We address the theoretical question which forces and moments measured at the base of a whisker (tactile sensor) allow for the prediction of the location in space of the point at which a whisker makes contact with an object. We deal with the general case of three-dimensional deformations as well as with the special case of planar configurations. All deformations are treated as quasi-static, and contact is assumed to be frictionless. We show that the minimum number of independent forces or moments required is three but that conserved quantities of the governing elastic equilibrium equations prevent certain triples from giving a unique solution in the case of contact at any point along the whisker except the tip. The existence of these conserved quantities depends on the material and geometrical properties of the whisker. For whiskers that are tapered and intrinsically curved, there is no obstruction to the prediction of the contact point. We show that the choice of coordinate system (Cartesian or cylindrical) affects the number of suitable triples. Tip and multiple point contact are also briefly discussed. Our results explain recent numerical observations in the literature and offer guidance for the design of robotic tactile sensory devices.

中文翻译：

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通过晶须基部的力和力矩测量来检测晶须

我们解决了一个理论问题，即在胡须（触觉传感器）底部测量的力和力矩允许预测胡须与物体接触点的空间位置。我们处理三维变形的一般情况以及平面配置的特殊情况。所有变形都被视为准静态，并且假设接触是无摩擦的。我们表明，所需的独立力或力矩的最小数量是三个，但控制弹性平衡方程的守恒量阻止某些三元组在除尖端外的晶须上的任何点接触的情况下给出唯一的解决方案。这些守恒量的存在取决于晶须的材料和几何特性。对于锥形和本质弯曲的晶须，接触点的预测没有障碍。我们表明坐标系（笛卡尔或圆柱）的选择会影响合适的三元组的数量。还简要讨论了尖端和多点接触。我们的结果解释了文献中最近的数值观察，并为机器人触觉传感设备的设计提供了指导。