# Design and Demonstration of a Flying-Squirrel-Inspired Jumping Robot with Two Modes
## 3 Analysis of Jumping Mechanism of Flying Squirrel  
The free activity inside confined spaces of an adult male southern flying squirrel (Glaucomys volans) was recorded using a Photron Fastcom Mini UX100 high-speed camera. Sequential images of the flying squirrel during jumping were captured at 2000 frames per second. Figures 3 and 4 exhibit the motional sequence of jumping for gliding and jumping for progress of the flying squirrel, respectively. As shown in Figure 3, the flying squirrel first curls up its hind limbs and supports the body with its forelimbs, then leans forward at the angle of approximately 0\({}^{\circ}\) between the body and the horizontal line. Next, it gradually stretches its hind limbs until leaving the hathpace. As shown in Figure 4, when jumping for progress, the flying squirrel likewise uses the stretching of hind limbs to takeoff, but the stance is markedly different: The angle between the body and the horizontal line is approximately 20\({}^{\circ}\). the hind limbs to the body. The toe joint acts as a takeoff steering and landing buffer. In addition, the femur and the tibofibrular are connected with the patagium and are able to deploy the patagium along with abduction of the hip joint in the gliding phase. In order to facilitate the analysis of the movement characteristics of the animal's hind limbs in the two jumping modes, the joints of hind limbs are simplified into revolute pairs with only one degree of freedom, as shown in Figure 6, where \(\beta_{0}\) represents the angle between the phalanx and the horizontal line, \(\beta_{1}\) represents the angle of toe joint, \(\beta_{2}\) represents the angle of ankle joint, \(\beta_{3}\) represents the angle of knee joint, and \(\beta_{4}\) represents the angle of hip joint. Reflective paint was used to mark each joint of the hind limbs of the flying squirrel. Then, under the same conditions, we made the flying squirrel repeat the jumping for gliding from a hathpace with a height of 2 m and the jumping for progress on the ground for times, respectively. In addition, the motion process was recorded with the high-speed camera. MATLAB software was used to extract the joint coordinates of the hind limbs on the motion images according to the markers, calculate the angle of each joint, and take the average of the five repetitions. Finally, the change curves of the angle of each joint in the whole motional sequence were plotted, as shown in Figures 7 and 8. Combined with the motional sequence of jumping for gliding of the flying squirrel, it can be seen from Figure 7 that: \(\beta_{0}\), \(\beta_{2}\), and \(\beta_{3}\) are nearly unchanged in the preparation stage of 0-0.03 s; \(\beta_{0}\) remains the same while \(\beta_{2}\) and \(\beta_{3}\) increase quickly with the identical rate of change 54 rad/s in the takeoff stage of 0.03-0.065 s; \(\beta_{0}\) increase quickly while \(\beta_{2}\) and \(\beta_{3}\) grow with slower rate in the launch stage of 0.065-0.075 s; \(\beta_{2}\) and \(\beta_{3}\) reach the maximum at 0.075 s. Throughout the stage, in addition, \(\beta_{4}\) keeps increasing and \(\beta_{1}\) almost keeps decreasing with the angle of change of about 85\({}^{\circ}\), which signify the flying squirrel's body leans forward considerably when it jumps for gliding. Combined with the motional  
Figure 5: Physiological structure of hind limbs of flying squirrels. Figure 6: Schematic of joints of hind limbs of flying squirrel. sequence of jumping for progress of the flying squirrel, it can be seen from Figure 8 that: \(\beta_{2}\) and \(\beta_{3}\) increase quickly with the identical rate of change 28 rad/s in the takeoff stage of 0.02-0.045 s; \(\beta_{4}\) and \(\beta_{1}\) increase and decrease by about 40\({}^{\circ}\), respectively. The comparison between Figures 7 and 8 indicate that the change trends of angle of hind limbs joints when the animal jump for progress are similar to that when jumping for gliding, but the initial value and the range are obviously different.