## 1 Introduction  
Insects and birds have provided significant inspiration for the development of flapping-wing micro aerial vehicles (FWMAV) and this bio-inspiration gives the performance of stealth, agility, and maneuverability to the FWMAV, which is of paramount significance in the reconnaissance of hostile environments [1; 2; 3; 4]. Thus, the aerodynamic and flight dynamic performance of the FWMAV has garnered significant interest and attention over the past several decades [5; 6; 7]. Among the studies for the flapping-wing system, symmetric feathering amplitudes are used in some of the research. For instance, [PERSON] et al. [8] investigated the aerodynamics of tandem-configured 2D flapping wings in forward flight through experimental and numerical methods. The results show that when the distance of the two wings is set as two times the chord length, the thrust of the tandem wings outperformed the combined thrust of two independently flapping single wings for phase angles ranging from approximately \(-90^{\circ}\) to \(90^{\circ}\). [PERSON] et al. [9] presents a multidisciplinary experimental method to investigate a flapping wing's aero-elasticity and thrust production. The results show that, under a specific deformation phase and amplitude, the interaction between aerodynamic loads and both the bending and twisting motion can improve wing performance. However, the symmetric feathering amplitudes of a real insect or bird should not be exactly symmetric. Thus, there is also much research focusing on the aerodynamic behavior of the FWMAV under asymmetric feathering amplitudes [10; 11]. For example, [PERSON] et al. [12] presented an analysis of the kinematics of a flapping membrane wing based on the experiment. They found that the ornithopter has a higher upper-range stroke angle (+30\({}^{\circ}\)) while the flexing of the wing results in the lower-range stroke angle of \(-20^{\circ}\). [PERSON] and [PERSON] [13] carried out a numerical analysis on the aerodynamic behavior of a 2D flapping wing with an asymmetric stroke angle in both hovering and forward flight. They found that the aerodynamic performance of the wing at a low Reynolds number can be enhanced under an appropriate asymmetric stroke. By combing the rotary motion of a rotorcraft and the flapping motion of a bird, a novel flapping-wing rotor (FWR) configuration was proposed [14; 15]. Unlike the insect-like flapping-wing system, the flapping-wing rotor (FWR) consists of a passive rotary motion which is caused by the reverse Karman vortex. The speed of the rotary motion is influenced by the flapping motion, twisting motion, as well as the wings' deformation, and can greatly affect the FWR's lift generation. This kind of configuration is capable of short-range take-off or landing and exhibit higher aerodynamic efficiency than insect-like FW when the Reynolds number ranges from 2600 to 5000 [16; 17]. In the past 10 years, a number of FWR models have been proposed. [PERSON] et al. [15] proposed a piezoelectric actuator as well as a multi-bar of flexure hinges to drive an FWR. [PERSON] et al. [18] designed an FWR with three wings and developed certain control mechanisms to control its pose. The hovering flight test shows their FWR can counteract the rotary-caused moment and maintain the attitude of their FWR. As declared before in this paper, although some of the research has involved the asymmetric feathering amplitudes for a flapping-wing system (such as Robobee) [19], few research involving in the asymmetric feathering amplitudes for an FWR system is found. Compared with a flapping-wing system, an FWR configuration shares a unique passive rotary motion caused by the reverse Karman vortex. Moreover, a different average stroke angle leads to a different speed of the rotary motion and thus leads to a different lift. According to the past studies, the effect of asymmetric feathering amplitudes on its lift and rotary speed remains unknown.