The ability to grip unhatched eggs is a skill exploited by the ants Harpegnathos venator, as they care their brood in tunneled nests, which is of extreme difficulty to keep the eggs intact while gripping. In this paper we propose a mathematical modeling method to elucidate the mechanism of such a gripping behavior in the ant mandibles. The new method can be subdivided into following steps. As a preliminary, the concavity geometry and mandible kinematics are examined experimentally. Second, coordinate transformation is used to predict the real-time spatial topology of the concavity. Third, we come up with a new method to quantify the workspace required to grip and the contact area between the concavity and ant egg. Our model indicates that the biaxial rotation fashion with specialized concavities can reduce workspace by 40% and increase contact area by 53% on average compared with the uniaxial rotation pattern, which augments success rate of gentle gripping. This methodology may have applications in evaluating mechanical performance in both natural and artificial grippers.

中文翻译：

---

阐明蚂蚁下颌骨和生物启发性爪爪综合抓地性能的数学建模方法

抓握未孵化卵的能力是蚂蚁Harpegnathos venator利用的一项技能，因为它们在隧道巢中照顾自己的卵，这对于在抓握时保持卵完整是极其困难的。在本文中，我们提出了一种数学建模方法，以阐明蚂蚁下颌骨中这种抓握行为的机理。新方法可以细分为以下步骤。首先，通过实验检查凹面几何形状和下颌运动学。其次，坐标变换用于预测凹面的实时空间拓扑。第三，我们提出了一种新的方法来量化握持所需的工作空间以及凹面和蚂蚁蛋之间的接触面积。我们的模型表明，与单轴旋转方式相比，具有特殊凹面的双轴旋转方式平均可减少40％的工作空间，并增加53％的接触面积，从而提高轻柔抓握的成功率。该方法可用于评估天然和人造抓具的机械性能。