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20
Human Hand as a Parallel Manipulator
Vladimir M. Zatsiorsky ad Mark L. Latash
Department of Kinesiology, The Pennsylvania State University
1. Introduction
When a human hand grasps an object the hand can be viewed as a parallel manipulator. In
general, the mathematical analyses of the human hands and multi-fingered robot hands
(Murray et al. 1994) are similar. In particular, concepts developed in robotics such as contact
models, e.g. soft-finger model, grasp matrix, form and force closure grasps, internal forces,
etc. can be applied to analyze the performance of the human hands. Multi-finger prehension
is an example of a mechanically redundant task: the same resultant forces on the object can
be exerted by different digit forces. People however do not use all the mechanically
available options; when different people perform a certain manipulation task they use a
limited subset of solutions.
Studies on human prehension deal with four main issues:
1. Description of the behavior: What are the regularities in force patterns applied at the
fingertip-object interfaces when people manipulate objects?
2. Are the observed patterns dictated by the task and hand mechanics? The mechanical
properties of the hand and fingers are complex, and it is not always evident whether the
findings are direct consequences of the mechanical properties of the hand or they are
produced by a neural control process.
3. If the observed facts/phenomena are not of mechanical origin are they mechanically
necessitated? In other words, can the task be performed successfully in another way?
4. If reproducible phenomena are not mechanical and not mechanically-necessitated, the
question arises why the central nervous system (CNS) facilitates these particular
phenomena. This is a central question of the problem of motor redundancy in general:
Why does the CNS prefer a certain solution over other existing solutions?
The present chapter briefly reviews some specific features of the human hand and the
involved control mechanisms. To date, the experimental data are mainly obtained for the so-
called prismatic grasps in which the thumb opposes the fingers and the contact surfaces are
parallel (Figure 1). The contact forces and moments are typically recorded with 6-
component force and moment sensors.
Experimental ‘inverted-T’ handle/beam apparatus commonly used to study the prismatic
precision grip. Five six-component force sensors (black rectangles) are used to register
individual digit forces. During testing, the suspended load could vary among the trials. The
load displacement along the horizontal bar created torques from 0 N⋅m to 1.5 N⋅m in both
directions. The torques are in the plane of the grasp. While forces in all three directions were
recorded the forces in Z direction were very small and, if not mentioned otherwise, were
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neglected. When the handle is oriented vertically the force components in the X and Y
directions are the normal and shear, (or tangential) forces, respectively. The figure is not
drawn to scale.
60 mm
Y
Z
Index
X
30 mm
Thumb
Middle
30 mm
Ring
30 mm
Little
Torque 0.0-1.5 Nm
Load 0.5 kg
Figure 1. Experimental ‘inverted-T’ handle/beam apparatus
2. Digit contacts
During an object manipulation the finger tips deform and the contact areas are not constant
(Nakazawa et al. 2000; Paré et al. 2002; Serina et al. 1997; Srinivasan, 1989; Srinivasan et al.
1992; Pataky et al. 2005). The fingers can also roll on the sensor surface. As a result, the point
of digit force application is not constant: it can displace by up to 5-6 mm for the fingers and
up to 11-12 mm for the thumb (Figure 2). Therefore the digit tip contacts should be as a rule
treated as the soft-finger contacts (Mason & Salisbury, 1985).
When a soft-finger model of the digit-object contact is employed, the contact is characterized
by six variables: three orthogonal force components (the normal force component is uni-
directional and the two tangential force components are bi-directional), free moment in the
plane of contact, and two coordinates of the point of force application on the sensor. To
obtain these data the six-component force and moment sensors are necessary. The
coordinates of the point of force application are not recorded directly; they are computed
from the values of the normal force and the moment around an axis in the contact plane.
Such a computation assumes that the fingers do not stick to the sensor surfaces, in other
words the fingers can only push but not pull on the sensors. In such a case the moment of
force about the sensor center is due to the application of the resultant force at a certain
distance from the center. The displacements of the points of digit force application change
the moment arms of the forces that the digits exert on the hand-held object and make the
computations more cumbersome.
Human Hand as a Parallel Manipulator
451
Figure 2. Displacement of the point of application of digit forces in the vertical direction at
the various torque levels. The results are for an individual subject (average of ten trials). The
positive direction of the torque is counterclockwise (pronation efforts), the negative
direction is clockwise (supination efforts). Adapted by permission from V.M. Zatsiorsky, F.
Gao, and M.L. Latash. Finger force vectors in multi-finger prehension. Journal of
Biomechanics, 2003a, 36:1745-1749.
3. Hand asymmetry and hierarchical prehension control
Asymmetry in the hand function is an important feature that differentiates the hand from
many parallel manipulators used in engineering as well as from some robotic hands (Fu &
Pollard 2006). The functional hand asymmetry is in part due to the hand design (e.g. the
thumb opposing other fingers, differences in the capabilities of index and little fingers, etc.)
and in part is due to the hand control.
Due to the specific function of the thumb opposing other fingers in grasping, the forces of
the four fingers can be reduced to a resultant force and a moment of force. This is
equivalent to replacing a set of fingers with a virtual finger, VF (Arbib et al. 1985, Iberall 1987;
Baud-Bovy & Soechting, 2001). A VF generates the same wrench as a set of actual fingers.
There are substantial differences between the forces exerted by individual fingers (IF) and
VF forces: (a) The IF force directions are as a rule dissimilar (for a review see Zatsiorsky &
Latash 2008) while their resultant (i.e., VF) force is in the desired direction (Gao et al. 2005).
(b) VF and IF forces adjust differently to modifications in task conditions (Zatsiorsky et al.
2002a, b). (c) IF forces are much more variable than VF forces (Shim et al. 2005a, b). The
desired performance at the VF level is achieved by a synergic co-variation among individual
finger forces at the IF level. The above facts support a hypothesis that multi-finger
prehension is controlled by a two-level hierarchical control scheme (reviewed in Arbib et al.
1985; Mackenzie & Iberall 1994). At the upper level, the required mechanical action on the
object is distributed between the thumb and the VF. At the lower level, action of the VF is
distributed among individual fingers.
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