Design and Integration of a Flapping Wing Apparatus

The outstanding performance of natural fliers has inspired the development of flapping wing aerial vehicles [1–5]. In nature, bats, insects, and birds excel at different modes of flight in a robust and efficient way compared to developed flapping flying robots [1,3,4,6]. One of the challenges is the complexity of the biological structures which makes it difficult to mimic and replicate in an engineering system. For example, the variety, distribution, and applicability of various sensors available on natural fliers’ wing although seems to be critical but are not thoroughly understood. Bat and insect wings include many sensors like strain sensors, air flow sensors, and speed sensors [7–9] which provide crucial information during the flight (Fig. 1). We seek to understand the applicability of wing sensors and in particular strain sensors during flapping flight and specially on wings with variable flexibility. Therefore, the goal in this paper is to present the design, manufacturing, and integration of a flapping wing apparatus to be used as a test bed for this purpose.

The majority of the flapping wing robots use either external real-time tracking sensors or internal sensors on the body like inertia measurement unit (IMU), rotary encoders, and GPS. Some of the notable accomplishments include COLIBRI [10], KUBeetle [6], Robobee [11], Delfly II [12], BatBot [1], and hummingbird robot [2]. Wood [3] developed an insect scale flapping wing robot that later Chirarattananon et al. [13] showed is capable of hovering in the presence of wind gusts. They used piezoelectric actuators directly connected to the wings and used real-time tracking of the different points on the robot as the main sensory information. Tu et al. [2] presented the design and prototyping of a hummingbird scale robot with two electric motors that each directly controls one wing. In their robot, the motor is connected to the wing through two gear spurs and therefore to generate flapping motion, motors should rotate and brake regularly. For the sensory information, they used IMU to measure the orientation of the body. He et al. [4] introduced a bird-scale flapping wing robot with three actuators total. They used spatial four-bar mechanism to actuate the two wings with one motor and presented the kinematics and dynamics of their design. Ramezani et al. [1] designed a tailless bat-scale flapping wing robot and demonstrated remarkable capabilities including banking and turning maneuvers. In these examples, the common approach is to focus on measuring the orientation of the body as the main source of sensory information.

In natural fliers, there are redundant availability of sensory signals [8,9]. Figure 1 shows two examples of bat and dragonfly wings with variety of sensors spread along them. However, it is not practical to provide that many sensors on a robotic system due to the increase in computational and building cost. Therefore, recognizing the important sensory signals in natural fliers and exploiting the use of the information to its utmost potential during flight is critical.

In this work, we aim at designing an apparatus as a framework on which to install various types of sensors on the wings and study their potential in providing flight information. This framework is aimed to be installed in a wind tunnel shown in Fig. 2. Moreover, we intend to use those sensors during flapping to study the effect of wing material texture and flexibility on aerodynamic force distribution. To design the apparatus, we first select the proper mechanism by comparing different alternatives for flapping wing systems and select the one that is the most suitable for our purpose. Then, we use the kinematic analysis to properly design the geometry of the mechanism accompanied by the dynamics of the entire system to model the behavior of the mechanism more accurately. We construct the dynamics of the entire apparatus using Lagrangian formulation and include the dynamics of the motor (both mechanical and electrical equations). After that, we present the aerodynamic modeling for the design purpose. Then we present the process for tradeoff between the gear ratio and motor characteristics. Then we present the manufacturing process for the different parts of the apparatus and explain the decision makings.

Our goal for this apparatus is to generate flapping motion on the two wings identically with minimal vibrations from the moving parts. To achieve identical flapping motion on the wings, we targeted mechanisms that are able to generate the same motion on the two wings using the proper mechanical mechanism of the system actuated by a single motor. Therefore, given the size constraints and goals of the apparatus, we consider the mechanisms shown in Fig. 3. In this figure, the mechanisms are: (a) crank-slider mechanism, (b) single-crank double-rocker mechanism, (c) double-crank double-rocker mechanism, (d) gearbox (transmission) direct connection, and (e) four-bar linkage mechanism. The crank-slider mechanism (Fig. 3(a)) can provide narrow width for the apparatus to minimize the interference to the flow in the wind tunnel while creating the identical flapping motion on the two wings. We can change the flapping angle amplitude in this mechanism, and a symmetrical down-stroke and upstroke motions can be easily generated by the mechanism. The single-crank double-rocker mechanism (Fig. 3(a)) is similar to the crank-slider mechanism from the apparatus width point of view, however it generates a phase difference between the motion of the two wings. Moreover, the sliders are free and oscillates in the horizontal direction during a wingbeat which applies undesired lateral vibration to the entire apparatus. The double-crank double-rocker mechanism shown in Fig. 3(c) resolves the problem with nonidentical wing motions but requires wider width for the apparatus and also imposes more moving parts to the mechanism making this less desirable compared to the crank-slider mechanism. From the kinematics point of view, it is similar to the four-bar linkage mechanism which we discuss later. The third mechanism that we consider is the direct gearbox (connection) between the motor and the wings as shown in Fig. 3(d). In this mechanism, the motor directly controls the wings through the gearbox which requires the motor to repeatedly reverse direction in order to generate flapping motion on the wings. This back and forth spinning motion of the motor applies undesired vibrations on the apparatus due to the inertia of the motor and the reflected inertia of the gearbox [2,14]. Moreover, the required width of the mechanism is increased. The last mechanism that we consider is a four-bar linkage shown in Fig. 3(e). This mechanism allows for the two wings to move identical as the motor spin continuously in one direction. However, beside the increased in the width of the apparatus, this mechanism has a singularity at the beginning and end of the upstroke and down-stroke. This singularity imposes an asymmetrical motion with respect to each stroke as shown in Fig. 4 [15]. This figure shows how the flapping angle and its velocity change during a wingbeat cycle. As can be seen, the upstroke and the down-stroke are not symmetrical. Moreover, the four-bar linkage mechanism is more sensitive to the resolution manufacturing of the parts [15]. This is due to the singular point in the mechanism that makes the flapping motion possible with unidirectional spinning of the motor. The flapping angle range is another restraint that the four-bar linkage imposes on the mechanism [16]. Although, all these mechanisms limit the flapping angle amplitude except the direct connection of the motor to the wings, but achieving the desired angle amplitude in the four-bar linkage requires some parts with smaller dimensions that is challenging to the manufacturing of those parts.

After comparing the different mechanisms, we choose the crank-slider mechanism (Fig. 3(a)) to use for this apparatus. This mechanism requires a narrow width and allows the motor to spin continuously in one direction while generating a symmetrical and identical flapping motion on the two wings.

In this section, we first present the kinematic analysis of the mechanism. Then, we derive the dynamical model of the moving parts to analyze the response and design the required gear ratio and the motor requirements. Finally, we present the aerodynamic force and torque on the wings as they are needed in the dynamical analysis.

We use the slider-crank mechanism (Fig. 5) to generate a flapping motion on the wings using a single motor rotating continuously in one direction. In addition to the movement of the motor, the dimensions in the mechanism determine the behavior of the flapping motion on the wings. Therefore, one of the objectives is to determine the geometry of the mechanism to result in the desired wing motion with a unidirectional motor speed control.

To find the geometric relationship between the wing kinematics, flapping angle (⁠$ϕ$⁠) and flapping angular velocity (⁠$ϕ˙$⁠), and the motor motion (⁠$θm$⁠,$θ˙m$⁠), we start from the flapping angle (⁠$ϕ$⁠) and move sequentially toward the motor. First, in Fig. 5 we can find the relationship between the vertical movement of the pin C (⁠$h$⁠) and the wing angle (⁠$ϕ$⁠) as: $tan(ϕ)=ha$⁠. Differentiating this equation gives us the vertical velocity of point C as a function of the flapping kinematics (⁠$ϕ$ and $ϕ˙$⁠): $h˙=aϕ˙(1+tan2(ϕ))$

By using these equations, we can construct the phase portraits of the wing kinematics (⁠$ϕ˙−ϕ$⁠) over one complete wingbeat cycle. Figure 6 shows the wing phase portraits for different dimensionless $l0/a$ and $R/a$ values based on the above kinematic equations. Each of the nine graphs in Fig. 6 presents the flapping angular velocity (⁠$ϕ˙$⁠) with the unit of (rad/s) as the vertical axis and the flapping angle (⁠$ϕ$⁠) with the unit of (rad) as the horizontal axis over a wingbeat cycle resulting from the corresponding $l0/a$ and $R/a$ values.

The results in Fig. 6 shows that for some combinations of $l0/a$ and $R/a$⁠, the response is not smooth and sometimes singular. Therefore, we choose the geometric ratios to be $l0a=2.0$ and $Ra=13≊0.57$ to first and foremost avoid singularities and abrupt changes. Second, due to the flapping angle amplitude to be $ϕ0=30deg$ (Fig. 7) to avoid the wing high-speeds at the mid upstrokes and down-strokes. Moreover, the capabilities and resolution of the resin printer and the manufacturing tolerance must be taken into account. Therefore, given the wind tunnel dimensions presented in Fig. 2, the geometric dimensions of the mechanism are chosen as: $R=1.0cm$⁠, $a=1.75≊3cm$⁠, and $l0=2a=3.5cm$⁠.

In this equation, $vm$ is the input voltage to the motor and $θ$ is the output which, by using Eq. (3), can be related to the wing kinematics (⁠$ϕ$ and $ϕ˙$⁠).

For the simulation we use matlab (R2022b, Mathworks Inc., Natick, MA) and its built-in integrator ode45 that uses Runge–Kutta fourth- and fifth-order formulas for solving the differential equations. The convergence is determined by checking the error from the relative and absolute tolerances that we choose to be $1×10−9$⁠.

To find a proper gear ratio for this apparatus, we simulate the dynamics of the system (Eq. (10)) for different gear ratios. Figure 8 shows how the flapping frequency is affected by the gear ratio and the required motor maximum torque and rotational velocity. Using the results in Fig. 8 and after considering the spur gear dimensions and arrangements through computer-aided design (CAD) modeling trials, we choose a gear ratio of $Ng=18$ to achieve a flapping frequency of at least 10 Hz at 24 V. Figure 9 shows the wing flapping angle and angular velocity from the simulation. More details about the gear selection will be discussed later in the paper.

To model the effect of the aerodynamic forces on the flapping wings we use the quasi-steady formulation [17,18,16,19]. Since the goal is to install the apparatus in the wind tunnel, the effective wind velocity on each element along the wings has freestream (⁠$V∞$⁠) and flapping (⁠$rϕ˙$⁠) components (Fig. 10). Then, the aerodynamic force on each element along the wing can be decomposed into a normal (⁠$dN$⁠) and tangential (⁠$dT$⁠) components [20] with respect to the wing surface.

The aerodynamic torque generated on each wing is shown in Fig. 11 for different freestream velocities at a constant flapping frequency.

In this section, we explain how the different components were designed in CAD, manufactured, and integrated into two prototypes shown earlier. We start with the wings, then we present the design process for the chassis prototypes followed by the gear arrangements in the transmission.

The wings’ dimension are determined based on the geometry of the wind tunnel, the chassis, and the mechanical characteristics of the materials. The wings’ length are directly determined based on the cross-sectional size of the wind tunnel presented earlier (Fig. 2). To avoid the boundary effect from the wind tunnel walls we choose the wings’ length to be 10 cm across all the samples. Moreover, the wings should sustain the stress due to aerodynamic forces and stay in the elastic region because of the repeatability of the flapping motion. To accomplish this goal, we use the maximum aerodynamic torque on the wings to confirm the integrity of the material and the wing thickness to stay in the elastic region.

The wing samples are $100mm×40mm$ length by width sheets and thicknesses ranging from 0.09 mm to 1.70 mm (Fig. 12). The materials are a spread of varying metals, plastics, and composites forming a total of 24 wing trials.

To connect the wings to the crank-slider mechanism, two wing grippers with press fit engagement are used (Fig. 12). They are designed to pivot around a pin at their midpoint where they are installed on the chassis to transform the linear movement of the crank-slider mechanism to flapping motion on the wings. It should be noted that the attachment points on the wing holder needs to be slotted to allow for the desired flapping angle amplitude of $±30deg$ (Fig. 7).

For assembling reasons, at the wing insertion area’s innermost section, a relief hole is needed to assist with linear clamp load on the wing element (Fig. 12). Also, we use two M4 screws retained with machine nuts while isolated from the resin material with 9 mm diameter machine washers. We realized through wing actuation trials that nylon M4 hardware is preferable for wing retention due to its weight and adequate grip instead of the alloy steel counterpart. Furthermore, a 2.5 mm offset feature on the midsection of the wing gripper design is incorporated for crank rocker meshing as well as to allow for a symmetric design.

Finally, to manufacture the gripper we use resin 3D printer and the material selection was determined experimentally. We started by the rigid 4000 grade resin, with a tensile and flexural modulus of 4.1 GPa and 3.4 GPa respectively with a tensile strength of 69 MPa. We found out that the wing holders constructed with the Rigid 4000 grade resin are prone to fractures during assembly and handling, but performed well for flapping cycles after installation. Due to the need to assemble multiple different wing materials, fractures during assembly would be undesirable. We found the tough 1500 grade resin to be an adequate alternative with a tensile and flexural modulus of 1.5 GPa and 1.4 GPa respectively.

The chassis is the central part of this apparatus on which the different elements including the transmission, the DC motor, and the wings are installed. Moreover, the chassis should be designed to comply with the installations and provide a reasonable tolerance for installing purposes. We developed the chassis in iterations through multiple 3D printing trials given the design constraints we explained in Sec. 2. Figure 13 shows the chassis iterations for the two prototypes we developed for this apparatus. It should be noted that the chassis needs to rigidly retain the DC motor, gear assembly, and the wing actuation linkages. Moreover, it should provide a fixed mounting location for the force sensor at the bottom as well as the ability to be mounted in the wind tunnel. The wind tunnel access point shown in Fig. 2 sets a target height for the entire apparatus and subsequently for the chassis.

The chassis is designed to incorporate the DC motor into the rear of the gearbox and to drive the transmissions via the motor integrated spur gear. We found out that gear interference is sensitive to 3D printer model and filament size which warranted dedicating a single 3D printing setup for chassis construction. We experimented several combinations of gear arrangements to find an appropriate design with a minimum number of moving components to be installed on the chassis. Then, the locations of the gears are designed in the CAD model of the chassis for 3D printing to ensure size and fitting compatibility.

The transmission is powered by a DC motor and a series of single and double spur gears. To achieve a gear ratio of $Ng=18$ as explained in Sec. 2, we combined multiple spur gears in CAD to fit the geometry and reach the desired gear ratio (Fig. 14(b)). The DC motor utilizes an integrated eight tooth spur gear and is press fit into the 3D printed chassis. We installed the other die cast plastic gears on the chassis using the 2 mm steel rod and pressed fit them into the proper locations on the chassis.

Figure 16 shows the setup of our experiment to verify the proper movement of the wings. We used marker tracker in order to track the movements of different points along the wings and the mechanism. Figure 17 shows the flapping angle and its velocity in simulation and experiment at a given constant voltage to the motor. Since the flapping angular velocity signal (⁠$ϕ˙$⁠) is noisy, we present a low-pass filter signal as well. The results show that the wing kinematics from the experiment (⁠$ϕ$ and $ϕ˙$⁠) match the simulation and confirms the design of the mechanism.

In this paper, we presented our process for the design and manufacturing of a flapping wing apparatus to be installed in a wind tunnel. First, we compared different alternatives for the flapping wing mechanism and selected the crank-slider mechanism given the requirements for our apparatus. Then, we presented the design process for this mechanism using both kinematic analysis and the dynamics of the entire system including the dynamics of the motor (both mechanical and electrical equations of the electric motor). We used the dynamics equation that relates the input voltage to the flapping motion on the wings in order to include the effect of the dynamical characteristics like motor inertia and damping on the performance of the apparatus in the design process. Using the dynamics of the entire system, we presented the design process to select the proper electric motor for the mechanism. Moreover, we presented the tradeoff between the gear ratio, motor maximum angular velocity, and motor maximum torque. For the aerodynamic torque, we used a quasi-steady formulation and developed a closed-form formulation for such a flapping wing system in the presence of freestream wind velocity for the purpose of design. This formulation can be used for selecting the motor and designing the wing structure in flapping wing robots for hovering and/or forward flight. We presented the process for manufacturing the parts of the apparatus and how we made the decisions for material selection and manufacturing method selection including 3D printing, resin printing, etc., for different parts of the apparatus. In presenting the manufacturing process we articulated the design constraints and the effect of the manufacturing limitations on the behavior of the mechanism. Furthermore, we discussed how the manufacturing limitations affected the design decisions during mechanism selection and design. Finally, we presented the constructed prototypes and the results from the experiment to confirm the design and manufacturing process.

This work is supported by the National Science Foundation under Grant No. 1931122.

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent was obtained for all individuals. Documentation provided upon request. This article does not include any research in which animal participants were involved.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.