The human hand detects high-frequency vibrations in all directions but cannot distinguish the direction, which suggests a multi-dimensional vibrotactile stimulus is haptically equivalent to some one-dimensional (1D) stimulus. In this article, we explore how a 6D vibrotactile stimulus rendered at the haptic interaction point (HIP) of a kinesthetic haptic interface, with the stylus held in a precision pen-hold grasp, is mapped to an equivalent 1D stimulus normalized by the detection threshold. We gather a large human-subjects data set in which we determine detection thresholds for 45 distinct combinations of three orthogonal forces and three orthogonal torques rendered at the HIP, at a single frequency of 108 Hz corresponding to the peak sensitivity in our prior study. Using this data set, we find a general quadratic weighting function to predict the 1D normalized stimulus for a given 6D vibrotactile stimulus. We find that including just seven (out of a possible 21) independent parameters in the symmetric weighting matrix is sufficient to capture the non-obvious coupling between forces and torques rendered at the HIP for dimensional reduction from 6D to 1D.

中文翻译：

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6D Vibrotactile 显示器的尺寸缩减

人手可以检测到各个方向的高频振动，但无法区分方向，这表明多维振动触觉刺激在触觉上等同于某些一维 (1D) 刺激。在本文中，我们探讨了在动觉触觉界面的触觉交互点 (HIP) 处呈现的 6D 振动触觉刺激如何映射到由检测阈值归一化的等效 1D 刺激. 我们收集了一个大型人类受试者数据集，其中我们确定了在 HIP 处呈现的三个正交力和三个正交扭矩的 45 种不同组合的检测阈值，单个频率为 108 Hz，对应于我们之前研究中的峰值灵敏度。使用这个数据集，我们找到了一个通用的二次加权函数来预测给定 6D 振动触觉刺激的 1D 归一化刺激。我们发现，在对称加权矩阵中仅包含七个（可能的 21 个）独立参数就足以捕获在 HIP 处呈现的力和扭矩之间的非明显耦合，以将尺寸从 6D 减少到 1D。