Symmetrically-driven bionic butterfly flapping wing mechanism and movement mechanism simulation method thereof

Abstract

The invention discloses a bionic butterfly flapping wing mechanism under symmetrical driving and a movement mechanism simulation method thereof, and belongs to the field of bionic machinery. The mechanism adopts a single-input and double-output symmetrical driving topological structure and comprises a driving subsystem, a transmission subsystem and an output subsystem, and differential amplitude and phase difference swinging of front and rear wings under single driving is realized through geometric asymmetry of a transmission chain and position offset of a supporting point. According to the simulation method, a mechanism model is constructed based on ADAMS, kinematics simulation is carried out, simulation data are processed through MATLAB, a difference amplitude ratio and a phase difference are calculated, and mechanism motion characteristics are verified. The device is compact in structure, simple to drive, controllable in difference amplitude characteristic and reliable in simulation method, is suitable for flapping wing structure design and optimization of a miniature bionic flight platform, and provides a new design thought and theoretical support for a multi-wing bionic flight mechanism.

Description

Technical Field

[0001] This invention relates to the field of biomimetic mechanics and motion simulation technology, and in particular to a biomimetic butterfly flapping wing mechanism under symmetrical drive and its motion mechanism simulation method. Background Technology

[0002] With the development of biomimetic flight and flapping wing mechanisms, mechanisms that mimic the movement patterns of insect or bird wings have been extensively studied. Traditional flapping wing mechanisms mostly employ single crank or four-bar linkages, whose main advantages are simple structure and ease of manufacturing, but they have significant limitations in output motion characteristics. Due to the singular motion transmission relationship between the drive end and the wing root, the wing surface amplitude is limited, making it difficult to simultaneously achieve phase and amplitude control of the forewing and hindwings in a lightweight structure, resulting in insufficient lift output and attitude adjustment capabilities.

[0003] Existing studies have explored various approaches to address these issues. One type of work uses double cranks or multi-degree-of-freedom mechanisms to achieve multi-point drive at the wing root, thereby increasing the flapping angle range. Another type of research introduces flexible connections or cam slides to improve airfoil deformation and phase adjustability. These methods have achieved certain results in improving the biomimicry of the airfoil, but most of them have complex structures, long transmission chains, and high manufacturing precision requirements, making them difficult to apply on micro-flight platforms. At the same time, existing mechanisms often focus on aerodynamic performance verification and lack a systematic analysis of the kinematic transmission laws of the mechanism itself [7].

[0004] To address the aforementioned problems, this invention proposes a novel flapping wing mechanism based on a double-crank-double-rocker symmetrical drive. This mechanism, through geometric amplitude and phase design, enables differentiated motion of the fore and rear wings under the same drive, thereby expanding output motion characteristics while maintaining a compact structure. This invention employs ADAMS for motion simulation and combines it with MATLAB to process and compare displacement, velocity, and acceleration data, aiming to verify whether the mechanism can achieve the expected wing flapping angle and phase difference characteristics. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of existing flapping wing mechanisms, which are complex in structure and have simple motion characteristics. It provides a biomimetic butterfly flapping wing mechanism under symmetrical drive and a simulation method for its motion mechanism, so as to realize the differential swing and phase difference control of the fore and hind wings under a single drive input. At the same time, the feasibility and stability of the mechanism's motion law are verified through simulation.

[0006] A symmetrically driven biomimetic butterfly flapping mechanism adopts a single-input, dual-output symmetrical drive topology, including a drive subsystem, a transmission subsystem, and an output subsystem;

[0007] The drive subsystem includes a drive point A and a crank AB. The drive point A is the power input center and rotates at a constant angular velocity. One end of the crank AB is connected to the drive point A and moves in a circular motion around point A.

[0008] The transmission subsystem includes the forewing transmission chain ABE and the hindwing transmission chain ABC. The connecting rods BE and CB have the same length, but the spatial arrangement angles of the two transmission chains are different.

[0009] The output subsystem includes a forewing EF and a hindwing CD. Point E is the connection point at the root of the forewing and is connected to the other end of the connecting rod BE. Point C is the connection point at the root of the hindwing and is connected to the other end of the connecting rod BC. Points F and D are fixed support points for the frame. Point F is located directly below the drive point A and is perpendicular to it. Point D is offset from the drive point A by 19.26°. The distance between the two points is 5mm.

[0010] The lengths and angles of the forewing drive chain ABE and the hindwing drive chain ABC together determine the motion amplification factor and the phase response difference.

[0011] Furthermore, the constant angular velocity of the driving point A is 1800° / s; the structural geometric dimensions are AB = 6mm, BE = CB = 18mm, |DF| = 5mm, ∠DFA = 90°, and ∠DAF = 19.26°.

[0012] Furthermore, the difference in amplitude and phase between the forewing and hindwing originates from geometric asymmetry: the spatial arrangement angles of the forewing drive chain ABE and the hindwing drive chain ABC are different, resulting in differences in the projection components of the same driving angular displacement in the two drive chains; the offset positions of the frame support points F and D cause the geometric constraint propagation path lengths of the two drive chains to be different, ultimately resulting in the motion amplitude of point E being smaller than that of point C, and the motion phase of point E lagging behind that of point C.

[0013] A simulation method for the motion mechanism of a biomimetic butterfly flapping wing mechanism under symmetrical actuation includes the following steps:

[0014] S1: Establish the geometric model of the mechanism

[0015] Driving point A rotates at a constant angular velocity ω, and its angular displacement can be expressed as:

[0016] θ(t)=ωt (1)

[0017] In the formula, θ is the driving angle, t is time, and ω is the angular velocity constant;

[0018] As the driving point A rotates, the connecting rod AB makes circular motion around point A, which is transmitted to the output end E via the connecting rod BE and to the output end C via the connecting rod CB, causing the two points to produce periodic displacement in the XZ plane; this motion can be regarded as the driving function of the time parameter t on the spatial coordinates of the output point.

[0019] S1.1: Establishing geometric constraints and position equations

[0020] Establish a fixed coordinate system with the driving point A as the origin, the X-axis horizontal, and the Z-axis vertically upward; the lengths of crank AB, connecting rod BE, and connecting rod CB remain constant during motion; when the driving point A rotates, the position of point B is:

[0021]

[0022] The condition for a constant link length is:

[0023] (X E -X B ) 2 +(Z E -Z B ) 2 =BE 2 (3)

[0024] (X C -X B ) 2 +(Z C -Z B ) 2 =CB 2 (4)

[0025] Based on the geometric relationship between the fixed support points F and D of the frame: |DF|=5mm, ∠DFA=90°, ∠DAF=19.26°, the spatial coordinates of the output points E and C at any time can be obtained from the mechanism constraints.

[0026]

[0027] Equations (2), (3), and (4) are the basic kinematic equations of the mechanism, which describe the mapping relationship between time and spatial position. These two functions directly determine the motion trajectory and amplitude characteristics of the output terminals E and C.

[0028] S1.2: Calculate the relationship between velocity and acceleration

[0029] Taking the time derivative of equation (5), we can obtain the velocities and accelerations of the output terminals E and C:

[0030]

[0031] Among them, Z · and Z ·· These represent the velocity and acceleration in the Z direction, respectively, corresponding to the V and A data in the simulation output. These two sets of equations reflect the law of change of the wing root's swing velocity and acceleration over time.

[0032] S1.3: Definition of amplitude and phase difference

[0033] To quantify the difference in movement between the forewings and hindwings, the amplitude and phase difference of the Z-axis displacement are defined; the output amplitude is defined as:

[0034]

[0035] The amplitude ratio is defined as:

[0036]

[0037] When K A When the amplitude is less than 1, the forewing's swing amplitude is less than that of the hindwing, resulting in differential motion;

[0038] The phase difference is obtained by comparing the peak times of the Z-axis velocity curves; let the maximum Z-axis velocities of the forewing and hindwing occur at time t, respectively. E,max With t C,max The phase difference is then defined as:

[0039] Δφ=t E，max -t C，max (10)

[0040] When Δφ>0, the forewing movement lags behind the hindwing; when Δφ<0, the forewing leads the hindwing.

[0041] S1.4: Draw the temporally correlated spatial trajectory

[0042] Plotting the result of equation (5) as a three-dimensional curve yields the trajectory diagram of the output point in the ZXt coordinate system. The results show that the forewing trajectory envelope is smaller and the motion lags behind; the hindwing trajectory amplitude is larger and the response is earlier.

[0043] S1.5: Analysis of the Amplitude Formation Mechanism

[0044] According to the combined formulas (2)–(10), under the same driving angular velocity conditions, the spatial layout of the two transmission chains A–B–E and A–B–C has geometric differences;

[0045] S2: Simulation Verification

[0046] A mechanism simulation model was built using ADAMS software, and the output data was processed using MATLAB.

[0047] S2.1: Simulation Model and Parameter Settings

[0048] The simulation uses the same geometric parameters as the theoretical model:

[0049] AB=6mm, BE=CB=18mm, DF=5mm

[0050] The angles between the fixed support points are ∠DFA = 90° and ∠DAF = 19.26°; the driving point A is the rotation center of the mechanism, and the input angular velocity ω = 1800° / s; the mechanism is arranged symmetrically on the left and right, with F and D being the fixed support points of the frame for the front and rear wings, respectively; the simulation step size is set to 0.001s, and the total duration is 1.5s; in ADAMS, a uniform angular velocity drive is applied to the driving point A, and the system constraints are established according to the actual geometric relationship; the displacement, velocity, and acceleration of the output terminals E and C are extracted along the Z direction, and the trajectory in the X direction is recorded for motion path analysis.

[0051] S2.2: Simulation Results and Trajectory Characteristics

[0052] The amplitude A can be calculated from the Z-axis displacement data. E A C And according to equations (8) and (9), the amplitude ratio K is obtained. A ;

[0053] The results showed that the amplitude of the forewing EF was significantly smaller than that of the hindwing CD, and the peak occurred later; this phenomenon is consistent with the prediction of the theoretical model.

[0054] The phase difference is calculated by comparing the peak occurrence times according to equation (10). The results show A positive value indicates that the forewing movement lags behind the hindwing movement.

[0055] S2.3: Motion Law and Amplitude Verification

[0056] Statistical analysis of simulation curves shows that: forewing A E Smaller amplitude; hindwing A C The amplitude is relatively large; the difference in amplitude ratio K A =A E / A C <1; Phase difference It is a positive value.

[0057] Furthermore, in step S1.5, due to the different spatial arrangement angles of AB, BE, CB and frame points D and F, the driving force is decomposed into components in different directions during transmission, resulting in differences in the displacement amplitude and time response of points E and C; the output amplitude of the forewing EF is smaller and the phase is lagging, while the output amplitude of the rearwing CD is larger and the phase is advancing. This difference originates from the geometric characteristics of the mechanism itself, rather than the influence of the driving signal or external load.

[0058] Furthermore, the mechanism can achieve stable periodic motion: as can be seen from the ZXt trajectory, the motion is smooth and the period is consistent, which is consistent with the constant speed drive assumption; the amplitude and phase difference are obvious: the amplitude and phase difference of the fore and hind wings are consistent with the theoretical prediction; the geometric design dominates the output characteristics: under no-load conditions, the amplitude difference phenomenon is completely determined by the angle of the rod and the length of the connecting rod.

[0059] The beneficial effects of this invention are as follows:

[0060] 1. Compact structure and simple drive: The present invention adopts a symmetrical topology structure with single input and dual output, which does not require multiple drive units or complex flexible components. The transmission path is clear, the overall size is small and the weight is light, and it is suitable for micro biomimetic flight platforms.

[0061] 2. Controllable amplitude characteristics: By optimizing the geometric arrangement angle of the transmission chain and the position of the support point, the amplitude ratio and phase difference of the fore and hind wings can be flexibly adjusted to meet the wing movement requirements of different biomimetic flight scenarios.

[0062] 3. High motion stability: The differential motion of the mechanism originates from the inherent characteristics of the geometric structure, requiring no additional control algorithm or power adjustment. The motion process is smooth and the cycle consistency is good.

[0063] 4. Reliable simulation method: Through the co-simulation of ADAMS and MATLAB, the kinematic parameters of the mechanism can be accurately extracted, the amplitude characteristics can be quantitatively verified, and a quantitative basis can be provided for the structural optimization of the mechanism. Attached Figure Description

[0064] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 This is a modeling diagram of the biomimetic butterfly flapping wing mechanism of the present invention;

[0066] Figure 2 This is a theoretical modeling diagram of the biomimetic butterfly flapping wing mechanism of the present invention;

[0067] Figure 3 Comparison of ZXt trajectories for forewings and hindwings;

[0068] Figure 4 Comparison curves of ZXt displacement between forewing and hindwing;

[0069] Figure 5 Comparison of the Z-axis velocity curves of the forewing and hindwing. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0071] A symmetrically driven biomimetic butterfly flapping mechanism is disclosed. This mechanism adopts a single-input, dual-output symmetrical drive form.

[0072] 1 Overall structural design

[0073] Drive point A serves as the power input center, transmitting rotational motion to the roots of the fore and aft wings via a crank-connecting rod system, thus achieving periodic oscillation of the wings. The two mechanisms are topologically symmetrical, but their geometric arrangements differ slightly, which is crucial for achieving differential motion. Drive point A rotates counterclockwise at a constant angular velocity of 1800° / s, and the motion of both mechanisms is confined to the XZ plane.

[0074] The drive chains for the fore and hind wings are A–B–E–F and A–B–C–D, respectively, where E and C are at the roots of the fore and hind wings, and F and D are at the frame support points. The rotation of crank A–B is transmitted to E (or C) via connecting rod B–E (or B–C), generating periodic vibrations. Due to the different spatial arrangement angles of the two drive chains, E and C exhibit amplitude and phase differences under the same driving conditions. Figure 1 A schematic diagram of the mechanism model.

[0075] 1.1 Functional Zoning and Transmission Relationship

[0076] The mechanism consists of three parts: drive, transmission, and output. The drive subsystem includes point A and crank AB; the transmission subsystem consists of connecting rod chains A–B–E and A–B–C; and the output subsystem consists of EF and CD, which drive the movement of the fore and rear wing roots, respectively.

[0077] F and D are fixed points on the frame. F is located directly below point A and perpendicular to it, while D is offset by 19.26° relative to A. The distance between the two points is 5mm. Under the same input angular velocity, the output displacement and time response differ due to the different projection direction of the transmission path and the different angles of the connecting rod.

[0078] 1.2 Geometric Parameters and Features

[0079] The main geometric dimensions of the mechanism are AB = 6mm, BE = CB = 18mm, |DF| = 5mm, ∠DFA = 90°, and ∠DAF = 19.26°. F and D are fixed, while E and C connect to the roots of the front and rear winglets, respectively. The lengths and angles of the two transmission chains together determine the motion amplification factor and phase response difference. The overall system structure is compact, the transmission path is clear, and dual outputs can be achieved under single-input conditions.

[0080] 1.3 Mechanism of amplitude difference formation

[0081] The generation of differential motion comes from geometric asymmetry.

[0082] The different angles between the A–B–E chain and the A–B–C chain result in different transmission projections of the same input angular displacement in the two chains, leading to a smaller output displacement obtained by the forewing (EF).

[0083] On the other hand, the support directions of F and D are inconsistent, and the lengths of the geometric constraint propagation paths differ, resulting in a time delay in the movement of the forewing relative to the hindwing. This difference in amplitude and phase is an inherent geometric result of the mechanism structure itself and does not depend on additional control or dynamic adjustment.

[0084] 2 Theoretical Modeling

[0085] Driving point A rotates at a constant angular velocity ω, and its angular displacement can be expressed as:

[0086] θ(t)=ωt (1)

[0087] In the formula, θ is the driving angle, t is time, and ω is the angular velocity constant.

[0088] As point A rotates, link AB undergoes circular motion around point A, which is transmitted to output terminals E and C via BE (or CB), causing periodic displacement of the two points in the XZ plane. This motion can be considered as a driving function of the time parameter t on the spatial coordinates of the output point. Figure 2 Modeling diagram for mechanism theory.

[0089] 2.1 Geometric Constraints and Position Equations

[0090] Establish a fixed coordinate system with point A as the origin, the X-axis horizontal, and the Z-axis vertically upward. The lengths of crank AB and connecting rod BE (or CB) remain constant during motion. When point A rotates, the position of point B is:

[0091]

[0092] The condition for a constant link length is:

[0093] (X E -X B ) 2 +(Z E -Z B ) 2 =BE 2 (3)

[0094] (X C -X B ) 2 +(Z C -ZB ) 2 =CB 2 (4)

[0095] Based on the geometric relationship between the frame support points F and D (|DF|=5mm, ∠DFA=90°, ∠DAF=19.26°), the spatial coordinates of the output points E and C at any given time can be obtained from the mechanism constraints:

[0096]

[0097] Equations (2), (3), and (4) are the basic kinematic equations of the mechanism, describing the mapping relationship between time and spatial position. These two functions directly determine the motion trajectory and amplitude characteristics of the output terminals E and C.

[0098] 2.2 Relationship between velocity and acceleration

[0099] Taking the time derivative of equation (5), we can obtain the velocities and accelerations of the output terminals E and C:

[0100]

[0101] Among them, Z · and Z ·· These represent the velocity and acceleration in the Z direction, respectively, corresponding to the V and A data in the simulation output. These two sets of equations reflect the changes in the wing root's oscillation velocity and acceleration over time.

[0102] 2.3 Definitions of Amplitude and Phase Difference

[0103] To quantify the difference in forewing and hindwing motion, the amplitude and phase difference of the Z-axis displacement are defined. The output amplitude is defined as:

[0104]

[0105] The amplitude ratio is defined as:

[0106]

[0107] When K_A<1, the amplitude of the forewing's waving is smaller than that of the hindwing, resulting in differential motion.

[0108] The phase difference is obtained by comparing the peak times of the Z-axis velocity curves. Let the maximum Z-axis velocities of the forewing and hindwing occur at time t. E，max With t C,max The phase difference is then defined as:

[0109] Δφ=t E，max -t C,max (10)

[0110] When Δφ>0, the forewing movement lags behind the hindwing; when Δφ<0, the forewing leads the hindwing.

[0111] 2.4 Temporally Correlated Spatial Trajectory

[0112] Plotting the result of equation (5) as a three-dimensional curve yields the trajectory of the output point in the ZXt coordinate system, as shown below. Figure 3 As shown.

[0113] from Figure 3 As can be seen, the forewing trajectory envelope is smaller and the motion lags behind; the hindwing trajectory amplitude is larger and the response is earlier. This pattern is consistent with the calculation results of equations (9) and (10), indicating that the amplitude and phase difference are structural results caused by geometric transmission characteristics.

[0114] 2.5 Analysis of the Amplitude Difference Formation Mechanism

[0115] As can be seen from equations (2)–(10), under the same driving angular velocity conditions, there are geometric differences in the spatial layout of the two transmission chains A–B–E and A–B–C.

[0116] Due to the different spatial arrangement angles of AB, BE, CB, and frame points D and F, the driving force is decomposed into components in different directions during transmission, resulting in differences in the displacement amplitude and time response at points E and C. The output amplitude of the forewing (EF) is smaller and the phase lags, while the output amplitude of the rearwing (CD) is larger and the phase advances. This difference stems from the inherent geometric characteristics of the mechanism itself, rather than from the influence of the driving signal or external load.

[0117] 3. Simulation Verification

[0118] This chapter establishes a mechanism simulation model using ADAMS software and processes the output data using MATLAB. The purpose of the simulation is to verify whether the kinematic characteristics of the mechanism conform to the theoretical model derivation results, with a focus on observing the amplitude and phase difference between the fore and hind wings.

[0119] A simulation method for the motion mechanism of a biomimetic butterfly flapping wing mechanism under symmetrical actuation includes the following steps:

[0120] 1.1 Simulation Model and Parameter Settings

[0121] The simulation uses the same geometric parameters as the theoretical model:

[0122] AB=6mm, BE=CB=18mm, DF=5mm

[0123] The angles between the fixed support points are ∠DFA = 90° and ∠DAF = 19.26°. The driving point A is the rotation center of the mechanism, with an input angular velocity ω = 1800° / s. The mechanism is symmetrically arranged left and right, with F and D being the support points for the front and rear wings, respectively. The simulation step size is set to 0.001s, and the total duration is 1.5s. In ADAMS, a uniform angular velocity drive is applied to point A, and system constraints are established according to the actual geometric relationships. The displacement, velocity, and acceleration of the output terminals E and C are extracted along the Z-direction, while the trajectory in the X-direction is recorded for motion path analysis.

[0124] 1.2 Simulation Results and Trajectory Characteristics

[0125] Figure 4 The X and Z direction motion curves of the connecting rod between the forewing EF and the hindwing CD are displayed. The amplitude A can be calculated from the Z-direction displacement data. E A C And according to equations (8) and (9), the amplitude ratio K is obtained. A .

[0126] The results show that the amplitude of the forewing EF swing is significantly smaller than that of the hindwing CD, and the peak occurs later. This phenomenon is consistent with the prediction of the theoretical model, indicating that the geometric difference does indeed lead to the output amplitude difference.

[0127] Figure 5 The Z-axis velocity curves of the two points are displayed. The phase difference is calculated according to equation (10) by comparing the peak occurrence times. The results show A positive value indicates that the movement of the forewings lags behind that of the hindwings.

[0128] 1.3 Motion Laws and Amplitude Verification

[0129] Statistical analysis of simulation curves shows that: forewing A E Smaller amplitude; hindwing A C The amplitude is relatively large; the difference in amplitude ratio K A =AE / A C <1; Phase difference It is a positive value.

[0130] This indicates that, under the same angular velocity input, the forewing oscillation phase lags and the amplitude decreases, verifying the differential amplitude characteristics derived above. This differential amplitude originates from the asymmetric transmission of the mechanism's geometry, rather than from differences in driving force or mass distribution.

[0131] 1.4 Results Analysis and Discussion

[0132] Simulation results show that:

[0133] 1. The mechanism can achieve stable periodic motion: As can be seen from the ZXt trajectory, the motion is smooth and the period is consistent, which is consistent with the constant speed drive assumption.

[0134] 2. Significant amplitude and phase differences exist: The amplitude and phase differences of the forewing and hindwings are consistent with theoretical predictions, proving the effectiveness of the geometric design.

[0135] 3. Geometric design dominates output characteristics: Under no-load conditions, the amplitude difference phenomenon is entirely determined by the angle of the link and the length of the link, reflecting the inherent kinematic characteristics of the mechanism.

[0136] Overall, the simulation verified that the symmetrical drive mechanism based on geometric difference can achieve differential motion of the fore and wing under a single input, providing a structural basis for subsequent aerodynamic performance research.

[0137] In summary, this invention proposes a biomimetic butterfly flapping wing mechanism based on geometric difference and its motion mechanism simulation method. The mechanism adopts a single-input, symmetrically driven structure, achieving differential oscillation through the geometric differences in the transmission of the fore and hind wings. This invention focuses on three aspects: mechanism design, theoretical modeling, and simulation verification. The main conclusions are as follows:

[0138] (1) The mechanism consists of crank AB, connecting rods BE and CB, and support points F and D. When point A rotates at a constant angular velocity, the motion is transmitted to the output terminals E and C through different geometric paths, resulting in periodic motions with different amplitudes and phases.

[0139] (2) Theoretical analysis shows that the geometric difference makes the displacement amplitude and time response of the output point in the XZ plane inconsistent. The difference ratio and phase difference can be obtained from the displacement and velocity curves, which are inherent geometric output characteristics of the mechanism.

[0140] (3) The ADAMS simulation results are consistent with the theoretical predictions. The amplitude of the forewing EF is smaller and the phase lags, while the amplitude of the hindwing CD is larger and the phase advances, which verifies the amplitude difference characteristics caused by geometric asymmetry transmission.

[0141] This mechanism achieved stable differential motion under single-drive conditions, verifying the direct influence of geometry on motion output. The results of this invention provide a theoretical basis and design reference for the geometric design and motion characteristic optimization of biomimetic flapping wing mechanisms.

[0142] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A symmetrical driven bionic butterfly flapping mechanism, characterized in that, The single-input and double-output symmetric driving topology includes a driving subsystem, a transmission subsystem and an output subsystem; The driving subsystem includes a driving point A and a crank AB, the driving point A is a power input center, the driving point A rotates at a constant angular velocity, one end of the crank AB is connected with the driving point A and makes a circular motion around the point A; The transmission subsystem includes a front wing transmission chain A-B-E and a rear wing transmission chain A-B-C, the length of the connecting rod BE is the same as that of the connecting rod CB, and the spatial arrangement angles of the two transmission chains are different; The output subsystem includes a front wing EF and a rear wing CD, the point E is a front wing root connecting point and is connected with the other end of the connecting rod BE, the point C is a rear wing root connecting point and is connected with the other end of the connecting rod BC; the points F and D are rack fixed support points, the point F is located directly below the driving point A and forms a right angle with the driving point A, the point D is offset by 19.26° relative to the driving point A, and the distance between the two points is 5 mm; The length and angle of the front wing transmission chain A-B-E and the rear wing transmission chain A-B-C jointly determine the motion amplification coefficient and the phase response difference.

2. The symmetrically driven biomimetic butterfly flapping mechanism according to claim 1, wherein, The constant angular velocity of the driving point A is 1800° / s; the structure geometric dimensions are AB=6 mm, BE=CB=18 mm, |DF|=5 mm, ∠DFA=90°, and ∠DAF=19.26°.

3. The symmetrically driven biomimetic butterfly flapping mechanism of claim 1, wherein, The amplitude difference and phase difference of the front and rear wings are derived from the geometric asymmetry: the spatial arrangement angles of the front wing transmission chain A-B-E and the rear wing transmission chain A-B-C are different, so that the projection components of the same driving angular displacement in the two transmission chains are different; the positions of the rack support points F and D are offset, so that the geometric constraint propagation path lengths of the two transmission chains are different, finally resulting in that the motion amplitude of the point E is less than that of the point C, and the motion phase of the point E lags behind that of the point C.

4. A method for simulating the motion mechanism of the bionic butterfly flapping mechanism driven by the symmetrical drive according to any one of claims 1-3, characterized in that, The method comprises the following steps: S1: establishing a geometric model of the mechanism The angular displacement of the driving point A can be represented as: θ(t)=ωt (1) In the formula, θ is the driving angle, t is the time, and ω is the angular velocity constant; With the rotation of the driving point A, the connecting rod AB makes a circular motion around the point A, is transmitted to the output end E through the connecting rod BE, and is transmitted to the output end C through the connecting rod CB, so that the two points produce periodic displacement in the XZ plane; the motion can be regarded as the driving function of the time parameter t to the spatial coordinates of the output point; S1.1: establishing geometric constraints and position equations A fixed coordinate system is established, the driving point A is taken as the origin, the X axis is horizontal, and the Z axis is vertical upward; the lengths of the crank AB, the connecting rod BE and the connecting rod CB remain unchanged in the motion; when the driving point A rotates, the position of the point B is: The constant length condition of the connecting rod is: (X E -X B ) 2 +(Z E -Z B ) 2 =BE 2 (3) (X C -X B ) 2 +(Z C -Z B ) 2 =CB 2 (4) Combined with the geometric relationship of the rack fixed support points F and D: |DF|=5 mm, ∠DFA=90°, and ∠DAF=19.26°, the spatial coordinates of the output points E and C at any time can be obtained from the mechanism constraints: The formulas (2), (3) and (4) are the basic kinematic equations of the mechanism, which describe the mapping relationship between the time and the spatial position, and the two functions directly determine the motion trajectory and amplitude difference characteristics of the output ends E and C; S1.2: calculating the velocity and acceleration relationship The time derivative of formula (5) can be obtained, and the velocity and acceleration of the output ends E and C are: where Z · and Z ·· respectively represent the Z-direction velocity and acceleration, corresponding to the V and A data in the simulation output, and the two sets of equations reflect the law of the wing root swing velocity and acceleration changing with time. S1.3: Definition of amplitude and phase difference In order to quantify the difference between the front and rear wing motion, the amplitude and phase difference of Z-direction displacement are defined; the output amplitude is defined as: The amplitude ratio is defined as: When K A <1, the amplitude of the forewing is smaller than that of the hindwing, forming a differential motion. The phase difference is obtained by comparing the peak time of the Z-velocity curves; let the maximum values of the Z-velocity of the front and rear wings appear at times t E,max and t C,max The phase difference is defined as: Δφ = t E,max -t C,max (10) When Δφ>0, the front wing lags behind the rear wing; when Δφ<0, the front wing leads the rear wing; S1.4: Draw time-dependent spatial trajectory The results of equation (5) are plotted as a three-dimensional curve to obtain the trajectory of the output point in the Z-X-t coordinate; the results show that the front wing trajectory envelope is small and the motion lags behind; the rear wing trajectory amplitude is larger and the response is ahead of time; S1.5: Analysis of the formation mechanism of amplitude difference Based on equations (2)-(10), under the same driving angular velocity, there is a geometric difference between the spatial layout of the A-B-E and A-B-C transmission chains; S2: Simulation verification The ADAMS software is used to establish the mechanism simulation model, and the MATLAB is used to process the output data; S2.1: Simulation model and parameter setting The simulation uses the same geometric parameters as the theoretical model: AB=6mm, BE=CB=18mm, DF=5mm The angle between the fixed support points is ∠DFA=90° and ∠DAF=19.26°; the driving point A is the center of the mechanism rotation, the input angular velocity ω=1800° / s; the mechanism is symmetrically arranged on the left and right, F and D are the fixed support points of the front and rear wing frames respectively; the simulation step is set to 0.001s and the total time is 1.5s; in ADAMS, the driving point A is driven by uniform angular velocity, and the system constraints are established according to the actual geometric relationship; the displacement, velocity and acceleration of the output ends E and C are extracted along the Z direction, and the X direction trajectory is recorded for motion path analysis; S2.2: Simulation results and trajectory characteristics The amplitude A can be calculated from the Z displacement data E , A C , and the differential amplitude ratio K is obtained according to equations (8), (9) A ; The results show that the swing amplitude of the front wing EF is significantly smaller than that of the rear wing CD, and the peak value appears later; this phenomenon is consistent with the prediction of the theoretical model; The phase difference is calculated according to equation (10) by comparing the peak occurrence time The results show If the value is positive, it means that the forewing motion lags behind the hindwing. S2.3: Motion law and amplitude difference verification The amplitude of the former wing A E is smaller; the amplitude of the latter wing A C is larger; the amplitude difference ratio K A = A E / A C <1; the phase difference is positive.

5. The motion mechanism simulation method according to claim 4, characterized by: In step S1.5, due to the different spatial arrangement angles of AB, BE, CB and the frame points D and F, the driving force is decomposed into different directional components during transmission, resulting in differences in displacement amplitude and time response between points E and C; the output amplitude of the front wing EF is small and the phase lags behind, while the output amplitude of the rear wing CD is large and the phase is ahead; this difference is due to the geometric characteristics of the mechanism itself, rather than the influence of the driving signal or external load.

6. The motion mechanism simulation method according to claim 4, characterized in that: The mechanism can realize stable periodic motion: from the Z-X-t trajectory, the motion is smooth and consistent, which meets the assumption of constant speed driving; the amplitude difference and phase difference are obvious: the amplitude and phase difference of the front and rear wings are consistent with the theoretical prediction; the geometric design dominates the output characteristics: under no load condition, the amplitude difference phenomenon is completely determined by the rod angle and link length.

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