Fig. 3. Wing kinematics. The figure illustrates the parameters of the left forewing; those of the other three wings are defined by the same way. (A) Definition of flapping angle . Point B1 represents the wingbase of the left forewing, point T1 the wingtip of that. The line B1-T1 denotes the leading edge of the wing. The stroke plane is defined by three points: the wingbase B1, and the wingtip at the maximum and minimum angular positions (T1_H and T1_L) in a flapping cycle based on the local body-centered coordinate system. (Note that the stroke plane of the left wing is generally different from that of the right wing without any assumption of kinematic symmetry, i.e. the stroke planes with respect to the left and right wing are not in one plane.) The line L1 represents the intersection of the plane X'—O'—Y' and the stroke plane. The flapping angle is defined as the angular position of the wing in the stroke plane, measured from dorsal reversal (start of downstroke) to ventral reversal (start of upstroke). =0 for the leading edge in the plane X'—O'—Y'. (B) Definition of the angle of attack, the torsional angle and camber deformation. The plane , which is normal to the leading edge and at a spanwise position of 50% of the total wing length, is defined as the mid-span chord plane. The intersection arch of the wing surface and the plane is the mid-span arch . The mid-span chord vector MN is corresponding to the arch , whose direction definition is from the wing trailing edge (M) to leading edge (N). The line L is the intersection of the plane and the stroke plane , which denotes the tangent of the wing's trajectory. The line L' is the perpendicular of the line L. The angle of attack is defined as the included angle between the vector MN and the line L and the torsional angle is defined as the included angle between the vector MN and the line L'. Note that and are complementary angles. When MNL, =0; =+90° (if downstroke) or =-90° (if upstroke). The two-dimensional coordinate system (o', x', y') is established in the plane with the x-direction from N to M, the y-direction from the lower surface to the upper surface of the wing and the origin in the leading edge. The camber deformation [UNK] is defined as the ratio of the maximum arch rise H_max to the mid-span chord length MN|.

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