Motor control goes beyond physics: differential effects of gravity and inertia on finger forces during manipulation of hand-held objects

Abstract

According to basic physics, the local effects induced by gravity and acceleration are identical and cannot be separated by any physical experiment. In contrast-as this study shows-people adjust the grip forces associated with gravitational and inertial forces differently. In the experiment, subjects oscillated a vertically-oriented handle loaded with five different weights (from 3.8 N to 13.8 N) at three different frequencies in the vertical plane: 1 Hz, 1.5 Hz and 2.0 Hz. Three contributions to the grip force-static, dynamic, and stato-dynamic fractions-were quantified. The static fraction reflects grip force related to holding a load statically. The stato-dynamic fraction reflects a steady change in the grip force when the same load is moved cyclically. The dynamic fraction is due to acceleration-related adjustments of the grip force during oscillation cycles. The slope of the relation between the grip force and the load force was steeper for the static fraction than for the dynamic fraction. The stato-dynamic fraction increased with the frequency and load. The slope of the dynamic grip force-load force relation decreased with frequency, and as a rule, increased with the load. Hence, when adjusting grip force to task requirements, the central controller takes into account not only the expected magnitude of the load force but also such factors as whether the force is gravitational or inertial and the contributions of the object mass and acceleration to the inertial force. As an auxiliary finding, a complex finger coordination pattern aimed at preserving the rotational equilibrium of the object during shaking movements was reported.

Fig. 1

a,b Effects of object weight and inertial force on the grip force. The inertial forces are due to an up-and-down oscillation of the vertically oriented handle. a An expected relation between the grip and load forces in the event that the grip force adjustments to the weight and inertial forces are identical. The expected dynamic grip force adjustments (open ellipses) are oriented along the same line as the static grip force-load force relation. b If the effects on the grip force of moving the handle differ from the static relation, the ellipses may be expected to shift with respect to the static line and to be oriented differently. Three fractions of the grip force—static (solid straight line), stato-dynamic (dotted line), and dynamic (ellipses)—are explained further in the text (see Fig. 3)

Fig. 2

Schematic drawing of the experimental set-up (the drawing is not to scale)

Fig. 3

Expanding the grip force into three fractions: static, stato-dynamic and dynamic. W is the object weight. The static relation is represented by a straight line. The dynamic relation is represented by an ellipse. The L-G vector (not shown in the picture) goes from the ellipse center to the star representing an L-G pair selected for the analysis

Fig. 4

The normal force of the thumb versus the normal force of the virtual finger (VF). The virtual finger is an imaginary finger that generates the same mechanical effect as the four fingers combined. Data for a representative subject are illustrated

Fig. 5

The time history of the difference between the tangential forces of the thumb and virtual finger (VF) in a typical trial. The frequency was 2 Hz, the weight was 13.8 N. Data for a representative subject are shown. To obtain the torque generated by this difference it should be multiplied by the moment arm (the width of the grasp: 60 mm)

Fig. 6

Changes in the sharing pattern of the normal finger forces during a trial as a percentage of the total force. To avoid a messy figure only the sharing percentages of the index and little fingers are shown. Normal forces of these fingers produce opposite moments of force about the thumb as a pivot. Hence, an increase in the sharing percentage of one finger with a simultaneous decrease of the other finger alters the moment of the normal forces exerted on the object. Frequency 2 Hz, weight 13.8 N. Data for a representative subject are shown

Fig. 7

Static, dynamic and stato-dynamic relations between the grip and load forces. The inertial forces are due to an oscillation of the vertically-oriented handle at 1.5 Hz over about 10 cm in the vertical plane. The weights are 3.8, 6.3, 8.8, 11.3, and 13.8 N. The total force of five digits is shown for a representative subject, Subject 1. W is the object weight, the load force L=W+ma

Fig. 8

a–c Static, stato-dynamic and dynamic contributions to the grip force at various loads and oscillation frequencies. The dynamic contribution was computed by projecting the major axes of the force ellipses onto the grip force axis. Group averages and standard errors of the mean are shown. Frequency: a 1 Hz; b 1.5 Hz; c 2 Hz. LD1–LD5 correspond to the weight values 3.8, 6.3, 8,8, 11.3 and 13.8 N, respectively

Fig. 9

Stato-dynamic fractions at various frequencies and loads. The data are group averages. The vertical bars are standard errors of the mean

Fig. 10

Slopes of the dynamic and static grip force–load force relations. Equal increments of the load force may induce unequal increments of the grip force

Fig. 11

Grip force and load force (N) time histories. Subject 6, frequency 1 Hz. The lower panel shows a close-up of the upper panel, the peak values of the curves are labeled with circles