Scale effects in steering law tasks.
Interaction tasks on a computer screen can technically be scaled to a much larger or much smaller sized input control area by adjusting the input device's control gain or the control-display (C-D) ratio. However, human performance as a function of movement scale is not a well concluded topic. This study introduces a new task paradigm to study the scale effect in the framework of the steering law. The results confirmed a U-shaped performance-scale function and rejected straight-line or no-effect hypotheses in the literature. We found a significant scale effect in path steering performance, although its impact was less than that of the steering law's index of difficulty.  We analyzed the scale effects in two plausible causes: movement joints shift and motor precision limitation. The theoretical implications of the scale effects to the validity of the steering law, and the practical implications of input device size and zooming functions are discussed in the paper.
INTRODUCTION
This research addresses the following questions: Can we successfully
accomplish the two steering tasks in Figure 1 in the
same amount of time? Can a large input device be substituted
with a small one without significantly impacting user
performance? Does size matter to input control quality? Can
a small-sized input area be compensated by higher control
gain (i.e. control-display ratio)? What are the scale effects
in movement control, if any? How sensitive are the scale
effects?
There are many practical reasons to ask these questions. One
concerns the miniaturization of the computing devices. We
are indeed stepping into the long-awaited era of inexpensive,
powerful and portable computers. In the rush towards minia-
turization, input devices are expected to adapt to the system
physical constraints: trackballs now come in a much smaller
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SIGCHI'01, March 31-April 4, 2001, Seattle, WA, USA.

Figure

1: The two circular tunnels are equivalent in
steering law difficulty but they differ in movement
scale. Does it take the same amount of time to steer
through the two tunnels?
diameter than before and touchpads are designed with a fairly
small contact surface, for instance. It is not clear whether
these reduced-size input devices still maintain the same level
of performance as their predecessors.
If we push the question of scale to the extreme, the answer
is obvious: of course size matters. Humans can not do well
in movement scales that are either greater than their arm's
reach or smaller than their absolute motor precision toler-
ance. Within these extremes, however, the question is much
more difficult to answer.
RELATED WORK AND LITERATURE
One might imagine that the scale effects in input control
should be a well documented topic in the human-machine
system literature. In reality, however, the results were scattered
and controversial. The scale effects were often studied
and reported under two related concepts: control gain and
control-display (CD) ratio. When the display (output) size
is fixed, these two concepts correspond to control movement
scale. Major handbooks [5, 6, 15] tend to suggest that human
performance is an inverted U-shaped function of control gain
or CD ratio: it reaches the highest point in a medium range
of the control gain and deteriorates in both directions away
from this range. Such a U function was usually found in studies
that involved control systems with higher order dynamics
(e.g. rate control system, or systems with inertia or lag).
Hess [11] is a common source regarding the U-shaped func-
tion. In his experiment, subjects performed tracking tasks by
manipulating a near-isometric joystick in rate control. A U-shaped
function was found between participants' subjective
rating and the system control gain 1 .
Gibbs [9] provided the most comprehensive set of data on
control gain. He studied control gain in both positional and
rate control systems and found that the target acquisition time
follows the function:
0:02G 0:106
0:003
G
(1)
where G is the control gain and L is the system lag. The
function produced U-shaped curve when L was greater than
zero. When L was zero (no system lag), the performance-
gain function produces a straight line - the greater the gain
was (which means the smaller the movement scale was), the
worse the performance was.
Buck [7] called into question the views on the significance
of CD gain. Based on results from a target alignment exper-
iment, he argued that target width on both the control device
and the display were important, but their ratio was not.
Arnaut and Greenstein [3] conducted a rather convoluted study
in which control input magnitude (movement scale), display
output magnitude, display target width, control target
width and Fitts' index of difficult were varied in two experi-
ments. They found that a greater movement scale increased
gross movement time but decreased fine adjustment time.
Gross and fine movements were defined by the initial entry
point in the target. The total completion time, in the case
of a tablet, was a U-shaped function. In the case of a track-
ball, however, the greater movement scale increased the total
completion time monotonically. They concluded that a combination
of gain and Fitts' index of difficulty could be a more
useful predictor than either of them alone.
Jellinek and Card studied users' performance as a function
of the control gain in a computer mouse [12]. They found
a U-shaped performance-gain function, but argued against
its status as a basic human performance characteristic. They
believed the performance loss in case of a large control gain
was due to the loss of relative measurement resolution (i.e. a
quantization effect). If there were not a resolution limit, and
as long as the control gain was in a "moderate" range, a user's
performance should have stayed constant, so they argued.
It is necessary to clarify that the most basic construct, in our
view, should be the "control movement scale". Other vari-
ables, such as control gain and CD ratio, are derivative or sec-
ondary. We think the concept of C-D ratio (or gain) in itself
is partially responsible for the contradictions in the literature.
By definition, C-D ratio is a compound variable between the
display scale and the control movement scale. The same relative
C-D ratio could have very different implications on input
1 Note that the notion of control gain is related but not always interchangeable
with movement scale or C-D ratio. Control gain, a term originated
in feedback control theory, exists in both zero order (position control)
and higher order systems. Control display ratio and movement scale only
exist in position control systems. For example, since a force joystick was
used, there was no control movement scale per se in Hess' study [11].
control, depending on the display size. Control movement
scale, on the other hand, is absolute and can be compared to
human body measurements. Furthermore, between the display
and the control movement scale, the former is more relevant
to perception and the latter is more directly relevant to
control performance.
One implication of movement scale is the limb segments (or
motor joints) involved in executing a task. Although limb
segments rarely work in isolation, a large movement (e.g.
m), tends to be carried out primarily by the arm (shoulder
and elbow joints), a medium range by the hand (wrist joint),
a small range (e.g. 10 mm) by the fingers. Langolf et al. [13]
demonstrated that Fitts' law gave different slopes and intercepts
in finger, wrist, and forearm scales 2 . They came to
the conclusion that the smaller the scale, the greater the aiming
performance, which in terms of primary limb segments
means that:
fingers > wrist > forearm (2)
This performance order was confirmed by Balakrishnan et
al. [4], who found that a combined use of multiple fingers
resulted in higher performance than other limb segments.
However they noted that "the finger(s) do not necessarily perform
better than the other segments of the upper limb" when
a single finger was involved 3 .
In a six degrees of freedom docking task, Zhai et al. [16]
showed that relative performance of 6-DOF devices did depend
on the muscle groups used. More specifically, they
demonstrated that the user performance was superior with the
fingers involved (together with the wrist and the arm) in operating
the control device than without (wrist and arm only).
It is natural to ask the question of scale in light of the well-known
Fitts' law [8, 14]), which predicts that the time T to
select a target of width W that lies at distance A is:
A
where a and b are empirically determined constants. The
logarithmic transformation of the ratio between A and W is
called the index of difficulty of the task. Some researchers
argue that control scale should not matter in view of Fitts'
law [12]. If a reaching task is scaled by a factor of two, both
the distance A and the width W will be twice as large and
hence cancel each other in the index of difficulty measure.
On the other hand, the impact of scale could be reflected in a
and b, as shown in [13].
The validity of index of difficulty as the sole determinant of
aimed movement has been recently called into question by
Guiard [10]. He argued that the way Fitts' law was studied
and applied in the past was problematic; both difficulty
and scale should be viewed as the basic dimensions of aimed
movement.
Some objections have been raised about this study, suggesting a faulty
experimental design [4]. But the finding that the index of performance varies
with movement scale is widely accepted.
3 Note that in the Balakrishnan study, however, the finger movement was
controlled in the lateral direction, which does not occur frequently in natural
movement
We recently established a movement law that models human
performance in a different class of tasks: trajectory-based
tunnel steering [1]. It is both theoretically and practically
necessary to study the scale effects in relation to the steering
law. Theoretically, it is important to investigate how the
steering law prediction is affected by movement scale. Prac-
tically, the steering law may serve as a platform based on a
new class of tasks for studying the control movement scale
effects, which may guide the design and selection of inter-action
devices and techniques. Some input devices, such as
tablet, are primarily designed for trajectory-based tasks.
To move a stylus tip or a cursor through a tunnel or path (see

Figure

1 for examples) without crossing the boundaries is a
steering task. One common steering task in HCI is traversing
multi-layered menus. In a recent study [1], we proposed and
validated a theoretical model for the successful completion
of steering tasks. This model, called the steering law, comes
in both an integral and a local form.
Integral form
The integral form of the steering law states that the difficulty
for steering through a generic tunnel C can be determined
by integrating the inverse of the path width along the tunnel
(see [1] for details). Formally, we define the index of difficulty
ID C for steering though C by:
Z
ds
where the integration variable s stands for the curvilinear abscissa
along the path. As in Fitts' law, the steering task difficulty
ID C predicts the time T needed to steer through tunnel
C in a simple linear form:
where a and b are constants. Finally, by analogy to Fitts'
law, we define the index of performance IP in a steering task
by This quantity is usually used for comparing
steering performance between experimental conditions.
The steering law also has a local formulation, which states
that the instantaneous speed at any point in a steering movement
is proportional to the permitted variability at that point:
where v(s) is the velocity of the limb at the point of curvilinear
abscissa s, W (s) is the width of the path at the same
point, and  is an empirically determined time constant.
Types of tunnels
Equation 4 allows the calculation of steering difficulty for a
wide range of tunnel shapes. In [1], three shapes were tested:
straight, narrowing and spiral tunnels. It was suggested [2]
that the properties of a great variety of tunnel shapes could be
captured by two common tunnel shapes: a linear tunnel and
a circular one (Figure 2). For both of the two steering tasks,
the steering law can be reduced to the following simple form:
where A is the tunnel length in the case of linear tunnels
and the perimeter of the center circle in the case of circular
tunnels (Figure 2). In both cases W stands for the path width.
a and b are experimentally determined constants. They were
found to be different for linear and circular tunnels, due to
the very different nature of steering in the two cases.
PSfrag replacements
A
(a) Linear tunnel
PSfrag replacements
A
(b) Circular tunnel

Figure

2: Two steering tasks
Influence of scale
One will notice from Equation 7 that the argument against
scale effects based on Fitts' law can also be found here: in
both the linear circular path, the steering difficulty depends
on the length/width ratio, such that dividing both the length
and the width of the steering path by a factor k gives the same
index of difficulty. In other words, although the speed in a
tunnel of width W
k will be k times slower than in a tunnel of
width W , this decrease in speed should be fully compensated
by the shortened steering length by the same ratio, such that
the movement time remains the same.
It is thus pertinent to ask whether the steering law still holds
over very different scales and, if not, how significant the scale
impact is.
The experimental task was steering through linear and circular
tunnels at five different scales. The scales were chosen
to cover a broad range of movement amplitudes so as to
guarantee that different combinations of motor joints were
tested. The input device used in the experiment was a graphics
tablet, which, in comparison to other input devices, provided
the most direct interaction, hence allowing us to focus
on more fundamental human performance characteris-
tics. Depending on the movement scale the movement of a
tablet stylus may be controlled by the fingers, the wrist, or the
arm joints. When operating the stylus, multiple fingers work
in conjunction, which should be much better than a single
finger working in isolation [4].
Ten volunteers participated in the experiment. All were right-handed
and had no or little experience using graphics tablets.
Apparatus
The experiment was conducted on a PC running Linux, with
a 24-inch GW900 Sony monitor (19201200 pixels resolu-
tion), and equipped with a Wacom UD-1218E tablet (455
303 mm active area, 12761277 dpi resolution). The computer
system was sufficiently fast that the input or feedback
lag was not perceptible. The size of the active view of the
monitor was set exactly equal to the size of the active area of
the tablet, which gives an approximate 107100 dpi screen
resolution. Different portions of the tablet area were mapped
onto the screen depending on the movement scale currently
being tested (mappings are detailed in the design section).
All experiments were done in full-screen mode, with the background
color set to black.
Procedure
Subjects performed two types of steering tasks: linear tunnel
and circular tunnel steering (Figure 2). At the beginning of
each trial, the path to be steered was presented on the screen,
in green color. After placing the stylus on the tablet (to the
left of the start segment) and applying pressure to the stylus
tip, the subject began to draw a blue line on a screen, showing
the stylus trajectory. When the cursor crossed the start
segment, left to right, the line turned red, as a signal that the
task had begun and the time was being recorded. When the
cursor crossed the end segment, also left to right, all drawings
turned yellow, signaling the end of the trial. Crossing
the borders of the path resulted in the cancellation of the trial
and an error being recorded. Releasing pressure on the stylus
after crossing the start segment and before crossing the
second, but without crossing the tunnel border, resulted in
an invalid trial, but no error was recorded 4 . Subjects were
asked to minimize errors. Finally, linear tunnels were all oriented
horizontally and were to be steered left to right; as for
circular steering, it had to be done clockwise.
Design
A fully-crossed, within-subject factorial design with repeated
measures was used. Independent variables were movement
scale detailed below), test phase
first and second block), task type linear and circular
tunnels), tunnel length
width on the screen pixels). The tunnel
lengths and widths define 6 different IDs, ranging from 4 to
33. The order of testing of the five scales (S conditions) was
balanced between five groups of subjects according to a Latin
square pattern. Within each S condition, subjects performed
a practice session, consisting of 1 trial in each of the 6 ID
conditions, in both linear and circular steering. The practice
session was followed by two identical sets of the 12 T -A-
conditions presented in random order, during which data
was actually collected. Subjects performed 3 trials in each
S-P -T -A-W condition.
The five scales were chosen considering the maximummove-
ment amplitude for each arm segment and in order to cover
the maximum number of motor "strategies". They were:
very large scale (S =1): the whole active area of the tablet
(455303 mm) was used, which corresponded to standard
4 Subjects sometimes released the pressure by mistake, but this could not
be attributed to the constraints imposed on movement variability.
A3 format. This scale involves movement amplitudes typically
around 20 cm, which require mainly forearm movements

large scale (S =2): the active tablet area was 227151 mm,
which was one half of the tablet in both dimensions. This
was equivalent to a A5-sized tablet. In this scale, movement
amplitudes are typically around 10 cm, which require mainly
wrist movements but involve to a certain extent the use of the
forearm.
medium scale (S =4): with an active area of 11476mm
of the tablet), movement amplitudes in this scale condition
are around 5 cm, which require mainly finger and wrist
movements and prevent the use of the forearm. This scale
was somewhat equivalent to a A6-format tablet.
small scale the tablet active area size was 57
of the tablet). Typical movement amplitudes in
that condition are ' 2 cm, which require finger movements
and to some extent wrist movements. This was the size of a
touchpad used in some notebook computers.
very small scale active area of
the tablet ( 1 =16 of the tablet) implied very small movements
amplitudes, around 1 cm, which require finger movements
exclusively, with the wrist and forearm joints stabilized on
the tablet surface. Note that this smallest scale tested was
still orders of magnitude above the tablet resolution, hence
preventing the possible machinery quantization effect in previous
studies.

Figure

3 illustrates the relative size of active areas of the
tablet for the different movement scales. The outermost box,
labeled S=1, corresponds to the whole tablet active area.
PSfrag replacements

Figure

3: Relative active tablet sizes at different scales

Table

1 shows the movement amplitudes and path widths in
input space for each scale condition: for instance, the tunnel
to be steered on the graphics tablet when S =4, W=60 and
A=250 has a width of 5 mm and a length of 14:8 mm.
Finally, in light of the movement scale vs. C-D ratio and display
scale discussion, the visual stimuli were kept in the same
size over all five movement scales, so that no visual perception
effect could influence the results. The experimental software
was identical for all scales; only the tablet scale settings
were changed.

Table

1: Movement amplitudes and path widths in input
space for each scale condition (in millimeters).
The results of the experiment include steering time, steering
speed and error rates.
Steering time
As expected, movement amplitude and tunnel width significantly
influenced steering time
and F there was also a
strong interaction between movement amplitude and tunnel
width which is consistent with
the fact that the steering time depends on the ratio of amplitude
and width. As in [2], steering type (linear vs. circular)
proved to be also a significant factor influencing steering time
As for the studied variable, movement
scale, it had a significant influence on steering performance
While the significant impact
of test phase shows a strong learning
effect, the non-significant interaction between test phase
and movement scale suggests that the
influence of scale is likely not to vary much with practice.
Paired t-tests between scale levels classified the scales into
three groups. The first group includes scales 2 and 4, the second
includes scales 1 and 8, and the last one is only composed
of scale 16. The differences were insignificant between
the two scales of the first group (p > :08) and the
scales of the second group (p > :31). The scales of the
first group outperformed significantly the scales of the second
group (with p< :0001 for all compared pairs), while the
last group is outperformed by both the first group (p< :0001)
and the second one (p< :0001). The ranking between movement
scales in terms of time performance is:
This grouping of scales and the ranking between groups held
in both linear and circular steering. Figure 4 summarizes the
average steering time depending on the movement scale and
steering task.
There was also a strong interaction between movement scale
and tunnel type which suggests that
the circular tasks were more sensitive to changes in movement
scale than the linear ones (see Figure 4). We also found
a significant interaction between scale and amplitude
3:2, p< :01), as well as between scale and width
:0001). The movement scale effects was greater when
the movement amplitude was greater or the tunnel width was
Scale
Steering
time
linear tunnel
circular tunnel

Figure

4: Steering time as a function of scale
smaller (Figure 5). This was especially true for the scale-16
conditions: very long amplitudes or very narrow tunnels in
this case were very difficult to steer, such that often subjects
could achieve the trial only after a couple of attempts (see error
rates analysis further). However, a significant interaction
between test phase and movement amplitude
p< :001) suggests that subjects tend to deal with long amplitudes
much better with practice.
As for the fitness to the steering law model, the integral form
of the steering law [1] proved to hold at all studied scales
with very good regression fitness (see Figure 6). The models
of steering time were, for linear steering (in ms):
and for circular steering:
The slope of linear regressions was significantly influenced
by tunnel type movement scale
:05). The intercept was not significantly
affected by tunnel type or by movement
scales
were rather small comparing to the total times involved,
which is consistent with previous results [1, 2].
Similar to the results found on steering times, the relationship
between the steering law index of performance and the
movement scale was an (inverted) U-shaped function (Fig-
ure 7), with the best performance in the medium scale 2 and
Movement amplitude
Steering
time
(ms)
scale 1
scale 2
scale 4
scale 8
scale
circular steering
linear steering
(a) Interaction between movement amplitude and movement scale
Tunnel width
Steering
time
(ms)
scale 1
scale 2
scale 4
scale 8
scale
circular steering
linear steering
(b) Interaction between tunnel width and movement scale

Figure

5: Steering time against scale depending on
movement amplitude and tunnel width
slightly higher than scale 4 in linear steering)
and lower performance in scale 1 and 8, and lowest in scale
16. All scales resulted in almost equivalent performance for
very easy tasks, but significant differences appeared for very
difficult tasks; this was characterized by the statistical interaction
between scale and index of difficulty of the tasks
In conclusion, the time performance was the highest when
the movement scale was between scale 2 and scale 4. In
terms of tablet size, this corresponds to A4/A5-sized tablets.
In terms of motor joints involved, it was when the wrist and
the fingers were the primary movement carriers. A3-sized
tablets seemed to be too large and require too much movement
efforts, while tablets smaller than A6 format were likely
to amplify noise beyond reasonable rates.
Steering
time
(ms)
scale 1
scale 2
scale 4
scale 8
scale
(a) Linear steering
Steering
time
(ms)
scale 1
scale 2
scale 4
scale 8
scale
(b) Circular steering

Figure

Steering time against ID
Errors
Besides the expected main effects on error rates of movement
amplitude
scale had a strong influence on error
occurrence
steering resulted in more errors than linear steering
95, p < :0001). A significant interaction between scale and
tunnel type shows that the number
of errors increases much faster for circular steering than
for linear steering when the movement scale decreases (see

Figure

8). Finally interactions between movement scale and
width movement
scale and movement amplitude
that it is more likely to make errors in long or narrow
tunnels when the tablet is very small: in the scale-16 con-
ditions, natural tremor and biomechanical noise was greatly
amplified such that subjects systematically made a few failed
trials in a sequence, even though they did their best.
scale
IP
(bits/s)515 linear tunnel
circular tunnel

Figure

7: Index of performance against scale
Scale
Average
number
of
linear tunnel
circular tunnel

Figure

8: Average number of errors in each scale
To conclude, the smaller the scale, the higher the error rates.
Considering that the optimal scales were 2 and 4 for time
performance, it appeared that the scale-2 condition had the
best overall performance while considering both time performance
and error rate.
DISCUSSION AND CONCLUSION
Movement scale, control gain, control-display ratio and motor
joints performance differences, are a set of related concepts
in input control literature without consistent conclu-
sions. In terms of movement scale or control gain effects,
some researchers found a U-shaped function [11, 3]; others
straight linear function [9], and yet others did not believe gain
or scale should matter much [12, 7]. Traditionally these issues
have been studied in the framework of target acquisition
tasks. We have conducted a systematic study on these issues
in a new paradigm - the steering law. Furthermore, we focused
on the most fundamental concept of them all - control
movement scale.
Our results supported the U-shaped performance-scale func-
tion: scale does matter. The U-shaped function is easily plausible
in the two extrema: too large a scale is beyond the arm's
reach and too small a scale is beyond motor control precision.
But even within the "moderate" range we tested, the U shape
was still clearly demonstrated. The cause for the U-shaped
function in this range is likely to be twofold: motor joints
shift and the human motor precision limitation.
The best performance appeared in the middle range (scale 2
and 4), when the movements were carried out by all parts of
the upper limb (arm, hand, and finger), although the arm's
role might be lesser than the hand and finger. In this range,
the steering IP was (in bits=ms) 1=62 and 1=74 for linear
steering; and 1=179 and 1=174 for circular steering. On the
larger scale side, when the movements were primarily carried
out by the arm movement, steering performance dropped to
1=81 for linear and 1=200 for circular steering.
On the smaller scale side (scale 8 and 16), when the movements
were carried out mostly by fingers, the performance
also dropped (to 1=85 and 1=227 for scale 16). However,
we can not make a conclusion that the fingers are inferior,
because the other factor, motor control precision limitation,
was increasingly more limiting as the movement scale de-
creased. This was clearly demonstrated by the number of
errors (failed attempts to complete the entire steering path)
shown in Figure 6: participants increasingly "accidentally"
moved out of the tunnel. Note that because we maintained
the same visual display size for all scale conditions, the error
had to be on the motor precision side.
The more theoretical implication of the results pertains the
validity of the steering law [1]. Similar to Fitts' law, the steering
law states that the difficulty of movement lies in relative
accuracy. The two steering tasks in Figure 1 are exactly the
same in steering law terms. This study shows that while the
fitness of the steering law held very well in all levels tested,
the movement scale does have an impact on steering law's
index of performance. A steering law model with strictly the
same index of performance is only valid if the scale does not
vary so widely that the motor joint combination shift fundamentally
or the control precision becomes the primary limiting
factor.
It is interesting to realize that the impact of scale is much
less significant than the steering law's index of difficulty. For
example, the range of scale we tested varied by a factor of
16, but the largest steering time difference was only 17% -
an impact equivalent to only 17% change of the steering ID
(either 17% longer or 15% narrower tunnel).
There are also many practical implications in our results. For
example, the size of a computer input device (tablet or mouse
and its pad) should be such that the fingers, wrists and to a
lesser extent forearm are all allowed in the operation. Another
practical implication lies in the design and use of zooming
interface. In fact users often unconsciously make effort
to stay at the bottom of the U-shaped scale function by zooming
up when their motor precision limits their performance,
and zooming down when too much of the movement had to
be carried out by large arm movement. How we can deliberately
apply the findings in the present study to assist zooming
is an interesting future research issue.
Based on the results of this study, we can begin to answer
some of the questions we raised at the beginning of this paper
on a more scientific ground. First, we found that device
size and movement scale indeed affects input control quality:
people do not accomplish the two steering tasks in Figure 1
in the same amount of time. Furthermore, small scale tends
to be limited by motor precision, large scale limited by the
arm dexterity, but scale in the medium range does not significantly
influence performance. Consequently, substituting
a large input device with a small one will not significantly
impact user performance if there is no fundamental change
in the muscle groups involved; but it will if the substituted
input device is too small that human motor control precision
becomes a limiting factor. The scale effects are also not very
sensitive in comparison to the steering law index of difficulty
effects (e.g. change the tunnel width while keeping the same
length). Finally, the question with regard to control gain or
control-display ration is ill-posed, because what matters is
the control movement scale: for the same movement scale,
the appropriate control gain depends on the display size.
In summary, we have 1) introduced a new task paradigm to
study scale effect; 2) contributed to the literature of scale ef-
fect, confirming the U-shaped function and rejecting straight-line
or no-effect hypotheses; improved the understanding
of the steering law; guidelines to practical input
design and selection issues.

ACKNOWLEDGMENTS

We would like to thank Fr-ed-eric Lepied of the XFree86 team
for his advice on the Wacom tablet configuration.



--R

Beyond Fitts' law: models for trajectory
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Is display/control gain a useful metric for optimizing an interface?
Performance differences in the fingers

Engineering data com- pendium: Human perception and performance
Motor performance in relation to control-display gain and target width
The information capacity of the human motor system in controlling the amplitude of move- ment
Controller design: Interactions of controlling limbs
Difficulty and scale as the basic dimensions of aimed movement.
Nonadjectival rating scales in human response experiments.
Powermice and user per- formance
An investigation of Fitts' law using a wide range of movement amplitudes.
Fitts' law as a research and design tool in human-computer interaction
Human Factors Design Handbook.
The influence of muscle groups on performance of multiple degree-of- freedom input
--TR
Powermice and user performance
Is display/control gain a useful metric for optimizing an interface?
The influence of muscle groups on performance of multiple degree-of-freedom input
Beyond Fitts'' law
Performance differences in the fingers, wrist, and forearm in computer input control
Performance evaluation of input devices in trajectory-based tasks

--CTR
Mary Czerwinski, Humans in human-computer interaction, The human-computer interaction handbook: fundamentals, evolving technologies and emerging applications, Lawrence Erlbaum Associates, Inc., Mahwah, NJ, 2002
Robert Pastel, Measuring the difficulty of steering through corners, Proceedings of the SIGCHI conference on Human Factors in computing systems, April 22-27, 2006, Montral, Qubec, Canada
Sergey Kulikov , I. Scott MacKenzie , Wolfgang Stuerzlinger, Measuring the effective parameters of steering motions, CHI '05 extended abstracts on Human factors in computing systems, April 02-07, 2005, Portland, OR, USA
Yves Guiard , Michel Beaudouin-Lafon, Target acquisition in multiscale electronic worlds, International Journal of Human-Computer Studies, v.61 n.6, p.875-905, December 2004
Raghavendra S. Kattinakere , Tovi Grossman , Sriram Subramanian, Modeling steering within above-the-surface interaction layers, Proceedings of the SIGCHI conference on Human factors in computing systems, April 28-May 03, 2007, San Jose, California, USA
Yves Guiard , Renaud Blanch , Michel Beaudouin-Lafon, Object pointing: a complement to bitmap pointing in GUIs, Proceedings of the 2004 conference on Graphics interface, p.9-16, May 17-19, 2004, London, Ontario, Canada
Marcelo Mortensen Wanderley , Nicola Orio, Evaluation of Input Devices for Musical Expression: Borrowing Tools from HCI, Computer Music Journal, v.26 n.3, p.62-76, Fall 2002
Tue Haste Andersen, A simple movement time model for scrolling, CHI '05 extended abstracts on Human factors in computing systems, April 02-07, 2005, Portland, OR, USA
Ken Hinckley, Input technologies and techniques, The human-computer interaction handbook: fundamentals, evolving technologies and emerging applications, Lawrence Erlbaum Associates, Inc., Mahwah, NJ, 2002
Carl Gutwin , Amy Skopik, Fisheyes are good for large steering tasks, Proceedings of the SIGCHI conference on Human factors in computing systems, April 05-10, 2003, Ft. Lauderdale, Florida, USA
David Ahlstrm, Modeling and improving selection in cascading pull-down menus using Fitts' law, the steering law and force fields, Proceedings of the SIGCHI conference on Human factors in computing systems, April 02-07, 2005, Portland, Oregon, USA
Taher Amer , Andy Cockburn , Richard Green , Grant Odgers, Evaluating swiftpoint as a mobile device for direct manipulation input, Proceedings of the eight Australasian conference on User interface, p.63-70, January 30-February 02, 2007, Ballarat, Victoria, Australia
Shumin Zhai , Johnny Accot , Rogier Woltjer, Human action laws in electronic virtual worlds: an empirical study of path steering performance in VR, Presence: Teleoperators and Virtual Environments, v.13 n.2, p.113-127, April 2004
Xiang Cao , Shumin Zhai, Modeling human performance of pen stroke gestures, Proceedings of the SIGCHI conference on Human factors in computing systems, April 28-May 03, 2007, San Jose, California, USA
input device;movement scale;C-D ratio;joints;elbow;motor control;finger;control gain;steering law;wrist;device size