Velocity-dependent changes of rotational axes in the non-visual control of unconstrained 3D arm motions.

We examined the roles of inertial (e(3)), shoulder-centre of mass (SH-CM) and shoulder-elbow articular (SH-EL) rotation axes in the non-visual control of unconstrained 3D arm rotations. Subjects rotated the arm in elbow configurations that yielded either a constant or variable separation between these axes. We hypothesized that increasing the motion frequency and the task complexity would result in the limbs' rotational axis to correspond to e(3) in order to minimize rotational resistances. Results showed two velocity-dependent profiles wherein the rotation axis coincided with the SH-EL axis for S and I velocities and then in the F velocity shifted to either a SH-CM/e(3) trade-off axis for one profile, or to no preferential axis for the other. A third profile was velocity-independent, with the SH-CM/e(3) trade-off axis being adopted. Our results are the first to provide evidence that the rotational axis of a multi-articulated limb may change from a geometrical axis of rotation to a mass or inertia based axis as motion frequency increases. These findings are discussed within the framework of the minimum inertia tensor model (MIT), which shows that rotations about e(3) reduce the amount of joint muscle torque that must be produced by employing the interaction torque to assist movement.

The role of the inertia tensor in kinesthesis.

We report experiments directed at the ability of humans to perceive the spatial orientation of occluded objects, to position an occluded limb relative to targets or directions in the environment, and to match the spatial orientation of occluded contralateral limbs. Results suggest that each of these abilities is tied to the inertial eigenvectors of each object or limb, which correspond to the object's or limb's principal axes of rotational inertia. It is suggested that the mechanisms supporting the perception of intact limbs, neuropathic or anesthetized limbs, prosthetic devices, and hand-held tools and implements via kinesthesis may be one and the same--the detection of movement-produced physical invariants such as the inertia tensor. While the research reported presently has focused on the perception of intact limbs and hand-held objects, future research should be directed at possible generalizations of this work to a variety of clinical populations, including those involving peripheral neuropathies and prosthetic devices.

Perceiving the lengths of rods wielded in different media.

In two experiments, we investigated the ability of participants to report the lengths of rods wielded in air or water. Homogeneous aluminum rods were employed in Experiment 1. The inertia of the rods was manipulated in Experiment 2 through the use of attached masses. Although the torques required in order to wield rods in water are substantially greater than those required to wield rods in air, the perceived lengths of rods wielded in the two media were very similar. Perceived length was found to be a function primarily of inertia in both media. The experiments also revealed a small influence of resistance due to the denser medium of water. The results demonstrate the ability of perceivers to extract a physical invariant from a complex array of forces. The discussion is focused on the role of invariants in dynamic touch.

Comparing measures of monocular distance perception: verbal and reaching errors are not correlated.

Monocular perception of egocentric distance via optic flow generated by head movement toward a target was investigated with a helmet-mounted video camera and display. Ability to perceive target distance was assessed with 2 response measures: verbal reports and reaches. Systematic and random errors differed as a function of the response measure. Verbal estimates of targets within and beyond reach were obtained before and after the performance of reaches to targets within reach. Systematic errors of verbal estimates changed but did not decrease overall. Random error decreased. Verbal estimates and reaches were performed concurrently to targets within reach. Verbal and reaching errors were uncorrelated. Verbal judgments appear to have been anchored using the range of distances experienced while reaching rather than being calibrated to the perceptual information itself. Discussion focuses on the advantages of action response measures.

The necessity of a perception-action approach to definite distance perception: monocular distance perception to guide reaching.

In this investigation of monocular perception of egocentric distance, the authors advocate the necessity of a perception-action approach because calibration is intrinsic to definite distance perception. A helmet-mounted camera and display were used to isolate optic flow generated by participants' head movements toward a target, and participants' reaches to place a stylus either in a target hole (Experiments 1, 2, and 4) or aligned under a target surface (Experiment 3) were analyzed. Conclusions are that binocular distance perception is accurate, monocular distance perception yields compression that is not eliminated by feedback, but feedback is used to eliminate underestimation generated by restriction of the size of the visual field.

Exteroception and exproprioception by dynamic touch are different functions of the inertia tensor.

When an object is held and wielded, a time-invariant quantity of the wielding dynamics is the inertia tensor Iij. The 3 x 3 quantity Iij is composed of moments of inertia (on the diagonal) and products of inertia (off the diagonal). Examination of Iij as a function of different locations at which a cylindrical object is grasped revealed that the products related systematically to grip position (a direction), and both the products and moments taken together related systematically to the extent of the rod to one side of the hand (a magnitude in a direction). In two experiments, observers wielded an occluded rod that was held at an intermediate point along its length and reproduced both the felt grip position and partial rod length. In both experiments, perceived grip position was a function of the rod's products of inertia and perceived partial rod length was a function of the moments and products. Discussion focuses on the specificity of exteroception and exproprioception to Iij.

The inertia tensor as a basis for the perception of limb orientation.

The ability of humans to perceive the spatial orientation of an occluded arm was investigated. It was hypothesized that this ability is tied to the arm's inertial eigenvectors, invariant mechanical parameters corresponding to a limb's axes of rotational symmetry. By breaking the coincidence between the eigenvectors of the arm and its longitudinal axis, 3 experiments were directed at the possibility that the perceived orientation of an occluded arm would vary as a function of the eigenvectors. Overall, the angles in which the arm was positioned were affected by the direction in which the eigenvectors of the limb were oriented by small appended masses. Discussion focused on the importance of physical invariants for proprioception.

Role of the inertia tensor in haptically perceiving where an object is grasped.

When an object is held and wielded, a time-invariant quantity of the wielding dynamics is the inertia tensor Iij. Examination of Iij as a function of different locations at which a cylindrical object is grasped revealed that the off-diagonal components of Iij--the products of inertia--related most systematically to grip position. In 3 experiments, Ss wielded an occluded rod held at an intermediate point along its length and reproduced, with the other hand, the felt grip position on a visible rod. In Experiment 1, the wielded rods were homogeneous; in Experiments 2 and 3, weights were added on either side of the grasp, with different manners of grasp contrasted in Experiment 3. In all 3 experiments, perceived hand position was predicted by Iij. Discussion was focused on the role of Iij's eigenvalues in perceiving the magnitudes of objects and Iij's eigenvectors in perceiving hand-object relations (e.g., position of grasp).

Tensorial basis to the constancy of perceived object extent over variations of dynamic touch.

Subjects wielded occluded rods, with or without attached masses, and reported the distances reachable with their distal tips. Experiments 1-3 compared wielding about the wrist, the elbow, and the shoulder. Experiments 4 and 5 compared free wielding, using the whole arm, with wielding only about the wrist. The two comparisons, respectively, were of spatial and temporal variations in the rod's rotational inertia. Perceived extent was found to be constant in both comparisons. This constancy was tied to the inertia tensor Iij defined about a point that remains a fixed distance from the object during wielding--an invariant of the spatially and temporally dependent patterning of mechanical energy impressed upon the tissues of the body. Discussion focused on the reciprocal action and perception capabilities of multisegmented limbs, the tensorial relations in the neurobiology of dynamic touch, and the strategy of understanding perceptual constancy through invariants.

Eigenvectors of the inertia tensor and perceiving the orientation of a hand-held object by dynamic touch.

Subjects wielded an object, hidden from view, and reported the orientation in which the object was positioned in the hand. The object consisted of a stem with two branches forming a V attached perpendicularly to the stem's distal end. The branches were differentially weighted so that the same spatial orientation of the object was associated with different orientations of its principal (symmetry) axes or eigenvectors. Perceived orientation was found to be dependent on the eigenvectors of the object's inertia tensor, computed about the point of rotation in the wrist, rather than on its spatial orientation. The results underscore the significance of the inertia tensor to understanding the perception of spatial properties by dynamic touch.

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.