A variable stiffness rolling joint flexible arm and its variable stiffness method

Abstract

The present invention relates to a variable-rigidity rolling joint flexible arm and a method for varying its rigidity, wherein the variable-rigidity rolling joint flexible arm comprises a flexible arm frame, a rigidity enhancing mechanism, a positioning device, a driving platform, and a driving cable; the flexible arm frame is a hollow structure, the rigidity enhancing mechanism passes through the flexible arm frame, and the rigidity enhancing mechanism and the flexible arm frame are combined to form a variable-rigidity flexible arm; the flexible arm frame is fixed on the positioning device, and a plurality of driving cables pass through the flexible arm frame and the positioning device in sequence and are connected to the driving platform; the driving platform is used to control the movement of the driving cables to drive the movement of the variable-rigidity rolling joint flexible arm. The present invention realizes the adjustability of the joint rigidity without changing the posture of the flexible arm itself, and provides a method for varying its rigidity, establishes a rigidity model, realizes the adjustable control of the flexible arm rigidity, and effectively increases the rigidity effect of the rolling joint flexible arm.

Description

Technical Field

[0001] The present invention relates to the field of robots, in particular to a variable-rigidity rolling joint flexible arm and a method for varying the rigidity thereof. Background Art

[0002] As robotic tasks become increasingly diverse, traditional rigid mechanical robots struggle to meet increasingly complex demands, especially in unstructured environments. New flexible robots are gaining increasing attention, appearing one after another, and rapidly advancing toward practical application. Flexible robotic arms, as a key component of robotics, offer advantages such as efficient operation, lightweight, and flexible motion, making them crucial for applications in aerospace, surgery, and other fields. While excellent compliance provides flexibility and safety, it significantly reduces efficiency when faced with precision-critical contact operations, as they cannot withstand excessive loads. Variable stiffness addresses the trade-off between compliance and operational precision. Existing approaches to variable stiffness rely on materials with adjustable stiffness, which suffer from slow response and significant environmental susceptibility. Therefore, a variable stiffness flexible arm mechanism is needed that can achieve high stiffness for precise positioning under high loads while maintaining low stiffness for maneuvering in complex environments, improving adaptability. Summary of the Invention

[0003] The purpose of the present invention is to provide a variable stiffness rolling joint flexible arm and a method for varying stiffness thereof in order to overcome the defects of the above-mentioned prior art.

[0004] The purpose of the present invention can be achieved by the following technical solutions:

[0005] A variable stiffness rolling joint flexible arm, comprising a flexible arm frame, a stiffness enhancing mechanism, a positioning device, a driving platform and a driving cable;

[0006] The flexible arm frame is a hollow structure, the stiffness enhancement mechanism passes through the flexible arm frame, and the stiffness enhancement mechanism and the flexible arm frame are combined to form a variable stiffness flexible arm;

[0007] The flexible arm frame is fixed on the positioning device, and a plurality of driving cables pass through the flexible arm frame and the positioning device in sequence and are connected to the driving platform;

[0008] The driving platform is used to control the movement of the driving cable to drive the movement of the variable stiffness rolling joint flexible arm.

[0009] Furthermore, the flexible arm skeleton includes an elastic rope and a rolling joint;

[0010] The rolling joints include a plurality of rolling joints, each of which is stacked in sequence;

[0011] Each rolling joint is provided with a small hole, and the elastic rope passes through the small holes on each rolling joint in sequence to connect the rolling joints. The elastic rope is used to prevent slippage between the rolling joints;

[0012] The drive cable passes through each rolling joint in sequence, and all the rolling joints are connected in series to form a two-degree-of-freedom flexible arm. The drive cable is used to drive the flexible arm to achieve left and right movement and up and down movement.

[0013] Furthermore, the stiffness enhancement mechanism includes a connection cover, a silicone tube, a hose connector and an air pump tube;

[0014] The silicone tube passes through the interior of the flexible arm skeleton;

[0015] The first end of the silicone tube is connected to the connecting cover, and the connecting cover is used to seal the first end of the silicone tube;

[0016] The second end of the silicone tube is connected to the first end of the hose connector, the second end of the hose connector is connected to the first end of the air pump tube, and the second end of the air pump tube passes through the positioning module and is connected to the air source;

[0017] The air source inflates the silicone tube through the air pump tube, so that the flexible arm skeleton exhibits different stiffness properties.

[0018] Furthermore, the positioning device includes a cable extension device and a flexible arm fixing seat;

[0019] The top of the cable extension device is fixedly connected to the flexible arm fixing seat; the flexible arm fixing seat is connected to the through hole at the proximal end of the flexible arm frame through a steel column;

[0020] The cable extension device has multiple tracks at the bottom, each track is embedded with a pulley, the drive cable is connected to the pulley, and the pulley is used to guide and extend the direction of the drive cable to facilitate the connection between the drive cable and the drive platform.

[0021] Furthermore, the driving platform includes a plurality of screw stepper motors, the number of the screw stepper motors is the same as the number of the driving cables, and each screw stepper motor is correspondingly connected to each driving cable;

[0022] The lead screw stepper motor is used to control the extension and contraction of the drive cable, thereby driving the flexible arm to move in different directions.

[0023] A method for varying the stiffness of a variable stiffness rolling joint flexible arm is applied to the variable stiffness rolling joint flexible arm described above, comprising the following steps:

[0024] S1, the screw stepper motor outputs power and pulls the drive cable. The initial tension applied to the drive cable is recorded as T0;

[0025] S2, inflating the silicone tube through an air source to achieve a change in the stiffness of the flexible arm of the variable stiffness rolling joint;

[0026] S3, constructing a mathematical model of the flexible arm skeleton;

[0027] S4. Based on the air spring assumption, establish the stiffness model of the silicone tube;

[0028] S5. Establishing a stiffness model of the stiffness enhancement mechanism;

[0029] S6. Based on the mathematical model of the flexible arm skeleton, the stiffness model of the silicone tube, and the stiffness model of the stiffness enhancement mechanism, a stiffness model of the variable stiffness rolling joint flexible arm is established to obtain the stiffness of the variable stiffness rolling joint flexible arm system;

[0030] Wherein, step S2 includes the following process:

[0031] S21. When the silicone tube is not inflated, the stiffness of the flexible arm is kept in its original state. At this time, the stiffness adjustment of the flexible arm is in state 1. P a is the inflation pressure in the silicone tube, P a =0;

[0032] S22: When the silicone tube begins to be inflated and the silicone tube has not yet contacted the hollow inner wall of the flexible arm frame, the flexible arm stiffness adjustment is in state 2, and the wall thickness is recorded as Δd. si , P m The pressure inside the silicone tube when it just touches the inner wall, 0<P a ≤P m ;

[0033] S23. When the air pressure inflated into the silicone tube causes the silicone tube to contact the hollow inner wall of the flexible arm frame, the silicone tube produces a slight protrusion at the part of the notch of the flexible arm frame. At this time, the flexible arm stiffness adjustment is in state three, and the wall thickness is recorded as Δd. msi , P a >P m .

[0034] Furthermore, the mathematical model of the flexible arm skeleton includes a kinematic model representing the mapping relationship from the joint space to the drive space; for the left and right movement of the flexible arm, the expression of the kinematic model is:

[0035]

[0036]

[0037] Where Δd l is the length change of the left drive cable, Δd ris the length change of the right driving cable, θ is the rotation angle of a single rolling joint, R is the rolling radius of the rolling joint, and α is the effective half angle of the rolling joint.

[0038] Furthermore, the stiffness model of the silicone tube includes a vertical stiffness model, and the expression of the vertical stiffness model is:

[0039]

[0040] Where P0 is atmospheric pressure, P a A is the air pressure inside the silicone tube. eff is the effective bearing area, V0 is the air pressure P a The internal volume of the silicone tube when

[0041] When the flexible arm stiffness adjustment is in state 2, the specific expressions of the relevant parameters are:

[0042]

[0043]

[0044] Where D si is the outer diameter of the silicone tube in state 2, d si is the inner diameter of the silicone tube in state 2, Δd si is the wall thickness of the silicone tube in state 2, and h is the effective length of the silicone tube;

[0045] When the flexible arm stiffness adjustment is in state three, the specific expressions of the relevant parameters are:

[0046]

[0047]

[0048] Where D msi is the outer diameter of the state three silicone tube, d msi is the inner diameter of the silicone tube in state three, Δd msi is the wall thickness of the state three silicone tube, and l0 is the effective length of a single discrete air spring.

[0049] Furthermore, the step of constructing the stiffness model of the stiffness enhancement mechanism includes:

[0050] S1. When the flexible arm stiffness adjustment is in state 1, the stiffness enhancement is 0, and the stiffness of the stiffness enhancement mechanism is equivalent to two linear springs with stiffness k1=0 connected in parallel;

[0051] S2. When the flexible arm stiffness adjustment is in state 2, the stiffness enhancement is based on the stiffness of the entire silicone tube. The stiffness of the stiffness enhancement mechanism is equivalent to two linear springs with a stiffness of k2 in parallel, with an increased compensation coefficient λ2. The expression for k2 is:

[0052]

[0053] K si2 is the vertical stiffness model of the silicone tube in state 2;

[0054] S3. When the flexible arm stiffness adjustment is in state three, the stiffness enhancement is based on the stiffness of the discrete silicone tube. The stiffness of the stiffness enhancement mechanism is equivalent to four linear springs with a stiffness of k3 connected in series and then in parallel. The expression is:

[0055] k3=2λ3K si3

[0056] K si3 This is the vertical stiffness model of the silicone tube in state three.

[0057] Furthermore, according to the principle of conservation of energy, the static equilibrium equation of the variable stiffness rolling joint flexible arm is obtained, and the static equilibrium equation is expressed as:

[0058] Π=∑W wire +∑W spring -∑W F

[0059] Where π is the total energy of the flexible arm in equilibrium state, W wire The work done to drive the cable, W spring To simplify the work done by the linear spring, W F The work done for an external load;

[0060] According to the different stiffness states of the flexible arm, the specific process includes the following:

[0061] S1. When the flexible arm stiffness adjustment is in state 1, the equilibrium equation is expressed as:

[0062]

[0063] Where ΔL l0 is the initial length of the left drive cable, ΔL l is the final length of the left drive cable, ΔL r0 is the initial length of the right drive cable, ΔL r is the final length of the right driving cable, ΔL is the total change of the driving cable, and s is the horizontal displacement under the external load F;

[0064] S2. When the flexible arm stiffness adjustment is in state 2, the equilibrium equation is expressed as:

[0065]

[0066] S3. When the flexible arm stiffness adjustment is in state three, the equilibrium equation is expressed as:

[0067]

[0068] The static equilibrium equation includes the linear mechanical model of the drive cable, joint angle constraints, and load displacement constraints. The linear mechanical model of the drive cable is expressed as:

[0069] T wire =ax+T0

[0070] Where a is the coefficient, T0 is the initial driving cable tension;

[0071] The joint angle constraint condition expression is:

[0072]

[0073] Where Θ is the total bending angle of the initial flexible arm, θ i is the bending angle of each motion joint, n is the number of motion joints;

[0074] For the left-right motion of the flexible arm, the specific expression of the load displacement constraint condition is:

[0075] s=3Hsinθ1+Hsin(θ1+θ2)+3Hsin(θ1+θ2+θ3)+H1sin(θ1+θ2+θ3+θ4)

[0076] =7Hθ1+4Hθ2+3Hθ3+H1(θ1+θ2+θ3+θ4)

[0077] Where H is the height of a single rolling joint in the middle of the flexible arm, and H1 is the height of the rolling joints at the proximal and distal ends of the flexible arm;

[0078] According to the minimum energy principle, the equilibrium equation expression is:

[0079]

[0080] The specific angle value of each joint is obtained by simultaneous solution;

[0081] The stiffness model expression of the variable stiffness rolling joint flexible arm is:

[0082]

[0083] Substituting the specific angle values ​​of each joint into the obtained value, the stiffness of the variable stiffness rolling joint flexible arm system is obtained.

[0084] Compared with the prior art, the present invention has the following beneficial effects:

[0085] The present invention provides a variable stiffness rolling joint flexible arm and a method for varying stiffness. By designing a stiffness enhancement mechanism in the flexible hollow inner cavity and by changing the size of the air cavity pressure, the joint stiffness is made adjustable without changing the posture of the flexible arm itself. Based on the changing process of the flexible arm stiffness enhancement, the present invention proposes three states of flexible arm stiffness change, from a continuous stiffness enhancement state to a discrete stiffness enhancement state, and provides a simple method for varying stiffness. Combining kinematics, air spring theory, and statics, a stiffness model of the rolling joint flexible arm is established for different stiffness change states, solving the problem of stiffness modeling. This allows the variable stiffness flexible robotic arm to achieve high-rigidity precise positioning under high-load operation, and to move in complex environments with lower stiffness, with high adaptability to the environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0086] Figure 1 1 is a schematic structural diagram of a variable stiffness rolling joint flexible arm in Example 1 of the present invention;

[0087] Figure 2-1 is a structural schematic diagram of the stiffness enhancement mechanism in Example 1 of the present invention;

[0088] Figure 2-2 is a schematic structural diagram of the cable extension device in Example 1 of the present invention;

[0089] Figure 3 This is a schematic diagram of a method for varying the stiffness of a variable stiffness rolling joint flexible arm in Example 2 of the present invention;

[0090] Figure 4 This is a simplified model diagram of a variable stiffness method for a variable stiffness rolling joint flexible arm in Example 2 of the present invention;

[0091] Figure 5 Schematic diagram of force balance of a flexible arm of a variable stiffness rolling joint in Example 2 of the present invention;

[0092] Figure 6 This is a schematic diagram of the stiffness change process of a variable stiffness rolling joint flexible arm in Example 2 of the present invention.

[0093] The correspondence between the numbers in the accompanying drawings and the various components is: 1-flexible arm frame, 2-rigidity enhancement mechanism, 3-positioning device, 4-driving platform, 6-air pump tube, 7-driving cable, 8-screw stepper motor, 9-connecting cover, 10-silicone tube, 11-hose connector, 12-elastic rope, 13-rolling joint, 14-cable extension device, 15-flexible arm fixing seat, 16-pulley. DETAILED DESCRIPTION

[0094] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0095] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, if there are terms such as "upper", "lower", "left", "right", etc. indicating directions or positional relationships, they are based on the directions or positional relationships shown in the drawings, which are only for the convenience of describing the present invention and simplifying the description. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0096] Example 1

[0097] In response to the problems in the existing technology such as slow response speed, great influence of the environment, and inability to simultaneously meet high load requirements and high precision requirements of flexible robotic arms, the present invention proposes a variable stiffness rolling joint flexible arm and a method for changing its stiffness.

[0098] like Figure 1 and Figure 2-1 、 2-2 FIG. 1 is a preferred embodiment of a variable stiffness rolling joint flexible arm proposed by the present invention, comprising a flexible arm skeleton 1, a stiffness enhancement mechanism 2, a positioning device 3, a driving platform 4 and a driving cable 7;

[0099] The flexible arm frame 1 is a hollow structure, the stiffness enhancement mechanism 2 passes through the flexible arm frame 1, and the stiffness enhancement mechanism 2 and the flexible arm frame 1 are combined to form a variable stiffness flexible arm; the flexible arm frame 1 is fixed on the positioning device 3, and multiple drive cables 7 pass through the flexible arm frame 1 and the positioning device 3 in turn and are connected to the drive platform 4; the drive platform 4 is used to control the movement of the drive cables 7 to drive the movement of the variable stiffness rolling joint flexible arm.

[0100] like Figure 2-1 As shown, the flexible arm skeleton 1 includes several rolling joints 13, elastic cords 12, and four drive cables 7. The rolling joints 13 are stacked in a certain manner and connected in series through the drive cables 7 to form a two-degree-of-freedom flexible arm, realizing left-right and up-and-down movement. Each rolling joint 13 has a small hole, and the elastic cords 12 pass through the small holes of each rolling joint 13 in sequence to connect the rolling joints 13. The elastic cords 12 are used to prevent slippage between the rolling joints.

[0101] like Figure 1 、 2-1As shown, the stiffness enhancement mechanism 2 includes a connecting cover 9, a silicone tube 10, a hose connector 11, and an air pump tube 6; the silicone tube 10 passes through the interior of the flexible arm skeleton 1; the first end of the silicone tube 10 is connected to the connecting cover 9, and the connecting cover 9 is used to seal the first end of the silicone tube 10; the second end of the silicone tube 10 is connected to the first end of the hose connector 11, and the second end of the hose connector 11 is connected to the first end of the air pump tube 6, and the second end of the air pump tube 6 passes through the positioning module 3 and is connected to the air source; the air source inflates the silicone tube 10 through the air pump tube 6, so that the flexible arm skeleton 1 exhibits different stiffness performance.

[0102] like Figure 1 、 2-1 As shown, the positioning device 3 includes a cable extension device 14 and a flexible arm fixing seat 15;

[0103] The top of the cable extension device 14 is fixedly connected to the flexible arm fixing seat 15. The bottom of the cable extension device 14 is provided with four tracks. The four tracks together form an "X" shape. A pulley 16 is embedded in each track. The drive cable 7 is connected to the pulley 16. The pulley 16 is used to guide and extend the direction of the drive cable 7 to facilitate the connection between the drive cable 7 and the drive platform 4.

[0104] The air pump tube 6 passes through the cable extension device 14 and is led out from the intersection of each track;

[0105] The flexible arm fixing seat 15 is connected to the through hole at the proximal end of the flexible arm frame 1 through a steel column. The variable stiffness rolling flexible arm determines its initial position with the assistance of the positioning device 3 .

[0106] like Figure 1 As shown, the driving platform 4 includes four screw stepper motors 8. The motors are driven by a single chip microcomputer to achieve the extension and contraction of the driving cable 7, thereby achieving the movement of the flexible arm in different directions.

[0107] Example 2

[0108] like Figures 3 to 6 The figure shows an embodiment of a method for changing the stiffness of a variable stiffness rolling joint flexible arm of the present invention, which is applied to a variable stiffness rolling joint flexible arm as described in Example 1. The proximal end of the flexible arm is fixed and the flexible arm is in an upright state. This embodiment is explained using a plane in the left and right movement direction as an example, and the same applies to up and down movement.

[0109] like Figure 3 As shown in FIG, the variable stiffness method includes the following steps:

[0110] S1. The screw stepper motor 8 outputs power and pulls the four drive cables 7. The initial tension applied to the drive cables is T0.

[0111] S2. The stiffness enhancement mechanism inflates the silicone tube via an air source, thereby changing the stiffness of the flexible arm of the rolling joint.

[0112] Wherein, step S2 includes the following process:

[0113] S21. When the silicone tube is not inflated, that is, there is no gas drive, the stiffness of the flexible arm remains in its original state. At this time, the flexible arm stiffness adjustment is said to be in state 1, P a =0;

[0114] S22. When the silicone tube begins to be inflated and the silicone tube has not yet contacted the hollow inner wall of the flexible arm frame, the entire silicone tube can be regarded as an air spring. At this time, the flexible arm stiffness adjustment is in state 2, and the wall thickness of the silicone tube is Δd. si , P a is the inflation pressure in the silicone tube, P m is the air pressure inside the tube when it just touches the inner wall, so the air pressure inside the tube in this state is 0<P a ≤P m ;

[0115] S23. When the air pressure inflating the silicone tube causes it to contact the hollow inner wall of the flexible arm frame, the silicone tube produces a slight protrusion at the part of the flexible arm frame where the gap is. At this time, the silicone tube's stiffness enhancement effect is only reflected in the tiny protrusion. Therefore, the silicone tube can be regarded as a series of discrete air springs. At this time, the flexible arm stiffness adjustment is said to be in state three, and the wall thickness of the silicone tube is Δd. msi , the pressure inside the tube is P a >P m .

[0116] Based on the above variable stiffness method, its stiffness model is established. According to the spatial geometric relationship, the mathematical model of the flexible arm skeleton is first established. Then, based on the air spring assumption, the stiffness model of the silicone tube is established. Then, the stiffness model of the stiffness enhancement mechanism is established. Finally, the stiffness model of the variable stiffness rolling joint flexible arm is established. Here, the plane of the left and right movement direction is taken as an example, and the same applies to the up and down movement.

[0117] The mathematical model of the flexible arm skeleton includes a kinematic model that represents the mapping relationship from the joint space to the drive space, which is expressed as follows:

[0118]

[0119]

[0120] Where Δd l is the length change of the left drive cable, Δd r is the length change of the right driving cable, θ is the rotation angle of a single joint, R is the rolling radius of the rolling joint, and α is the effective half angle of the rolling joint.

[0121] Furthermore, the stiffness model of the silicone tube includes a vertical stiffness model, which is expressed as follows:

[0122]

[0123] Where P0 is atmospheric pressure, P a A is the air pressure inside the silicone tube. eff is the effective bearing area, V0 is the air pressure P a The internal volume of the silicone tube at .

[0124] When the flexible arm stiffness adjustment is in state 2, the specific expressions of the relevant parameters are:

[0125]

[0126]

[0127] Where D si is the outer diameter of the silicone tube in state 2, d si is the inner diameter of the silicone tube in state 2, Δd si is the wall thickness of the silicone tube in state 2, and h is the effective length of the silicone tube. Substituting expressions (4) and (5) into (3) yields K si2 .

[0128] When the flexible arm stiffness adjustment is in state three, the specific expressions of the relevant parameters are:

[0129]

[0130]

[0131] Where D msi is the outer diameter of the state three silicone tube, d msi is the inner diameter of the silicone tube in state three, Δd msi is the wall thickness of the state three silicone tube, l0 is the effective length of a single discrete air spring. Substituting expressions (6) and (7) into (3) we can get K si3 .

[0132] like Figure 4 As shown in Figure 2, the stiffness model of the stiffness enhancement mechanism can be further simplified, specifically including the following steps:

[0133] S1. When the flexible arm stiffness adjustment is in state 1, the stiffness enhancement is 0, or the stiffness of the stiffness enhancement mechanism is equivalent to two linear springs with stiffness k1 = 0 in parallel;

[0134] S2. When the flexible arm stiffness adjustment is in state 2, the silicone tube has not yet contacted the inner wall. The stiffness enhancement is based on the stiffness of the entire silicone tube. The stiffness of the stiffness enhancement mechanism can be equivalent to two linear springs with a stiffness of k3 in parallel, with an additional compensation coefficient λ2. The expression for k2 is:

[0135]

[0136] S3. When the flexible arm stiffness adjustment is in state three, the silicone tube is completely in contact with the inner wall. The stiffness enhancement is based on the stiffness of the discrete silicone tube. The stiffness of the stiffness enhancement mechanism can be equivalent to four linear springs with a stiffness of k3 connected in series and then in parallel. The compensation coefficient λ3 is added. The expression for k3 is:

[0137] k3=2λ3K si3 (9)

[0138] like Figure 5 As shown in Figure 2, when the end of the flexible arm is subjected to an external load, the upright flexible arm will bend in an S-shape. According to the principle of conservation of energy, the static equilibrium equation of the flexible arm with variable stiffness rolling joint can be obtained as follows:

[0139] Π=∑W wire +∑W spring -∑W F (10)

[0140] Where π is the total energy of the flexible arm in equilibrium state, W wire The work done to drive the cable, W spring To simplify the work done by the linear spring, W F The work done for an external load.

[0141] According to the different stiffness states of the flexible arm, the specific process includes the following:

[0142] S1. When the flexible arm stiffness adjustment is in state 1, the equilibrium equation is expressed as:

[0143]

[0144] Where ΔL l0 is the initial length of the left drive cable, ΔL l is the final length of the left drive cable, ΔL r0 is the initial length of the right drive cable, ΔL r is the final length of the right driving cable, ΔL is the total change of the driving cable, and s is the horizontal displacement under the external force F.

[0145] S2. When the flexible arm stiffness adjustment is in state 2, the equilibrium equation is expressed as:

[0146]

[0147] S3. When the flexible arm stiffness adjustment is in state 3, the equilibrium equation is expressed as:

[0148]

[0149] The static equilibrium equation includes the linear mechanical model of the drive cable, the joint angle constraint conditions, and the load displacement constraint conditions. The linear mechanical model expression of the drive cable can be obtained as follows:

[0150] T wire =ax+T0 (14)

[0151] Where a is the coefficient, which can be obtained through experimental fitting, and T0 is the initial driving cable tension.

[0152] The joint angle constraint expression is:

[0153]

[0154] Where Θ is the total bending angle of the initial flexible arm, θ i is the bending angle of each motion joint, n is the number of motion joints, and in this embodiment, n is 4.

[0155] Since the change in joint angle produced by the variable stiffness flexible arm under the action of external force F is small, the equivalent infinitesimal replacement formula can be used, sinθ≈θ, so the specific expression of the load displacement s constraint condition is:

[0156]

[0157] Where H is the height of a single rolling joint in the middle of the flexible arm, and H1 is the height of the rolling joints at the proximal and distal ends of the flexible arm.

[0158] According to the minimum energy principle, the equilibrium equation expression is:

[0159]

[0160] Substituting expressions (14), (15), and (16) into expression (17), we can solve for the specific angle values ​​of each joint.

[0161] Furthermore, the stiffness model expression of the variable stiffness rolling joint flexible arm is:

[0162]

[0163] Substitute the angle value of the joint obtained in expression (17) into expression (18), and finally obtain the stiffness of the variable stiffness rolling joint flexible arm system.

[0164] like Figure 6 As shown in the figure, it is the fitting curve of the stiffness change process of the flexible arm. The theoretical stiffness value is calculated for different air pressure values. It can be seen that when the air pressure is P m Near the edge, the stiffness has a relatively obvious sudden change. When the pressure is less than P m When the pressure is greater than P, the stiffness increases slowly. m , the stiffness changes faster. This trend is consistent with the stiffness enhancement mechanism of the flexible arm, thus confirming that the variable-stiffness rolling joint flexible arm has a good ability to change stiffness. Therefore, the variable-stiffness flexible arm proposed in this invention can achieve high-stiffness precision positioning under high-load operation while also maintaining low stiffness in complex environments, demonstrating high adaptability to the environment.

[0165] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A method for changing the stiffness of a variable stiffness rolling joint flexible arm, characterized in that: The variable stiffness rolling joint flexible arm comprises a flexible arm frame (1), a stiffness enhancing mechanism (2), a positioning device (3), a driving platform (4) and a driving cable (7); The flexible arm frame (1) is a hollow structure, the stiffness enhancement mechanism (2) passes through the flexible arm frame (1), and the stiffness enhancement mechanism (2) and the flexible arm frame (1) are combined to form a variable stiffness flexible arm; The flexible arm frame (1) is fixed on the positioning device (3), and a plurality of drive cables (7) pass through the flexible arm frame (1) and the positioning device (3) in sequence and are connected to the drive platform (4); The driving platform (4) is used to control the movement of the driving cable (7) to drive the movement of the variable stiffness rolling joint flexible arm; The method comprises the following steps: S1, the screw stepper motor outputs power and pulls the drive cable. The initial tension applied to the drive cable is recorded as ; S2, inflating the silicone tube through an air source to achieve a change in the stiffness of the flexible arm of the variable stiffness rolling joint; S3, constructing a mathematical model of the flexible arm skeleton; S4. Based on the air spring assumption, establish the stiffness model of the silicone tube; S5. Establishing a stiffness model of the stiffness enhancement mechanism; S6. Based on the mathematical model of the flexible arm skeleton, the stiffness model of the silicone tube, and the stiffness model of the stiffness enhancement mechanism, a stiffness model of the variable stiffness rolling joint flexible arm is established to obtain the stiffness of the variable stiffness rolling joint flexible arm system; Wherein, step S2 includes the following process: S21. When the silicone tube is not inflated, the rigidity of the flexible arm is kept in its original state. At this time, the rigidity adjustment of the flexible arm is said to be in state 1. The air pressure in the silicone tube is ; S22. When the silicone tube begins to be inflated and the silicone tube has not yet contacted the hollow inner wall of the flexible arm frame, the flexible arm stiffness adjustment is in state 2, and the wall thickness is recorded as , It is the air pressure inside the tube when the silicone tube just touches the inner wall. ; S23. When the air pressure inflated into the silicone tube causes the silicone tube to contact the hollow inner wall of the flexible arm frame, the silicone tube produces a small protrusion at the part of the notch of the flexible arm frame. At this time, the flexible arm stiffness adjustment is in state three, and the wall thickness is recorded as , ; The stiffness model of the silicone tube includes a vertical stiffness model, and the expression of the vertical stiffness model is: , In the formula is atmospheric pressure, It is the air pressure inside the silicone tube. is the effective bearing area, The air pressure is The internal volume of the silicone tube when When the flexible arm stiffness adjustment is in state 2, the specific expressions of the relevant parameters are: In the formula is the outer diameter of the silicone tube in state 2, is the inner diameter of the silicone tube in state 2, is the wall thickness of the silicone tube in state 2, is the effective length of the silicone tube; When the flexible arm stiffness adjustment is in state three, the specific expressions of the relevant parameters are: In the formula is the outer diameter of the state three silicone tube, is the inner diameter of the state three silicone tube, The wall thickness of the state three silicone tube, is the effective length of a single discrete air spring.

2. The method for varying stiffness according to claim 1, characterized in that: The flexible arm frame (1) comprises an elastic rope (12) and a rolling joint (13); The rolling joints (13) include a plurality of rolling joints (13), and the rolling joints (13) are stacked in sequence; Each rolling joint (13) is provided with a small hole, and the elastic rope (12) passes through the small holes on each rolling joint (13) in sequence to connect the rolling joints (13), and the elastic rope (12) is used to prevent slippage between the rolling joints; The driving cable (7) passes through each rolling joint (13) in sequence, and all the rolling joints (13) are connected in series to form a two-degree-of-freedom flexible arm. The driving cable (7) is used to drive the flexible arm to achieve left-right movement and up-down movement.

3. The method for varying stiffness according to claim 2, characterized in that: The stiffness enhancement mechanism (2) comprises a connection cover (9), a silicone tube (10), a hose connector (11) and an air pump tube (6); The silicone tube (10) passes through the interior of the flexible arm skeleton (1); The first end of the silicone tube (10) is connected to the connecting cover (9), and the connecting cover (9) is used to seal the first end of the silicone tube (10); The second end of the silicone tube (10) is connected to the first end of the hose connector (11), the second end of the hose connector (11) is connected to the first end of the air pump tube (6), and the second end of the air pump tube (6) passes through the positioning device (3) and is connected to the air source; The air source inflates the silicone tube (10) through the air pump tube (6), so that the flexible arm skeleton (1) exhibits different stiffness properties.

4. The method for varying stiffness according to claim 3, characterized in that: The positioning device (3) includes a cable extension device (14) and a flexible arm fixing seat (15); The top of the cable extension device (14) is fixedly connected to the flexible arm fixing seat (15); the flexible arm fixing seat (15) is connected to the through hole at the proximal end of the flexible arm frame (1) via a steel column; The cable extension device (14) has a plurality of tracks at the bottom, each track being embedded with a pulley (16), the drive cable (7) being connected to the pulley (16), and the pulley (16) being used to guide and extend the direction of the drive cable (7), thereby facilitating the connection of the drive cable (7) with the drive platform (4).

5. The method for varying stiffness according to claim 1, characterized in that: The driving platform (4) includes a plurality of screw stepper motors (8), the number of the screw stepper motors (8) is the same as the number of the driving cables (7), and each screw stepper motor (8) is correspondingly connected to each driving cable (7); The screw stepper motor (8) is used to control the extension and contraction of the drive cable (7), thereby driving the flexible arm to achieve movement in different directions.

6. The method for varying stiffness according to claim 1, characterized in that: The mathematical model of the flexible arm skeleton includes a kinematic model that represents the mapping relationship from the joint space to the drive space. For the left-right movement of the flexible arm, the expression of the kinematic model is: In the formula is the length change of the left drive cable, is the length change of the right drive cable, is the rotation angle of a single rolling joint, is the rolling radius of the rolling joint, is the effective half angle of the roll joint.

7. The method for varying stiffness according to claim 1, wherein: The step of constructing the stiffness model of the stiffness enhancement mechanism includes: S1. When the flexible arm stiffness adjustment is in state 1, the stiffness enhancement is 0, and the stiffness of the stiffness enhancement mechanism is equivalent to two stiffnesses of Linear springs in parallel; S2. When the flexible arm stiffness adjustment is in state 2, the stiffness enhancement is based on the stiffness of the entire silicone tube, and the stiffness of the stiffness enhancement mechanism is equivalent to two stiffnesses of Linear springs are connected in parallel to increase the compensation coefficient , The expression is: is the vertical stiffness model of the silicone tube in state 2; S3. When the flexible arm stiffness adjustment is in state three, the stiffness enhancement is based on the stiffness of the discrete silicone tube, and the stiffness of the stiffness enhancement mechanism is equivalent to four stiffnesses. The linear springs are discretely connected in series and then in parallel, and the expression is: This is the vertical stiffness model of the silicone tube in state three.

8. The method for varying stiffness according to claim 7, characterized in that: According to the principle of energy conservation, the static equilibrium equation of the flexible arm of the variable stiffness rolling joint is obtained, and the static equilibrium equation is expressed as: In the formula is the total energy of the flexible arm in equilibrium state, The work done to drive the cable, To simplify the work done by the linear spring, The work done for an external load; According to the different stiffness states of the flexible arm, the specific process includes the following: S1. When the flexible arm stiffness adjustment is in state 1, the equilibrium equation is expressed as: In the formula is the initial left drive cable length, is the final length of the left drive cable, is the initial right drive cable length, is the final length of the right drive cable, is the total change of the driving cable, External load Horizontal displacement under action; S2. When the flexible arm stiffness adjustment is in state 2, the equilibrium equation is expressed as: S3. When the flexible arm stiffness adjustment is in state three, the equilibrium equation is expressed as: The static equilibrium equation includes the linear mechanical model of the drive cable, joint angle constraints, and load displacement constraints. The linear mechanical model of the drive cable is expressed as: In the formula is the coefficient, is the initial driving cable tension; The joint angle constraint condition expression is: In the formula is the total bending angle of the initial flexible arm, is the bending angle of each moving joint, is the number of motion joints; For the left-right motion of the flexible arm, the specific expression of the load displacement constraint condition is: In the formula is the height of a single rolling joint in the middle of the flexible arm, is the height of the proximal and distal rolling joints of the flexible arm; According to the minimum energy principle, the equilibrium equation expression is: The specific angle value of each joint is obtained by simultaneous solution; The stiffness model expression of the variable stiffness rolling joint flexible arm is: Substituting the specific angle values ​​of each joint into the obtained value, the stiffness of the variable stiffness rolling joint flexible arm system is obtained.

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