Radial force distribution changes associated with tangential force production in cylindrical grasping, and the importance of anatomical registration.
ABSTRACT Radial force (F(r)) distributions describe grip force coordination about a cylindrical object. Recent studies have employed only explicit F(r) tasks, and have not normalized for anatomical variance when considering F(r) distributions. The goals of the present study were (i) to explore F(r) during tangential force production tasks, and (ii) to examine the extent to which anatomical registration (i.e. spatial normalization of anatomically analogous structures) could improve signal detectability in F(r) data. Twelve subjects grasped a vertically oriented cylindrical handle (diameter=6 cm) and matched target upward tangential forces of 10, 20, and 30 N. F(r) data were measured using a flexible pressure mat with an angular resolution of 4.8°, and were registered using piecewise-linear interpolation between five manually identified points-of-interest. Results indicate that F(r) was primarily limited to three contact regions: the distal thumb, the distal fingers, and the fingers' metatacarpal heads, and that, while increases in tangential force caused significant increases in F(r) for these regions, they did not significantly affect the F(r) distribution across the hand. Registration was found to substantially reduce between-subject variability, as indicated by both accentuated F(r) trends, and amplification of the test statistic. These results imply that, while subjects focus F(r) primarily on three anatomical regions during cylindrical grasp, inter-subject anatomical differences introduce a variability that, if not corrected for via registration, may compromise one's ability to draw anatomically relevant conclusions from grasping force data.
- [show abstract] [hide abstract]
ABSTRACT: Gripping and push forces, also named coupling forces, have induced effects on the transmission of the vibration in the upper limb. The assessment of the vibration exposure with powered tools thus requires that these man/machine coupling parameters are controlled and monitored. To date, no reliable metrological systems enable their precise measurements. This study first investigated how much precision could be expected from the pressure mapping technique for the determination of coupling forces by means of numerical integration. Then a specific procedure was worked out and validated to instrument hand-held tools and measure the coupling forces with regard to the appropriate current standards. The proposed method was applied as a case study on an ordinary breaker and an anti-vibration breaker.Ergonomics 03/2008; 51(2):168-91. · 1.67 Impact Factor
Article: Multifinger prehension: an overview.[show abstract] [hide abstract]
ABSTRACT: The authors review the available experimental evidence on what people do when they grasp an object with several digits and then manipulate it. The article includes three parts, each addressing a specific aspect of multifinger prehension. In the first part, the authors discuss manipulation forces (i.e., the resultant force and moment of force exerted on the object) and the digits' contribution to such forces' production. The second part deals with internal forces defined as forces that cancel each other and do not disturb object equilibrium. The authors discuss the role of the internal forces in maintaining the object stability, with respect to such issues as slip prevention, tilt prevention, and resistance to perturbations. The third part is devoted to the motor control of prehension. It covers such topics as prehension synergies, chain effects, the principle of superposition, interfinger connection matrices and reconstruction of neural commands, mechanical advantage of the fingers, and the simultaneous digit adjustment to several mutually reinforcing or conflicting demands.Journal of Motor Behavior 10/2008; 40(5):446-76. · 1.04 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: Pheasant and O'Neill's torque model (1975) was modified to account for grip force distributions. The modified model suggests that skin friction produced by twisting an object in the direction of fingertips causes flexion of the distal phalanges and increases grip force and, thus, torque. Twelve subjects grasped a cylindrical object with diameters of 45.1, 57.8, and 83.2 mm in a power grip, and performed maximum torque exertions about the long axis of the handle in two directions: the direction the thumb points and the direction the fingertips point. Normal force on the fingertips increased with torque toward the fingertips, as predicted by the model. Consequently, torque toward the fingertips was 22% greater than torque toward the thumb. Measured torque and fingertip forces were compared with model predictions. Torque could be predicted well by the model. Measured fingertip force and thumb force were, on average, 27% less than the predicted values. Consistent with previous studies, grip force decreased as the handle diameter increased from 45.1 to 83.2 mm. This may be due not only to the muscle length-strength relationship, but also to major active force locations on the hand: grip force distributions suggest that a small handle allows fingertip force and thumb force to work together against the palm, resulting in a high reaction force on the palm, and, therefore, a high grip force. For a large handle, fingertip force and thumb force act against each other, resulting in little reaction force on the palm and, thus, a low grip force.Journal of Biomechanics 02/2007; 40(14):3236-43. · 2.72 Impact Factor
Radial force distribution changes associated with tangential force
production in cylindrical grasping, and the importance of
Todd C. Pataky1, Gregory P. Slota2, Mark L. Latash2, and Vladimir M. Zatsiorsky2
1Department of Bioengineering, Shinshu University, Japan
2Department of Kinesiology, Pennsylvania State University, USA
January 26, 2013
Radial force (Fr) distributions describe grip force coordination about a cylindrical object. Re-
cent studies have employed only explicit Fr tasks, and have not normalized for anatomical
variance when considering Frdistributions. The goals of the present study were (i) to explore
Frduring tangential force production tasks, and (ii) to examine the extent to which anatomi-
cal registration (i.e. spatial normalization of anatomically analogous structures) could improve
signal detectability in Frdata. Twelve subjects grasped a vertically-oriented cylindrical handle
(diameter = 6 cm) and matched target upward tangential forces of 10, 20, and 30 N. Frdata were
measured using a flexible pressure mat with an angular resolution 4.8 deg, and were registered
using piecewise-linear interpolation between five manually identified points-of-interest. Results
indicate that Fr was primarily limited to three contact regions: the distal thumb, the distal
fingers, and the fingers’ metatacarpal heads, and that, while increases in tangential force caused
significant increases in Frfor these regions, they did not significantly a↵ect the Frdistribution
across the hand. Registration was found to substantially reduce between-subject variability, as
indicated by both accentuated Frtrends, and amplification of the test statistic. These results im-
ply that, while subjects focus Frprimarily on three anatomical regions during cylindrical grasp,
inter-subject anatomical di↵erences introduce a variability that, if not corrected for via regis-
tration, may compromise one’s ability to draw anatomically relevant conclusions from grasping
Prehension requires fine coordination amongst contact forces. During precision grip and pinch
these forces are paramount, and a large body of literature exists regarding endpoint force coordi-
nation amongst the digits (reviewed in Zatsiorsky and Latash, 2008). Since these studies measure
only endpoint forces they neglect pressure distributions across the hand, yet many grasping modes
involve continuous contact across the palmar hand. For example: power grip to hold a tool han-
dle, cylindrical grip to hold a glass of water, and spherical grip to hold a baseball. In these tasks
endpoint forces cannot describe all mechanically-relevant contact information.
Consequently a variety of studies have explored contact force distribution, and the most widely
studied model is cylindrical grasp (Gurram et al., 1993; Shimojo et al., 1995; Hall, 1997; Welcome
et al., 2004). As an aside we note that ‘cylindrical grasp’ is a type of ‘power grasp’, a grasping
mode for which forces are distributed across the palmar surface of the hand; we presently use the
term ‘cylindrical grasp’ to refer to power grasp of a cylindrical object. Cylindrical grasp studies
reveal a non-uniform force distribution, with grip forces primarily focussed on the distal phalanges
and metacarpal heads, but with non-negligible forces between these points as well (Kargov et al.,
2004). They also reveal that cylindrical grasp force distribution can be quite di↵erent from other
power grasp modes (Wimer et al., 2009), suggesting that cylindrical grasp is worthwhile, if not
necessary to study in isolation.
We believe that there are three key issues which have not yet been explored in the cylindrical
grasp literature. The first is tangential load. For many natural cylindrical grasp tasks, like holding
a glass of liquid or handling a steering wheel, the tangential forces are the task-relevant forces while
normal forces may be regarded as secondary, necessary primarily for slip prevention and sensory
ending loading . While cylindrical grasp has been studied using explicit grasp force tasks, as well
as pulling and pushing tasks (Welcome et al., 2004), there are none, to our knowledge, that have
investigated tangential force tasks.
The second and third issues we believe warrant further attention are anatomical normalization
and continuous radial force distribution analysis. We use the term ‘radial force’ (Fr) to mean the
component of force directed toward the cylinder’s central axis (Fig.1); this force component is often
referred to as ‘normal force’ in the literature, but we believe Frmore adequately distinguishes cylin-
drical grip from other grasping modes. For example: if an object, like a steering wheel, has a bump
or dimple on its surface, normal forces will not necessarily be directed toward the object center, but
Frwill. And by ‘anatomical normalization’ we mean accounting for anatomical di↵erences amongst
subjects. Presently we use a form of anatomical normalization known as ‘registration’ (Maintz and
Viergever, 1998; Sadeghi et al., 2003; Kneip et al., 2000) to align analogous structures within the
continuous Frdistribution. We believe that continuous Frcharacterization and previous forms of
anatomical normalization represent two sides of the investigative coin: previous studies that have
valued anatomical normalization sacrificed continuous Frcharacterization, and studies that have
valued the latter sacrificed the former. But we believe that, with registration, this sacrifice is not
necessary. To explain:
Anatomical normalization has been implicitly adopted in studies which use individual sensors
at pre-determined points on the palmar surface of the hand (Gurram et al., 1993; Shimojo et
al., 1995; Hall, 1997; Welcome et al., 2004; Pylatiuk et al., 2006). However this measurement
scheme constrains analyses to those particular points-of-interest, and thus cannot characterize the
continuous Frdistribution in a completely objective manner.
Similarly, Fr distribution has been characterized using discrete sensors dispersed around the
cylinder (Wimer et al., 2009) or using finer pressure sensor arrays (Aldien et al., 2005; Lemerle et
al., 2007; Seo et al., 2007; Young et al., 2010), but in these studies the Frdata were described with
respect to the handle rather than with respect to the hand. This may be problematic in cases of
non-negligible inter-subject hand size variation, where positions on the handle cannot be mapped
directly to hand structures.
Registration overcomes these di?culties by transforming the Frdistribution to an anatomically
normalized space. Some studies employed registration to study the Frdistribution (Aldien et al.,
2005; Seo et al., 2007), even using impressive 3D kinematic models to do so (Sinsel et al., 2010),
but these studies employed region-of-interest discretization, e↵ectively breaking up the continuous
Frdistribution into discrete, comparatively low-resolution chunks. This process e↵ectively returns
the data to the discrete domain, as if Fr had been measured with large discrete sensors. This
is important because such discretization can corrupt the underlying data via regional conflation
(Pataky et al., 2008).
The purposes of this study were thus: (i) to describe how cylindrical grasp’s radial contact forces
are shared across the palmar surface of the hand during tangential force production, and (ii) to
determine the extent to which registration can improve continuous Frsignal detection. Based on the
literature we expected uniform Frincreases around the handle surface with increasing tangential
load (Zatsiorsky and Latash, 2008), that the greatest Fr would occur at the distal phalanges
and metacarpal heads with negligible forces elsewhere (Hall, 1997; Kargov et al., 2004), and that
registration would reduce inter-subject Fr distribution variability (Sadeghi et al., 2003), thereby
improving the statistical detection of the aforementioned e↵ects.
Twelve right-handed male subjects participated in this study (age: 32 ±8.1 years, height: 178.0
±6.6 cm, mass: 81.5 ±14.8 kg, hand length: 18.6 ±1.0 cm – from the proximal palmar crease to
the tip of the third digit, hand width: 9.1±0.6 cm – at the metacarpal heads). None reported
neurological or upper extremity pathology, and each provided informed consent according to The
Pennsylvania State University Institutional Review Board.
2.2Equipment and experiment
Subjects were secured with two shoulder/waist straps to a height-adjustable chair so that their
upper and lower arms were parallel to the horizontal plane and so that their shoulder and elbow
angles in the horizontal plane were 0 and 90 deg, respectively (Fig.1). Subjects grasped a vertically-
oriented cylindrical polyvinyl chloride (PVC) handle (diameter = 6 cm) just large enough to prevent
finger-thumb touching around the handle. The handle base was fixed to a 6-axis load cell (Mini-85,
ATI Industrial Automation, Apex, NC, USA) which was free to move in the xy plane via low-
friction sliders. Force data were measured at 1000 Hz using LabView 8.2 (National Instruments,
Austin, TX, USA).
A flexible pressure mat (PX200:100:100:10, XSENSOR Technology Corp., Calgary, Canada)
was fixed to the PVC handle using overnight pre-dried adhesive spray (Photo Mount, 3M, St.
Paul, MN, USA). While the adhesive supported the weight of the light mat, the mat’s data cables
were supported by cords, which were wrapped around steel ceiling rafters and then fastened to the
mat edges and data cables using metal clips. The device (thickness: 2 mm, sensing area: 25 ⇥ 25
cm, resolution: 2.54 mm, 16 Hz) was manufacturer-calibrated to a range of 1-200 kPa.
The task was to produce an upward vertical force (Fz = 10, 20, or 30 N) via bar-plot visual
feedback. Three repetitions of each target Fzwere conducted in a randomized order, yielding nine
trials per subject. Data were collected for 5 s, including both force development and steady-state
about the target Fz. Subjects were instructed to maintain a constant grasping posture between
trials (20 s). A foam-covered PVC half-pipe arm-rest was suspended from rafter cables; subjects
were permitted to use this arm-rest only between trials.
2.3 Data processing
The time window between 2 and 4 s was selected for analyses; this window was verified to follow
the initial Fzramping period, and was cut short of the 5 s period to avoid anticipatory relaxation.
Both the pressure data, originally in a 3D laboratory coordinate system (Fig.2), and the Fzdata
were averaged within these time windows. The averaged, unwrapped pressure images (Fig.3a),
which were originally on a 100 ⇥ 100 grid, were manually cropped to a size of 52 ⇥ 75 (132 ⇥ 190
mm) to exclude pressure cells that were not under the hand. Five points of interest, to be used in
subsequent analyses, were manually digitized on the cropped images: distal thumb phalanx - DP1,
first and second metacarpophalangeal joints - MCP1, MCP2, distal phalanges of index and middle
fingers - DP2, DP3.
Radial force (Fr) distributions (Fig.3b) were then computed by summing along the vertical (z)
direction as follows:
where ✓ is the polar angle (Fig.1b), A is the area of a single sensor (6.45 mm2), ?r is the angular
distance between pressure cells (0.083 rad), and I(✓,z) is the pressure recorded at the handle’s
(✓,z) coordinates. The resulting Frdistributions (Fig.3b) are 1D distributed loads (units: N/rad).
Just as pressure (i.e. N/mm2, a 2D distributed load) is more informative than absolute force when
using pressure measurement systems with arbitrary spatial resolution, the present units (N/rad) are
more informative than absolute force units when measuring Frwith arbitrary angular resolution.
The data were then averaged within-subjects, separately for each Fz (10, 20, 30 N), yielding
three Frdistributions per subject. The Frdata were analyzed as both distributed Fr(units: N/rad)
and as ‘force sharing’ (units: % grip force), where we presently define ‘grip force’ as:
grip force ⌘
Anatomically analogous Fr(✓) features were initially unaligned (Fig.4a). To compensate we
used a piecewise-linear spatial warping registration procedure (Kneip et al., 2000) between the
five manually digitized points of interest (Fig.3a). The result was improved analogous alignment
(Fig.4b). Rather than directly analyzing registration e↵ects via a comparison of pre- and post-
registered (dis)similarity metrics like mean squared error, the e↵ects of registration were presently
examined indirectly, through separate statistical analyses of original and registered data. That
is, we presently sought to examine only the extent to which registration amplified the ultimate
Frdistributions were analyzed using Statistical Parametric Mapping (SPM), a set of methods
developed in the neuroimaging literature (Friston et al., 2007), but which have also been shown
to be useful for a variety of smoothly varying biomechanics datasets (Pataky, 2010). Briefly, SPM
uses random field theory (Adler, 1981) to search the entire lattice-sampled measurement space for
both the location and extent of experimentally-induced signals. After one computes a test statistic
curve, for example as a set of t values at each point in the measurement space, a family-wise
error-rate, usually 0.05, is used to determine a t threshold below which results are not considered
significant. In this sense SPM is very much like traditional univariate or multivariate statistical
testing. However, SPM’s main di↵erence is that, since the underlying data have spatial structure
and are spatially smooth, values surviving the threshold tend to form connected clusters. It can
be shown that statistical inference, or p-value computation, can be comprehensively conducted
on cluster-specific metrics like cluster size and height (Adler, 1981). Just as in univariate testing
precise p values depend on the experimental degrees of freedom, but for SPM analyses p values
are also dependent on the underlying field smoothness, which can be estimated directly from the
spatial derivates of the statistical model residuals (Friston et al., 2007).
Presently SPM was used to assess the linear relation between Fzand Fr(✓) using the regression
Fri(✓) = ?(✓)Fzi+ ?(✓) + ✏i(✓)(3)
where i indexes observations, ? and ? are the regression slope and the intercept, respectively, and
where ✏iis the residual of the ith observation. First, least-squares estimates of ? were obtained
separately for each subject. Next, in a second-level mixed-e↵ects analysis the test statistic was
where n is the number of subjects,b?jis the estimated slope for subject j, and ˆ ? is the estimated
standard deviation. Statistical inference was conducted using a family-wise error rate of ↵ = 0.05
and the radial extent of clusters that survived the corresponding t(✓) threshold (Friston et al.,
2007). General analyses were implemented in Python 2.7 using the Enthought Python Distribution
7.0 (Enthought Inc., Austin, TX, USA), and SPM analyses were conducted using SPM1D (Pataky,
Irrespective of Fz, radial forces were primarily limited to three regions: MCP2, DP2, and DP1
(Fig.5a,b), and angular windows of 30 deg around these three regions accounted for a median 75.1%
of the total grip force (range: 45.9% – 99.3%; across all subjects and conditions). Fr tended to
increase with Fz(Fig.5a,b), and statistical analyses found this trend to reach significance (Fig.5c,d),
especially at DP1, but also continuously along the handle surface from MCP2 to DP2.
The magnitude of the Fz-induced Frincrease was region-dependent (Fig.5b), partially because
the three main contact points did not form an equilateral triangle and thus static equilibrium would
not be maintained with equal force increases. All aforementioned Frresults were both qualitatively
and statistically accentuated by registration, as indicated by t statistic amplification (Fig.5c,d).
Force sharing (Fig.6a,b) exhibited the opposite trend: Fr(% grip force) decreased with increased
Fz, implying that Frwas spread over a larger contact area, likely via increased tissue deformation.
Despite these trends, and while the distal portion of the fingers’ distal phalanges approached the
threshold for significance (Fig.6d), ANOVA found no di↵erences amongst the three Fzconditions
(p > 0.05). We note that, like a typical univariate case, the present ANOVA yields a critical F
threshold based on the a priori Type I error rate of ↵ = 0.05, and F values below this threshold are
deemed non-significant. We finally note that, like the absolute Frresults, registration accentuated
the Frsharing trends, as indicated by F statistic amplification (Fig.6c,d).
The present findings of distally focussed forces agrees with many previous studies on maximal
grasp (Gurram et al., 1993; Shimojo et al., 1995; Wimer et al., 2009; Hall, 1997; Lemerle et al., 2007;
Sinsel et al., 2010). That distal force concentration is consistent for sub-maximal and maximal tasks
suggests that the distal phalanges are likely the most important e↵ector for Fr production. The
present basic force distribution (DP1, DP2-3, MCP) has also been reported elsewhere (Gurram
et al., 1993; Hall, 1997), but the angular Fr distribution, and specifically the isolation to these
three regions has not been shown as clearly before, due mainly to previously insu?cient angular
One study (Pylatiuk et al., 2006) reported distally concentrated forces (37%), but also found
reasonably high forces at the middle (25%) and proximal (12%) phalanges. Another (Enders and
Seo, 2011) reported similar percentages: 47%, 25%, and 28%, respectively. While the present results
showed very little force sharing by the middle and proximal phalanges (Fig.6), the di↵erences
between the present and former studies may partially be explained by small tangential forces;
Pylatiuk et al. (2006) required a total vertical force of only 5-10 N. Di↵erences between the present
and latter studies may be partially explained by hand dominance and task constraints; Enders and
Seo (2011) measured the non-dominant hand and placed a single sensor under only one phalanx
segment at a time, potentially creating a segment-specific task perception. Regardless, the present
study also found systematic Frincreases with Fzalong the lumped finger segment from MCP2 to
DP2 (Fig.5d). Thus, while forces are almost certainly concentrated distally, it is also apparent that
more proximal portions of the finger phalanges contribute to the mechanical task in a non-trivial
Finally, since Frdid not increase equally at all contact points (Fig.5b,d), we can infer that the
hand did not behave in a clamp-like manner. That is, the hand did not simply squeeze the handle
more tightly. Rather, grasp forces were increased in a coordinated manner.
4.2Statistical parametric mapping (SPM)
We presently used SPM to analyze Frdistributions. In the present context SPM’s main advan-
tage was its anatomical detail, with statistical results having the same angular resolution as the
original dataset. This is in contrast to previous studies, which either measured Frdistributions at
low angular resolution (e.g. Wimer et al. ; 2009), or analyzed higher-resolution data with gross
regionalization schemes (e.g. Aldien et al. ; 2005). The importance of analysis resolution is echoed
by Young et al. (2010), who wrote (p.1159): “When the surface of the handle is lumped into 5
equal zones, the observed (force) trend is lost.” Since analysis resolution can a↵ect biomechani-
cal conclusions, we would submit that SPM, or another similar method, is needed for maximum
Failing to register data is double-edged: the higher inter-subject variability in non-registered
data (Fig.4) at once reduces the t signal magnitude (Fig.5) and raises the critical t threshold. The
latter occurs because SPM-based statistical inference depends on the underlying field smoothness
(Friston et al., 2007); when the underlying field is rough one is more likely to observe high t values
simply by chance. In plainer terms, the sensitivity with which one can detect signals is directly
related to registration.
While we currently employed a simple, manual, piecewise registration procedure (Kneip et al.,
2000), we note that there have been considerably more sophisticated methods employed in the
hand pressure literature. In particular, Buczek et al. (2011) used cone frustra to model finger
kinematics, and then to fit this model to observed hand pressure distributions (Sinsel et al., 2010).
Such techniques would likely be helpful to increase registration objectivity, and are likely necessary
to objectively study 2D pressure distributions.
Although we recorded 2D surface pressures (Fig.3a,b), we presently analyzed only Fr. This
was done primarily to make the present data comparable to previous studies which either report
polar force distributions (Pylatiuk et al., 2006; Wimer et al., 2009; Young et al., 2010), or which
report radial forces measured at arbitrary angular resolution. We presently preferred to focus on
Frin interest of simplicity, as only Frdata were necessary to emphasize registration’s importance
to cylindrical grasp analyses. We intend to explore the Fzdistributions and 2D pressure data in
It has been shown that many factors such as handle diameter (Seo et al., 2007) and surface
properties (Enders and Seo, 2011) can a↵ect Frcoordination. We presently did not consider these
factors, again in interest of a simpler message regarding registration.
Finally, since we measured only pressures, we were unable to determine potential e↵ects of
local shear. It has been shown, for example, that radial forces are not typically balanced during
power grip, that local shear forces are necessary for xy planar equilibrium (see Fig.1) (Wimer et
al., 2009). Local shears are clearly important for gaining a more complete perspective of the hand’s
management of quasi-static equilibrium.
This study examined radial force (Fr) distributions during cylindrical grasping while subjects
produced tangential force. The main findings were that: (i) Frincreased significantly with tangen-
tial forces, but only at the distal thumb and along the lateral digits, not between the distal thumb
and the fingers’ metacarpal heads, (ii) Frwas concentrated primarily on the distal phalanges and
the fingers’ metacarpal heads, and (iii) anatomical registration qualitatively and statistically ac-
centuated all trends. We presently argue that anatomical registration is necessary for maximum
objectivity, and that continuous analysis of force distributions is necessary for maximum anatomical
Funding for this work was provided by JSPS Wakate B Grant#22700465 and by NIH grant#AR-
Conflict of interest statement
The authors report that no conflicts of interest, financial or otherwise, influenced this work.
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Figure 1. Experimental apparatus. (a) Side view. (b) Top view, with an exploded handle
view indicating the polar coordinate system. The task was to produce tangential force in
the upward (+z) direction.
Figure 2. Example data, laboratory coordinate system. The thick line indicates the radial