Exp Brain Res (1994) 98:535-541
9 Springer-Verlag 1994
Reinoud J. Bootsma. Ronald G. Marteniuk
Christine L. MacKenzie 9 Frank T.J.M. Zaal
The speed-accuracy trade-off in manual prehension:
effects of movement amplitude, object size
and object width on kinematic characteristics
Received: 21 July 1993 / Accepted: 8 November 1993
Abstract Earlier studies have suggested that the size of
an object to be grasped influences the time taken to
complete a prehensile movement. However, the use of
cylindrical objects in those studies confounded the effects of object size - extent orthogonal to the reach axis
and object width - extent along the reach axis. In
separating these effects, the present study demonstrates
that movement time is not affected by manipulation of
object size, as long as the latter does not approach the
maximal object size that can be grasped. Object width,
on the other hand, is shown to exert a systematic influence on movement time: Smaller object widths give rise
to longer movement times through a lengthening of the
deceleration phase of the movement, thus reproducing
the effect of target width on the kinematics of aiming
movements. As in aiming, movement amplitude also affects the movement time in prehension, influencing primarily the acceleration phase (i.e. peak velocity attained). The effects of object width and movement amplitude were found to combine in a way predicted by
Fitts' law, allowing a generalisation of the latter to the
transport component in prehensile actions. With respect
to the grasp component, both object size and object
width are shown to affect peak hand aperture. Increasing object width thus lowers the spatial accuracy demands on the transport component, permitting a faster
movement to emerge. At the same time, the hand opens
to a larger grip in order to compensate for eventual
directional errors that result. Finally, with respect to the
control mode of the grasp component, it was found that
peak finger closing velocity scales to distance to be cov-
R. J. Bootsma ([~)
Faculty of Sport Sciences, University of Aix-Marseille II,
163 Av. de Luminy, F-13009 Marseille, France
R. G. Marteniuk - C. L. MacKenzie
Department of Kinesiology, Simon Fraser University,
Burnaby BC, Canada
F. T. J. M. Zaal
Faculty of Human Movement Sciences, Free University,
Amsterdam, The Netherlands
ered, defined as the peak hand aperture minus object
size.
Key words Motor control 9 Speed-accuracy trade-off
Prehension. Human
Introduction
In 1899 Woodworth demonstrated that in a task requiring a pencil to be moved between three target points
arranged in a triangular manner speeding up the movement resulted in a loss of accuracy. However, it was not
until Fitts refined these early experiments in 1954 that
the speed-accuracy trade-off in movement assumed its
present status within the field of motor control, Instead
of using target points, Fitts required his subjects to reverse their movement within (two) designated target areas. By varying target width and inter-target distance
(amplitude), Fitts demonstrated that a lawful relation
exists between the speed and the accuracy of movement:
The time taken to complete the movement was shown
to be a function of the index of difficulty, the latter being
the logarithm (to the base 2) of twice the movement
amplitude divided by the target width. The same kind of
relation was subsequently demonstrated to hold for discrete aiming movements by Fitts and Peterson (1964).
Although there is currently some discussion on whether
the logarithmic function is, in general, the most appropriate description of the speed-accuracy trade-off (e.g.
Meyer et al. 1988), the basic proposition that movement
time increases when aiming movements are directed toward smaller or targets further away has received much
experimental support (Jagacinski et al. 1980; Kerr 1973;
Meyer et al. 1982; Wade et al. 1978).
While the underlying assumption of research on simple aiming movements is that the findings will generalise
to other, more complex tasks, the question whether
Fitts' law also holds for a task like prehension has, however, not yet been answered. This question is nevertheless of particular interest, as the control and coordina-
536
tion of components in the latter task has been the subject of much discussion during the last decade (Arbib
1981, 1985; Bootsma and Van Wieringen 1992; Chieffi
and Gentilucci 1993; Haggard and Wing 1991; Jakobson and Goodale 1991; Jeannerod, 1981, 1984, 1988;
Marteniuk et al. 1987, 1990; Paulignan et al. 1991a,b;
Wallace and Weeks 1988; Wallace et al. 1990, 1992;
Wing et al. 1986). A prehensile act can be considered as
two coordinated functional components that allow the
hand to eventually establish the required contact with
the object for manipulation to ensue. The transport
component is responsible for bringing the hand/wrist
system into the vicinity of the object to be grasped, and
the grasp component is responsible for the formation of
the grip. Jeannerod (1981, 1984), see also Arbib (1981,
1985), has suggested that these two components are
controlled via separate and independent visuo-motor
pathways, while their coordination is ensured by a
supra-ordinate control structure. The first question addressed in the present study is whether Fitts' law is to be
found in the behaviour of the transport component
(which can be considered to perform an aiming-type of
task) during a prehensile act. The second question concerns the independence (as proposed by Jeannerod
1981, 1984) of the control structures for the two components.
Fitts' law in prehension
The issue of relevance for an evaluation of Fitts' law in
prehension is, of course, the appropriate choice of the
variables corresponding to movement amplitude and
target width in aiming movements. We propose to
adopt the following criteria: the prehension task variables should (i) relate logically to the aiming task variables, and (ii) exert similar effects on the kinematics of
the movement. Importantly, in an aiming task,
MacKenzie et al. (1987) demonstrated that manipulation of movement amplitude and manipulation of target
width lead to quite different kinematic effects, with amplitude of movement affecting primarily the acceleration
phase - its duration and the peak velocity attained
and target width affecting the duration of the deceleration phase.
In prehension, movement amplitude may be taken to
be the distance between the starting point of the hand
and the object to be grasped. A number of studies have
demonstrated that this variable indeed affects the time
taken to complete a prehension movement (Jakobson
and Goodale 1991; Marteniuk et al. 1987; Zaal and
Bootsma 1993), with larger movement amplitudes giving rise to longer movement times. Moreover, these
studies also reproduced the scaling of peak velocity to
movement amplitude as has been found in aiming.
Identification of the prehension task variable(s) corresponding to target width in aiming is somewhat less
straightforward. A number of prehension studies have
demonstrated an effect of object size 1 on movement time
(Athenes 1992; Jakobson and Goodale 1991 ; Marteniuk
et al. 1987, 1990). The most extensive study on the topic
(Marteniuk et al. 1990), using ten different object sizes
ranging from 1 to 10 cm, reported a negative linear relationship between movement time and diameter of the
disk to be grasped. Object size, however, delineates a
constraint along a dimension that can be considered to
be functionally orthogonal (Haggard 1991) to the direction of motion of the transport component and would
thus not seem to represent the same type of constraint as
does target width in aiming tasks. Interestingly, in the
majority of studies that have varied object size cylindrical object forms were used. Increasing the diameter of a
cylindrical object not only influences the minimal aperture needed to encompass the object (i.e. object size in
the strict definition used here), but also affects the extension of the object along the primary dimension of movement of the transport component. Zaal and Bootsma
(1993) have suggested that this confounding of object
size - extent orthogonal to the reach axis - and object
extension (or object width as we will call it from here on)
- extent along the reach axis may have led to premature conclusions concerning the effect of object size on
movement time. A generalisation of Fitts' law to prehension leads to the hypothesis that it is object width
(and not object size) that influences the movement time.
In the present study we set out to evaluate the effects
of object size and object width on kinematic characteristics of the prehensile movement. By using non-cylindrical objects, we could vary the two object parameters
independently. If, as we hypothesise, object width (W)
influences movement time (MT), decreasing W should
lead to an increase in MT. Object size (S), on the other
hand, is not expected to influence MT, at least not until
it comes close to the maximal aperture attainable by the
subject. 2 Using 16 objects, differing in W (4 levels) and in
S (4 levels), and two amplitudes of movement, the question of whether Fitts' law also holds in prehension can
be addressed.
Component independence
In a prehensile act the spatio-temporal unfolding of the
transport component, on which we have focussed so far,
needs to be coordinated with the spatio-temporal unfolding of the grasp component, so that the fingers may
enclose the object. Jeannerod (1981, 1984) has suggested
that object location (i.e. distance and direction in an
egocentric frame of reference) affects the transport component, while object size affects the grasp component.
Moreover, the two visuomotor channels, for the trans1Object size refers to the intrinsic object property that defines the
hand aperture needed to enclose the object (Jeannerod 1981, 1984)
2When object size approaches the maximal aperture attainable,
this implies that severe spatial constraints are imposed on the
control of direction of movement of the transport component.
Hence, for large object sizes an increase in MT may be predicted
537
p o r t and grasp c o m p o n e n t s , should be considered as
operating independently. A n u m b e r of researchers have
d e m o n s t r a t e d that m a n i p u l a t i o n of the diameter of a
cylindrical object exerts an influence on the t r a n s p o r t
c o m p o n e n t , suggesting that this constitutes a violation
of the p r o p o s e d independence of the t r a n s p o r t c o m p o nent (Ath6nes 1992; M a r t e n i u k et al. 1990; Paulignan et
al. 1991b). As we have argued above, however, the effect
of object diameter on the t r a n s p o r t c o m p o n e n t need not
be due to changes in object size, but m i g h t stem from
concurrent changes in object width.
The p e a k aperture to which the h a n d is opened during a p p r o a c h has been shown to be a linear function of
the size of the object to be grasped ( J a k o b s o n and
G o o d a l e 1991; M a r t e n i u k et al. 1990; Zaal and Bootsm a 1993), However, for similar sized objects, Wing et al.
(1986) found a dependency of p e a k hand aperture on the
accuracy of m o v e m e n t of the t r a n s p o r t c o m p o n e n t , with
less accurate m o v e m e n t s (i.e. m o v e m e n t s carried out
without visual information) giving rise to larger p e a k
apertures (see also Chieffi and Gentilucci 1993; J a k o b son and G o o d a l e 1991). Hence these results question the
independent operation of the grasp c o m p o n e n t . In the
present study we m a n i p u l a t e d b o t h object size and
width, with the latter being hypothesised to constitute a
constraint on t r a n s p o r t c o m p o n e n t m o v e m e n t accuracy. The hypothesis of c o m p o n e n t independence suggests
that only m a n i p u l a t i o n of object size should affect p e a k
h a n d aperture. If, on the other hand, b o t h the size and
the width of the object to be grasped were found to
influence the p e a k h a n d aperture attained
with b o t h
larger object sizes and larger object widths giving rise to
larger p e a k h a n d apertures this would provide further
evidence for a functional coupling of grasp and transport components.
Materials and methods
amplitude conditions, for a total of 320 experimental trials, with
the order of presentation alternating over subjects. Under each
movement amplitude condition, the 16 different objects were presented in a randomised order. For each object, the subjects practised the movement one or two times, after which ten experimental
trials were recorded.
Data was collected using an OPTOTRAK/3010 opto-electrical registration system (Northern Digital Inc, Waterloo, Ontario),
consisting of three lenses mounted within a 1.1 m long bar. The
bar was placed 2.5 m above the floor facing the subject's
workspace at an angle of 40 deg. Four IREDs (Infrared emitting
diodes) were sampled with a frequency of 200 Hz. They were
placed on (i) the target, (ii) the upper medial corner of the thumb
nail, (iii) the upper lateral corner of the index finger nail, and (iv)
above the styloid process on the radial side of the wrist. The
OPTOTRAK was pre-calibrated and gave rise to a static error
(i.e. error observed for stationary IREDs) of less than 1 mm, and
a dynamic error (i.e. error observed for moving IREDs) of less
than 2 mm.
Data analysis
High frequency noise was removed from the three-dimensional
position signals of each of the four IREDs using a second order
recursive Butterworth filter with a cutoff frequency of 10 Hz. Time
derivatives were calculated using local second order polynomials.
Resultant velocity was calculated as the square root of the sum of
the squared velocities in X, Y, and Z-directions. Initiation of
movement was taken to be represented by the first movement of
the thumb in the direction of the target object. Movement termination was indicated by the reversal of the direction of motion of
the hand? The aperture of the hand was calculated for each frame
as the 3D distance between the IREDs on the thumb and index
finger.
Results
All dependent variables were analysed with 2 (movem e n t amplitude 20 and 30 c m ) x 4 (object size 3, 5, 7,
and 9 cm) x 4 (object width 0.5, 1.0, 1.5, and 2.0 cm) repeated measures analyses of variance. Figure 1 presents
illustrative examples of h a n d t r a n s p o r t and h a n d aperture profiles as a function of time.
Subjects
Five volunteers, one male and four female aged between 21 and 27
years, participated in the experiment.
Apparatus and procedure
Subjects were seated at a table, with the underarm and hand in
line with the shoulder in the sagittal plane. Prior to each movement they assumed a standardised initial hand position, with the
thumb and the index finger gently touching. The target objects
were situated either 20 cm or 30 cm away from the starting position along the sagittal plane. The subjects were asked to pick up
the target object as quickly as possible, using an index fingerthumb opposition, bring it to the starting position and then replace it on the target position (the orientation of the object for the
next trial was thus controlled by the subject himself). Following a
'ready' signal given by the experimenter, they could start moving
whenever they wanted.
Objects used were 16 rectangular wooden blocks, varying in
size (3, 5, 7, or 9 cm) and in width (always having square sides of
0.5, 1.0, 1.5, or 2.0 cm). The objects were always picked up by
bringing the fingers into contact with the sides. Each subject performed 160 experimental trials under each of the two movement
M o v e m e n t time
Significant m a i n effects on M T were found for the factors m o v e m e n t amplitude (F1, 4 = 26.27, P < 0.01), object
width
(F3,~2=10.37,
P<0.01),
and
object
size
(F3,12 = 8.57, P < 0 . 0 1 . N o n e of the interactions reached
significance. A larger m o v e m e n t amplitude gave rise to
3We chose to operationalise movement termination as the moment of reversal of direction of motion of the hand (see also Marteniuk et al. 1990), rather than the moment when the fingers contacted the object or the moment the object was lifted off the table,
for the following reasons. (i) This operationalisation involves only
the component for which we are trying to assess the applicability
of Fitts' law, namely the transport component; (ii) it remains as
close as possible to that used in reciprocal aiming tasks; (iii) it
does not give rise to different results with respect to the influence
of W and S, but only influences the absolute magnitude of the MT,
with MTs calculated on the basis of reversal of direction of motion
of the hand being, on average, 15 ms longer than MTs calculated
on the basis of first object movement
538
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sized objects, as compared to the others (NewmanKeuls test P < 0.05). On the average MTs were 492, 501,
495, and 524 ms for the 3, 5, 7, and 9 cm sized objects,
respectively.
Calculating the index of difficulty as log2(2A/W),
where A is amplitude and W object width, a significant
fit between MT and the index of difficulty was found
(r(32)=0.678, F1,30=25.45, P<0.001, see Fig. 2). Individual subject correlations between mean MT (for the
10 trials per condition) and ID ranged between 0.39 and
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calculated as log2(2A/W), for prehensile movements directed towards the 16 different objects, placed at two different distances.
The best fit line is described by M T = 317 + 34 * I D
a longer MT, with MT being on average 472 ms for the
20 cm and 534 ms for the 30 cm movement. Decreasing
object width resulted in increasing MTs (on average 486,
487, 512, and 528 ms for W equal to 2.0, 1.5, 1.0, and
0.5 cm, respectively). Post-hoc Newman-Keuls analysis
(P < 0.05) revealed that all means were different, except
two (between W = 2 . 0 and W = l . 5 cm and between
W = 1.0 and W = 0 . 5 cm). The effect of object size was
found to be caused solely by a longer MT for the 9 cm
Total movement time was partitioned into in an acceleration phase (from movement onset until peak velocity)
and a deceleration phase (from peak velocity until reversal of direction of motion of the hand). The lengthening
of total MT with decreasing W was found to be caused
by a lengthening of the duration of the deceleration
p h a s e (F3,12 = - 1 0 . 2 8 , P < 0.01), while the duration of the
acceleration phase was not affected (see Fig. 3). The effect of object size on total MT, caused by the lengthening of MT for the 9 cm sized objects, was also found to
be the result of a lengthening of the deceleration phase
for these objects only (overall main effect of S:
f 3 j 2 = 5.68, P < 0.05; Post-hoc Newman-Keuls P < 0.05).
The effect of movement amplitude on total MT (on average 64 ms) could not be attributed to a differential
lengthening of either phase, as the effect was found to be
partitioned over the duration of the acceleration phase
(27 ms longer for the 30 cm movement) and the duration
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Fig. 6 Peak finger closing velocity as a function of object width
for the 9, 7, 5, and 3 cm sized objects
of the deceleration phase (37 ms longer for the 30 cm averaged over amplitudes and object widths). Similarly,
movement). The interactions between movement ampli- increasing object width gave rise to proportional intude, object size, and object width did not reach signifi- creases in peak hand aperture, with the best fit line being
cance.
described by peak hand aperture (mm) = 91.5 + 0.77 * W
The magnitude of the peak hand velocity reached dur- (mm), r(4) = 0.985, F1,2= 65.02, P < 0.01 (data averaged
ing approach was affected by movement amplitude over amplitudes and object sizes).
(F1.4 = 58.13, P < 0.01), with a higher peak hand velocity
As was found for peak hand aperture, peak finger
being attained for the longer movement amplitude (on closing velocity was found to depend on both object size
average, 1151 and 1352 mm s 1 for the 20 and 30 cm (F3,~2= 19.28, P<0.001) and object width (F3,12=7.73,
movement amplitudes, respectively). Peak hand velocity P < 0.01), while their interaction was not significant (alwas also affected by object size (F3,12=3.79, P<0.05) though a tendency toward significance was to be disand object width (F3,12=4.41, P<0.05). The 7 cm sized cerned: F3,12 = 1.89, P<0.10, see Fig. 6). Increasing obobject gave rise to the highest peak hand velocity, while ject size resulted in a decreasing peak finger closing vedecreasing object width appeared to systematically low- locity (on the average 526, 490, 426, and 294 mm s-a for
er peak hand velocity (see Fig. 4). None of the interac- the 3, 5, 7, and 9 cm sized objects, respectively), while
tions reached significance.
increasing object width led to increasing peak finger
closing velocities (on average, 344, 409, 471, and
514 mm s-1 for the 0.5, 1.0, 1.5, and 2.0 cm object widths,
Grasp characteristics
respectively).
The magnitude of the peak hand aperture attained durZaal and Bootsma (1993) have suggested that peak
ing approach was found to depend on both object size finger closing velocity is a function of the distance to be
(F3,12 = 107.74, P < 0.001) and object width (F3.~2= 18.75, covered - calculated as peak hand aperture minus obP<0.001), while their interaction was not significant ject size similar to the scaling of peak hand velocity
(see Fig. 5). Increasing object size led to a proportional and movement amplitude discussed above. When disincrease in peak hand aperture, with the best fit line tance to be covered was calculated for all 32 combinabeing described by peak hand aperture (ram)= 60.2 + tions of movement amplitude, object size, and object
0.68 * S (mm), r(4)=0.998, F1,2=401.85, P<0.001 (data width, a strong linear relation was found to exist (see
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Fig. 7 Peak finger closing velocity as a function of distance to be
covered, calculated as peak hand aperture minus object size, for
prehensile movements directed towards the 16 different objects,
placed at two different distances
Fig. 7), with the best fit line being described by peak
finger closing velocity (mm s-1)=-94.5+ 12.9 * [peak
hand aperture - object size] (mm), r(32)=0.978,
fl,3o = 672.33, P < 0.001.
Discussion
Contrary to what has been suggested in the literature,
the results of the present study indicate that the size of
the object to be grasped does not systematically influence the time taken to complete a prehensile movement.
The reciprocal relation, reported by Marteniuk et al.
(1990), between the diameter of a cylindrical object and
MT most probably resulted from concurrent changes in
object width (i.e. surface area available for placement of
the fingers), as the present study has demonstrated that
smaller object widths (while maintaining constant object size) gave rise to longer MTs. This effect on MT is
brought about by a lengthening of the duration of the
deceleration phase, similar to the effect of decreasing
target width in aiming (MacKenzie et al. 1987). The latter observation, together with the fact that in prehension object width would appear to impose the same type
of constraint as does target width in aiming, leads us to
suggest that object width may be considered to be the
task variable corresponding to target width in aiming.
Because in prehension, as in aiming, movement amplitude affects MT while giving rise to a scaling of peak
velocity, the two task variables of interest for an evaluation of Fitts' taw in prehension have been identified. The
results of the present study indicate that in prehensile
movements the time taken to pick up an object indeed
increases as a linear function of the index of difficulty,
calculated as log2(2A/W), where A is movement amplitude and W target object width. The strength of the
relationship found (r(32)= 0.678) is somewhat less than
that reported for aiming movements (e.g. Fitts 1954;
Fitts and Peterson 1964; MacKenzie et al. 1987), as is
the effect of increasing the index of difficulty on MT (e.g.
the slope, 34 ms/bit). Nevertheless, the formal descrip-
tion of the speed-accuracy trade-off that has been found
to hold for simple aiming movements may be generalised to the more complex task of prehension. Many of
the manipulations that have been reported to influence
movement time in prehension tasks can thus be understood as stemming from the same underlying mechanism. For instance, the increase in MT, reported by
Marteniuk et al. (1990), for disks of a smaller diameter
can be viewed as a result of decreasing object width. The
pro-active effect on the approach phase of the type of
action to be performed with the object after it has been
acquired, reported by Marteniuk et al. (1987), can also
be understood along similar lines. Picking up an object
to place it in a tight-fitting well was shown to lead to
longer MTs (caused by a lengthening of the deceleration
phase) than picking up the same object to throw it in a
nearby box. We suggest that accuracy of the grip required, i.e. the precision of placement of the fingers, differed between these two conditions, with a smaller effective object width imposed for objects that needed to be
fitted into the well. Finally, the lengthening of MT as a
result of increasing the constraints on the motion of the
target object after acquisition, as reported by Wallace
and Weeks (1988), can also be understood as resulting
from decreasing effective target object width.
In prehension, transporting the hand needs to be
complemented with a preshaping of the fingers in anticipation of contact 4 (Jeannerod 1984). The size of the
object to be grasped does not by itself seem to influence
kinematic characteristics of the transport component,
although for sizes that demand a near-maximal hand
aperture (i.e. for the 9 cm sized objects in the present
experiment) an increase in MT can be observed that
results from the fact that severe spatial constraints now
come into operation for the control of direction of movement of the hand. The magnitude of the peak hand aperture attained, on the other hand, is adapted very accurately to the size of the object to be grasped (Athenes
1992: r(5)=1.00; Marteniuk et al. 1990: r(10)=0.99;
Zaal and Bootsma 1993: r(3)=1.00; present study:
r(4) = 1.00), although the slope of the relation between
peak hand aperture and object size is always found to be
smaller than unity (0.68 in the present study).
Peak hand aperture was, however, not only influenced by object size but also by object width, with larger
object widths being associated with larger peak apertures. As intimated in the introduction this constitutes a
violation of the assumption of independence of transport and grasp components. The data suggest the following interpretation: Increasing object width leads to a
lowering of the accuracy demands for the amplitude of
transport component movement, allowing a faster
movement to emerge. The lesser accuracy demanded
from the transport component, however, concurrently
gives rise to increased directional variability. This in4While this is, of course, true for all grasp formations, the current
research and hence its discussion only addresses the preshaping
for the precision grip
541
creased directional variability of the transport component is compensated for by a larger peak aperture attained during approach (grasp component), in line with
the suggestion of Wing et al. (1986) and Wallace and
Weeks (1988). In such a way the acquisition of the object
is subserved by two concurrent mechanisms, which
might explain the lesser slope found in the relation between MT and index of difficulty in prehension as compared to aiming. The velocity with which the hand is
closed following the attainment of peak hand aperture
seems to be a function of the distance to be covered only
(see Fig. 7). Thus the way in which the hand is closed
resembles the way in which the hand is transported toward the object.
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