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Fig. 1. Wing beat kinematics of a dragonfly, set-up of the robotic wing hinge, and
mechanical properties of the model wings as used in this study. (A) Diagram
showing wing tip path of fore- (green) and hindwing (purple) and orientation
of a freely flying dragonfly with near vertical thrust vector. Body
orientation, location of the wing hinges and wing tip path were plotted after
data published by Wakeling and Ellington
(1997). In this kinematic
study advance ratio, defined as the ratio between forward and wing flapping
speed, was 0.44. Due to the steep body angle with respect to the horizontal,
the wing hinges are aligned almost vertically and thus similar to the
alignment of the robotic wing hinges shown in (B). (B) Schematic diagram of
the robotic dragonfly setup, modeling aerodynamic characteristics on one side
of the functionally four-winged insect with the forewing and hindwing wingtip
trajectories of our generic dragonfly kinematics superimposed (see Materials
and methods for details). The kinematics used during fore- and hindwing motion
is identical in all experiments, yielding 100° stroke amplitude and
symmetrical wing rotation at dorsal and ventral stroke reversal. Kinematic
phase shift is the temporal offset between fore- and hindwing motion. (C) The
shape of the robotic forewing and hindwing used. The wings are driven by servo
motors mounted in a gear box that controls back/forth, up/down and rotational
wing motion. Forces and moments acting on the wing during motion are measured
on the surface mid point of the force sensor (blue circle). The center of
gravity of the wing including the mass of the wing's holder is indicated by a
red circle, respectively. lx, length of the horizontal
moment arm for the wing's center of gravitiy; ly, length
of the vertical moment arm between the wing's center of gravitiy and the
wing's rotational axis. (D) Wing deflection due to bending moments under
static load of the plexiglas model forewing (orange, red, black) and hindwing
(cyan, green, blue). Deflection during load was measured at two distinct
positions on the wing at two-third wing length (orange, cyan) and the wing tip
(red, black, green, blue). To load the wing, small metal weights were placed
on the upper wing surface either at two-third distance from the wing base
(**, red, green, cyan, orange) or on the wing tip (*,
black, blue). The vertical gray line indicates approximately mean force (0.3
N) measured throughout one complete stroke cycle on the wings during flapping
motion. Horizontal gray area shows the range of deflections for fore- and
hindwing, assuming the wing is loaded with mean force. The pictogram
illustrates the measurement procedure showing wing holder and the wing seen
parallel to the wing's surface.
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