Design of a Flapping Wings Butterfly Robot based on Aerodynamics Force

The study addresses the design and analysis of a flapping-wing butterfly robot that leverages aerodynamic and aeroelastic principles to generate lift and thrust efficiently. Motivated by the advantages of flapping-wing micro air vehicles (vertical take-off and landing, hovering, and maneuverability in complex environments), the research examines how quasi-steady aerodynamics of thin airfoils can be used to design larger, slower-flapping butterfly-like wings that consume less energy and potentially carry more payload than other insect-scale robots. It contrasts single-actuator crank mechanisms (shared wing trajectories, limited degrees of freedom, need extra actuator for yaw) with two-actuator mechanisms (independent wing trajectories enabling rotation). The goal is to derive wing-section forces, design a wing and flapping mechanism, and experimentally validate take-off and climb in still air.

Prior flapping-wing robots include Delfly, Nano Hummingbird, Purdue Hummingbird, and RoboBee, which demonstrated take-off and hover using either crank mechanisms (shared motion from a single actuator) or two independent actuators (greater degrees of freedom). Crank mechanisms are simpler but limit wing kinematics and require an extra actuator for rotation; two-actuator systems allow asymmetric wing motions and improved maneuverability. Theoretical foundations used include Jones’s unsteady lift for finite aspect ratio wings, Theodorsen’s theory of aerodynamic instability and flutter, and empirical formulations for skin-friction drag on laminar flat plates. These works inform the aerodynamic modeling choices (thin airfoil, quasi-steady assumptions, strip theory with finite AR corrections) and the design trade-offs in flapping mechanisms.

- Wing aerodynamic modeling: The butterfly wing is modeled as a thin airfoil with large aspect ratio, analyzed via strip theory where flow over each spanwise section is chordwise. Quasi-steady assumptions allow treating time-varying parameters as locally constant over small intervals. Section forces comprise circulation-induced normal force and added-mass normal force (aeroelastic contribution). The plunging motion is sinusoidal, and pitch/dihedral angles vary with flapping frequency and kinematics. - Unsteady aerodynamics: Relative angle of attack and velocity at quarter/half-chord are formulated using velocity diagrams and reduced frequency k = c·ω/(2U). Jones’s coefficient for finite aspect ratio is approximated using Scherer’s expressions for F′(k) and G′(k), with downwash related to free-stream velocity for an untwisted elliptical-planform wing. Chordwise forces include leading-edge suction, camber force, and viscous skin-friction drag (laminar plate approximation with Reynolds-number-based coefficient). - Lift and thrust estimation: Infinitesimal lift and thrust are obtained by resolving chordwise and normal forces into streamwise and normal components, then integrating along the wingspan. Average lift and thrust over a flapping period are computed by integrating instantaneous values over time, incorporating the section dihedral angle σ(t) = Γ cos(ωt). To maximize net lift, non-symmetric flapping is considered (fast downstroke, slow upstroke) due to the inability to fold insect wings during upstroke. - Flow simulation: Airflow around the designed wing in still air is simulated using incompressible Navier–Stokes equations for Newtonian fluid. The SIMPLER algorithm with Runge–Kutta time stepping is used to obtain numerical solutions under appropriate boundary conditions. Flowsquare+ is employed with a computational grid of 128×64×64 cells, inflow of 5 m/s in +x-direction to reach quasi-steady conditions rapidly, and dynamic viscosity set to 1.8×10⁻⁵ kg/(m·s). Simulations visualize vortices behind wing tips and pressure distribution, indicating pressure concentration near the wing’s center of mass and validating laminar flat-plate behavior when the wing is perpendicular to flow. - Mechanical design and construction: Wings are scaled to approximately 10× the real butterfly while maintaining shape and proportions (wingspan ~51 cm; area ~539 cm²). Each wing uses a transparent laminar plastic sheet with reinforced carbon fiber rods to achieve rigidity (thin airfoil). The robot employs two independent high-speed micro servos (KST MS325: 5.2 kg·cm torque; 60°/0.07 s at 8.4 V) coupled via 3D-printed servo holders and wing lockers (PLA). The main controller is an STM32 ARM Cortex-M3 (72 MHz via PLL). Servo positions are commanded via 50 Hz PWM RC signals (5–10% duty cycle), with motion profiles set to higher downstroke speed than upstroke. The robot structure is mounted on a sliding rod with a support platform for free vertical motion; external power is used to reduce payload. - Iterative refinement: Initial tests revealed wing bending under servo torque and aerodynamic loading, and undesired rotation due to asymmetric wing number compared to real butterflies. Wings were further reinforced with an additional carbon fiber layer and duct tape, and redesigned to be symmetric to condense pressure around the mass center and reduce rotation. The modified wing was re-simulated to confirm pressure location before re-testing.

- The robot achieved vertical take-off from a support platform and climbed to approximately 10 cm in about 1.02 s under non-symmetric flapping (fast downstroke, slow upstroke). - Average lift generated by the wings exceeded 1.0791 N, sufficient to lift the 110 g robot. A simple estimate (neglecting coupling velocity effects and inertia) suggests peak lift on the order of ~5.4 N and maximum body acceleration around 0.93 m/s² when wings are parallel to the ground. - Flow simulations showed vortical structures behind the wing tips and pressure concentration near the wing’s center of mass, informing the placement of reaction forces in dynamics considerations. - Initial wing bending and body rotation were mitigated by adding reinforcement (extra carbon fiber rods and duct tape) and redesigning the wings to be symmetric, resulting in unbent wings and reduced rotation. - Hardware parameters: total robot weight 110 g; component weights include wing with locker (25 g), two servos with plastic horns (23 g), servo holder (9 g), nuts/bolts (5 g). Servos operated via 50 Hz PWM; controller logic at 3.3 V with driver circuitry for 8.4 V servos.

The derived aerodynamic framework and simulations guided the wing sizing and reinforcement strategy, ensuring sufficient average lift for take-off in still air. Two independent servos enabled flexible wing kinematics and the potential for yaw control without a tail; however, asymmetric motion and structural differences initially induced rotation and wing bending. Redesigning to symmetric wings and adding reinforcement concentrated pressure near the center of mass, stabilizing flight during the downstroke and validating the quasi-steady thin-airfoil approach for larger, slow-flapping butterfly wings. The observed rapid descent during upstroke highlights the challenge of non-folding insect wings, where upstroke downforce combines with weight, limiting sustained hover and payload capacity. These results emphasize the need to optimize flapping kinematics (e.g., more asymmetric trajectories, pitch control, passive wing compliance) and to incorporate complete dynamics (mass/inertia and coupling effects) for controlled hovering and maneuvering.

The study derives and applies quasi-steady thin-airfoil aerodynamics, including circulation and added-mass effects, to design a butterfly-inspired flapping-wing robot. Numerical flow simulations (SIMPLER, Flowsquare+) validated laminar flat-plate behavior and informed reaction force locations. A two-servo flapping mechanism and reinforced symmetric wings enabled vertical take-off and ascent to a modest height, demonstrating that larger butterfly-like wings flapping at lower frequencies can generate adequate lift with lower energy consumption. Future work will develop a standalone robot with onboard payload, derive full dynamics using Euler–Lagrange methods (including masses, inertias, and coupling velocity effects), refine wing kinematics to reduce upstroke downforce, and conduct more comprehensive experiments for hover and maneuverability.

- Full robot dynamics (mass distribution, inertias, coupling velocity effects) were not modeled; lift estimates neglect inertia and coupling. - Experiments used external power to reduce payload; thus, results may not generalize to onboard-powered configurations. - Friction between the robot and sliding rod was neglected; environmental effects and disturbances were minimal (still indoor air). - Initial wing structure exhibited bending and induced rotation; while reinforcement and symmetry mitigated these, flexible wing behavior was not analyzed (no detailed aeroelastic beam model). - Sustained hover was not achieved due to upstroke downforce; control strategies and kinematic optimization remain to be addressed.