Limitations of a haptic device can cause distortions of the force feedback it presents. Just-noticeable difference (JND) in system dynamics is important for creating transparent haptic interaction. Based on the previous work, this article presents a unified model that extends the existing JND rule. Our approach projects the JNDs in the mechanical properties of a second-order mass-spring-damper system onto the real and imaginary components of the system's frequency response function (FRF). We discuss the results of two experiments and show that the JNDs obtained for both the real and imaginary components can be expressed as the same fraction of, and thus are proportional to, the magnitude of the total system's FRF. Furthermore, the findings are generalized to cases where the system's dynamics order is different than two. What results is a unified model that accurately describes the threshold for changes in human perception of any linear system dynamics with only two dimensions: the real and imaginary axes in the complex plane.

中文翻译：

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感知系统动力学变化的人类阈值模型

触觉设备的局限性会导致其呈现的力反馈失真。系统动力学中的恰到好处的差异 (JND) 对于创建透明的触觉交互非常重要。本文在之前的工作的基础上，提出了一个统一模型，扩展了现有的 JND 规则。我们的方法将二阶质量弹簧阻尼器系统的机械特性中的 JND 投影到系统频率响应函数 (FRF) 的实部和虚部。我们讨论了两个实验的结果，并表明实部和虚部获得的 JND 可以表示为整个系统 FRF 的相同分数，因此与总系统 FRF 的大小成正比。此外，这些发现被推广到系统的动态顺序不同于两个的情况。