Department of Ecology and Evolution, University of California, Irvine, CA 92697-2525, USA.
J Exp Biol. 2012 Apr 1;215(Pt 7):1231-45. doi: 10.1242/jeb.061465.
The geometry of an animal's skeleton governs the transmission of force to its appendages. Joints and rigid elements that create a relatively large output displacement per unit input displacement have been considered to be geared for speed, but the relationship between skeletal geometry and speed is largely untested. The present study explored this subject with experiments and mathematical modeling to evaluate how morphological differences in the raptorial appendage of a mantis shrimp (Gonodactylus smithii) affect the speed of its predatory strike. Based on morphological measurements and material testing, we computationally simulated the transmission of the stored elastic energy that powers a strike and the drag that resists this motion. After verifying the model's predictions against measurements of strike impulse, we conducted a series of simulations that varied the linkage geometry, but were provided with a fixed amount of stored elastic energy. We found that a skeletal geometry that creates a large output displacement achieves a slower maximum speed of rotation than a low-displacement system. This is because a large displacement by the appendage causes a relatively large proportion of its elastic energy to be lost to the generation of drag. Therefore, the efficiency of transmission from elastic to kinetic energy mediates the relationship between the geometry and the speed of a skeleton. We propose that transmission efficiency plays a similar role in form-function relationships for skeletal systems in a diversity of animals.
动物骨骼的几何形状决定了力向其附肢的传递。关节和刚性元件每单位输入位移产生相对较大的输出位移，被认为是为了速度而设计的，但骨骼几何形状与速度之间的关系在很大程度上尚未得到验证。本研究通过实验和数学建模来探讨这个问题，以评估螳螂虾（Gonodactylus smithii）捕食附肢的形态差异如何影响其捕食攻击的速度。基于形态测量和材料测试，我们通过计算模拟了存储弹性能量的传递，这些弹性能量为攻击提供动力，以及阻力抵抗这种运动。在根据冲击脉冲的测量结果验证了模型的预测之后，我们进行了一系列模拟，改变了连杆的几何形状，但提供了固定数量的存储弹性能量。我们发现，产生大输出位移的骨骼几何形状比低位移系统达到的最大旋转速度要慢。这是因为附肢的大位移会导致其弹性能量的相对较大比例因产生阻力而损失。因此，从弹性到动能的传递效率调节了骨骼的几何形状和速度之间的关系。我们提出，在各种动物的骨骼系统中，传递效率在形态-功能关系中起着类似的作用。
