Fig 1.
Seven-rigid-body system of Caudipteryx.
The simplified rigid body system illustrates the mechanism of moving parts, main body, wings, legs, neck and head, and the tail of the Caudipteryx. The masses of all parts are represented by lumped mass points and the muscles at the joints are replaced with springs (As damping coefficient does not significantly affect the natural frequency, we simplified the joints which are composed of tendons, muscles, ligaments and soft tissues as purely elastic springs with no damping). Different effective masses of these seven primary modes of the simplified Caudipteryx show different possibilities to be excited.
Fig 2.
Modal effective mass of Caudipteryx.
FE model of Caudipteryx by using modal effective mass illustrates that the most obvious flapping modes are occurred at the speeds of 2.50 m/s and 5.79 m/s. Y-axis is in the vertical direction and X and Z axes are in lateral directions.
Fig 3.
Biophysical vibration of the wings.
(A) Wearable devices to detect the performance of wings. The back bracket was manufactured through 3D printer with ABS plastics. The angular accelerometer sensor, force sensor and SD card were all mounted on the bracket (S3B Fig). The accelerometer sensor on the back and the wings were used to measure the rolling angle of body and wings respectively during locomotion on the ground. A force sensor is embedded between the arm and the body to measure the lift generated by the flapping wings (S3A Fig). (B) Simplified wing mechanism. Every wing has a flexible structure that is jointed with the body via elastic rubber belts, which are used to simulate the function of muscles. (C) Reconstruction of wings of different sizes. The first wing represents the forearm with filament feathers. From the second one to the fourth one, the length of feathers increases gradually. The second one represents the short feather, the third one represent middle feather while the fourth one with the longest feathers represents the largest wing (the realistic wing is the third one in accordance to the fossil).
Fig 4.
Forced vibrations of wings of Caudipteryx robot deduced by test rig (S1 Video) which approaches the flapping flight of modern birds [56].
Through curve iteration, we obtained the flapping function ϴright = 932.7sin(19.01t−3.35)+28.18sin(15.25t−5.103)+898.2 sin(19.16t+6.034) and ϴleft = 135.6 sin(6.453t+1.808)+1558 sin(0.4013t+6.198)+6.517 sin(18.87t + 0.4756). We here defined the anticlockwise motion of both wings as the positive direction. Therefore, the down stroke for the left wing is a positive motion while the down stroke for the right wing is a negative one.