To a first approximation, the mechanical behavior of all deformable solid objects can be expressed as f ϭ F s ϩ Kx ϩ Bẋ ϩ mẍ, which represents the relationship between the total force ( f ) applied on the object and the corresponding displacement (x), velocity (ẋ), and acceleration (ẍ); the frictional force (F s ), linear stiffness (K ), viscosity (B), and mass (M ) are the physical parameters that distinguish one object from another (we use lowercase letters for variables and uppercase for parameters). It is our goal to study manual resolution of all these physical variables and parameters and to provide basic psychophysical information that can be used to (1) advance our understanding of manual perception of object properties, (2) guide the development of design specifications for haptic interfaces that not only sense position and force commands from the human operator but also display such information to the operator in teleoperation and virtual environment systems (see, e.g., the recently published book on systems of this type edited by Durlach & Mavor, 1994), and (3) improve the design of autonomous robots that must make use of manual sensing and manipulation. This is the third in a series of papers concerned with how individual physical properties of objects are perceived. In the first paper of this series (Durlach et al., 1989) , we reported the results of a variety of experiments in which the subject was required to discriminate or identify object length (related to the variable x) by means of the fingerspan method. The just noticeable difference (JND) in length measured in discrimination experiments was roughly 1 mm for reference lengths of 10-20 mm, and increased to roughly 2.2 mm for a reference length of 80 mm. The results violated Weber's law. In the second paper (Pang, Tan, & Durlach, 1991) , we discussed experiments in which the subject was required to discriminate resistive force (represented by the parameter F s ) by means of active finger motion. The JND was found to be 7% of the reference force over a reference force range of 2.5-10.0 N, 1 a displacement range of 5-30 mm, an initial finger-span range of 45-125 mm, and a mean velocity range of 25-160 mm/sec. These results were roughly consistent with those reported for weight and force by other researchers (e.g., Jones, 1989; see also the review by Jones, 1986) . Manual perception of stiffness K (i.e., change in force divided by change in displacement) or, equivalently, compliance 1/K (i.e., change in displacement divided by change in force) is presumably based on the perception of both force and displacement, since humans possess no known special "stiffness/compliance sensors" in the peripheral sensory organs. During active touch, although both tac- Copyright 1995 Psychonomic Society, Inc. In these experiments, two plates were grasped between the thumb and the index finger and squeezed together along a linear track. The force resisting the squeeze, produced by an electromechanical system under computer control, was programmed to be either constant (in the case of the force discrimination experiments) or linearly increasing (in the case of the compliance discrimination experiments) over the squeezing displacement. After completing a set of basic psychophysical experiments on compliance resolution (Experiment 1), we performed further experiments to investigate whether work and/or terminal-force cues played a role in compliance discrimination. In Experiment 2, compliance and force discrimination experiments were conducted with a roving-displacement paradigm to dissociate work cues (and terminal-force cues for the compliance experiments) from compliance and force cues, respectively. The effect of trial-by-trial feedback on response strategy was also investigated. In Experiment 3, compliance discrimination experiments were conducted with work cues totally eliminated and terminal-force cues greatly reduced. Our results suggest that people tend to use mechanical work and force cues for compliance discrimination. When work and terminal-force cues were dissociated from compliance cues, compliance resolution was poor (22%) relative to force and length resolution. When work cues were totally eliminated, performance could be predicted from terminal-force cues. A parsimonious description of all data from the compliance experiments is that subjects discriminated compliance on the basis of terminal force.
The effects of force and work cues on compliance discrimination were surveyed in REF and the significant effect of force cues on discrimination was evident.
Manual discrimination of compliance using active pinch grasp: the roles of force and work cues, Perception
Psychophysics
Psychology Medicine