Static prehension of a horizontally oriented object in three dimensions

Abstract

We studied static prehension of a horizontally oriented object. Specific hypotheses were explored addressing such issues as the sharing patterns of the total moment of force across the digits, presence of mechanically unnecessary digit forces, and trade-off between multi-digit synergies at the two levels of the assumed control hierarchy. Within the assumed hierarchy, at the upper level, the task is shared between the thumb and virtual finger (an imagined finger producing a wrench equal to the sum of the wrenches of individual fingers). At the lower level, action of the virtual finger is shared among the four actual fingers. The subjects held statically a horizontally oriented handle instrumented with six-component force/torque sensors with different loads and torques acting about the long axis of the handle. The thumb acted from above while the four fingers supported the weight of the object. When the external torque was zero, the thumb produced mechanically unnecessary force of about 2.8 N, which did not depend on the external load magnitude. When the external torque was not zero, tangential forces produced over 80% of the total moment of force. The normal forces by the middle and ring fingers produced consistent moments against the external torque, while the normal forces of the index and little fingers did not. Force and moment variables at both hierarchical levels were stabilized by covaried across trials adjustments of forces/moments produced by individual digits with the exception of the normal force analyzed at the lower level of the hierarchy. There was a trade-off between synergy indices computed at the two levels of the hierarchy for the three components of the total force vector, but not for the moment of force components. Overall, the results have shown that task mechanics are only one factor that defines forces produced by individual digits. Other factors, such as loading sensory receptors may lead to mechanically unnecessary forces. There seems to be no single rule (for example, ensuring similar safety margin values) that would describe sharing of the normal and tangential forces and be valid across tasks. Fingers that are traditionally viewed as less accurate (e.g., the ring finger) may perform more consistently in certain tasks. The observations of the trade-off between the synergy indices computed at two levels for the force variables but not for the moment of force variables suggest that the degree of redundancy (the number of excessive elemental variables) at the higher level is an important factor.

Figure 1

The handle and subject position during experiment. (A) Digit sensors were attached to an aluminum handle, and a load could be attached at different points along a rigid, light-weight rod. An electromagnetic tracking device and a bubble level were attached to the handle. M_X, M_Y, and M_Z are the global moments with respect to the global X-, Y-, Z-axes; m_x, m_y, and m_z are the local moment with respect to the local x-, y-, and z-axes on each sensor. (B) The position of the subject. The subject maintained the handle horizontal by monitoring the orientation angles around the X- and Y-axes shown on the computer screen.

Figure 1

The handle and subject position during experiment. (A) Digit sensors were attached to an aluminum handle, and a load could be attached at different points along a rigid, light-weight rod. An electromagnetic tracking device and a bubble level were attached to the handle. M_X, M_Y, and M_Z are the global moments with respect to the global X-, Y-, Z-axes; m_x, m_y, and m_z are the local moment with respect to the local x-, y-, and z-axes on each sensor. (B) The position of the subject. The subject maintained the handle horizontal by monitoring the orientation angles around the X- and Y-axes shown on the computer screen.

Figure 2

Normal forces (Fⁿ) of the thumb (TH) and vitual finger (VF) exerted on the handle under different load conditions (0.1, 0.2, and 0.3 kg) and different lever arms (black bars: 0.08 m; white bars: 0.16 m; gray bars: 0.24 m). The averaged data across trials and subjects are presented with standard error bars. Both VF and thumb normal forces scaled with the load and lever arm.

Figure 3

Tangential forces (F^t,X) in the anterior-posterior direction (X-axis) by the thumb an VF under different loads (0.1, 0.2, and 0.3 kg) and lever arms (0.08, 0.16, and 0.24 m). Averaged data across trials and subjects are presented with standard error bars. The tangential forces of VF and thumb formed a force couple acting against the external torque. Magnitudes of both VF and thumb tangential forces scaled with the external load and its lever arm.

Figure 4

The sharing patterns of the VF tangential (gray bars) and normal (white bars) forces across the individual fingers. The averaged data across trials, subjects, and conditions are presented with standard error bars. Note that the shares of the “central” fingers (M and R) were smaller for the VF tangential force as compared to the normal force. I, M, R, and L stand for the index, middle, ring, and little fingers, respectively.

Figure 5

The moments about the Y-axis (M_Y) generated by the VF and thumb under different loads (0.1, 0.2, and 0.3 kg) and lever arms (0.08, 0.16, and 0.24 m). The averaged data across trials and subjects are presented with standard error bars. Note that the total moment against external torque was shared nearly equally between moments exerted by VF and thumb.

Figure 6

The sharing of total moment about the Y-axis (M_Y) between the moments generated by normal (Mⁿ – white bars) and tangential (M^t – gray bars) forces by all five digits. The averaged data across trials, subjects, and conditions are presented with standard error bars. Most of the total M_Y was produced by the tangential forces. Note that the “lateral” fingers (I - index and L - little) produced higher M^t, while their Mⁿ, on average, was close to zero.

Figure 7

The changes in the anterior-posterior coordinate (X-axis) of the center of pressure (COP^X) with the external load (0.1, 0.2, and 0.3 kg) and lever arm (0.08, 0.16, and 0.24 m) for the thumb and VF. The averaged data across trials and subjects are presented with standard error bars. Only for the thumb, COP^X showed an increase with both load magnitude and lever arm.

Figure 8

The safety margin (SM) values of the thumb across trial conditions. (A) The SM values across lever arms (0.08, 0.16, and 0.24 m). (B) The SM values across external load magnitudes (0.1, 0.2, and 0.3 kg). The bars show SM values after Fisher transformation (averaged across subjects with standard error bars), while the values in parentheses refer to data before Fisher transformation. SM values dropped with both lever arm and load magnitude.

Figure 9

Indices of co-variation of elemental variables (ΔV) averaged across subjects for all six component of the force and moment of force vectors. (A) and (C) show ΔV across lever arms at the VF-TH and IF level, respectively. (B) and (D) show ΔV across external loads at the VF-TH and IF level, respectively. Note that ΔV are predominantly positive at both levels (with the exception of Fⁿ at the IF level), and changes in the lever arm and load magnitude had only minor effects on ΔV.

Figure 10

The relations between indices values after Fisher transformation (ΔV_Z) averaged across subjects and trial conditions at the VF and IF levels for (A) the three force components and (B) the three moment of force components. Note that there was a strong negative relation between the ΔV_Z at the VF-TH and IF levels across the force variables, but not across the moment of force variables. Linear regression equations are shown with correlation coefficients; * - p < 0.05.

Figure 11

An illustration of the sagittal view of the handle with the force vectors and COP^X of each digit at (A) the VF–TH level and at (B) the IF level. The averaged data across trials, subjects, and conditions are illustrated. The aluminum beam to which the external load attached is truncated. The subscripts (TH, VF, I, M, R, and L) refer to the thumb, virtual finger, index, middle, ring, and little fingers, respectively.