WO2021082520A1 - Model building method for variable-stiffness soft robot - Google Patents

Model building method for variable-stiffness soft robot Download PDF

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Publication number
WO2021082520A1
WO2021082520A1 PCT/CN2020/100791 CN2020100791W WO2021082520A1 WO 2021082520 A1 WO2021082520 A1 WO 2021082520A1 CN 2020100791 W CN2020100791 W CN 2020100791W WO 2021082520 A1 WO2021082520 A1 WO 2021082520A1
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film tube
particles
spherical particles
particle
soft robot
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PCT/CN2020/100791
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French (fr)
Chinese (zh)
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徐丰羽
江丰友
余洪亮
蒋国平
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南京南邮信息产业技术研究院有限公司
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Publication of WO2021082520A1 publication Critical patent/WO2021082520A1/en

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators

Definitions

  • the invention relates to the technical field of driving travel, in particular to a modeling method of a variable stiffness soft robot.
  • the mechanism needs to have better variable stiffness performance, that is, better flexibility and rigidity.
  • it Before coming into contact with the object, it needs to have good flexibility and be able to realize its own movement through active deformation, so as to better adapt to external objects and obtain a larger contact area.
  • After full contact with the object it needs to have good rigidity to increase the pressure between the objects in contact, and then increase the friction between the objects in contact.
  • Pneumatic structure has good position control performance, but due to the characteristics of its material itself, the stiffness of the mechanism made of it is not high, and the introduction of a blocking system can increase the stiffness of the soft robot to adapt to more applications.
  • the pneumatic drive has the characteristics of fast response, high power density, and high switching speed.
  • the materials constituting the soft robot are usually flexible, the pressure is always maintained at a low level when driven by air pressure, which enables the soft robot to achieve corresponding motions and at the same time has high safety.
  • Variable stiffness is an effective way for soft structures (natural or man-made) to interact with the environment.
  • the inherent flexibility of the software structure deforms itself to adapt to the external environment, and the safe interaction prevents the external environment from damaging the entity. But at the same time, it also needs to strengthen its own rigidity to increase the force applied to the external environment.
  • variable stiffness method based on particle clogging is a more effective method of using vacuum pressure to control stiffness.
  • Particle blockage is to cause a large number of particles to undergo a phase change, transitioning between a fluid state and a solid state. If the particles are placed in a sealing film under normal conditions, due to the large gaps between the particles and the small friction between the particles, they can flow arbitrarily, thus exhibiting a fluid-like behavior. At this time, a large number of particles are wrapped.
  • the sealing film can be changed in any shape. When the air in the sealing film is discharged, a large number of particles are compressed together. At this time, due to the increase of the contact surface pressure between the particles, the friction between the particles rises sharply. At this time, the particles are restricted and cannot flow freely. , So that the filling particles present a solid state, and the sealing film and the particles as a whole show a certain degree of rigidity.
  • variable stiffness software driver software arm and software platform based on blocking mechanism
  • the application is The author discloses a variable stiffness soft drive based on the blocking mechanism, which is mainly composed of a flexible frame, a trachea, an outer flexible layer, a blocking mechanism, a deformable plug and a blocking plug.
  • the blocking mechanism is mainly composed of a supporting frame, an elastic connecting rope, and a large ball. It is composed of particles, small ball particles, tightening spring and sealing film, which can have greater flexibility and rigidity through the principle of variable stiffness.
  • the technical problem to be solved by the present invention is to address the above-mentioned shortcomings of the prior art, and provide a modeling method of a variable stiffness soft robot.
  • the modeling method of the variable stiffness soft robot takes all the filling particles and the film tube in the film tube into consideration. As a whole particle block, the small spherical particles are equivalent to fluid, the film tube is equivalent to a closed space, the sphere-plane Hertz contact model is established, and the locking force is established based on the Hertz contact theory and the Hertz contact model of two spheres. And the model of the locking torque, so as to control the stiffness of the variable stiffness soft robot as required.
  • a modeling method of a variable stiffness soft robot includes the following steps.
  • Step 1 the design of the locking force FL between the filling particles, includes the following steps.
  • Step 11 support frame selection.
  • the support frame in the blocking mechanism is selected as a rhombus frame, and the sealing film is selected as a film tube.
  • the large spherical particles and small spherical particles in the film tube are collectively referred to as filler particles.
  • Step 12 Establish a particle block model.
  • all the filling particles in the film tube are rigid and are restricted as a whole, that is, all the filling particles in the film tube and the film tube, When taken as a whole piece of pellets.
  • Step 13 the design of the locking force FL between the filling particles.
  • the particle block receives an external force
  • the small spherical particles in the filled particles are equivalent to a fluid.
  • the calculation formula of the locking force FL between the filled particles is obtained as follows.
  • P′ is the equivalent pressure in the film tube
  • R 1 is the radius of the diamond-shaped skeleton
  • ⁇ is the sharp apex angle of the diamond-shaped skeleton
  • R 2 is the radius of the large spherical particles
  • ⁇ 1 is the friction coefficient between the small spherical particles and the diamond-shaped skeleton
  • ⁇ 2 is the friction coefficient between small spherical particles and large spherical particles.
  • Step 2 Calculate the equivalent pressure P'in the film tube.
  • the radius of the small spherical particles is much smaller than the radius of the film tube, and the area of the film tube facing the single small spherical particle is small. Therefore, the film tube in contact with the single small spherical particle can be regarded as a flat surface.
  • the sphere-plane Hertz contact model according to the Hertz contact theory and the Hertz contact model of two spheres, the calculation formula for the equivalent pressure P′ in the membrane tube is obtained as follows.
  • R 3 is the radius of the small spherical particles
  • v 1 is the Poisson's ratio of the diamond-shaped framework
  • v 2 is the Poisson's ratio of the small spherical particles
  • E 1 is the Young's modulus of the diamond-shaped framework
  • E 2 is the Young's ratio of the small spherical particles.
  • Modulus P is the vacuum pressure in the film tube.
  • Step 3 Establish the corresponding relationship between the locking force FL and the vacuum pressure P in the film tube. Substituting the equivalent pressure P'in the membrane tube calculated in step 2 into the locking force FL designed in step 1, the corresponding relationship between the locking force FL and the vacuum pressure P in the membrane tube is obtained as shown in the following formula.
  • Step 4 Design the locking torque ML of the particle block.
  • the design formula is shown below.
  • d is the radius of the film tube.
  • step 5 establishing the corresponding relationship between the locking torque M L and the hardness S 1 of the pellets.
  • the corresponding relationship between the Young's modulus value and the Shore hardness value the corresponding relationship between the locking torque M L and the hardness S 1 of the small spherical particles is established as follows.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • step 6 the design of the deformation angle ⁇ of the film tube.
  • the film tube will deform in contact with the small spherical particles, and the deformation angle ⁇ of the film tube is calculated using the following formula.
  • the calculation method of the deformation angle ⁇ of the film tube includes the following steps.
  • Step 61 Calculate the relative radial deformation displacement ⁇ of the thin film tube. According to the sphere-plane Hertzian contact model established in step 2, and then according to the Hertzian contact theory and the two-sphere Hertzian contact model, the relative radial deformation displacement ⁇ of the membrane tube is obtained to satisfy the following calculation formula.
  • Step 62 Establish a corresponding relationship between the deformation angle ⁇ of the membrane tube and the relative radial deformation displacement ⁇ of the membrane tube.
  • the corresponding relationship between the deformation angle ⁇ of the membrane tube and the relative radial deformation displacement ⁇ of the membrane tube is calculated as follows.
  • Step 63 Calculate the deformation angle ⁇ of the film tube. Substituting the relative radial deformation displacement ⁇ of the thin film tube calculated in step 61 into step 62, it is obtained that the deformation angle ⁇ of the thin film tube satisfies the following formula.
  • step 13 according to the static balance equation and Pascal's law, the method of calculating the locking force FL between the filled particles includes the following steps.
  • the particle block includes an upper particle block and a lower particle block, wherein the lower particle block is located on the side of the object to be locked and the bottom is in contact with the object to be locked, and the upper particle is located on the side away from the object to be locked.
  • the locking force of the lower particle block needs to resist the external moment. Therefore, the upper particle block and the lower particle block slide relative to each other in the horizontal direction. According to the static balance equation of the particle block, the locking force F L described as.
  • f L is the friction force of the particle block in the contact area with the diamond-shaped skeleton
  • f P is the static force of the particle block on the locking area
  • f U is the friction force of the lower particle block and the large spherical particles in the horizontal direction.
  • Step 13b f P is calculated.
  • the small spherical particles are equivalent to fluid, and the film tube is equivalent to a closed space.
  • Several small spherical particles are filled in the closed space to form a static fluid model. Then the static force f P applied by the particle block in the horizontal direction of the locking area , Will be provided by the pressure between the particle block and the diamond skeleton, specifically.
  • R 1 is the radius of the rhombus skeleton
  • ⁇ is the apex angle of the rhombus skeleton
  • P′ is the equivalent pressure in the film tube.
  • Step 13c f L is calculated.
  • the frictional force f L of the particle block in the contact area with the diamond-shaped skeleton is.
  • ⁇ 1 is the friction coefficient between the particle block and the diamond-shaped skeleton.
  • Step 13d f U is calculated.
  • the frictional force f U between the lower layer of particles and the large spherical particles in the horizontal direction is.
  • ⁇ 2 is the friction coefficient between small spherical particles and large spherical particles.
  • step 13e the f P , f L and f U calculated in steps 13b, 13c, and 13d are substituted into step 13a respectively to obtain the calculation formula of the locking force FL between the filling particles.
  • the vacuum pressure P in the membrane tube is adjusted by the vacuum pump, and then the stiffness of the variable stiffness soft robot is adjusted.
  • the vacuum pressure P in the membrane tube increases, the deformation angle ⁇ and the locking torque M L of the membrane tube will increase, and the stiffness of the variable stiffness soft robot will increase.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • the radius R 3 of the small ball particle is larger, the locking torque M L is smaller, and the rigidity of the variable-rigidity soft robot will decrease.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • the radius R 1 of the rhombus skeleton is larger, the locking torque M L is larger, and the rigidity of the variable-rigidity soft robot will increase.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • the radius R 2 of the large ball particle is larger, the locking torque M L is larger, and the rigidity of the variable-rigidity soft robot will increase.
  • the invention has the following beneficial effects: the particles are quickly divided into upper and lower layers, and the locking force of the lower layer of particle blocks resists the external moment.
  • the upper and lower layers of particle blocks slide relatively in the horizontal direction.
  • the small spherical particles are equivalent to a fluid
  • the film tube is equivalent to a closed space.
  • the inside of the tube is filled with small spherical particles.
  • the locking force is obtained according to the static balance equation of the particle block.
  • the film area where a single particle is facing If the area is small, it can be regarded as a plane, then the film and particle block are analyzed using the Hertzian contact theory, the sphere-plane Hertzian contact model is established, and the relationship between the hardness of the small ball and the locking torque is obtained.
  • the apex angle and radius of the rhombus skeleton By adjusting the apex angle and radius of the rhombus skeleton, the radius of the large spherical particles, the radius of the small spherical particles, the hardness, the vacuum pressure and other parameters, the required stiffness of the variable stiffness soft robot can be obtained.
  • the model established by the invention is simulated through variable stiffness characteristics, and the simulation result is consistent with the established model, so the reliability is high and it is convenient for popularization and utilization.
  • Figure 1 shows a schematic structural diagram of a blocking mechanism in a variable stiffness soft robot of the present invention.
  • Figure 2 shows a longitudinal cross-sectional view of a blocking mechanism in a variable stiffness soft robot of the present invention.
  • Fig. 3 shows an exploded analysis diagram of the force on the end of the blocking mechanism in a variable stiffness soft robot of the present invention.
  • Figure 4 shows a cross-sectional view of the longitudinal plane where all the large spherical particles connected by the same tightening spring are located.
  • Figure 5 shows a schematic diagram of the force analysis of the lower particle block.
  • Figure 6 shows a schematic diagram of the fluid pressurization model.
  • Figure 7 shows a schematic diagram of the force analysis of the blocking mechanism in the present invention.
  • Figure 8 shows the Hertz model of two balls in contact.
  • Figure 9 shows the particle-plane Hertz contact model of the small spherical particles in contact with the film tube.
  • Figure 10 shows the simplified model diagram of Figure 9.
  • Figure 11 shows the corresponding relationship between the deformation angle ⁇ and the vacuum pressure P.
  • Figure 12 shows the corresponding relationship between the locking torque M L and the vacuum pressure P.
  • Figure 13 shows the corresponding relationship between the locking torque M L and the radius R 3 of the small spherical particles.
  • Figure 14 shows the corresponding relationship between the locking torque M L and the radius R 1 of the diamond skeleton.
  • Figure 15 shows the corresponding relationship between the locking torque M L and the radius R 2 of the large spherical particles.
  • Figure 16 shows the corresponding relationship between the locking torque M L and the hardness S 1 of the pellets.
  • variable stiffness soft robot For details, please refer to the invention patent application filed on August 31, 2017 with the application number CN201710768485.2.
  • the name of the invention is "variable stiffness soft driver, soft arm and software platform based on clogging mechanism.” "This application does not improve the structure of the blocking mechanism itself, but selects the support frame in the blocking mechanism as the diamond-shaped frame 32, and the sealing film as the film tube 31.
  • the large spherical particles 34 and the small spherical particles 35 in the film tube are collectively referred to as filling particles.
  • the elastic connecting rope is selected as a flexible rope 33, and vacuum pressure is provided into the film tube through a vacuum pump 40.
  • the specific structure is shown in Figs. 1 and 2.
  • a modeling method of a variable stiffness soft robot includes the following steps.
  • Step 1 the design of the locking force FL between the filling particles, includes the following steps.
  • Step 11 support frame selection.
  • Step 12 Establish a particle block model.
  • all the filling particles in the film tube are rigid and are restricted as a whole, that is, all the filling particles in the film tube and the film tube, When taken as a whole piece of pellets.
  • Step 13 the design of the locking force FL between the filling particles.
  • the particle block When the particle block receives an external force, the small spherical particles in the filled particles are equivalent to a fluid. According to the static balance equation and Pascal's law, the calculation formula of the locking force FL between the filled particles is obtained as follows.
  • P′ is the equivalent pressure in the film tube
  • R 1 is the radius of the diamond-shaped skeleton
  • ⁇ is the sharp apex angle of the diamond-shaped skeleton
  • R 2 is the radius of the large spherical particles
  • ⁇ 1 is the friction coefficient between the small spherical particles and the diamond-shaped skeleton
  • ⁇ 2 is the friction coefficient between small spherical particles and large spherical particles.
  • the above method for calculating the locking force FL between filled particles according to the static balance equation and Pascal's law includes the following steps.
  • the particle block includes an upper particle block 51 and a lower particle block 52, wherein the lower particle block is located on the side of the object to be locked and the bottom is in contact with the object to be locked, and the upper particle is located on the side away from the object to be locked.
  • the particle block receives an external force F E
  • the locking force of the lower particle block needs to resist the external moment. Therefore, the upper particle block and the lower particle block slide relative to each other in the horizontal direction.
  • the static balance equation of the particle block, then the locking force FL is described as.
  • f L is the friction force of the particle block on the contact area 10 with the diamond-shaped skeleton
  • f P is the static force of the particle block on the locking area 60
  • f U is the horizontal friction between the lower particle block and the large spherical particles. force.
  • Step 13b f P is calculated.
  • the static force f P of the particle block on the locking area can be estimated by the fluid pressure model.
  • the fluid in a confined space exerts pressure on the fluid, can be transferred from the fluid to all directions in the space with the same magnitude.
  • Figure 6 and Pascal's law we can get:
  • the small spherical particles are equivalent to a fluid, and the film tube is equivalent to a closed space, and its interior is filled with small spherical particles, which constitutes a static fluid model as shown in Figure 7.
  • the force applied on each side It can be calculated by the above formula.
  • FN2 is the positive pressure of the particle block on the diamond-shaped skeleton, as shown in Figure 7, R 1 is the radius of the diamond-shaped skeleton, ⁇ is the apex angle of the diamond-shaped skeleton, and P'is the equivalent pressure applied by the particle block to the diamond-shaped skeleton and the big sphere. , Which is the equivalent pressure in the film tube.
  • the above-mentioned diamond-shaped skeleton radius R 1 refers to the radius of the radial large circle in the diamond-shaped skeleton in Fig. 3, which is infinitely close to the radius d of the film tube and can be approximately equal.
  • the apex angle ⁇ of the rhombus skeleton refers to the apex angle on the flexible rope, which is an acute angle.
  • Step 13c f L calculation: the friction force f L of the particle block in the contact area with the diamond-shaped skeleton is:
  • ⁇ 1 is the friction coefficient between the particle block and the diamond-shaped skeleton
  • a 1 is the equivalent area of the contact area between the particle block and the diamond-shaped skeleton.
  • Step 13d the frictional force f U between the lower layer of particles and the large spherical particles in the horizontal direction is:
  • F N1 is the positive pressure of the particle block on the large spherical particle
  • R 2 is the radius of the large spherical particle
  • ⁇ 2 is the friction coefficient between the small spherical particle (filling particle) and the large spherical particle
  • a 2 is the particle block and the large spherical particle. The equivalent area of particle contact.
  • step 13e the f P , f L and f U calculated in steps 13b, 13c, and 13d are substituted into step 13a respectively to obtain the calculation formula of the locking force FL between the filling particles.
  • Step 2 Calculate the equivalent pressure P'in the film tube.
  • Ra is the radius of the ball a in Figure 8
  • R b is the radius of the ball b
  • v a is the Poisson's ratio of the ball a
  • v b is the Poisson's ratio of the ball b
  • E a is the Young's modulus of the ball a
  • E b is b Ball Young's modulus.
  • the radius of the small spherical particle is much smaller than the radius of the film tube, and the area of the film tube facing the single small spherical particle is small. Therefore, the film tube in contact with the single small spherical particle can be regarded as a flat surface.
  • the relative radial deformation displacement of the ⁇ film tube R 3 is the radius of the small spherical particles
  • v 1 is the Poisson's ratio of the diamond-shaped framework
  • v 2 is the Poisson's ratio of the small spherical particles
  • E 1 is the Young's modulus of the diamond-shaped framework
  • E 2 is the Young's modulus of the small spherical particles
  • P is the vacuum pressure in the film tube.
  • Step 3 Establish the corresponding relationship between the locking force FL and the vacuum pressure P in the film tube. Substituting the equivalent pressure P'in the membrane tube calculated in step 2 into the locking force FL designed in step 1, the corresponding relationship between the locking force FL and the vacuum pressure P in the membrane tube is obtained as shown in the following formula.
  • Step 4 Design the locking torque ML of the particle block.
  • the design formula is shown below.
  • d is the radius of the film tube.
  • Step 5 Establish the corresponding relationship between the locking torque M L and the hardness S 1 of the small ball particles.
  • E is the Young's modulus in MPa
  • S is the hardness in accordance with ASTM D2240. This formula is suitable for materials with a hardness of 20 to 80, which is close to the material properties of small spherical particles.
  • the corresponding relationship between the Young's modulus value and the Shore hardness value is established as follows.
  • the stiffness of the variable stiffness soft robot is adjusted.
  • Step 6 the design of the deformation angle ⁇ of the film tube.
  • the film tube When the particle block is subjected to an external force, the film tube will deform in contact with the small spherical particles, and the deformation angle ⁇ of the film tube is calculated using the following formula.
  • the calculation method of the deformation angle ⁇ of the film tube includes the following steps.
  • Step 61 Calculate the relative radial deformation displacement ⁇ of the thin film tube. According to the sphere-plane Hertzian contact model established in step 2, and then according to the Hertzian contact theory and the two-sphere Hertzian contact model, the relative radial deformation displacement ⁇ of the membrane tube is obtained to satisfy the following calculation formula.
  • step 2 the above calculation formula can be obtained, which is only for reference here.
  • Step 62 Establish a corresponding relationship between the deformation angle ⁇ of the membrane tube and the relative radial deformation displacement ⁇ of the membrane tube.
  • Step 63 Calculate the deformation angle ⁇ of the film tube. Substituting the relative radial deformation displacement ⁇ of the thin film tube calculated in step 61 into step 62, it is obtained that the deformation angle ⁇ of the thin film tube satisfies the following formula.
  • the relationship between the locking torque M L and the vacuum pressure P as shown in Fig. 12 is obtained. It can be seen from the figure that the greater the vacuum pressure P, the greater the locking torque M L. Therefore, the stiffness of the mechanism can be controlled by adjusting the vacuum pressure.
  • the relationship between the locking torque M L and the radius R 3 of the small spherical particles shown in Fig. 13 is obtained. It can be seen from the figure that the larger the radius R 3 of the pellets, the smaller the locking torque M L. And as the size of small particles decreases, the decrease of the locking torque M L becomes smaller and smaller under the same size reduction.
  • the relationship between the locking torque M L and the radius size R2 of the large spherical particles shown in Fig. 15 can be obtained. It can be seen that the larger the radius of the large spherical particles, the larger the locking torque M L. And with the increase of the radius of the large spherical particles, the increase of the locking torque M L becomes larger and larger under the same size increment.
  • the invention first theoretically studies and analyzes the principle of variable stiffness of the plugging variable stiffness structure, first simplifying the modeling, and applying the Pascal model and Hertz contact theory to establish the mechanical model of the plugging mechanism, and derive the locking torque and vacuum at the end of the mechanism
  • the relationship between the pressure, the hardness of the small spherical particles and the radius of the large spherical particles The relationship between the stiffness of the mechanism and the degree of vacuum, the radius of the diamond skeleton and the size of the large spherical particles is obtained, and the simulation analysis is performed. It is convenient for the subsequent design of the cavity shape and wall thickness of the driver to have better bending performance and better meet the design requirements.

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  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
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Abstract

A model building method for a variable-stiffness soft robot comprises: step 1, designing a locking force between filler particles; step 2, calculating an equivalent pressure in a thin film tube (31); step 3, establishing a correspondence relationship between the locking force and a vacuum pressure in the thin film tube (31); step 4, designing a locking torque of a particle block; step 5, establishing a correspondence relationship between the locking torque and a hardness of small spherical particles (35); and step 6, calculating a deformation angle of the thin film tube (31). The method treats all filler particles (34, 35) in the thin film tube (31) and the thin film tube (31) as an integrated particle block, considers the small spherical particles (35) as an equivalent of a fluid and the thin film tube (31) as an equivalent of a closed space, and establishes a Hertzian sphere-plane contact model. Models for the locking force and the locking torque are established according to the Hertz contact theory and a Hertzian two-sphere contact model. In this way, the invention enables control of the stiffness of the variable-stiffness soft robot, and the established model is reliable since the result obtained by variable-stiffness characteristic simulation is consistent with the model.

Description

一种变刚度软体机器人的建模方法A modeling method of variable stiffness soft robot 技术领域Technical field
本发明涉及驱动行进技术领域，特别是一种变刚度软体机器人的建模方法。The invention relates to the technical field of driving travel, in particular to a modeling method of a variable stiffness soft robot.
背景技术Background technique
根据软体驱动器的应用环境，需要机构具备较好的变刚度性能，即较好的柔顺性和刚性。在与物体接触前，需要有较好柔顺性，能通过主动变形实现自身运动，以较好的适应外界物体，获得更大的接触面积。与物体充分接触后，则需要具备较好的刚性，以提高物体接触间的压力，进而增大物体接触间的摩擦力。According to the application environment of the software driver, the mechanism needs to have better variable stiffness performance, that is, better flexibility and rigidity. Before coming into contact with the object, it needs to have good flexibility and be able to realize its own movement through active deformation, so as to better adapt to external objects and obtain a larger contact area. After full contact with the object, it needs to have good rigidity to increase the pressure between the objects in contact, and then increase the friction between the objects in contact.
同时，驱动器也需要其具备较好的位置控制性能，以较好的躲避障碍物。气动结构具有较好的位置控制性能，但由于其材料本身的特性，由其制成的机构刚度不高，而引入阻塞***则可增加软体机器人的刚度，以适应更多的应用场合。At the same time, the driver also needs to have better position control performance to better avoid obstacles. Pneumatic structure has good position control performance, but due to the characteristics of its material itself, the stiffness of the mechanism made of it is not high, and the introduction of a blocking system can increase the stiffness of the soft robot to adapt to more applications.
气压驱动方式与其他物理驱动方式相比，具有响应速度快、功率密度高、开关速度高等特点。同时，由于构成软体机器人的材料通常具有良好的柔性，气压驱动时压力始终维持在较低的水平上，既能够使软体机器人实现相应的运动，同时又具有较高的安全性。Compared with other physical drive methods, the pneumatic drive has the characteristics of fast response, high power density, and high switching speed. At the same time, since the materials constituting the soft robot are usually flexible, the pressure is always maintained at a low level when driven by air pressure, which enables the soft robot to achieve corresponding motions and at the same time has high safety.
变刚度是软体结构(自然或人造)与环境相互作用的有效方式。软体结构固有的柔软性使自身发生变形以适应外界环境，安全的相互作用防止外界环境对实体的损害。但同时，也需要加强自身刚度以增加施加到外界环境的力。Variable stiffness is an effective way for soft structures (natural or man-made) to interact with the environment. The inherent flexibility of the software structure deforms itself to adapt to the external environment, and the safe interaction prevents the external environment from damaging the entity. But at the same time, it also needs to strengthen its own rigidity to increase the force applied to the external environment.
基于颗粒堵塞的变刚度方法是一种利用真空压力控制刚度较有效的方法。颗粒阻塞是使大量的颗粒发生相变，在流体状态与固态之间进行转变。若在常态下将颗粒置于密封薄膜中，由于颗粒之间具有较大的空隙，颗粒之间的摩擦力较小，则其可以任意流动，因此表现出类流体行为，此时包裹大量颗粒的密封薄膜可产生任意形状的变化。当密封薄膜中的空气被排出后，大量的颗粒被压缩在一起，此时由于颗粒之间的接触面压力增大，使得颗粒间的摩擦力急剧上升，此时颗粒被限制住，不能随意流动，从而使填充颗粒呈现固态，密封薄膜和颗粒整体表现出一定的刚度。The variable stiffness method based on particle clogging is a more effective method of using vacuum pressure to control stiffness. Particle blockage is to cause a large number of particles to undergo a phase change, transitioning between a fluid state and a solid state. If the particles are placed in a sealing film under normal conditions, due to the large gaps between the particles and the small friction between the particles, they can flow arbitrarily, thus exhibiting a fluid-like behavior. At this time, a large number of particles are wrapped. The sealing film can be changed in any shape. When the air in the sealing film is discharged, a large number of particles are compressed together. At this time, due to the increase of the contact surface pressure between the particles, the friction between the particles rises sharply. At this time, the particles are restricted and cannot flow freely. , So that the filling particles present a solid state, and the sealing film and the particles as a whole show a certain degree of rigidity.
申请人于2017年8月31日申请的申请号为CN201710768485.2的发明专利申请，其发明创造名称为“基于堵塞机理的变刚度软体驱动器、软体手臂和软体平台”，在该专利中，申请人公开了一种主要由柔性骨架、气管、外柔性层、堵塞机构、形变堵头和堵塞堵头组成的基于堵塞机理的变刚度软体驱动器，堵塞机构主要通过支撑骨架、弹性连接绳索、大球颗粒、小球颗粒、收紧弹簧和密封薄膜组成，其通过变刚度原理，既能具有较大柔性，又能具有较大刚性。The applicant applied for an invention patent application with the application number CN201710768485.2 on August 31, 2017, and the name of the invention creation is "variable stiffness software driver, software arm and software platform based on blocking mechanism". In this patent, the application is The author discloses a variable stiffness soft drive based on the blocking mechanism, which is mainly composed of a flexible frame, a trachea, an outer flexible layer, a blocking mechanism, a deformable plug and a blocking plug. The blocking mechanism is mainly composed of a supporting frame, an elastic connecting rope, and a large ball. It is composed of particles, small ball particles, tightening spring and sealing film, which can have greater flexibility and rigidity through the principle of variable stiffness.
当前的软体驱动器由于采用软体材料制成，材料本征非线性明显，建模和控制困难，离人们期望的性能(与生物肌肉相媲美)，还需要进一步进行探索和实践。因而，建模技术是本领域的难点。软体驱动器建模技术目前并不成熟，这也制约了软体机器人的发展和应用。Because the current soft actuator is made of soft materials, the intrinsic nonlinearity of the material is obvious, modeling and control are difficult, and it is far from the expected performance (comparable to biological muscle), and further exploration and practice are needed. Therefore, modeling technology is a difficult point in this field. The software driver modeling technology is currently immature, which also restricts the development and application of software robots.
发明内容Summary of the invention
本发明要解决的技术问题是针对上述现有技术的不足，而提供一种变刚度软体机器人的建模方法，该变刚度软体机器人的建模方法将薄膜管内的所有填充颗粒和薄膜管，当作为一个整体的颗粒块，并将小球颗粒等效成流体，薄膜管等效为一个密闭空间，建立球体-平面赫兹接触模型，根据赫兹接触理论和两圆球赫兹接触模型，建立锁紧力和锁紧力矩的模型，从而能根据需要控制变刚度软体机器人的刚度。The technical problem to be solved by the present invention is to address the above-mentioned shortcomings of the prior art, and provide a modeling method of a variable stiffness soft robot. The modeling method of the variable stiffness soft robot takes all the filling particles and the film tube in the film tube into consideration. As a whole particle block, the small spherical particles are equivalent to fluid, the film tube is equivalent to a closed space, the sphere-plane Hertz contact model is established, and the locking force is established based on the Hertz contact theory and the Hertz contact model of two spheres. And the model of the locking torque, so as to control the stiffness of the variable stiffness soft robot as required.
为解决上述技术问题，本发明采用的技术方案是：In order to solve the above technical problems, the technical solutions adopted by the present invention are:
一种变刚度软体机器人的建模方法，包括如下步骤。A modeling method of a variable stiffness soft robot includes the following steps.
步骤1，填充颗粒间的锁紧力F L设计，包括如下步骤。 Step 1, the design of the locking force FL between the filling particles, includes the following steps.
步骤11，支撑骨架选择。堵塞机构中的支撑骨架选择为菱形骨架，密封薄膜选择为薄膜管。薄膜管中的大球颗粒和小球颗粒均统称为填充颗粒。 Step 11, support frame selection. The support frame in the blocking mechanism is selected as a rhombus frame, and the sealing film is selected as a film tube. The large spherical particles and small spherical particles in the film tube are collectively referred to as filler particles.
步骤12，建立颗粒块模型。为分析填充颗粒对变刚度软体机器人刚度的影响，在真空压力作用下，假定薄膜管内的所有填充颗粒都是刚性的，且被限制为一个整体，也即将薄膜管内的所有填充颗粒和薄膜管，当作为一个整体的颗粒块。Step 12: Establish a particle block model. In order to analyze the influence of the filling particles on the stiffness of the variable stiffness soft robot, under the action of vacuum pressure, it is assumed that all the filling particles in the film tube are rigid and are restricted as a whole, that is, all the filling particles in the film tube and the film tube, When taken as a whole piece of pellets.
步骤13，填充颗粒间的锁紧力F L设计。当颗粒块受到外力时，将填充颗粒中的小球颗粒等效成流体，根据静力平衡方程和帕斯卡定律，得到填充颗粒间锁紧力F L的计算公式如下。 Step 13, the design of the locking force FL between the filling particles. When the particle block receives an external force, the small spherical particles in the filled particles are equivalent to a fluid. According to the static balance equation and Pascal's law, the calculation formula of the locking force FL between the filled particles is obtained as follows.
Figure PCTCN2020100791-appb-000001
Figure PCTCN2020100791-appb-000001
其中，P′为薄膜管内等效压强，R 1为菱形骨架半径，α为菱形骨架的锐形顶角，R 2为大球颗粒半径，μ 1为小球颗粒与菱形骨架之间的摩擦系数，μ 2为小球颗粒与大球颗粒之间的摩擦系数。 Among them, P′ is the equivalent pressure in the film tube, R 1 is the radius of the diamond-shaped skeleton, α is the sharp apex angle of the diamond-shaped skeleton, R 2 is the radius of the large spherical particles, and μ 1 is the friction coefficient between the small spherical particles and the diamond-shaped skeleton , Μ 2 is the friction coefficient between small spherical particles and large spherical particles.
步骤2，薄膜管内等效压强P′计算。自然状态下，小球颗粒半径远小于薄膜管半径，单个小球颗粒正对着的薄膜管区域面积较小，因而，能将与单个小球颗粒接触的薄膜管近似看成是一块平面，建立球体-平面赫兹接触模型，根据赫兹接触理论和两圆球赫兹接触模型，得到薄膜管内等效压强P′的计算公式如下。 Step 2. Calculate the equivalent pressure P'in the film tube. In the natural state, the radius of the small spherical particles is much smaller than the radius of the film tube, and the area of the film tube facing the single small spherical particle is small. Therefore, the film tube in contact with the single small spherical particle can be regarded as a flat surface. The sphere-plane Hertz contact model, according to the Hertz contact theory and the Hertz contact model of two spheres, the calculation formula for the equivalent pressure P′ in the membrane tube is obtained as follows.
Figure PCTCN2020100791-appb-000002
Figure PCTCN2020100791-appb-000002
其中，R 3为小球颗粒半径，v 1为菱形骨架的泊松比，v 2为小球颗粒的泊松比，E 1为菱形骨架杨氏模量，E 2为小球颗粒的杨氏模量，P为薄膜管内的真空压力。 Among them, R 3 is the radius of the small spherical particles, v 1 is the Poisson's ratio of the diamond-shaped framework, v 2 is the Poisson's ratio of the small spherical particles, E 1 is the Young's modulus of the diamond-shaped framework, and E 2 is the Young's ratio of the small spherical particles. Modulus, P is the vacuum pressure in the film tube.
步骤3，建立锁紧力F L与薄膜管内真空压力P的对应关系。将步骤2中计算的薄膜管内等效压强P′代入步骤1设计的锁紧力F L中，得到如下式所示的锁紧力F L与薄膜管内真空压力P的对应关系。 Step 3: Establish the corresponding relationship between the locking force FL and the vacuum pressure P in the film tube. Substituting the equivalent pressure P'in the membrane tube calculated in step 2 into the locking force FL designed in step 1, the corresponding relationship between the locking force FL and the vacuum pressure P in the membrane tube is obtained as shown in the following formula.
Figure PCTCN2020100791-appb-000003
Figure PCTCN2020100791-appb-000003
步骤4，颗粒块的锁紧力矩M L设计，设计公式如下所示。 Step 4. Design the locking torque ML of the particle block. The design formula is shown below.
Figure PCTCN2020100791-appb-000004
Figure PCTCN2020100791-appb-000004
其中，d为薄膜管半径。Among them, d is the radius of the film tube.
还包括步骤5，建立锁紧力矩M L与小球颗粒硬度S 1的对应关系。根据杨氏模量值与肖氏硬度值的对应关系，建立锁紧力矩M L与小球颗粒硬度S 1的对应关系如下。 It also includes step 5, establishing the corresponding relationship between the locking torque M L and the hardness S 1 of the pellets. According to the corresponding relationship between the Young's modulus value and the Shore hardness value, the corresponding relationship between the locking torque M L and the hardness S 1 of the small spherical particles is established as follows.
Figure PCTCN2020100791-appb-000005
Figure PCTCN2020100791-appb-000005
通过调整小球颗粒的硬度S 1，进而调整变刚度软体机器人的刚度。小球颗粒的硬度S 1越大，变刚度软体机器人的刚度越大。 By adjusting the hardness S 1 of the small ball particles, the stiffness of the variable stiffness soft robot is adjusted. The greater the hardness S 1 of the pellets, the greater the rigidity of the variable-rigidity soft robot.
还包括步骤6，薄膜管变形角β的设计。颗粒块受到外力时，薄膜管将与小球颗粒发生接触变形，则薄膜管的变形角β采用如下公式进行计算得出。It also includes step 6, the design of the deformation angle β of the film tube. When the particle block is subjected to an external force, the film tube will deform in contact with the small spherical particles, and the deformation angle β of the film tube is calculated using the following formula.
Figure PCTCN2020100791-appb-000006
Figure PCTCN2020100791-appb-000006
薄膜管变形角β的计算方法，包括如下步骤。The calculation method of the deformation angle β of the film tube includes the following steps.
步骤61，薄膜管的相对径向形变位移δ的计算。根据步骤2中建立的球体-平面赫兹接触模型，再根据赫兹接触理论和两圆球赫兹接触模型，得到薄膜管的相对径向形变位移δ满足如下计算公式。Step 61: Calculate the relative radial deformation displacement δ of the thin film tube. According to the sphere-plane Hertzian contact model established in step 2, and then according to the Hertzian contact theory and the two-sphere Hertzian contact model, the relative radial deformation displacement δ of the membrane tube is obtained to satisfy the following calculation formula.
Figure PCTCN2020100791-appb-000007
Figure PCTCN2020100791-appb-000007
步骤62，建立薄膜管变形角β与薄膜管相对径向形变位移δ的对应关系。根据球体-平面赫兹接触模型，计算得出薄膜管变形角β与薄膜管相对径向形变位移δ的对应关系如下。Step 62: Establish a corresponding relationship between the deformation angle β of the membrane tube and the relative radial deformation displacement δ of the membrane tube. According to the sphere-plane Hertz contact model, the corresponding relationship between the deformation angle β of the membrane tube and the relative radial deformation displacement δ of the membrane tube is calculated as follows.
Figure PCTCN2020100791-appb-000008
Figure PCTCN2020100791-appb-000008
步骤63，薄膜管变形角β的计算。将步骤61中计算得到的薄膜管相对径向形变位移δ代入步骤62中，得出薄膜管变形角β满足如下公式。Step 63: Calculate the deformation angle β of the film tube. Substituting the relative radial deformation displacement δ of the thin film tube calculated in step 61 into step 62, it is obtained that the deformation angle β of the thin film tube satisfies the following formula.
Figure PCTCN2020100791-appb-000009
Figure PCTCN2020100791-appb-000009
步骤13中，根据静力平衡方程和帕斯卡定律，计算填充颗粒间锁紧力F L的方法，包括如下步骤。 In step 13, according to the static balance equation and Pascal's law, the method of calculating the locking force FL between the filled particles includes the following steps.
步骤13a，锁紧力描述。颗粒块包括上层颗粒块和下层颗粒块，其中，下层颗粒块位于待锁紧物体一侧且底部与待锁紧物体相接触，上层颗粒则位于背离待锁紧物体的一侧。当颗粒块受到外力时，下层颗粒块的锁紧力需抵抗外力矩，因而，上层颗粒块和下层颗粒块沿水平方向发生相对滑动，根据颗粒块的静力平衡方程，则锁紧力F L描述为。 Step 13a, description of the locking force. The particle block includes an upper particle block and a lower particle block, wherein the lower particle block is located on the side of the object to be locked and the bottom is in contact with the object to be locked, and the upper particle is located on the side away from the object to be locked. When the particle block is subjected to an external force, the locking force of the lower particle block needs to resist the external moment. Therefore, the upper particle block and the lower particle block slide relative to each other in the horizontal direction. According to the static balance equation of the particle block, the locking force F L described as.
F L＝2f U+f p+f L F L ＝2f U +f p +f L
其中，f L是颗粒块在与菱形骨架接触区域上的摩擦力，f P是颗粒块在锁紧区域上的静态力，f U是下层颗粒块与大球颗粒在水平方向上的摩擦力。 Among them, f L is the friction force of the particle block in the contact area with the diamond-shaped skeleton, f P is the static force of the particle block on the locking area, and f U is the friction force of the lower particle block and the large spherical particles in the horizontal direction.
步骤13b，f P计算。将小球颗粒等效成流体，薄膜管等效为一个密闭空间，密闭空间内填充若干小球颗粒，从而构成一个静态流体模型，则颗粒块作用在锁紧区域水平方向上的静态力f P，将由颗粒块与菱形骨架间的压力提供，具体为。 Step 13b, f P is calculated. The small spherical particles are equivalent to fluid, and the film tube is equivalent to a closed space. Several small spherical particles are filled in the closed space to form a static fluid model. Then the static force f P applied by the particle block in the horizontal direction of the locking area , Will be provided by the pressure between the particle block and the diamond skeleton, specifically.
f P＝πR 1 2P′sinα f P ＝πR 1 2 P′sinα
其中，R 1为菱形骨架半径，α为菱形骨架顶角，P′为薄膜管内等效压强。 Among them, R 1 is the radius of the rhombus skeleton, α is the apex angle of the rhombus skeleton, and P′ is the equivalent pressure in the film tube.
步骤13c，f L计算。颗粒块在与菱形骨架接触区域上的摩擦力f L为。 Step 13c, f L is calculated. The frictional force f L of the particle block in the contact area with the diamond-shaped skeleton is.
f L＝πR 1 2P′μ 1 f L ＝πR 1 2 P′μ 1
其中，μ 1为颗粒块与菱形骨架之间的摩擦系数。 Among them, μ 1 is the friction coefficient between the particle block and the diamond-shaped skeleton.
步骤13d，f U计算。下层颗粒块与大球颗粒在水平方向上的摩擦力f U为。 Step 13d, f U is calculated. The frictional force f U between the lower layer of particles and the large spherical particles in the horizontal direction is.
Figure PCTCN2020100791-appb-000010
Figure PCTCN2020100791-appb-000010
其中，μ 2为小球颗粒与大球颗粒之间的摩擦系数。 Among them, μ 2 is the friction coefficient between small spherical particles and large spherical particles.
步骤13e，将步骤13b、13c和13d计算的f P、f L和f U，分别代入步骤13a中，即得到填充颗粒间锁紧力F L的计算公式。 In step 13e, the f P , f L and f U calculated in steps 13b, 13c, and 13d are substituted into step 13a respectively to obtain the calculation formula of the locking force FL between the filling particles.
通过真空泵调整薄膜管内的真空压力P，进而调整变刚度软体机器人的刚度。当薄膜管内的真空压力P增大时，薄膜管的变形角β和锁紧力矩M L均将增大，变刚度软体机器人的刚度增大。 The vacuum pressure P in the membrane tube is adjusted by the vacuum pump, and then the stiffness of the variable stiffness soft robot is adjusted. When the vacuum pressure P in the membrane tube increases, the deformation angle β and the locking torque M L of the membrane tube will increase, and the stiffness of the variable stiffness soft robot will increase.
通过调整小球颗粒半径R 3，进而调整变刚度软体机器人的刚度。当小球颗粒半径R 3越大，锁紧力矩M L越小，变刚度软体机器人的刚度将减小。 By adjusting the radius of the small ball particle R 3 , the stiffness of the variable stiffness soft robot is adjusted. When the radius R 3 of the small ball particle is larger, the locking torque M L is smaller, and the rigidity of the variable-rigidity soft robot will decrease.
通过调整菱形骨架半径R 1，进而调整变刚度软体机器人的刚度。当菱形骨架半径R 1越大，锁紧力矩M L越大，变刚度软体机器人的刚度将增大。 By adjusting the radius of the diamond skeleton R 1 , the stiffness of the variable stiffness soft robot is adjusted. When the radius R 1 of the rhombus skeleton is larger, the locking torque M L is larger, and the rigidity of the variable-rigidity soft robot will increase.
通过调大球颗粒半径R 2，进而调整变刚度软体机器人的刚度。当大球颗粒半径R 2越大，锁紧力矩M L越大，变刚度软体机器人的刚度将增大。 By increasing the radius of the spherical particle R 2 , the stiffness of the variable stiffness soft robot is adjusted. When the radius R 2 of the large ball particle is larger, the locking torque M L is larger, and the rigidity of the variable-rigidity soft robot will increase.
本发明具有如下有益效果：将颗粒快分为上、下两层，下层颗粒块的锁紧力抵抗外力矩，当末端受到外力时，上、下两层颗粒块沿水平方向发生相对滑动，将小球颗粒等效成流体，薄膜管等效为一个密闭空间，其内部被小球颗粒这一流体填满，根据颗粒块的静力平衡方程得到锁紧力，单个颗粒正对着的薄膜区域面积较小，看成是一块平面，则利用赫兹接触理论对薄膜和颗粒块进行分析，建立球体-平面赫兹接触模型，得出小球颗粒硬度与锁紧力矩的关系。通过调整菱形骨架的顶角、半径，大球颗粒的半径，小球颗粒的半径、硬度，真空压力 等参数，即可得到所需要的变刚度软体机器人的刚度。本发明建立的模型，通过变刚度特性仿真，仿真所得结果与建立的模型保持一致，因而可靠度高，便于推广利用。The invention has the following beneficial effects: the particles are quickly divided into upper and lower layers, and the locking force of the lower layer of particle blocks resists the external moment. When the end receives an external force, the upper and lower layers of particle blocks slide relatively in the horizontal direction. The small spherical particles are equivalent to a fluid, and the film tube is equivalent to a closed space. The inside of the tube is filled with small spherical particles. The locking force is obtained according to the static balance equation of the particle block. The film area where a single particle is facing If the area is small, it can be regarded as a plane, then the film and particle block are analyzed using the Hertzian contact theory, the sphere-plane Hertzian contact model is established, and the relationship between the hardness of the small ball and the locking torque is obtained. By adjusting the apex angle and radius of the rhombus skeleton, the radius of the large spherical particles, the radius of the small spherical particles, the hardness, the vacuum pressure and other parameters, the required stiffness of the variable stiffness soft robot can be obtained. The model established by the invention is simulated through variable stiffness characteristics, and the simulation result is consistent with the established model, so the reliability is high and it is convenient for popularization and utilization.
附图说明Description of the drawings
图1显示了本发明一种变刚度软体机器人中堵塞机构的结构示意图。Figure 1 shows a schematic structural diagram of a blocking mechanism in a variable stiffness soft robot of the present invention.
图2显示了本发明一种变刚度软体机器人中堵塞机构的纵剖面图。Figure 2 shows a longitudinal cross-sectional view of a blocking mechanism in a variable stiffness soft robot of the present invention.
图3显示了本发明一种变刚度软体机器人中堵塞机构末端受力的***分析图。Fig. 3 shows an exploded analysis diagram of the force on the end of the blocking mechanism in a variable stiffness soft robot of the present invention.
图4显示了同一收紧弹簧连接的所有大球颗粒所在纵向平面的剖面图。Figure 4 shows a cross-sectional view of the longitudinal plane where all the large spherical particles connected by the same tightening spring are located.
图5显示了下层颗粒块受力分析示意图。Figure 5 shows a schematic diagram of the force analysis of the lower particle block.
图6显示了流体加压模型示意图。Figure 6 shows a schematic diagram of the fluid pressurization model.
图7显示了本发明中堵塞机构的受力分析示意图。Figure 7 shows a schematic diagram of the force analysis of the blocking mechanism in the present invention.
图8显示了两圆球接触赫兹模型。Figure 8 shows the Hertz model of two balls in contact.
图9显示了小球颗粒与薄膜管接触的颗粒与平面赫兹接触模型。Figure 9 shows the particle-plane Hertz contact model of the small spherical particles in contact with the film tube.
图10显示了图9的简化模型图。Figure 10 shows the simplified model diagram of Figure 9.
图11显示了变形角β与真空压力P的对应关系。Figure 11 shows the corresponding relationship between the deformation angle β and the vacuum pressure P.
图12显示了锁紧力矩M L与真空压力P的对应关系。 Figure 12 shows the corresponding relationship between the locking torque M L and the vacuum pressure P.
图13显示了锁紧力矩M L与小球颗粒半径R 3的对应关系。 Figure 13 shows the corresponding relationship between the locking torque M L and the radius R 3 of the small spherical particles.
图14显示了锁紧力矩M L与菱形骨架半径R 1的对应关系。 Figure 14 shows the corresponding relationship between the locking torque M L and the radius R 1 of the diamond skeleton.
图15显示了锁紧力矩M L与大球颗粒半径R 2的对应关系。 Figure 15 shows the corresponding relationship between the locking torque M L and the radius R 2 of the large spherical particles.
图16显示了锁紧力矩M L与小球颗粒硬度S 1的对应关系。 Figure 16 shows the corresponding relationship between the locking torque M L and the hardness S 1 of the pellets.
其中有：Including:
10.接触区域；20.末端菱形骨架；21.径向大圆；10. Contact area; 20. End diamond-shaped skeleton; 21. Radial great circle;
31.薄膜管；31a.薄膜管变形前；31b.薄膜管变形后；32.菱形骨架；33.柔性绳索；34.大球颗粒；35.小球颗粒；31. Film tube; 31a. Before the film tube is deformed; 31b. After the film tube is deformed; 32. Rhombus skeleton; 33. Flexible rope; 34. Large spherical particles; 35. Small spherical particles;
40.真空泵；40. Vacuum pump;
51.上层颗粒块；52.下层颗粒块；51. Upper particle block; 52. Lower particle block;
60.锁紧区域。60. Locking area.
具体实施方式Detailed ways
下面结合附图和具体较佳实施方式对本发明作进一步详细的说明。The present invention will be further described in detail below in conjunction with the drawings and specific preferred embodiments.
本发明的描述中，需要理解的是，术语“左侧”、“右侧”、“上部”、“下部”等指示的方 位或位置关系为基于附图所示的方位或位置关系，仅是为了便于描述本发明和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作，“第一”、“第二”等并不表示零部件的重要程度，因此不能理解为对本发明的限制。本实施例中采用的具体尺寸只是为了举例说明技术方案，并不限制本发明的保护范围。In the description of the present invention, it should be understood that the orientation or positional relationship indicated by the terms "left", "right", "upper", "lower", etc. are based on the orientation or positional relationship shown in the drawings, and only In order to facilitate the description of the present invention and simplify the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, "first", "second", etc. do not indicate the nature of parts. The degree of importance cannot therefore be understood as a limitation of the present invention. The specific dimensions used in this embodiment are only used to illustrate the technical solution, and do not limit the protection scope of the present invention.
一种变刚度软体机器人，其结构具体参见2017年8月31日申请的申请号为CN201710768485.2的发明专利申请，其发明创造名称为“基于堵塞机理的变刚度软体驱动器、软体手臂和软体平台”，本申请未对堵塞机构结构本身进行改进，只是将堵塞机构中的支撑骨架选择为菱形骨架32，密封薄膜选择为薄膜管31。薄膜管中的大球颗粒34和小球颗粒35均统称为填充颗粒，弹性连接绳索选择为柔性绳索33，通过真空泵40向薄膜管内提供真空压力，具体结构如图1和图2所示。A variable stiffness soft robot. For details, please refer to the invention patent application filed on August 31, 2017 with the application number CN201710768485.2. The name of the invention is "variable stiffness soft driver, soft arm and software platform based on clogging mechanism." "This application does not improve the structure of the blocking mechanism itself, but selects the support frame in the blocking mechanism as the diamond-shaped frame 32, and the sealing film as the film tube 31. The large spherical particles 34 and the small spherical particles 35 in the film tube are collectively referred to as filling particles. The elastic connecting rope is selected as a flexible rope 33, and vacuum pressure is provided into the film tube through a vacuum pump 40. The specific structure is shown in Figs. 1 and 2.
一种变刚度软体机器人的建模方法，包括如下步骤。A modeling method of a variable stiffness soft robot includes the following steps.
步骤1，填充颗粒间的锁紧力F L设计，包括如下步骤。 Step 1, the design of the locking force FL between the filling particles, includes the following steps.
步骤11，支撑骨架选择。 Step 11, support frame selection.
步骤12，建立颗粒块模型。为分析填充颗粒对变刚度软体机器人刚度的影响，在真空压力作用下，假定薄膜管内的所有填充颗粒都是刚性的，且被限制为一个整体，也即将薄膜管内的所有填充颗粒和薄膜管，当作为一个整体的颗粒块。Step 12: Establish a particle block model. In order to analyze the influence of the filling particles on the stiffness of the variable stiffness soft robot, under the action of vacuum pressure, it is assumed that all the filling particles in the film tube are rigid and are restricted as a whole, that is, all the filling particles in the film tube and the film tube, When taken as a whole piece of pellets.
步骤13，填充颗粒间的锁紧力F L设计。 Step 13, the design of the locking force FL between the filling particles.
当颗粒块受到外力时，将填充颗粒中的小球颗粒等效成流体，根据静力平衡方程和帕斯卡定律，得到填充颗粒间锁紧力F L的计算公式如下。 When the particle block receives an external force, the small spherical particles in the filled particles are equivalent to a fluid. According to the static balance equation and Pascal's law, the calculation formula of the locking force FL between the filled particles is obtained as follows.
Figure PCTCN2020100791-appb-000011
Figure PCTCN2020100791-appb-000011
其中，P′为薄膜管内等效压强，R 1为菱形骨架半径，α为菱形骨架的锐形顶角，R 2为大球颗粒半径，μ 1为小球颗粒与菱形骨架之间的摩擦系数，μ 2为小球颗粒与大球颗粒之间的摩擦系数。 Among them, P′ is the equivalent pressure in the film tube, R 1 is the radius of the diamond-shaped skeleton, α is the sharp apex angle of the diamond-shaped skeleton, R 2 is the radius of the large spherical particles, and μ 1 is the friction coefficient between the small spherical particles and the diamond-shaped skeleton , Μ 2 is the friction coefficient between small spherical particles and large spherical particles.
上述根据静力平衡方程和帕斯卡定律，计算填充颗粒间锁紧力F L的方法，包括如下步骤。 The above method for calculating the locking force FL between filled particles according to the static balance equation and Pascal's law includes the following steps.
步骤13a，锁紧力描述。颗粒块包括上层颗粒块51和下层颗粒块52，其中，下层颗粒块位于待锁紧物体一侧且底部与待锁紧物体相接触，上层颗粒则位于背离待锁紧物体的一侧。如图3、图4和图5所示，当颗粒块受到外力F E时，下层颗粒块的锁紧力需抵抗外力矩，因而，上层颗粒块和下层颗粒块沿水平方向发生相对滑动，根据颗粒块的静力平衡方程，则锁 紧力F L描述为。 Step 13a, description of the locking force. The particle block includes an upper particle block 51 and a lower particle block 52, wherein the lower particle block is located on the side of the object to be locked and the bottom is in contact with the object to be locked, and the upper particle is located on the side away from the object to be locked. As shown in Figure 3, Figure 4 and Figure 5, when the particle block receives an external force F E , the locking force of the lower particle block needs to resist the external moment. Therefore, the upper particle block and the lower particle block slide relative to each other in the horizontal direction. The static balance equation of the particle block, then the locking force FL is described as.
F L＝2f U+f p+f L F L ＝2f U +f p +f L
其中，f L是颗粒块在与菱形骨架接触区域10上的摩擦力，f P是颗粒块在锁紧区域60上的静态力，f U是下层颗粒块与大球颗粒在水平方向上的摩擦力。 Among them, f L is the friction force of the particle block on the contact area 10 with the diamond-shaped skeleton, f P is the static force of the particle block on the locking area 60, and f U is the horizontal friction between the lower particle block and the large spherical particles. force.
步骤13b，f P计算。 Step 13b, f P is calculated.
颗粒块在锁紧区域上的静态力f P，可通过流体加压模型来估算。根据帕斯卡定律，密闭空间内的流体，施加到流体上压强，能够大小不变的由流体向空间各个方向传递。根据图6和帕斯卡定律，我们可得出： The static force f P of the particle block on the locking area can be estimated by the fluid pressure model. According to Pascal's law, the fluid in a confined space, exerts pressure on the fluid, can be transferred from the fluid to all directions in the space with the same magnitude. According to Figure 6 and Pascal's law, we can get:
Figure PCTCN2020100791-appb-000012
Figure PCTCN2020100791-appb-000012
图6中，密闭空间上表面和下表面面积相等，均为A 2，F ext相当于步骤13a中颗粒块受到的外力F E。 In Fig. 6, the upper surface and the lower surface area of the enclosed space are equal, both are A 2 , and F ext is equivalent to the external force F E received by the particle block in step 13a.
所以，施加在图6区域A 1上的力为： Therefore, the force applied to area A 1 in Figure 6 is:
Figure PCTCN2020100791-appb-000013
Figure PCTCN2020100791-appb-000013
将小球颗粒等效成流体，薄膜管等效为一个密闭空间，其内部被小球颗粒这一流体填满，则构成了一个如图7所示的静态流体模型，施加在每一面的力可以通过上式来计算。The small spherical particles are equivalent to a fluid, and the film tube is equivalent to a closed space, and its interior is filled with small spherical particles, which constitutes a static fluid model as shown in Figure 7. The force applied on each side It can be calculated by the above formula.
则，颗粒块在锁紧区域A 3上的静态力f P： Then, the static force f P of the particle block on the locking area A 3 :
f P＝F N2sinα＝P′A 3sinα＝πR 1 2P′sinα f P =F N2 sinα=P′A 3 sinα=πR 1 2 P′sinα
其中，F N2为颗粒块对菱形骨架的正压力，如图7所示，R 1为菱形骨架半径，α为菱形骨架顶角，P'为颗粒块施加给菱形骨架和大球的等效压强，也即为薄膜管内等效压强。 Among them, FN2 is the positive pressure of the particle block on the diamond-shaped skeleton, as shown in Figure 7, R 1 is the radius of the diamond-shaped skeleton, α is the apex angle of the diamond-shaped skeleton, and P'is the equivalent pressure applied by the particle block to the diamond-shaped skeleton and the big sphere. , Which is the equivalent pressure in the film tube.
上述菱形骨架半径R 1，是指图3中菱形骨架中径向大圆所在直径面中的半径，无限接近薄膜管半径d，可以近似相等。菱形骨架顶角α，是指位于柔性绳索上的顶角，为锐角。 The above-mentioned diamond-shaped skeleton radius R 1 refers to the radius of the radial large circle in the diamond-shaped skeleton in Fig. 3, which is infinitely close to the radius d of the film tube and can be approximately equal. The apex angle α of the rhombus skeleton refers to the apex angle on the flexible rope, which is an acute angle.
步骤13c，f L计算：颗粒块在与菱形骨架接触区域上的摩擦力f L为： Step 13c, f L calculation: the friction force f L of the particle block in the contact area with the diamond-shaped skeleton is:
f L＝μ 1P′·A 1＝πR 1 2P′μ 1 f L ＝μ 1 P′·A 1 ＝πR 1 2 P′μ 1
其中μ 1为颗粒块与菱形骨架之间的摩擦系数，A 1为颗粒块与菱形骨架接触区域的等效面积。 Among them, μ 1 is the friction coefficient between the particle block and the diamond-shaped skeleton, and A 1 is the equivalent area of the contact area between the particle block and the diamond-shaped skeleton.
步骤13d，f U计算：下层颗粒块与大球颗粒在水平方向上的摩擦力f U为： Step 13d, f U calculation: the frictional force f U between the lower layer of particles and the large spherical particles in the horizontal direction is:
Figure PCTCN2020100791-appb-000014
Figure PCTCN2020100791-appb-000014
其中F N1为颗粒块对大球颗粒的正压力,R 2为大球颗粒半径，μ 2为小球颗粒(填充颗粒)与大球颗粒之间的摩擦系数，A 2为颗粒块与大球颗粒接触的等效面积。 Among them, F N1 is the positive pressure of the particle block on the large spherical particle, R 2 is the radius of the large spherical particle, μ 2 is the friction coefficient between the small spherical particle (filling particle) and the large spherical particle, and A 2 is the particle block and the large spherical particle. The equivalent area of particle contact.
步骤13e，将步骤13b、13c和13d计算的f P、f L和f U，分别代入步骤13a中，即得到填充颗粒间锁紧力F L的计算公式。 In step 13e, the f P , f L and f U calculated in steps 13b, 13c, and 13d are substituted into step 13a respectively to obtain the calculation formula of the locking force FL between the filling particles.
步骤2，薄膜管内等效压强P′计算。 Step 2. Calculate the equivalent pressure P'in the film tube.
根据赫兹接触理论和图8所示的两圆球赫兹接触模型，则两球体相接触后，其中心相对变形位移和应力分别为：According to the Hertzian contact theory and the Hertzian contact model of the two spheres shown in Figure 8, the relative deformation displacement and stress of the center of the two spheres after contact are as follows:
Figure PCTCN2020100791-appb-000015
Figure PCTCN2020100791-appb-000015
Figure PCTCN2020100791-appb-000016
Figure PCTCN2020100791-appb-000016
其中，R a为图8中a球半径,R b为b球半径，v a为a球泊松比，v b为b球泊松比，E a为a球杨氏模量，E b为b球杨氏模量。 Among them, Ra is the radius of the ball a in Figure 8, R b is the radius of the ball b, v a is the Poisson's ratio of the ball a, v b is the Poisson's ratio of the ball b, E a is the Young's modulus of the ball a, and E b is b Ball Young's modulus.
自然状态下，小球颗粒半径远小于薄膜管半径，单个小球颗粒正对着的薄膜管区域面积较小，因而，能将与单个小球颗粒接触的薄膜管近似看成是一块平面，利用赫兹接触模型对薄膜管和颗粒块进行分析，建立球体-平面赫兹接触模型，令上述公式中的的R a＝∞,R b＝R 3，并将薄膜管和小球颗粒的参数代入，得到薄膜管内等效压强P′的计算公式如下： In the natural state, the radius of the small spherical particle is much smaller than the radius of the film tube, and the area of the film tube facing the single small spherical particle is small. Therefore, the film tube in contact with the single small spherical particle can be regarded as a flat surface. The Hertzian contact model analyzes the film tube and the particle block, and establishes the sphere-plane Hertzian contact model. Let Ra = ∞, R b = R 3 in the above formula, and substitute the parameters of the film tube and the small spherical particles to obtain The calculation formula of the equivalent pressure P′ in the film tube is as follows:
Figure PCTCN2020100791-appb-000017
Figure PCTCN2020100791-appb-000017
Figure PCTCN2020100791-appb-000018
Figure PCTCN2020100791-appb-000018
其中，δ薄膜管的相对径向形变位移，R 3为小球颗粒半径，v 1为菱形骨架的泊松比，v 2为小球颗粒的泊松比，E 1为菱形骨架杨氏模量，E 2为小球颗粒的杨氏模量，P为薄膜管内的真空压力。 Among them, the relative radial deformation displacement of the δ film tube, R 3 is the radius of the small spherical particles, v 1 is the Poisson's ratio of the diamond-shaped framework, v 2 is the Poisson's ratio of the small spherical particles, and E 1 is the Young's modulus of the diamond-shaped framework , E 2 is the Young's modulus of the small spherical particles, and P is the vacuum pressure in the film tube.
步骤3，建立锁紧力F L与薄膜管内真空压力P的对应关系。将步骤2中计算的薄膜管内等效压强P′代入步骤1设计的锁紧力F L中，得到如下式所示的锁紧力F L与薄膜管内真空压力P的对应关系。 Step 3: Establish the corresponding relationship between the locking force FL and the vacuum pressure P in the film tube. Substituting the equivalent pressure P'in the membrane tube calculated in step 2 into the locking force FL designed in step 1, the corresponding relationship between the locking force FL and the vacuum pressure P in the membrane tube is obtained as shown in the following formula.
Figure PCTCN2020100791-appb-000019
Figure PCTCN2020100791-appb-000019
步骤4，颗粒块的锁紧力矩M L设计，设计公式如下所示。 Step 4. Design the locking torque ML of the particle block. The design formula is shown below.
Figure PCTCN2020100791-appb-000020
Figure PCTCN2020100791-appb-000020
其中，d为薄膜管半径。Among them, d is the radius of the film tube.
当真空压力P取极限真空度P m＝101kPa，并将数值代入上式中，则得到最大锁紧力矩M Lm＝304.5N.mm。 When the vacuum pressure P takes the ultimate vacuum degree P m =101kPa, and the value is substituted into the above formula, the maximum locking torque M Lm =304.5N.mm is obtained.
步骤5，建立锁紧力矩M L与小球颗粒硬度S 1的对应关系。 Step 5: Establish the corresponding relationship between the locking torque M L and the hardness S 1 of the small ball particles.
基于经典线弹性理论，A.N.Gent提出杨氏模量值E与肖氏硬度值S的关系，为：Based on the classical linear elastic theory, A.N.Gent proposed the relationship between the Young's modulus value E and the Shore hardness value S, as:
Figure PCTCN2020100791-appb-000021
Figure PCTCN2020100791-appb-000021
其中E为以MPa为单位的杨氏模量，S是以ASTM D2240标准的硬度计示数。该公式适用于硬度为20到80的物质，与小球颗粒的物质属性想接近。Where E is the Young's modulus in MPa, and S is the hardness in accordance with ASTM D2240. This formula is suitable for materials with a hardness of 20 to 80, which is close to the material properties of small spherical particles.
根据上述杨氏模量值与肖氏硬度值的对应关系，建立锁紧力矩M L与小球颗粒硬度S 1的对应关系如下。 According to the above-mentioned corresponding relationship between the Young's modulus value and the Shore hardness value, the corresponding relationship between the locking torque M L and the hardness S 1 of the small spherical particles is established as follows.
Figure PCTCN2020100791-appb-000022
Figure PCTCN2020100791-appb-000022
通过调整小球颗粒的硬度S 1，进而调整变刚度软体机器人的刚度。小球颗粒的硬度S 1越大，变刚度软体机器人的刚度越大。 By adjusting the hardness S 1 of the small ball particles, the stiffness of the variable stiffness soft robot is adjusted. The greater the hardness S 1 of the pellets, the greater the rigidity of the variable-rigidity soft robot.
步骤6，薄膜管变形角β的设计。 Step 6, the design of the deformation angle β of the film tube.
颗粒块受到外力时，薄膜管将与小球颗粒发生接触变形，则薄膜管的变形角β采用如下公式进行计算得出。When the particle block is subjected to an external force, the film tube will deform in contact with the small spherical particles, and the deformation angle β of the film tube is calculated using the following formula.
Figure PCTCN2020100791-appb-000023
Figure PCTCN2020100791-appb-000023
薄膜管变形角β的计算方法，包括如下步骤。The calculation method of the deformation angle β of the film tube includes the following steps.
步骤61，薄膜管的相对径向形变位移δ的计算。根据步骤2中建立的球体-平面赫兹接触模型，再根据赫兹接触理论和两圆球赫兹接触模型，得到薄膜管的相对径向形变位移δ满足如下计算公式。Step 61: Calculate the relative radial deformation displacement δ of the thin film tube. According to the sphere-plane Hertzian contact model established in step 2, and then according to the Hertzian contact theory and the two-sphere Hertzian contact model, the relative radial deformation displacement δ of the membrane tube is obtained to satisfy the following calculation formula.
Figure PCTCN2020100791-appb-000024
Figure PCTCN2020100791-appb-000024
本发明中，在步骤2，已能得出上述计算公式，此处仅为引用。In the present invention, in step 2, the above calculation formula can be obtained, which is only for reference here.
步骤62，建立薄膜管变形角β与薄膜管相对径向形变位移δ的对应关系。Step 62: Establish a corresponding relationship between the deformation angle β of the membrane tube and the relative radial deformation displacement δ of the membrane tube.
根据如9所示的球体-平面赫兹接触模型及如图10所示的简化模型，由等腰∠ABC、∠AEC和直角∠ADC、∠EDC的性质，可得出以下关系：According to the sphere-plane Hertz contact model shown in Figure 9 and the simplified model shown in Figure 10, the following relationships can be derived from the properties of isosceles ∠ABC, ∠AEC and right angles ∠ADC, ∠EDC:
Figure PCTCN2020100791-appb-000025
Figure PCTCN2020100791-appb-000025
Figure PCTCN2020100791-appb-000026
Figure PCTCN2020100791-appb-000026
∠ABC＝2∠DAC＝∠β∠ABC＝2∠DAC＝∠β
上述三式联立，计算得出薄膜管变形角β与薄膜管相对径向形变位移δ的对应关系如下：Combining the above three formulas, the corresponding relationship between the deformation angle β of the membrane tube and the relative radial deformation displacement δ of the membrane tube is calculated as follows:
Figure PCTCN2020100791-appb-000027
Figure PCTCN2020100791-appb-000027
步骤63，薄膜管变形角β的计算。将步骤61中计算得到的薄膜管相对径向形变位移δ代入步骤62中，得出薄膜管变形角β满足如下公式。Step 63: Calculate the deformation angle β of the film tube. Substituting the relative radial deformation displacement δ of the thin film tube calculated in step 61 into step 62, it is obtained that the deformation angle β of the thin film tube satisfies the following formula.
Figure PCTCN2020100791-appb-000028
Figure PCTCN2020100791-appb-000028
变刚度特性仿真：Simulation of variable stiffness characteristics:
利用步骤6设计的薄膜管变形角β，将机构的参数设置为：菱形骨架半径R 1＝14mm，大球颗粒半径R 2＝6.5mm，填充颗粒半径R 3＝3mm，得到了图11所示的薄膜变形角β与真空压力P之间的关系。从图中可看出，真空压力P越大，薄膜变形角β也越大。同时，随着压力逐渐增大，压力增量相同时，薄膜变形角的增量不断减小。 Using the deformation angle β of the thin film tube designed in step 6, set the parameters of the mechanism as: diamond-shaped skeleton radius R 1 =14mm, large spherical particle radius R 2 =6.5mm, filling particle radius R 3 =3mm, and the result shown in Figure 11 The relationship between the film deformation angle β and the vacuum pressure P. It can be seen from the figure that the greater the vacuum pressure P, the greater the film deformation angle β. At the same time, as the pressure gradually increases, when the pressure increment is the same, the increment of the film deformation angle continues to decrease.
根据步骤3中建立的锁紧力F L与薄膜管内真空压力P对应关系，将参数设置为：R 1＝14mm，R 2＝6.5mm，R 3＝3mm，P＝80kPa，薄膜管半径d＝16mm。得到如图12所示的锁紧力矩M L和真空压力P之间的关系。从图中可见，真空压力P越大，锁紧力矩M L越大。因此，可通过调整真空压力来控制机构刚度。 According to the corresponding relationship between the locking force F L established in step 3 and the vacuum pressure P in the film tube, the parameters are set as: R 1 =14mm, R 2 =6.5mm, R 3 =3mm, P=80kPa, the film tube radius d= 16mm. The relationship between the locking torque M L and the vacuum pressure P as shown in Fig. 12 is obtained. It can be seen from the figure that the greater the vacuum pressure P, the greater the locking torque M L. Therefore, the stiffness of the mechanism can be controlled by adjusting the vacuum pressure.
根据步骤4设计的颗粒块的锁紧力矩M L，将机构的参数设置为：R 1＝14mm，R 2＝6.5mm，P＝80kPa，d＝16mm，并将R 3范围设置在2mm～6mm之间。得到图13所示锁紧力矩M L与小球颗粒半径R 3之间的关系。从图中可知，小球颗粒半径R 3越大，锁紧力矩M L越小。且随着小颗粒尺寸的减小，相同尺寸减量下，锁紧力矩M L的减量越来越小。 According to the locking torque M L of the particle block designed in step 4, set the parameters of the mechanism as: R 1 =14mm, R 2 =6.5mm, P=80kPa, d=16mm, and set the range of R 3 to 2mm～6mm between. The relationship between the locking torque M L and the radius R 3 of the small spherical particles shown in Fig. 13 is obtained. It can be seen from the figure that the larger the radius R 3 of the pellets, the smaller the locking torque M L. And as the size of small particles decreases, the decrease of the locking torque M L becomes smaller and smaller under the same size reduction.
根据步骤4设计的颗粒块的锁紧力矩M L，将机构的参数设置为：R 2＝6.5mm，R 3＝3mm，d＝16mm，P＝80kPa，并将菱形骨架半径R 1范围设置在10mm～15mm之间。得到图14所示锁紧力矩M L与菱形骨架R 1之间的关系。从图中可知，菱形骨架的半径R 1越大，锁紧力矩M L越大。 According to the locking moment M L of the particle block designed in step 4, set the parameters of the mechanism as: R 2 =6.5mm, R 3 =3mm, d=16mm, P=80kPa, and set the diamond-shaped skeleton radius R 1 in the range Between 10mm～15mm. The relationship between the locking torque M L and the diamond-shaped skeleton R 1 shown in FIG. 14 is obtained. It can be seen from the figure that the larger the radius R 1 of the diamond-shaped skeleton is, the larger the locking torque M L is.
根据步骤4设计的颗粒块的锁紧力矩M L，将机构的参数设置为:R 1＝14mm，R 3＝3mm，d＝16mm，P＝80kPa，并将大球颗粒半径R 2设置为3mm～7mm之间。可得图15所示锁紧力矩M L与大球颗粒半径尺寸R2之间的关系。可见大球颗粒半径尺寸越大，锁紧力矩M L越大。且随着大球颗粒半径的增大，相同尺寸增量下，锁紧力矩M L的增量越来越大。 According to the locking torque M L of the particle block designed in step 4, set the parameters of the mechanism as: R 1 =14mm, R 3 =3mm, d=16mm, P=80kPa, and set the radius R 2 of the large spherical particle to 3mm ～7mm. The relationship between the locking torque M L and the radius size R2 of the large spherical particles shown in Fig. 15 can be obtained. It can be seen that the larger the radius of the large spherical particles, the larger the locking torque M L. And with the increase of the radius of the large spherical particles, the increase of the locking torque M L becomes larger and larger under the same size increment.
根据步骤4设计的颗粒块的锁紧力矩M L，将机构的参数设置为:R1＝14mm，R 2＝6.5mm，R 3＝3mm，d＝16mm，P＝80kPa。然后得到图16所示锁紧力矩M L与颗粒硬度S1之间的关系。 从图中可见，小颗粒硬度S1越大，锁紧力矩M L越大。且随着小颗粒硬度的增大，相同增量下，锁紧力矩M L的增量越来越小。 The tightening torque M L grain block design in step 4, the parameter setting means: R1 = 14mm, R 2 = 6.5mm, R 3 = 3mm, d = 16mm, P = 80kPa. Then, the relationship between the locking torque M L and the particle hardness S1 shown in Fig. 16 is obtained. It can be seen from the figure that the greater the hardness S1 of the small particles, the greater the locking torque M L. And with the increase of the hardness of the small particles, the increase of the locking torque M L becomes smaller and smaller under the same increment.
本发明首先从理论上对堵塞变刚度结构变刚度原理进行研究进行分析，先简化建模，并应用帕斯卡模型和赫兹接触理论，建立堵塞机构的力学模型，推导出机构末端的锁紧力矩与真空压力，小球颗粒硬度和大球颗粒半径之间的关系。得出机构刚度与真空度、菱形骨架半径和大球颗粒尺寸的关系，并进行仿真分析。便于后续驱动器空腔形状和壁厚尺寸的设计，以便具备更好的弯曲性能，更符合设计要求。The invention first theoretically studies and analyzes the principle of variable stiffness of the plugging variable stiffness structure, first simplifying the modeling, and applying the Pascal model and Hertz contact theory to establish the mechanical model of the plugging mechanism, and derive the locking torque and vacuum at the end of the mechanism The relationship between the pressure, the hardness of the small spherical particles and the radius of the large spherical particles. The relationship between the stiffness of the mechanism and the degree of vacuum, the radius of the diamond skeleton and the size of the large spherical particles is obtained, and the simulation analysis is performed. It is convenient for the subsequent design of the cavity shape and wall thickness of the driver to have better bending performance and better meet the design requirements.
以上详细描述了本发明的优选实施方式，但是，本发明并不限于上述实施方式中的具体细节，在本发明的技术构思范围内，可以对本发明的技术方案进行多种等同变换，这些等同变换均属于本发明的保护范围。The preferred embodiments of the present invention are described in detail above. However, the present invention is not limited to the specific details in the above-mentioned embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention. These equivalent transformations All belong to the protection scope of the present invention.

Claims (10)

  1. 一种变刚度软体机器人的建模方法，其特征在于：包括如下步骤：A modeling method for a variable stiffness soft robot, which is characterized in that it comprises the following steps:
    步骤1，填充颗粒间的锁紧力F L设计，包括如下步骤： Step 1, the design of the locking force FL between the filling particles, including the following steps:
    步骤11，支撑骨架选择：堵塞机构中的支撑骨架选择为菱形骨架，密封薄膜选择为薄膜管；薄膜管中的大球颗粒和小球颗粒均统称为填充颗粒；Step 11, support frame selection: the support frame in the blocking mechanism is selected as a diamond frame, and the sealing film is selected as a film tube; the large spherical particles and small spherical particles in the film tube are collectively referred to as filler particles;
    步骤12，建立颗粒块模型：为分析填充颗粒对变刚度软体机器人刚度的影响，在真空压力作用下，假定薄膜管内的所有填充颗粒都是刚性的，且被限制为一个整体，也即将薄膜管内的所有填充颗粒和薄膜管，当作为一个整体的颗粒块；Step 12: Establish a particle block model: In order to analyze the effect of the filling particles on the stiffness of the variable stiffness soft robot, under the action of vacuum pressure, it is assumed that all the filling particles in the film tube are rigid and restricted as a whole, that is, the inside of the film tube All the filled particles and film tubes are treated as a whole particle block;
    步骤13，填充颗粒间的锁紧力F L设计：当颗粒块受到外力时，将填充颗粒中的小球颗粒等效成流体，根据静力平衡方程和帕斯卡定律，得到填充颗粒间锁紧力F L的计算公式如下： Step 13, the locking force F L between the design of filler particles: when the external force is applied grain block, pellets equivalent granular fill fluid particles, according to the static equilibrium equations and Pascal's law, the locking force between the filler particles to give The calculation formula of FL is as follows:
    Figure PCTCN2020100791-appb-100001
    Figure PCTCN2020100791-appb-100001
    其中，P′为薄膜管内等效压强，R 1为菱形骨架半径，α为菱形骨架的锐形顶角，R 2为大球颗粒半径，μ 1为小球颗粒与菱形骨架之间的摩擦系数，μ 2为小球颗粒与大球颗粒之间的摩擦系数； Among them, P′ is the equivalent pressure in the film tube, R 1 is the radius of the diamond skeleton, α is the sharp apex angle of the diamond skeleton, R 2 is the radius of the large spherical particles, and μ 1 is the friction coefficient between the small spherical particles and the diamond skeleton. , Μ 2 is the friction coefficient between small spherical particles and large spherical particles;
    步骤2，薄膜管内等效压强P′计算：自然状态下，小球颗粒半径远小于薄膜管半径，单个小球颗粒正对着的薄膜管区域面积较小，因而，能将与单个小球颗粒接触的薄膜管近似看成是一块平面，建立球体-平面赫兹接触模型，根据赫兹接触理论和两圆球赫兹接触模型，得到薄膜管内等效压强P′的计算公式如下：Step 2. Calculate the equivalent pressure P′ in the film tube: In the natural state, the radius of the small spherical particle is much smaller than the radius of the film tube, and the area of the film tube facing the single small spherical particle is small. Therefore, it can be compared with the single small spherical particle. The contacting membrane tube is approximately regarded as a plane, and the sphere-plane Hertz contact model is established. According to the Hertz contact theory and the two-sphere Hertz contact model, the calculation formula of the equivalent pressure P′ in the membrane tube is obtained as follows:
    Figure PCTCN2020100791-appb-100002
    Figure PCTCN2020100791-appb-100002
    其中，R 3为小球颗粒半径，v 1为菱形骨架的泊松比，v 2为小球颗粒的泊松比，E 1为菱形骨架杨氏模量，E 2为小球颗粒的杨氏模量，P为薄膜管内的真空压力； Among them, R 3 is the radius of the small spherical particles, v 1 is the Poisson's ratio of the diamond-shaped framework, v 2 is the Poisson's ratio of the small spherical particles, E 1 is the Young's modulus of the diamond-shaped framework, and E 2 is the Young's ratio of the small spherical particles. Modulus, P is the vacuum pressure in the film tube;
    步骤3，建立锁紧力F L与薄膜管内真空压力P的对应关系：将步骤2中计算的薄膜管内等效压强P′代入步骤1设计的锁紧力F L中，得到如下式所示的锁紧力F L与薄膜管内真空压力P的对应关系： Step 3. Establish the corresponding relationship between the locking force FL and the vacuum pressure P in the membrane tube: Substitute the equivalent pressure P′ in the membrane tube calculated in step 2 into the locking force FL designed in step 1, and obtain the following formula Corresponding relationship between locking force F L and vacuum pressure P in the film tube:
    Figure PCTCN2020100791-appb-100003
    Figure PCTCN2020100791-appb-100003
    步骤4，颗粒块的锁紧力矩M L设计，设计公式如下所示： Step 4. Design the locking torque ML of the particle block. The design formula is as follows:
    Figure PCTCN2020100791-appb-100004
    Figure PCTCN2020100791-appb-100004
    其中，d为薄膜管半径。Among them, d is the radius of the film tube.
  2. 根据权利要求1所述的变刚度软体机器人的建模方法，其特征在于：还包括步骤5，建立锁紧力矩M L与小球颗粒硬度S 1的对应关系：根据杨氏模量值与肖氏硬度值的对应关系，建立锁紧力矩M L与小球颗粒硬度S 1的对应关系如下： The modeling method of a variable stiffness soft robot according to claim 1, characterized in that it further comprises step 5, establishing the corresponding relationship between the locking torque M L and the hardness S 1 of the small spherical particles: according to the Young's modulus value and the Shore Corresponding relationship of the hardness value, the corresponding relationship between the locking torque M L and the hardness S 1 of the small ball particles is established as follows:
    Figure PCTCN2020100791-appb-100005
    Figure PCTCN2020100791-appb-100005
  3. 根据权利要求2所述的变刚度软体机器人的建模方法，其特征在于：通过调整小球颗粒的硬度S 1，进而调整变刚度软体机器人的刚度；小球颗粒的硬度S 1越大，变刚度软体机器人的刚度越大。 The modeling method of the variable stiffness soft robot according to claim 2, characterized in that: the stiffness of the variable stiffness soft robot is adjusted by adjusting the hardness S 1 of the small spherical particles ; the greater the hardness S 1 of the small spherical particles, the change Stiffness The greater the stiffness of the soft robot.
  4. 根据权利要求2所述的变刚度软体机器人的建模方法，其特征在于：还包括步骤6，薄膜管变形角β的设计：颗粒块受到外力时，薄膜管将与小球颗粒发生接触变形，则薄膜管的变形角β采用如下公式进行计算得出：The modeling method of a variable stiffness soft robot according to claim 2, characterized in that it further comprises step 6, the design of the deformation angle β of the film tube: when the particle block receives an external force, the film tube will deform in contact with the small spherical particles, Then the deformation angle β of the film tube is calculated using the following formula:
    Figure PCTCN2020100791-appb-100006
    Figure PCTCN2020100791-appb-100006
  5. 根据权利要求4所述的变刚度软体机器人的建模方法，其特征在于：薄膜管变形角β的计算方法，包括如下步骤：The modeling method of a variable stiffness soft robot according to claim 4, wherein the method for calculating the deformation angle β of the film tube includes the following steps:
    步骤61，薄膜管的相对径向形变位移δ的计算：根据步骤2中建立的球体-平面赫兹接触模型，再根据赫兹接触理论和两圆球赫兹接触模型，得到薄膜管的相对径向形变位移δ满足如下计算公式：Step 61: Calculation of the relative radial deformation displacement δ of the membrane tube: According to the sphere-plane Hertz contact model established in step 2, and then according to the Hertz contact theory and the two-sphere Hertz contact model, the relative radial deformation displacement of the membrane tube is obtained. δ satisfies the following calculation formula:
    Figure PCTCN2020100791-appb-100007
    Figure PCTCN2020100791-appb-100007
    步骤62，建立薄膜管变形角β与薄膜管相对径向形变位移δ的对应关系：根据球体-平面赫兹接触模型，计算得出薄膜管变形角β与薄膜管相对径向形变位移δ的对应关系如下：Step 62: Establish the corresponding relationship between the deformation angle β of the membrane tube and the relative radial deformation displacement δ of the membrane tube: According to the sphere-plane Hertz contact model, the correspondence relationship between the deformation angle β of the membrane tube and the relative radial deformation displacement δ of the membrane tube is calculated as follows:
    Figure PCTCN2020100791-appb-100008
    Figure PCTCN2020100791-appb-100008
    步骤63，薄膜管变形角β的计算：将步骤61中计算得到的薄膜管相对径向形变位移δ代入步骤62中，得出薄膜管变形角β满足如下公式：Step 63: Calculation of the deformation angle β of the thin film tube: Substituting the relative radial deformation displacement δ of the thin film tube calculated in step 61 into step 62, it is obtained that the deformation angle β of the thin film tube satisfies the following formula:
    Figure PCTCN2020100791-appb-100009
    Figure PCTCN2020100791-appb-100009
  6. 根据权利要求1所述的变刚度软体机器人的建模方法，其特征在于：步骤13中，根据静力平衡方程和帕斯卡定律，计算填充颗粒间锁紧力F L的方法，包括如下步骤： The modeling method of a variable stiffness soft robot according to claim 1, characterized in that: in step 13, according to the static balance equation and Pascal's law, the method of calculating the locking force FL between the filled particles includes the following steps:
    步骤13a，锁紧力描述：颗粒块包括上层颗粒块和下层颗粒块，其中，下层颗粒块位于待锁紧物体一侧且底部与待锁紧物体相接触，上层颗粒则位于背离待锁紧物体的一侧；当颗粒块受到外力时，下层颗粒块的锁紧力需抵抗外力矩，因而，上层颗粒块和下层颗粒块沿水平方向发生相对滑动，根据颗粒块的静力平衡方程，则锁紧力F L描述为： Step 13a, description of locking force: the particle block includes an upper particle block and a lower particle block, where the lower particle block is located on the side of the object to be locked and the bottom is in contact with the object to be locked, while the upper particle is located away from the object to be locked When the particle block is subjected to an external force, the locking force of the lower particle block needs to resist the external moment. Therefore, the upper particle block and the lower particle block slide relative to each other in the horizontal direction. According to the static balance equation of the particle block, the lock The tightening force FL is described as:
    F L＝2f U+f p+f L F L ＝2f U +f p +f L
    其中，f L是颗粒块在与菱形骨架接触区域上的摩擦力，f P是颗粒块在锁紧区域上的静态力，f U是下层颗粒块与大球颗粒在水平方向上的摩擦力； Among them, f L is the friction force of the particle block in the contact area with the diamond-shaped skeleton, f P is the static force of the particle block on the locking area, and f U is the friction force of the lower particle block and the large spherical particles in the horizontal direction;
    步骤13b，f P计算：将小球颗粒等效成流体，薄膜管等效为一个密闭空间，密闭空间内填充若干小球颗粒，从而构成一个静态流体模型，则颗粒块作用在锁紧区域水平方向上的静态力f P，将由颗粒块与菱形骨架间的压力提供，具体为： Step 13b, f P calculation: the small spherical particles are equivalent to a fluid, and the film tube is equivalent to a closed space, and a number of small spherical particles are filled in the closed space to form a static fluid model, and the particle block acts on the level of the locked area The static force f P in the direction will be provided by the pressure between the particle block and the diamond skeleton, specifically:
    f P＝πR 1 2P′sinα f P ＝πR 1 2 P′sinα
    其中，R 1为菱形骨架半径，α为菱形骨架顶角，P′为薄膜管内等效压强； Among them, R 1 is the radius of the diamond-shaped framework, α is the apex angle of the diamond-shaped framework, and P′ is the equivalent pressure in the film tube;
    步骤13c，f L计算：颗粒块在与菱形骨架接触区域上的摩擦力f L为： Step 13c, f L calculation: the friction force f L of the particle block in the contact area with the diamond-shaped skeleton is:
    f L＝πR 1 2P′μ 1 f L ＝πR 1 2 P′μ 1
    其中，μ 1为颗粒块与菱形骨架之间的摩擦系数； Among them, μ 1 is the friction coefficient between the particle block and the diamond-shaped skeleton;
    步骤13d，f U计算：下层颗粒块与大球颗粒在水平方向上的摩擦力f U为： Step 13d, f U calculation: the frictional force f U between the lower layer of particles and the large spherical particles in the horizontal direction is:
    Figure PCTCN2020100791-appb-100010
    Figure PCTCN2020100791-appb-100010
    其中，μ 2为小球颗粒与大球颗粒之间的摩擦系数； Among them, μ 2 is the friction coefficient between small spherical particles and large spherical particles;
    步骤13e，将步骤13b、13c和13d计算的f P、f L和f U，分别代入步骤13a中，即得到填充颗粒间锁紧力F L的计算公式。 In step 13e, the f P , f L and f U calculated in steps 13b, 13c, and 13d are substituted into step 13a respectively to obtain the calculation formula of the locking force FL between the filling particles.
  7. 根据权利要求5所述的变刚度软体机器人的建模方法，其特征在于：通过真空泵调整薄膜管内的真空压力P，进而调整变刚度软体机器人的刚度；当薄膜管内的真空压力P增大时，薄膜管的变形角β和锁紧力矩M L均将增大，变刚度软体机器人的刚度增大。 The modeling method of the variable stiffness soft robot according to claim 5, characterized in that: the vacuum pressure P in the membrane tube is adjusted by a vacuum pump, thereby adjusting the stiffness of the variable stiffness soft robot; when the vacuum pressure P in the membrane tube increases, Both the deformation angle β and the locking moment M L of the membrane tube will increase, and the stiffness of the variable stiffness soft robot will increase.
  8. 根据权利要求5所述的变刚度软体机器人的建模方法，其特征在于：通过调整小球颗粒半径R 3，进而调整变刚度软体机器人的刚度；当小球颗粒半径R 3越大，锁紧力矩M L越小，变刚度软体机器人的刚度将减小。 The modeling method of the variable stiffness soft robot according to claim 5, characterized in that: the rigidity of the variable stiffness soft robot is adjusted by adjusting the radius R 3 of the small spherical particle; when the radius R 3 of the small spherical particle becomes larger, the locking The smaller the torque M L, the lower the stiffness of the variable stiffness soft robot.
  9. 根据权利要求5所述的变刚度软体机器人的建模方法，其特征在于：通过调整菱形骨架半径R 1，进而调整变刚度软体机器人的刚度；当菱形骨架半径R 1越大，锁紧力矩M L越大，变刚度软体机器人的刚度将增大。 The method for modeling a variable stiffness soft robot according to claim 5, characterized in that: the rigidity of the variable stiffness soft robot is adjusted by adjusting the radius R 1 of the rhombic skeleton; when the radius R 1 of the rhombus becomes larger, the locking torque M The larger L is, the rigidity of the variable rigidity soft robot will increase.
  10. 根据权利要求5所述的变刚度软体机器人的建模方法，其特征在于：通过调大球颗粒半径R 2，进而调整变刚度软体机器人的刚度；当大球颗粒半径R 2越大，锁紧力矩M L越大，变刚度软体机器人的刚度将增大。 The modeling method of claim 5 variable stiffness software robot as claimed in claim wherein: the ball transfer large particle radius R 2, and further adjusted by varying the stiffness of the software robot; when large spherical particles larger radius R 2, the locking The greater the torque M L, the greater the stiffness of the variable stiffness soft robot.
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