PCTCN2022131817-appb-000119
上述仅为本发明的优选实施例而已，并不对本发明起到任何限制作用。任何所属技术领域的技术人员，在不脱离本发明的技术方案的范围内，对本发明揭露的技术方案和技术内容做任何形式的等同替换或修改等变动，均属未脱离本发明的技术方案的内容，仍属于本发明的保护范围之内。

Claims (6)

  1. 一种自锁式欠驱动夹持器，包括驱动机构(1)，其特征在于，所述驱动机构(1)的上端面安装着镜像对称设置的夹持机构，所述夹持机构自下而上由首指节组件(2)、中指节组件(3)和末指节组件(4)相连构成；其中，
    所述的驱动机构(1)包括气缸体(5)，所述气缸体(5)上端面左右隔离安装有镜像对称的气动滑块(6)，所述气动滑块(6)上通过螺栓固定连接有传动滑块(7)，所述传动滑块(7)上方转动连接着驱动连杆(8)的下端，所述驱动连杆(8)的上端转动连接着首指节传动连杆(9)的下端，所述气缸体(5)的后端对应传动滑块(7)固定设置有镜像对称的支撑臂(10)，所述首指节传动连杆(9)的上端与支撑臂(10)上端的转轴转动连接；
    所述首指节组件(2)包括首指节框架(11)，所述首指节框架(11)的下边框的中间转动连接着支撑臂(10)上端的转轴，所述首指节框架(11)通过螺栓从下到上依次夹持固定着首指节下导向件(12)、首指节上导向件(13)和首指节L型杆(14)，所述首指节L型杆(14)的上端旋转连接在中指节三角架(15)弧形处的左端，所述首指节下导向件(12)包括相互平行的第一工字件(16)和第二工字件(17)，所述第一工字件(16)和第二工字件(17)分别固定在首指节框架(11)的左边框间和右边框间，所述第一工字件(16)和第二工字件(17)间夹持固定着左端口封闭右端口导通的第一导向管(18)，所述第一导向管(18)内装有第一弹簧(19)，所述第一弹簧(19)的右端支撑在首指节下压簧杆(20)左端部，所述首指节下压簧杆(20)的左端上还固定着与其轴线垂直的第一销轴(21)，所述第一销轴(21)在第一导向管(18)沿轴向所开槽内左右移动，所述首指节下压簧杆(20)的右端固定在首指节夹持块(22)的左下部，所述首指节上导向件(13)包括相互平行的第三工字件(23)和第四工字件(24)，所述第三工字件(23)和第四工字件(24)同样分别固定在首指节框架(11)的左边框间和右边框间，所述第三工字件(23)和第四工字件(24)间夹持固定着左端口封闭右端口导通的第二导向管(25)，所述第二导向管(25)内装有第二弹簧(26)，所述第二弹簧(26)的右端支撑在首指节上压簧杆(27)左端部，所述首指节上压簧杆(27)的右端固定在首指节夹持块(22)的左上部，所述首指节下压簧杆(20)和首指节上压簧杆(27)共同支撑着首指节夹持块(22)，所述首指节框架(11)中间横杆上与首指节曲杆(28)的转折处转动连接，所述首指节曲杆(28)下端槽口内嵌着且能沿槽滑动的第一销轴(21)，所述首指节曲杆(28)的上端转动连接着中指节传动连杆(29)的下端；
    所述中指节组件(3)包括中指节框架(30)，所述中指节框架(30)通过螺栓从下到上依次夹持固定装有中指节三角架(15)、中指节下导向件(31)、中指节上导向件(32)和中指节T型杆(33)，所述中指节三角架(15)弧形处的右端转动连接着中指节传动连杆(29)的上端，所述中指节下导向件(31)和首指节下导向件(12)结构一样，包括第五工字件(34)、第六工字件(35)、第三导向管(36)、第三弹簧(37)、中指节下压簧杆(38)和第二销轴(39)，所述中指节下压簧杆(38)的右端固定在中指节夹持块(40)的左下部，所述中指节上导向件(32)和首指节上导向件(13)结构一样，包括第七工字件(41)、第八工字件(42)、第四导向管(43)、第四弹簧(44)和中指节上压簧杆(45)，所述中指节上压簧杆(45)的右端固定在中指节夹持块(40)的左上部，所述中指节下压簧杆(38)和中指节上压簧杆(45)共同支撑着中指节夹持块(40)，所述中指节框架(30)中间横杆上与中指节曲杆(46)的转折处转动连接，所述中指节曲杆(46)下端槽口内嵌着且能沿槽滑动的第二销轴(39)，所述中指节曲杆(46)的上端转动连接着末指节传动连杆(47)的下端；
    所述末指节组件(4)包括末指节夹持块(48)，所述末指节夹持块(48)的右下端转动连接着末指节传动连杆(47)的上端，所述末指节夹持块(48)的左下端转动连接着中指节T型杆(33)的上端；
    所述末指节组件(4)，包括末指节夹持块(48)，所述末指节夹持块(48)的左下端转动连接着中指节T型杆(33)的上端，所述末指节夹持块(48)的右下端转动连接着末指节传动连杆(47)的上端。
  2. 如权利要求1所述的一种自锁式欠驱动夹持器，其特征在于：所述首指节夹持块(22)为包括安装面和夹持面的凹形结构件，且凹部内侧为弧形状。
  3. 如权利要求1所述的一种自锁式欠驱动夹持器，其特征在于：所述中指节夹持块(40)为包括安装面和夹持面的凹形结构件，且凹部内侧为弧形状。
  4. 如权利要求1所述的一种自锁式欠驱动夹持器，其特征在于：所述末指节夹持块(48)为包括安装端和夹持端的刀形结构件，用于安装的刀柄部设有两个连接孔，用于夹持的刀片部为凹形结构，且凹部内侧为弧形状。
  5. 如权利要求1所述的一种自锁式欠驱动夹持器，其特征在于：所述首指节夹持块(22)，所述中指节夹持块(40)和所述末指节夹持块(48)的夹持面上均设置有防冲击、防滑层。
  6. 一种如权利要求1至5任意一项所速的一种自锁式欠驱动夹持器的结构优化方法，其特征在于：包括夹持器夹持接触力模型建立、夹持器结构参数优化方法和夹持器结构参数优化流程，
    一、所述夹持器夹持接触力模型建立，包括以下内容和步骤：
    (1)根据夹持器结构建立几何模型和静力学模型；
    鉴于自锁式欠驱动夹持器呈左右对称结构，以左边三指节为例进行模型建立和结构优化；所述建立几何模型是将所述驱动机构(1)中的所述驱动连杆(8)等效为AB杆，将所述首指节传动连杆(9)等效为BC 2杆，将所述首指节框架(11)等效为C 1C 3C 4E 1四边形，将所述首指节曲杆(28)等效为QD 2D 3折杆，将所述首指节框架(11)中间横杆的左端到首指节曲杆(28)转折处的部分等效为D 1D 2杆，将所述中指节传动连杆(29)等效为QP杆，将所述中指节框架(30)等效为E 1E 2E 5G 1四边形，将所述中指节曲杆(46)等效为RE 4E 3折杆，将所述中指节框架(30)中间横杆的左端到中指节曲杆(46)转折处的部分等效为E 6E 4杆，将所述末指节传动连杆(47)等效为RU，将所述末指节夹持块(48)等效为G 1G 2G 3G 4四边形，由于第一弹簧(19)和第二弹簧(26)同步拉伸和压缩，且变形量一样，在模型计算时将两者受力等效到弹簧D 4D 3上，且用s 1表示弹簧D 4D 3；同理将第三弹簧(37)和第四弹簧(44)受力等效到弹簧E 7E 3上，且用s 2表示弹簧E 7E 3；定义杆C 1C 3、D 1D 2、E 1E 2、G 1U和E 6E 4的长度分别为a 1、a 2、a 3、a 4和a 5；定义杆E 1B、G 1E 1、G 1G 4、D 1B和E 1E 6的长度为d 1、d 2、d 3、d 4和d 5；定义杆D 2D 3、D 2Q、PQ、E 3E 4、E 4R和RU的长度为l 1、l 2、l 3、l 4、l 5和l 6；
    所述建立静力学模型是定义所述驱动机构(1)的力矩为T 1，定义所述弹簧s 1和s 2的驱动力分别为T 2和T 3；定义所述首指节组件(2)、中指节组件(3)和末指节组件(4)夹持物体的接触力分别为F 1、F 2和F 3；定义C 1点距F 1力的距离为h 1，定义E 1点距F 2力的距离为h 2，定义G 1点距F 3力的距离为h 3；定义杆E 2P与杆QP的夹角，杆PQ与杆D 2Q的夹角，杆G 2U与杆RU的夹角，杆UR与杆E 4R的夹角，杆C 4E 1与杆C 1E 1的夹角分别为α 1、α 2、α 3、α 4、α 5；定义杆E 1C 1与水平反向线的夹 角，杆G 1E 1与杆C 1E 1反向延长线的夹角，杆G 4G 1与杆E 1G 1反向延长线的夹角分别为β 1、β 2、β 3；定义杆C 3C 1与水平线的夹角，杆PE 1与水平线的夹角，杆UG 1与水平线的夹角分别为
    Figure PCTCN2022131817-appb-100001
    (2)基于虚功原理建立夹持器各指节虚功方程：
    Figure PCTCN2022131817-appb-100002
    式中，
    Figure PCTCN2022131817-appb-100003
    为力矩T 1作用于首指节上的虚角速度，v s1、v s2分别为弹簧s 1和s 2上的虚速度；v F1、v F2、v F3分别为接触力F 1、F 2、F 3在接触点处的虚速度；
    令T＝[T 1 F 1+T 2 F 2+T 3] T，F＝[F 1 F 2 F 3] T，
    Figure PCTCN2022131817-appb-100004
    V F＝[v F1 v F2 v F3] T，虚功方程可以简化为：F TV F＝T TW；
    (3)基于刚体速度公式建立夹持器各指节虚速度V F＝[v F1 v F2 v F3] T为：
    Figure PCTCN2022131817-appb-100005
    式中，
    Figure PCTCN2022131817-appb-100006
    δ β1、δ β2、δ β3分别为转角β 1、β 2和β 3的角速度；
    将虚速度V F写成矩阵形式：V F＝J v[δ β1 δ β2 δ β3] T；
    式中，
    Figure PCTCN2022131817-appb-100007
    (4)由于所述中指节传动连杆(29)(PQ)和末指节传动连杆(47)(UR)都对所在指节组件有直接作用力，计算两杆的虚速度v PQ、v UR：
    Figure PCTCN2022131817-appb-100008
    因为，
    Figure PCTCN2022131817-appb-100009
    Figure PCTCN2022131817-appb-100010
    Figure PCTCN2022131817-appb-100011
    Figure PCTCN2022131817-appb-100012
    所以，所述中指节传动连杆(29)(PQ)和末指节传动连杆(47)(UR)的虚速度v PQ、v UR为：
    Figure PCTCN2022131817-appb-100013
    针对五连杆机构E 1PQD 2D 1，以E 1 D 1为x轴正方向，指向圆盘工件方向为y轴正方向，列出其矢量封闭方程：
    Figure PCTCN2022131817-appb-100014
    将其分解为x、y方向：
    Figure PCTCN2022131817-appb-100015
    对α 6+β 2、
    Figure PCTCN2022131817-appb-100016
    求导：
    Figure PCTCN2022131817-appb-100017
    因为α 6为固定角，所以δ α6＝0，根据同一构件角速度关系可得：
    Figure PCTCN2022131817-appb-100018
    令上式等号右边项为m，则上式整理可得：
    Figure PCTCN2022131817-appb-100019
    同样针对五连杆机构G 1URE 4E 6，列出其矢量封闭方程：
    Figure PCTCN2022131817-appb-100020
    即：
    Figure PCTCN2022131817-appb-100021
    对α 7+β 3、
    Figure PCTCN2022131817-appb-100022
    求导，并整理可得：
    Figure PCTCN2022131817-appb-100023
    由于α 7为固定角，则δ α7＝0，根据同一构件角速度关系可得：
    Figure PCTCN2022131817-appb-100024
    令上式的等号右边项为n，则其可整理得：
    Figure PCTCN2022131817-appb-100025
    由于
    Figure PCTCN2022131817-appb-100026
    将
    Figure PCTCN2022131817-appb-100027
    和
    Figure PCTCN2022131817-appb-100028
    代入虚速度v PQ、v UR中，并整理可得：
    Figure PCTCN2022131817-appb-100029
    式中，
    Figure PCTCN2022131817-appb-100030
    Figure PCTCN2022131817-appb-100031
    Figure PCTCN2022131817-appb-100032
    (5)计算弹簧s 1和s 2上的虚速度v s1、v s2；
    根据夹持器的所述几何模型和静力学模型中结构件间几何关系，可以得出：
    Figure PCTCN2022131817-appb-100033
    所以弹簧s 1和s 2上的虚速度：
    Figure PCTCN2022131817-appb-100034
    式中，
    Figure PCTCN2022131817-appb-100035
    Figure PCTCN2022131817-appb-100036
    (6)计算夹持器接触力F＝[F 1 F 2 F 3] T；
    根据同一构件角速度关系可得：
    Figure PCTCN2022131817-appb-100037
    再结合弹簧s 1和s 2上虚速度v s1和v s2，可以将上面的W写为矩阵相乘形式：W＝J ω[δ β1 δ β2 δ β3] T；
    式中，
    Figure PCTCN2022131817-appb-100038
    将虚速度V F、W代入简化的虚功方程，可得：F TJ v＝T TJ ω，
    则接触力为：
    Figure PCTCN2022131817-appb-100039
    式中，
    Figure PCTCN2022131817-appb-100040
    且
    Figure PCTCN2022131817-appb-100041
    Figure PCTCN2022131817-appb-100042
    Figure PCTCN2022131817-appb-100043
    鉴于弹簧s 1和s 2的驱动力T 2和T 3远小于夹持力F，所以将其忽略并获得夹持力F：
    Figure PCTCN2022131817-appb-100044
    进一步化简可得F：
    Figure PCTCN2022131817-appb-100045
    上式给出了接触力F＝[F 1 F 2 F 3] T与T 1之间的关系，由式可以看出，接触力F受β 1～β 3、
    Figure PCTCN2022131817-appb-100046
    等角度以及手指机构尺寸的影响；
    二、夹持器结构参数优化方法，包括基于群体效应的免疫优化算法，所述基于群体效应的免疫进化算法是在基本免疫优化算法的算子(包括免疫选择算子O s、免疫交叉算子O c和免疫变异算子O m)基础上，根据群体效应设计了新的免疫集聚算子O g和免疫扩散算子O d进行算法优化提升；
    已知第k代含有n个个体的种群A(k)＝[a 1(k),a 2(k),…,a n(k)]，则免疫选择算子O s可以描述为：
    Figure PCTCN2022131817-appb-100047
    免疫交叉算子O c可以描述为：
    Figure PCTCN2022131817-appb-100048
    Figure PCTCN2022131817-appb-100049
    免疫变异算子O m可以描述为：
    Figure PCTCN2022131817-appb-100050
    Figure PCTCN2022131817-appb-100051
    所述免疫集聚算子O g，主要是让种群中优势个体组成集聚种群对适应度差的劣势个体形成号召影响，进而提高劣势个体的性能；
    设集聚数为m，集聚距离为l(l<n)，适应度差的劣势个体数为n，免疫集聚算子流程为：
    (1)从免疫变异后种群A″′(k)中选择适应度最好的个体a*(k)；
    (2)根据a*(k)生成与其集聚距离小于l的m个优势个体，并组成集聚种群
    Figure PCTCN2022131817-appb-100052
    Figure PCTCN2022131817-appb-100053
    |·|表示汉明距离；
    (3)从种群A″′(k)中选择z个适应度最差的个体，并组成劣势种群W(k)＝[w 1(k),w 2(k),…,w z(k)]；
    (4)从W(k)中提取个体w i(k)(i∈[1，z])，将其与G(k)中个体分别进行异或操作，并得到G'(k)＝[g' 1(k),g' 2(k),…,g' m(k)]；
    (5)提取G'(k)＝[g' 1(k),g' 2(k),…,g' m(k)]中最优个体与w i(k)比较，若前者优于后者则替换后者，否则保留后者；
    (6)判断W(k)中所有个体是否都与G(k)中个体完成异或操作？若否，则转步骤(4)，否则退出；
    免疫集聚算子O g可以描述为：
    Figure PCTCN2022131817-appb-100054
    所述免疫扩散算子O d，主要是让种群中高浓度个体进行扩散，以防止个体陷入局部极小；
    设扩散距离为r(r<n)，扩散数为s，免疫扩散算子流程为：
    (1)从免疫集聚后种群A IV(k)中选取浓度最高的s个抗体，并组成扩散种群D(k)＝[d 1(k),d 2(k),…,d s(k)]；
    (2)随机产生1个初始个体a 0(k)，且其元素为1的数量大于r并小于等于n；
    (3)从D(k)中取出个体d i(k)(i∈[1，s])与个体a 0(k)进行异或操作，并得到新个体d i'(k)；
    (4)将个体d i(k)与d i'(k)进行对比，若后者优于前者则替换前者，否则保留前者；
    (5)判断D(k)中所有抗体是否都与a 0(k)完成异或操作？若否，则转步骤(3)，否则退出；
    免疫扩散算子O d可以描述为：
    Figure PCTCN2022131817-appb-100055
    三、夹持器结构参数优化流程，包括以下内容与步骤：
    (1)基于夹持器夹持力F，并以夹持时接触力尽可能分布均匀且相等为目标，建立夹持器稳定夹持状态下参数优化的目标函数：
    minf(X)＝min((F 1-F 2) 2+(F 1-F 3) 2+(F 2-F 3) 2)；
    式中，X为夹持器结构参数变量集且
    Figure PCTCN2022131817-appb-100056
    Figure PCTCN2022131817-appb-100057
    (2)设定夹持器参数变量集X的约束范围；
    (3)初始化基于群体效应的免疫优化算法参数，及初始种群A(k)＝[a 1(k),a 2(k),…,a n(k)]，k←0；
    (4)免疫选择：A′(k)←O s(A(k))＝[a′ 1(k),a′ 2(k),…,a′ n(k)]；
    (5)免疫交叉：A″(k)←O c(A′(k))＝[a″ 1(k),a″ 2(k),…,a″ n(k)]；
    (6)免疫变异：A″′(k)←O m(A″(k))＝[a″′ 1(k),a″′ 2(k),…,a″′ n(k)]；
    (7)免疫集聚：
    Figure PCTCN2022131817-appb-100058
    (8)免疫扩散：
    Figure PCTCN2022131817-appb-100059
    (9)终止条件判定，进化代数k是否达到最大代数？若是，则算法终止，并输出最优变量X*；否则k←k+1，并返回步骤(4)。
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