Role of the inertia tensor in perceiving object orientation by dynamic touch.

Ss wielded an occluded L-shaped rod and attempted to perceive the direction in which the rod was pointing with respect to the hand. The pattern of the rod's different resistances to rotation in different directions, quantified by the inertia tensor, changes systematically with the rod's orientation. Perception of orientation by wielding is possible if the tissue deformation consequences of the rod's inertia tensor are detectable. It was shown that perceived orientation was a linear function of actual orientation for both free and restricted wielding and for rods of different-size branches. The eigenvectors of the inertia tensor were implicated as the basis for this haptic perceptual capability. Results were discussed in reference to information-perception specificity and its implications for effortful or dynamic touch.

Can shape be perceived by dynamic touch?

The possibility that some aspects of the shapes of solid objects can be perceived through dynamic touch, even when the objects are not touched, but simply wielded with a handle, was investigated in four experiments. Wooden solids were constructed of three sizes and five shapes: hemisphere, cylinder, parallelepiped, cone, and pyramid. Experiments 1 and 2 involved comparisons (judgments of same or different) between and among wielded objects of the same mass. In Experiments 3 and 4, subjects were required to wield an object and to select a match from a visible arrangement of objects of the five shapes; the wielded objects were of two sizes, each different from that of the visible objects. The success of subjects at these tasks, and the patternings of errors, are seen to involve the characteristic moment of inertia profiles of each shape, and a ratio of the object's resistances to rotation around orthogonal axes is shown to be a strong predictor of performance in the identification experiments. The results are discussed with reference to dynamic touch and to the notion of shape invariants that do not reduce to aspects of object surface.

An ecological analysis of knowing by wielding.

The ecological approach to perception, as developed by James Gibson, is described and applied to how one knows, by means of the haptic perceptual system, various properties of hand-held objects. Four sets of experiments are reviewed in which subjects reported on the extent, orientation, shape, and fractional components of unseen objects wielded freely. For each task, an invariant specific to the object property in question is identified in the structured arrays of rotational moments and strains produced by the act of wielding. Results are discussed in relation to the concepts of attention and stimulation, as reformulated by the ecological approach, and the general theory of perception as information pickup.

Perceiving extents of rods by wielding: haptic diagonalization and decomposition of the inertia tensor.

We report two experiments on the length-perception capabilities of the hand-related haptic subsystem. On each trial, a visually occluded rod was wielded by the subject at a position intermediate between its two ends. The position was either 1/2 or 3/4 of the rod's length. On two-thirds of the trials, a weight was attached to the rod at a point either above or below its center of gravity and not coincident with the hand's position. In Experiment 1, the subject's task was to perceive the distance reachable with the portion of the rod extending beyond the position of the grasp. In the second experiment, the subject's task was to perceive the distance reachable with the entire rod if it were held at its proximal end. In Experiment 1, perceived reaching distance was a function of the moment of inertia of the amount of rod forward of the grasp about an axis through the proximal end of the rod segment. In Experiment 2, perceived reaching distance was a function of the moment of inertia of the entire rod about the given axis of rotation intermediate between the rod's ends. The results are discussed in terms of (a) the notion of smart perceptual instruments capitalizing on invariant properties of the inertia tensor and (b) how the haptic decomposition of moments of inertia follows the principle of equivalence of forces.

Haptically perceiving the distances reachable with hand-held objects.

Nine experiments are reported on the ability of people to perceive the distances reachable with hand-held rods that they could wield by movements about the wrist but not see. An observed linear relation between perceived and actual reaching distances with the rods held at one end was found to be unaffected by the density of the rods, the direction relative to the body in which they were wielded, and the frequency at which they were wielded. Manipulating (a) the position of an attached weight on an otherwise uniformly dense rod and (b) where a rod was grasped revealed that perceived reaching distance was governed by the principal moment(s) of inertia (I) of the hand-rod system about the axis of rotation. This dependency on moment of inertia (I) was found to hold even when the reaching distance was limited to the length of rod extending beyond an intermediate grasp. An account is given of the haptic subsystem (hand-muscles-joints-nerves) as a smart perceptual instrument in the Runeson (1977) sense, characterizable by an operator equation in which one operator functionally diagonalizes the inertia and strain tensors. Attunement to the invariants of the inertia tensor over major physical transformations may be the defining property of the haptic subsystem. This property is discussed from the Gibsonian (ecological) perspectives of information as invariants over transformations and of intentions as extraordinary constraints on natural law.