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Modeling Human Difference Threshold in Perceiving Mechanical Properties From Force

We discuss an extension of the basic principles underlying the human haptic just noticeable difference (JND) in perceiving a manipulator's mechanical properties from force feedback. Two cases are studied: first, the JND in perceiving the stiffness of manipulators with various masses and, second, the JND in perceiving the damping of a combined mass–spring–damper system with varying stiffness and mass. The extended JND laws are obtained through mapping psychophysical findings to JND formulations based on frequency response functions. We first present two human-factor experiments in which subjects discriminated between different levels of manipulator stiffness/damping while moving the manipulator with a prescribed sinusoidal deflection. For the two testing cases, both JNDs violate Weber's law: Due to the increases in mass, the normalized stiffness JND (the Weber fraction) decreases as the reference stiffness level increases; the damping JND for a constant reference damping increases with higher combined responses of stiffness and mass. On the basis of weighting the frequency response magnitude of mechanical properties, we performed model identification that fit the experimental observations and extended the JND laws for the two testing cases. Our extended JND laws indicate that, first, the stiffness and mass affect the stiffness JND in the same way, the stiffness JND is a fixed proportion of the combined frequency response of stiffness and mass, and, second, the frequency response magnitude of the damping JND is a fixed proportion of the frequency response magnitude of the combined system (the mass–spring–damper system).