Dynamics modeling and kinematics calculation of webbed-feet during cormorant's take-off
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摘要:
鸬鹚在水面起飞的过程中，进行周期性扑翼运动的同时，其脚蹼也不断进行周期性拍水运动。为探究脚蹼周期性拍击水面对鸬鹚水面起飞的贡献以及定量计算每个拍水周期中脚蹼力的大小，探讨了鸬鹚起飞过程中后肢力量的贡献以及需要腿部力量辅助的原因；同时，比较自然界生物在水面行走或奔跑方式的异同，从而研究鸬鹚等水栖鸟类在水面上连续拍水的机理。通过蛇怪蜥蜴和鸬鹚脚蹼水上运动模式和机理的对比，类比研究脚蹼对水面冲击而产生支持身体冲量的大小与脚蹼在拍水时与水接触变化的过程；定义鸬鹚腿部自由度，建立鸬鹚起飞过程脚蹼周期性拍水运动的运动学模型，分析腿部关节角度与脚蹼中心坐标的D-H矩阵，并研究关节角速度与脚蹼中心速度的雅可比矩阵，通过现有的视频分析验证模型可靠性，并对鸬鹚脚掌运动以及水平、竖直方向的运动做了基本计算。
Abstract:The process of taking off from the surface of water for cormorant is a combination of flapping its wings and its webbed-feet periodically. In order to look into the contribution of the latter that helps in taking off and to compute each period in fixed quantity of the amount of force in each flapping action, this article explores the contribution of hind limb power to the process of taking off as well as the reasons of the need of leg strength for assistance. At the same time, through introducing various types of water walking living creatures and looking at the differences and similarities in the ways that nature creatures walk or run on the water surface, the continuous flapping mechanism of cormorant and other aquatic birds on water surface is studied. Moreover, by comparing the different modes and mechanism of water movement of basilisk lizard and cormorant, an analogy is made to study the impulse generated by the webbed-feet which sustains the body as well as the changes of webbed-feet beating the water. With the DOF of cormorant's webbed-feet defined, the periodic flapping kinematics model during cormorant taking off is established. The D-H matrix of the leg joint angle and the webbed-feet center coordinates, as well as the Jacobian matrix of the joint angular velocity and the webbed-feet center speed are analyzed. Through the existing video analysis, the reliability of the model is verified, and the basic calculation is made for the movement of the cormorant's webbed-feet and the horizontal and vertical direction.
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图 6 鸬鹚腿部关节角度及简化模型D-H坐标系
Figure 6. Cormorant's leg joint angle and simplified model D-H coordinate system
图 11 鸬鹚竖直、水平位移-时间曲线及运动轨迹竖直-水平位移曲线
Figure 11. Vertical, horizontal displacement-time curve and vertical-horizontal displacement curve of cormorant
表 1 D-H参数
Table 1. D-H parameters
序号 关节角θ 连杆偏距d 连杆长度a 连杆转角α 1 π+δ+θ1 0 D2 0 2 π-θ2 0 D3 0 注：序号1、2表示髋关节与膝关节的D-H转换关系。 
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表 2 关节角度测量值表示
Table 2. Expression of joint angle measurements
测量值 横坐标表示 纵坐标表示 A xA yA B xB yB C xC yC D xD yD E xE yE θ1 
θ2 
注：dot和norm在MATLAB中分别表示点乘和取模的函数。
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表 4 竖直方向位移测量值表示
Table 4. Expression of vertical displacement measurement
测量值 横坐标表示 纵坐标表示 A xA yA M xM yM N xN yN Sv 
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表 5 水平方向位移测量值表示
Table 5. Expression of horizontal displacement measurement
测量值 横坐标表示 纵坐标表示 A xA yA X1 x1 y1 X2 x2 y2 Xn xN yN Sh 
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