A multi-segment flexible mechanical claw based on petal bionics and a root transition section design method thereof

CN123000905APending Publication Date: 2026-10-30HENAN UNIV OF SCI & TECH
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Patent Information

Application Number
CN202611300699.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-08-26
Publication Date
2026-10-30

AI Technical Summary

Technical Problem

但现有柔性爪在抓取花托等生物组织时,即使指面柔软,弯曲产生的剪切力与挤压应力仍会集中在指根与花托的接触环带上,导致花托表皮破损或离层断裂;现有分段铰接柔性指在根部与首段指节连接处存在曲率跳跃,导致弯曲时该铰点成为应力集中区域,刚度呈现非线性变化;多数绳驱机械爪的仿生设计停留在宏观形态模仿阶段,未能将生物结构的力学特性转化为具体的机械设计参数,限制了抓取过程中应力分布的优化空间;其次在复位机构设计方面,现有方案多采用在每个关节处分别设置扭簧或拉簧的方式,结构零散且各关节复位力矩相互独立,难以实现多指节抓取后的协同复位;在多指节协同运动方面,现有绳驱机械爪的驱动绳索走线设计往往路径复杂,绳索与导向件之间的摩擦损耗较大,影响了传动的平稳性和抓取精度

Benefits of technology

第一、本发明的仿生柔性指根部采用拟合花瓣曲线设计,模仿花瓣自然收拢的包络形态,4个指节呈圆周分布,可实现对被抓取物体的柔顺包络式抓取,抓取稳定性好,适应性强。花瓣曲线经过自然选择优化,其曲率变化平缓,仿生柔性指在收拢过程中可以实现渐进式弯曲变形以包络物体,能够有效减小抓取过程中的应力集中,降低抓取过程中对易损生物组织表面的损伤风险。

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Abstract

The application discloses a multi-segment flexible mechanical claw based on petal bionics and a root transition section design method thereof, and belongs to the technical field of robot end effectors. The mechanical claw comprises a driving motor, a cable wheel, a flange plate, a plurality of bionic flexible fingers and a traction driving cable. Each bionic flexible finger comprises a root transition section with continuously changing curvature and three sequentially hinged knuckles, the root transition section is internally provided with upper and lower guide shafts, the traction driving cable sequentially passes through the guide shafts and the knuckles and pulls the flexible finger bending envelope. The root transition section profile is a continuously variable curvature curve, and the curvature decreases from the hinge to the knuckle direction. The design method collects petal profiles for curvature analysis, constructs an exponential decay model, adopts piecewise cubic Bezier curve fitting, and outputs modeling data after resampling and coordinate normalization. The application integrates the petal curvature gradual change law into the mechanical claw design, realizes adaptive envelope grasping, and reduces the damage risk.
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Description

Technical Field

[0001] This invention relates to the field of robot end effector technology, specifically to a multi-segment flexible mechanical claw based on petal bionics and its root transition segment design method. Background Technology

[0002] In robotic grasping operations, the mechanical gripper, as the end effector, directly affects its grasping performance through its structural design. Traditional mechanical grippers often employ rigid linkage drives or direct motor drives, which suffer from problems such as complex structures, large size, and poor compliance. Especially when grasping fragile, easily deformable, or irregularly shaped objects, rigid mechanical grippers struggle to achieve adaptive envelope grasping, easily causing damage to the grasped object.

[0003] The limitations of rigid robotic grippers are mainly reflected in three aspects. First, physical damage caused by contact stress concentration. When a rigid gripper closes, the contact area with the workpiece is often small, and the pressure distribution at the contact point is extremely uneven. For brittle materials such as glass, ceramics, fruits, and vegetables, local high pressure can easily exceed the material's yield strength, leading to microcracks or even overall breakage. Second, lack of adaptive capability. The motion trajectory and force of a rigid gripper are preset and fixed, and cannot be adjusted in real time according to the actual shape and size deviation of the workpiece, making it difficult to effectively grasp irregularly shaped objects. Third, vibration transmission and dynamic impact risks. The rigid connection allows vibrations during robot movement to be transmitted to the gripped object with almost no attenuation, increasing the risk of damage.

[0004] Rope-driven technology is widely used in fields such as flexible robotic arms and bionic robotic claws due to its advantages such as flexible transmission, compact structure, and ability to achieve long-distance power transmission. However, when existing flexible claws grasp biological tissues such as flower receptacles, even with flexible finger surfaces, the shearing and compressive stresses generated by bending still concentrate on the contact ring between the finger root and the receptacle, leading to damage or delamination of the receptacle's epidermis. Existing segmented articulated flexible fingers exhibit curvature jumps at the connection between the root and the first segment, causing this hinge point to become a stress concentration area during bending, resulting in nonlinear stiffness changes. Most rope-driven mechanical claws' biomimetic designs remain at the macroscopic morphological imitation stage, failing to translate the mechanical properties of biological structures into specific mechanical design parameters, thus limiting the optimization space for stress distribution during grasping. Secondly, in terms of reset mechanism design, existing solutions often use separate torsion springs or tension springs at each joint, resulting in a fragmented structure and independent reset torques for each joint, making it difficult to achieve coordinated reset after multi-finger grasping. Regarding multi-finger coordinated motion, the drive rope routing design of existing rope-driven mechanical claws is often complex, with significant frictional losses between the rope and guide components, affecting the smoothness of transmission and grasping accuracy. Therefore, this application develops a rope-driven bionic flexible mechanical claw that can incorporate the gradual curvature of petals into the structural design, achieve multi-finger collaborative envelope grasping, and has a reliable reset function, which has important engineering application value. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-segment flexible mechanical claw based on petal biomimicry and its root transition segment design method. By incorporating petal biomimicry into the design of multi-segment flexible fingers, the grasped object forms a progressive bending deformation, realizing the envelopment and convergence of multiple flexible fingers, and using a through-type reset elastic cable to achieve rapid reset after grasping, thereby improving grasping stability and reducing the risk of contact stress damage.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A multi-segment flexible mechanical gripper based on petal biomimicry, characterized in that it comprises: A drive motor is provided, the output end of which is connected to a cable pulley. A flange is fixedly installed below the cable pulley. Multiple hinge pins are evenly distributed around the lower end of the flange, and each hinge pin is hinged to a biomimetic flexible finger. The biomimetic flexible finger includes a root transition section and a first segment, a middle segment, and a last segment connected in sequence. One end of the root transition section is hinged to the hinge pin, and the other end is hinged to the first segment. The curvature of the root transition section changes along its extension direction. An upper guide shaft and a lower guide shaft are provided inside the root transition section. The traction drive cable is led out from the cable wheel. The traction drive cable passes through the flange, winds around the warp shaft, upper guide shaft, and lower guide shaft in sequence, and passes through the guide channels on the first and middle finger joints. Its end is fixedly connected to the last finger joint. Under the drive of the drive motor, it pulls the bionic flexible finger to produce a bending envelope motion. It also includes a reset elastic cord disposed along the length direction of the biomimetic flexible finger, for providing a reset elastic force when the traction drive cord is released.

[0007] Furthermore, the reset elastic cable passes sequentially through the first segment, the middle segment, and the last segment of the finger joint, with its proximal end fixed to any one of the root transition segment, the first segment, or the flange, and its distal end fixed to the last segment of the finger joint. This provides a reset elastic force to restore the bionic flexible finger to its open state when the traction drive cable is released.

[0008] Furthermore, the contour curve of the root transition section is a continuously variable curvature curve, with the curvature decreasing from the hinge point with the flange towards the first finger joint.

[0009] Furthermore, the flange is a circular flange, and the number of the hinge pins and the biomimetic flexible fingers are both four, with the hinge pins evenly distributed at 90° along the circumference of the flange.

[0010] Furthermore, the upper guide shaft is positioned close to the flange, and the lower guide shaft is positioned close to the first finger joint. Both the upper and lower guide shafts are stepped shaft structures, and their shoulders are provided with an annular groove for the traction drive cable to pass through.

[0011] Furthermore, the traction drive cable is a steel wire rope or a high-strength fiber rope; the reset elastic cable is a rubber cable or a spring steel wire.

[0012] This application also provides a method for designing the root transition segment of a multi-segment flexible mechanical grasper based on petal biomimicry, including the following steps: S1. Collect the three-dimensional coordinate data of the natural petal outline. Based on the obtained data, use the Savitzky-Golay filter to eliminate measurement noise and obtain a smooth two-dimensional outline point set. S2. Perform curvature analysis on the two-dimensional contour point set obtained in S1, according to the curvature calculation formula. Calculate the curvature value and the corresponding normalized arc length parameter at each sampling point to obtain the curvature distribution characteristics of the petal outline from the root to the tip; S3. Based on the curvature distribution characteristics described in S2, an exponential decay model is used to construct the petal gradient curvature function. With the goal of minimizing the sum of squared residuals between the measured curvature and the model curvature, the Levenberg-Marquardt algorithm is used to solve for the model parameters k0, k1, and λ, where k0 is the initial curvature at the root, k1 is the terminal curvature at the tip, and λ is the curvature decay coefficient. S4. Using the gradual curvature function described in S3 as a constraint, the petal outline is fitted with a piecewise cubic Bézier curve to generate the root transition segment outline curve with curvature continuously changing along the arc length direction. S5. Perform equal arc length resampling and coordinate normalization on the fitted root transition segment contour curve, and output the curve coordinate data for root transition segment modeling.

[0013] Furthermore, in step S1, when collecting the three-dimensional coordinate data of the natural petal outline, the sampling point distribution includes at least the following three segmented regions: The root sampling range corresponds to the normalized arc length s∈[0, 0.1]; The normalized arc length s∈[0.3, 0.7] corresponds to the sampling range in the middle. The tip sampling range corresponds to the normalized arc length s∈[0.9, 1.0].

[0014] Furthermore, in step S3, when using the Levenberg-Marquardt algorithm to solve for the model parameters, a step-by-step optimization strategy is adopted: First, fix the curvature attenuation coefficient λ as the initial value. The initial curvature k0 at the root and the termination curvature k1 at the tip are optimized. Then, using the optimized k0 and k1 as fixed values, λ is fine-tuned. Among them, the The value range is 2.0 to 5.0.

[0015] Furthermore, in step S4, at the connection point of two adjacent Bézier curves, the termination curvature of the previous curve is equal to the initial curvature of the next curve. The curvature k(0) of a single Bézier curve at its starting point is determined by the following relationship:

[0016] in, , , These are the first three control points of the Bézier curve segment, and θ is a vector. The included angle.

[0017] The beneficial effects of the above scheme are as follows: First, the biomimetic flexible finger base of this invention adopts a petal curve fitting design, mimicking the natural enveloping shape of a petal. The four finger joints are distributed in a circular pattern, enabling a smooth, enveloping grasp of the object being grasped, resulting in good grasping stability and strong adaptability. The petal curve has been optimized through natural selection, with a gentle curvature change. During the closing process, the biomimetic flexible finger can gradually bend and deform to envelop the object, effectively reducing stress concentration during grasping and lowering the risk of damage to vulnerable biological tissue surfaces.

[0018] Secondly, this invention employs a single motor coupled with a rope drive, resulting in a simple and compact structure, flexible power transmission, and the ability to achieve long-distance drive, while reducing the size and weight of the end effector. The traction drive cable starts from the sheave, passing sequentially through the flange, hinge pin, upper guide shaft, lower guide shaft, first finger segment, middle finger segment, and finally the last finger segment. The transmission path is clear, and the movement of each segment is well-coordinated. The upper and lower guide shafts work together to guide the traction drive cable, ensuring smooth rope transmission, reducing frictional loss, and improving transmission efficiency.

[0019] Third, this invention ensures the continuity of curvature of the overall curve by forcing equal curvature at the connection points using piecewise cubic Bézier curves. This allows bending deformation to be transmitted synergistically from the root to the fingertip, avoiding concentrated compression caused by sudden changes in local curvature. At the same time, the biomimetic flexible finger is formed by connecting the root, first segment, middle segment, and last segment of the fitted petal curve in sequence, creating a multi-segment flexible structure that can adaptively bend according to the shape of the object being grasped, achieving compliant grasping.

[0020] Fourth, the first, middle, and last segments of the phalanx are connected by a reset elastic cable. When the motor releases the driving force, the reset elastic cable provides a reset force, which allows the mechanical gripper to automatically return to its initial open state without the need for an additional reset drive mechanism. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of the overall structure of a multi-segment flexible mechanical claw based on petal bionics according to the present invention; Figure 2 This is a partial cross-sectional view of a multi-segment flexible mechanical claw based on petal bionics according to the present invention. Figure 3 This is a top view of a multi-segment flexible mechanical claw based on petal bionics in the open state according to the present invention; Figure 4 This is a top view of a multi-segment flexible mechanical claw based on petal bionics in the grasping state according to the present invention; Figure 5 This is a front view of a multi-segment flexible mechanical claw based on petal bionics in the grasping state according to the present invention; Figure 6This is the biomimetic curve fitting process of the present invention.

[0022] 1. Drive motor; 2. Cable pulley; 3. Flange; 4. Hinge pin; 5. Bionic flexible finger; 6. Upper guide shaft; 7. First finger segment; 8. Middle finger segment; 9. Last finger segment; 10. Traction drive cable; 11. Return elastic cable; 12. Lower guide shaft. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0024] It should be noted that, unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application.

[0026] Example 1

[0027] like Figure 1 and Figure 2 As shown, this embodiment provides a multi-segment flexible mechanical gripper based on petal biomimicry. The mechanical gripper includes a drive motor 1, a pulley 2, a flange 3, a hinge pin 4, and a biomimetic flexible finger 5.

[0028] Specifically, the drive motor 1 serves as the power source, and its output end is connected to the cable pulley 2. A flange 3 is fixedly installed below the cable pulley 2. Multiple hinge pins 4 are evenly distributed around the lower end of the flange 3. Each hinge pin 4 is hinged to a bionic flexible finger 5, thereby forming the basic support and drive frame of the mechanical claw. It should be understood that although this embodiment shows a specific connection form between the flange 3 and the hinge pin 4, in other embodiments, an integrally formed base or other equivalent hinged connectors can be used instead, as long as the bionic flexible finger 5 can be rotatably connected relative to the drive end.

[0029] The biomimetic flexible finger 5 comprises a root transition section and sequentially connected first segment 7, middle segment 8, and last segment 9. One end of the root transition section is hinged to a hinge pin 4, and the other end is connected to the first segment 7. The curvature of the root transition section varies along its extension direction. Here, "curvature varying along the extension direction" means that the outline of the root transition section is not a traditional straight line or a single-radius arc, but a curve with continuously varying curvature. This variable curvature design allows the biomimetic flexible finger 5 to simulate the closing shape of natural flower petals during the initial bending stage. Compared to a constant curvature structure, it provides a smoother stress transition and a larger initial envelope area in the initial contact with the target object, effectively avoiding damage to fragile fruits and vegetables caused by rigid impacts. Simultaneously, the variable curvature shape ensures that the root transition section maintains good mechanical stability at different bending angles, reducing localized stress concentration.

[0030] To accommodate the aforementioned variable curvature shape and ensure transmission reliability, an upper guide shaft 6 and a lower guide shaft 12 are provided in the root transition section.

[0031] Specifically, the upper guide shaft 6 and the lower guide shaft 12 are spaced apart along the rope's direction within the root transition section, dividing the drive cable path, which might otherwise experience severe friction or deflection due to large curvature bending, into multiple controlled micro-segments. This multi-stage guiding structure not only provides the necessary radial support for the traction drive cable 10, preventing axial stacking or deviation from the predetermined trajectory within the variable curvature cavity, but also reduces single-point contact pressure through segmented guidance, significantly improving transmission efficiency and service life. It should be understood that the specific shapes of the upper guide shaft 6 and the lower guide shaft 12 are not limited to cylindrical shafts; they can also be pulleys with grooves, smooth pins, or guide ribs integrally formed within the finger body, as long as they can limit and guide the traction drive cable 10.

[0032] The traction drive cable 10 originates from the pulley 2, passes through the flange 3, and sequentially passes through the hinge pin 4, upper guide shaft 6, lower guide shaft 12, first finger segment 7, middle finger segment 8, and connects to the last finger segment 9. Driven by the drive motor 1, it pulls the bionic flexible finger 5 to produce a bending envelope motion. Through the above path, the traction drive cable 10 forms a closed and continuous force transmission chain between the variable curvature root transition section and the multi-segment finger segments. When the drive motor 1 rotates forward to tighten the traction drive cable 10, the tension is smoothly transmitted through the upper guide shaft 6 and lower guide shaft 12, acting sequentially on each finger segment, causing the bionic flexible finger 5 to produce a coordinated inward bending motion from the root to the end. Conversely, when the traction drive cable 10 is released, in conjunction with the reset elastic cable 11, the bionic flexible finger 5 can return to its open state. This structural combination achieves the dual effects of compliant initial envelope and smooth transmission, ensuring both the adaptability and safety of the gripping process, and ensuring the operational reliability of the rope drive system under complex deformation conditions.

[0033] Example 2

[0034] This embodiment further optimizes the overall spatial layout and reset mechanism of the mechanical gripper at the system level. Specifically, the flange 3 is a circular flange, and there are four hinge pins 4 and four biomimetic flexible fingers 5. The hinge pins 4 are evenly distributed at 90° along the circumference of the flange 3.

[0035] like Figure 3-5 As shown, this cross-symmetrical spatial layout constitutes the basic configuration for the robotic gripper to perform enveloping grasping operations. From the perspective of mechanical transmission and grasping stability, the equiangular distribution of the four biomimetic flexible fingers 5 in the circumferential direction allows the radial components generated by each finger during the retraction process to cancel each other out, retaining only the axial resultant force pointing towards the geometric center. This effectively avoids grasping posture deviation or lateral compression damage to the target object caused by uneven force distribution. Especially when harvesting nearly spherical fruits and vegetables such as apples and citrus fruits, the four-point evenly distributed contact pattern can form a stable spatial constraint. Combined with the compliant fitting characteristics of the variable curvature root transition section in the aforementioned embodiment, it can achieve adaptive envelopment of irregular surfaces, significantly improving the reliability and safety of grasping.

[0036] Specifically, such as Figure 2 As shown, the reset elastic cord 11 runs through the interior of each phalanx along the length of the bionic flexible finger 5 or is attached to the inner side of the phalanx. Its two ends are fixed to the proximal end of the first phalanx 7 and the distal end of the last phalanx 9 (or to the flange 3), forming an independent passive energy storage circuit. When the drive motor 1 tightens the traction drive cord 10 to make the bionic flexible finger 5 bend inward to grasp, the reset elastic cord 11 is stretched and stores elastic potential energy. When the grasping is completed or the target needs to be released, the drive motor 1 reverses or releases the traction drive cord 10. At this time, the elastic potential energy stored in the reset elastic cord 11 is instantly converted into mechanical kinetic energy, pulling each phalanx segment to move in the opposite direction, so that the bionic flexible finger 5 smoothly and quickly returns to its initial open state. This purely mechanical passive reset scheme does not require an independent reset motor or complex torsion spring mechanism for each finger. It not only greatly simplifies the internal structure and electrical wiring of the end effector, but also significantly reduces the overall weight and control complexity, making it particularly suitable for load-sensitive mobile robot picking platforms. The specific material selection for the reset elastic cord 11 can be flexibly chosen according to the requirements of gripping force and response speed. For example, a high-elasticity rubber cord can be used to obtain a gentle reset characteristic and a good damping buffering effect, or a spring steel wire can be used to obtain a more linear stiffness output and a longer fatigue life. In addition, the placement of the reset elastic cord 11 is not limited to inside the finger body. Without interfering with the external envelope surface, it can also be set in a dedicated channel on the back of the finger body to achieve an equivalent reset function.

[0037] Example 3

[0038] like Figure 6 This embodiment provides a design method for a root transition section. Specifically, the contour curve of the root transition section is a continuously variable curvature curve, with the curvature decreasing from the hinge point with the flange 3 towards the first finger joint 7.

[0039] The term "decreasing curvature" here refers to the gradual decrease in curvature value at various points along the contour line of the root transition section as it extends from the end near the hinge pin 4 to the end connecting the first finger segment 7. From a biomechanical and mechanical transmission perspective, this non-uniform curvature distribution has specific functional adaptability: the proximal end of the root transition section (i.e., the side near the flange 3) bears the maximum tensile torque from the traction drive cable 10 and the reaction torque of the external load during gripping operations. The larger initial curvature helps to form a more compact structural shape in this area, thereby improving the local bending stiffness and load-bearing capacity, and preventing structural failure or transmission efficiency loss due to excessive deformation. As the extension direction develops further, the curvature gradually decreases and tends to flatten, giving the connection area between the root transition section and the first finger segment 7 better flexibility and conformity. This allows for a gradual tangential fit when contacting spherical or irregular fruit and vegetable surfaces, avoiding hard compression points caused by sudden changes in local curvature, thus effectively protecting fragile targets.

[0040] Regarding the specific generation method of this continuous variable curvature curve, in this embodiment, it can be obtained by collecting the three-dimensional coordinate data of the natural petal outline and using spline curve or polynomial fitting methods. Natural petals, through long-term evolutionary selection, naturally possess optimal envelope mechanical properties; using them as a prototype for fitting can quickly obtain curve parameters that combine aesthetics and functionality.

[0041] For example, three-dimensional coordinate data of the outline of a natural petal are collected and saved as a CSV file. The data file contains three columns: x-coordinate, y-coordinate, and z-coordinate, corresponding to the positions of the petal outline points in three-dimensional space. The number of sampling points, n, is determined based on the petal size and accuracy requirements, typically n = 50~200. The collected data is then denoised and smoothed using a Savitzky-Golay filter to eliminate measurement noise and obtain a smooth petal outline curve. The filter window length is 11~21, and the polynomial order is 3~5.

[0042] Curvature analysis is performed on the smoothed petal contour curve. Let the petal contour parametric equation be (x(t), y(t)), where t is the arc length parameter. Then the formula for calculating the curvature k(t) is: Curvature analysis was used to obtain the curvature distribution characteristics of the petal curve from the root to the tip.

[0043] Curvature analysis range: The range of selected points at the root: s∈[0, 0.1], corresponding to the connection between the petals and the calyx, where the curvature changes drastically; The selected point range in the middle is s∈[0.3, 0.7], corresponding to the main body of the petals, where the curvature changes gently; The range of the tip selection point is s∈[0.9, 1.0], corresponding to the end of the petal, where the curvature tends to be stable.

[0044] Calculate the normalized arc length parameter s:

[0045] Among them, L i L is the cumulative arc length from the starting point to the i-th sampling point. total This represents the total arc length of the curve.

[0046] Based on the curvature analysis results, a petal gradient curvature function is constructed. Let the normalized arc length parameter s∈[0,1], where s=0 corresponds to the root and s=1 corresponds to the tip. The petal gradient curvature function adopts an exponential decay model.

[0047] Where k0 is the initial curvature at the root, k1 is the final curvature at the tip, and λ is the curvature decay coefficient.

[0048] Method for determining k0 and k1: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] The parameters for overall optimization are solved simultaneously using the nonlinear least squares method. The objective function is the sum of squared residuals between the measured curvature and the model curvature:

[0049]

[0050] Where, k i Let s be the measured curvature of the i-th sampling point. i Let be the normalized arc length corresponding to the i-th sampling point, and n be the total number of sampling points. The Levenberg-Marquardt algorithm solves the above nonlinear least squares problem to obtain the optimal parameters (k0, k1, λ). The Levenberg-Marquardt algorithm requires reasonable initial values:

[0051]

[0052] (Estimated based on curvature decay rate) Value range: Take the average value of the first 10% of the sampling points on the curvature distribution curve; Take the average value of the last 10% of sampling points on the curvature distribution curve; Choose according to the type of petals, ranging from 2.0 to 5.0.

[0053] The algorithm's iteration termination condition is: the parameter change is less than 1 / 3. Or the change in the objective function is less than .

[0054] Find the partial derivatives of k(s) with respect to k0, k1, and λ respectively:

[0055] At the root (s≈0). ≈1, ≈0, the root curvature is almost entirely determined by k0; the opposite is true at the tip (s≈1). This parameter separation characteristic means that k0 and k1 can be optimized independently, reducing the dimensionality of the fitting problem. When λ > 3, k0 and λ are nearly decoupled, and a step-by-step optimization strategy can be adopted: first fix λ=3 to optimize k0 and k1, and then fine-tune λ, which can improve computational efficiency by about 40%.

[0056] Based on the gradient curvature function, a piecewise cubic Bézier curve is used to fit the petal contour. Let the control points of the i-th Bézier curve be... The equation of the curve is:

[0057] in N s The number of segments is determined by selecting 3 to 5 segments based on the complexity of the curve.

[0058] The determination of control points must satisfy curvature constraints. At the connection points, the termination curvature of the preceding curve segment is equal to the initial curvature of the following curve segment, ensuring the curvature continuity of the overall curve. The relationship between curvature and Bézier curve control points is as follows:

[0059] Where θ is a vector The included angle. The positions of the control points are adjusted through an iterative optimization algorithm to ensure that each curve segment meets the preset gradual curvature constraint.

[0060] The fitted petal gradient curvature curve is resampled with equal arc lengths to generate uniformly distributed coordinate points. Let the total arc length of the curve be L, and the number of sampling points be N. Then the arc length interval between adjacent sampling points is Δs = L / (N-1).

[0061] The relationship between the arc length parameter s and the curve parameter t is determined by the following integral:

[0062] The arc length is calculated using numerical integration, and the inverse function t(s) is solved by Newton's iteration method to obtain the coordinates (x(sᵢ), y(sᵢ)) of the sampling points with equal arc length distribution.

[0063] Newton's iterative formula is:

[0064] in, Iteration termination condition .

[0065] The generated curve coordinates are translated to start from the origin (0,0), making it easier to import and use in 3D modeling software such as SolidWorks:

[0066]

[0067]

[0068] Through the refined design of the above geometric features, the designed biomimetic flexible finger 5 maximizes the adaptive envelope capability of the target object while ensuring the strength of the root structure, thus solving the technical problems of stress concentration and poor fit at the root of traditional flexible fingers.

[0069] Finally, it should be noted that any parts of this invention not described in detail are prior art. Those skilled in the art will understand that the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A multi-segment flexible mechanical gripper based on petal biomimicry, characterized in that, include: A drive motor (1) is connected to a cable wheel (2) at its output end. A flange (3) is fixedly installed below the cable wheel (2). Multiple hinge pins (4) are evenly distributed around the lower end of the flange (3). Each hinge pin (4) is hinged to a bionic flexible finger (5). Bionic flexible finger (5), the bionic flexible finger (5) includes a root transition section and a first segment (7), a middle segment (8) and a last segment (9) connected in sequence. One end of the root transition section is hinged to the hinge pin (4) and the other end is hinged to the first segment (7). The curvature of the root transition section changes along its extension direction. An upper guide shaft (6) and a lower guide shaft (12) are provided in the root transition section. The pulley (2) leads out the traction drive cable (10), which passes through the flange (3), and then winds around the warp shaft (4), the upper guide shaft (6), and the lower guide shaft (12) in sequence. It also passes through the guide channels on the first finger joint (7) and the middle finger joint (8). Its end is fixedly connected to the last finger joint (9). Under the drive of the drive motor (1), it pulls the bionic flexible finger (5) to generate a bending envelope motion. It also includes a reset elastic cord (11) arranged along the length direction of the bionic flexible finger (5) for providing a reset elastic force when the traction drive cord (10) is released.

2. The multi-segment flexible mechanical gripper based on petal biomimicry according to claim 1, characterized in that, The reset elastic cable (11) passes sequentially through the first segment (7), the middle segment (8), and the last segment (9), with its proximal end fixed to any one of the root transition section, the first segment (7), or the flange (3), and its distal end fixed to the last segment (9), and is used to provide a reset elastic force to restore the bionic flexible finger (5) to the open state when the traction drive cable (10) is released.

3. The multi-segment flexible mechanical gripper based on petal biomimicry according to claim 1, characterized in that, The contour curve of the root transition section is a continuous variable curvature curve, with the curvature decreasing from the hinge point with the flange (3) towards the first finger joint (7).

4. The multi-segment flexible mechanical gripper based on petal biomimicry according to claim 1, characterized in that, The flange (3) is a circular flange. There are four hinge pins (4) and four biomimetic flexible fingers (5). The hinge pins (4) are evenly distributed at 90° along the circumference of the flange (3).

5. The multi-segment flexible mechanical gripper based on petal biomimicry according to claim 1, characterized in that, The upper guide shaft (6) is located near the flange (3), and the lower guide shaft (12) is located near the first finger joint (7); both the upper guide shaft (6) and the lower guide shaft (12) are stepped shaft structures, and their shoulders are provided with annular grooves for the traction drive cable (10) to pass through.

6. The multi-segment flexible mechanical gripper based on petal biomimicry according to claim 2, characterized in that, The traction drive cable (10) is a steel wire rope or a high-strength fiber rope; the reset elastic cable (11) is a rubber cable or a spring steel wire.

7. A method for designing the root transition section of a multi-segment flexible mechanical grasper based on petal biomimicry, characterized in that, Includes the following steps: S1. Collect the three-dimensional coordinate data of the natural petal outline. Based on the obtained data, use the Savitzky-Golay filter to eliminate measurement noise and obtain a smooth two-dimensional outline point set. S2. Perform curvature analysis on the two-dimensional contour point set obtained in S1, according to the curvature calculation formula. Calculate the curvature value and the corresponding normalized arc length parameter at each sampling point to obtain the curvature distribution characteristics of the petal outline from the root to the tip; S3. Based on the curvature distribution characteristics described in S2, an exponential decay model is used to construct the petal gradient curvature function. With the goal of minimizing the sum of squared residuals between the measured curvature and the model curvature, the Levenberg-Marquardt algorithm is used to solve for the model parameters k0, k1, and λ, where k0 is the initial curvature at the root, k1 is the terminal curvature at the tip, and λ is the curvature decay coefficient. S4. Using the gradual curvature function described in S3 as a constraint, the petal outline is fitted with a piecewise cubic Bézier curve to generate the root transition segment outline curve with curvature continuously changing along the arc length direction. S5. Perform equal arc length resampling and coordinate normalization on the fitted root transition segment contour curve, and output the curve coordinate data for root transition segment modeling.

8. The root transition segment design method of a multi-segment flexible mechanical grasper based on petal biomimicry according to claim 7, characterized in that, In step S1, when collecting the three-dimensional coordinate data of the natural petal outline, the sampling point distribution includes at least the following three segmented regions: The root sampling range corresponds to the normalized arc length s∈[0, 0.1]; The normalized arc length s∈[0.3, 0.7] corresponds to the sampling range in the middle. The tip sampling range corresponds to the normalized arc length s∈[0.9, 1.0].

9. The root transition segment design method of a multi-segment flexible mechanical grasper based on petal biomimicry according to claim 7, characterized in that, In step S3, when using the Levenberg-Marquardt algorithm to solve for the model parameters, a step-by-step optimization strategy is adopted: First, fix the curvature attenuation coefficient λ as the initial value. The initial curvature k0 at the root and the termination curvature k1 at the tip are optimized. Then, using the optimized k0 and k1 as fixed values, λ is fine-tuned. Among them, the The value range is 2.0 to 5.

0.

10. The root transition segment design method of a multi-segment flexible mechanical grasper based on petal biomimicry according to claim 7, characterized in that, In step S4, at the connection point of two adjacent Bézier curves, the termination curvature of the previous curve is equal to the initial curvature of the next curve. The curvature k(0) of a single Bézier curve at its starting point is determined by the following relationship: in, , , These are the first three control points of the Bézier curve segment, and θ is a vector. The included angle.