University of Iowa
Iowa Research Online
Theses and Dissertations
Spring 2014
Starting hand position effects on arm configuration
for targeted reaching movements
Steven Ewart
University of Iowa
Copyright 2014 Steven Ewart
This thesis is available at Iowa Research Online: http://ir.uiowa.edu/etd/4625
Recommended Citation
Ewart, Steven. "Starting hand position effects on arm configuration for targeted reaching movements." MS (Master of Science) thesis,
University of Iowa, 2014.
http://ir.uiowa.edu/etd/4625.
Follow this and additional works at: http://ir.uiowa.edu/etd
Part of the Systems and Integrative Physiology Commons
STARTING HAND POSITION EFFECTS ON ARM CONFIGURATION FOR
TARGETED REACHING MOVEMENTS
by
Steven Ewart
A thesis submitted in partial fulfillment
of the requirements for the Master of
Science degree in Health and Human Physiology
in the Graduate College of
The University of Iowa
May 2014
Thesis Supervisor: Professor Warren Darling
Graduate College
The University of Iowa
Iowa City, Iowa
CERTIFICATE OF APPROVAL
_______________________
MASTER'S THESIS
_______________
This is to certify that the Master's thesis of
Steven Ewart
has been approved by the Examining Committee
for the thesis requirement for the Master of Science
degree in Health and Human Physiology at the May 2014 graduation.
Thesis Committee: ___________________________________
Warren Darling, Thesis Supervisor
___________________________________
Kelly Cole
___________________________________
Clayton Peterson
To those that made this possible
ii
“…even in man the crown of life is an action, not a thought…to move things is all that
mankind can do…for such the sole executant is muscle, whether in whispering a syllable
or felling a forest.”
Sir Charles S. Sherrington
Linacre Lecture, 1924
iii
ACKNOWLEDGMENTS
I would like to recognize the Department of Health and Human Physiology at the
University of Iowa for their involvement and support. I would also like to thank my
fellow graduate student colleagues during my time as a graduate student. Special thanks
are extended to Stephanie Hynes for her time with software help and getting the
experiment off the ground. I would also like to thank Dr. Clayton Peterson for setting the
programing groundwork required. Finally I would like to thank Dr. Warren Darling for
advising me and for his invaluable input, supervision, and many revisions of this
document, without which this study would not have been possible.
iv
TABLE OF CONTENTS
LIST OF FIGURES ........................................................................................................... vi
INTRODUCTION ...............................................................................................................1
MATERIALS AND METHODS .........................................................................................7
Subjects .............................................................................................................7
Experimental Setup ...........................................................................................7
Experimental Protocol ....................................................................................10
Data Analysis ..................................................................................................14
RESULTS.. ........................................................................................................................20
Upper Limb Angles and Paths of the Index Finger ........................................20
Profile of Quick Reaches Compared to Comfortable Reaches .......................27
Index Fingertip Endpoint Error Volume and Variability of Angle of
Inclination .......................................................................................................27
Mean Angles of Inclination of the Upper Limb in Different Reaching
Conditions .......................................................................................................29
Variability in Angles of Inclination of the Upper Limb .................................31
DISCUSSION ....................................................................................................................35
Comfortable Speed Movements .....................................................................35
Quick Reaching Movements...........................................................................37
Reaches to Grasp an Object ............................................................................39
Future Directions ............................................................................................42
Summary .........................................................................................................42
REFERENCES ..................................................................................................................45
v
LIST OF FIGURES
Figure 1: Experimental setup with dimensions. Top Left: Subject’s view of table
setup from the front. Top Right: Specific dimensions of experimental
setup from the side. The top shelf was 15.2 cm in depth, 19.7 cm in
height, and targets were placed 10.2 cm away from the edge of the table
or on the removable shelf. Bottom: The distance the subject is from the
table is a function of the subject’s acromion to fingertip length. ........................9
Figure 2: View of the seven starting hand locations from anterior perspective. The
subject would start with his or her hand in one of the seven locations
before a movement as described in detail within the protocol. The initial
four subjects only used starting positions 1-5. ..................................................12
Figure 3: Schematic of the cylinder used for experiments. The silver mark on the
top represents tape that was used to indicate the target over which the
index finger was placed in CR and QR experiments. The cylinder
weighed 340 grams. ...........................................................................................13
Figure 4: Target cylinder locations. A, B, and C were upper targets placed on a
removable shelf. D, E, and F were lower targets placed on the table itself.
The removable shelf was not present for trials when the subjects were
reaching for the lower targets. ...........................................................................14
Figure 5: Example of raw data for a subject 5 start position 3 to target F. The
fingertip X (green line), Y (black line), and Z (horizontal red line) data
are displayed here. The red vertical line marks the initiation of the
movement while the blue line signifies the completion. Y axis is cm
demarcated by 25.4 cm blocks for the top two position graphs and 49.53
cm/s blocks for the bottom velocity graphs. X axis is in seconds, with
each line representing 0.5 seconds. Top Left: Quick reach position. Top
Right: Comfortable reach position. Bottom Left: Quick reach velocity.
Bottom Right: Comfortable reach velocity. ......................................................18
Figure 6: Angles defining the posture of the arm. Three angles are required to
define the motion at the shoulder (η, θ, and ζ). The yaw angle (η)
represents a rotation of the arm about the vertical Z axis, measured
relative to the positive X direction. The elevation angle (θ) represents the
angle between the arm and the negative Z axis, measured in a vertical
plane. θ is 90o when the upper arm is in the horizontal (XY) plane. The
humeral rotation is defined by ζ, ζ being 0o when the plane of the arm is
vertical. φ corresponds to elbow extension. The vector p, perpendicular
to the plane of the arm, provides a succinct description of the arm’s
posture. Angle of inclination, ν, the acute angle between p and the
horizontal plane. ................................................................................................19
vi
Figure 7: Subject 6 forearm yaw angles at endpoint for two of each condition in
degrees, for targets A-F from the seven different starting positions. Each
plotted point is the final forearm yaw angle for one movement to a target.
Yaw calculated in the XY plane, with 0o being straight forward from the
subject and 90o being directly to the subjects left, along the positive Y
axis.....................................................................................................................21
Figure 8: Arm elevation at endpoint under each condition for subject 6 in degrees
for targets A-F from the seven different starting positions. Each plotted
point is the final arm elevation angle for one movement to a specific
target under a specific condition. Elevation is measured from the
negative Z axis, here 0o corresponds with the arm pointing straight down
and at 90o would be with the arm horizontal. ....................................................22
Figure 9: Arm roll at endpoint under each condition for subject 6 in degrees for
targets A-F from the seven different starting positions. Each plotted point
is the final arm roll angle for one movement to a specific target under a
specific condition. 0o corresponds to no internal, positive angle, or
external rotation, negative angle, at the shoulder joint......................................23
Figure 10: Elbow flexion at endpoint under each condition for subject 6 in degrees
for targets A-F from the seven different starting positions. Each plotted
point is the final elbow angle for one movement to specific target under a
specific condition. .............................................................................................24
Figure 11: Angle of inclination of the plane for the upper limb for subject 6 under
each condition in degrees for targets 1-6 A-F from the seven starting
locations. Each plotted point describes the final angle of inclination for
one movement to the target. Angle of inclination describes the
configuration of the arm in three dimensions by finding the vector, p,
angle in respect to the XY plane. ......................................................................25
Figure 12: An example set of paths of the index fingertip from the seven different
starting positions moving to target E in CR first block of subject 6. The
numbers within the green dots indicate the starting position used. The
points trace out the index fingertip path through the movement from each
starting position to target E (lower middle target), the red dot. ........................26
Figure 13: Scatterplot of variability (standard deviations) of angles of inclinations
of the plane of the upper limb at endpoint versus endpoint variability of
the tip of the index finger across all targets and conditions. Each plotted
point is the standard deviation of the angles of inclination of the upper
limb for all movements by one subject to a single target in a single
condition (comfortable reach [♦], quick reach [-], grasp [x]). ...........................28
Figure 14: Mean angle of inclination of the plane of the upper limb for different
targets. Top: Each plotted point is the mean angle of inclination across all
subjects to a specific target (A-F) under a specific condition (comfortable
reach, quick reach, or grasp). Vertical bars denote ± 1 standard error.
Bottom: Each plotted point is the individual subjects’ mean angle of
inclination to a specific target (A-F) under a specific condition
(comfortable reach, quick reach, or grasp). .......................................................30
vii
Figure 15: Variability of angle of inclination of the upper for targets A-F. Each bar
is the average of standard deviations of the inclination angles of the plane
of the upper limb for movements from different starting positions to a
single target across all subjects and across all conditions. Error bars
represent ± 1 S.D. * and ^ denote significant differences between
standard deviations of the angle of inclination of the plane of the upper
limb for targets A, D, and E. .............................................................................32
Figure 16: Variability of angle of inclination of the upper limb for all three
conditions, comfortable reach, quick reach, and grasp. Each plotted point
is one subject’s standard deviation in the angle of inclination to a specific
target under a specific condition. ......................................................................33
Figure 17: Aggregate data showing the mean variability of the angle of inclination
for six targets A-F (1-6) for the three conditions, comfortable reach,
quick reach, and grasp. Top: Each plotted point is the mean variability in
the angle of inclination for a specific target under a specific condition.
Vertical bars denote ± standard errors. Bottom: Each plotted point is the
individual subjects’ standard deviation in the angle of inclination for a
specific target (A-F) under a specific condition (comfortable reach, quick
reach, or grasp). .................................................................................................34
viii
1
INTRODUCTION
The central nervous system (CNS) is the only means through which humans
interact with the world around them. In order to effect change, the CNS activates muscles
to produce forces acting on the external environment. A complex multi-jointed system is
difficult to control, but the human brain is able to swiftly guide the upper limb accurately
to a point in space and with seemingly minimal effort. A possible theory for this swift
action is an internal “formula” that solves for the forces necessary to produce the
movement, where a final posture is defined by a specific location is space (Polit and Bizzi
1979; Rosenbaum et al. 1995; Desmurget and Prablanc 1997; Grea et al. 2000; Capaday
et al. 2013).
A solution like this has been described in the human eye (Alpern 1969; Nakayama
and Balliet, 1977; Tweed and Vilis, 1990). In this case, the eye, while a three dimensional
structure, is limited to movements in two dimensions, such that for each unique gaze
direction there exists a single corresponding eye position. To move to any point in the
available space, the eye makes a single rotation from the central position. These axis of
rotations all lie in a plane, known as Listing’s plane. In contrast to findings with eye
movements, head rotation axes were not confined to a two dimensional plane, but instead
existed as a warped surface (Misslisch et al. 1994a). The adherence to a warped surface
or a plane is known as Donders’ law. A body structure which obeys Donders’ law can
only assume one unique end configuration for each point in space. As such, the nervous
system would attempt to move the structure (e.g. eye, head, limb) to that specific ending
configuration regardless of variations in starting position, manifesting in a relatively
simple solution to a complex problem (Capaday et al. 2013).
Hore et al. (1992) found that the shoulder also followed Donders’ law in pointing
tasks with the elbow in full extension. In contrast, Soechting et al. (1995) extrapolated
Donders’ law to the entire upper limb for pointing movements and found that it did not
2
apply in humans. Specifically, the final upper limb configuration of a pointing gesture
depended on the initial position of the upper limb, and thus was not unique for a point in
space. Other work has shown that upper limb configurations in movement and grasping
do not completely obey Donders’ law, but approximate the law’s predictions to within a
few degrees (Gielen et al. 1997; Schot et al. 2010). Specifically, the axes of rotation for
the upper limb motion have a standard deviation relative to the axis that conforms to
Donders’ law of only 3-4o (Gielen et al. 1997), whereas the head only varied by ~2o
(Misslisch et al. 1994a) and the eye only varies by approximately 1o in pursuit
movements (Tweed and Vilis 1987, 1990; Misslisch et al. 1994b).
In different tasks, the eye does deviate from Donders’ law, and therefore Listing’s
plane. In the optokinetic reflex, the rotation vectors of the eye form a cloud ~8-10 ± 2.4o
(S.D.) thick compared to the ~2 ± 1.1o (S.D.) plane created by smooth pursuit. The
vestibuloocular reflex deviates even further, creating a cloud ~15 ± 3.7o (S.D.) in
thickness. From these data Misslisch et al. (1994b) conclude that Donders’ law does not
hold for the eye in the optokinetic reflex and vestibuloocular reflex.
Just as in the eye, ending arm configuration could also depend on the task and not
just initial position. Faster movements are known to be more variable in execution than
slow movements (Fitts 1954), and require greater consideration of energy requirements to
retard fatigue (Elliott et al. 2009). A proposed reason for this reduction in accuracy is
signal-dependent noise. Increased activity in motor neurons increases endpoint errors due
to accumulation of noise within the CNS, causing faster movements to become more
inaccurate (Harris and Wolpert 1998). This noise, or error, accumulation can be
generated in movement execution (Darling and Cooke 1987a) and movement planning
(Churchland et al. 2006). A recent study by Apker et al. (2010) presented evidence that
planning noise is dominant in movements, with error in execution playing a factor as a
function of movement direction, mainly in the depth axis, which is aligned with visual
line of sight.
3
There is another reason why faster movements produce larger endpoint errors.
When reaching at a comfortable speed the CNS may be able to better use feedback from
visual and proprioceptive sensors (Prablanc and Martin 1992; Gordon et al. 1995). Quick
movements are executed in less time than casual movements, thereby reducing the time
available for feedback signals to reach the CNS to influence the course of the movement.
Therefore fast movements receive less online corrections than slower movements,
causing greater errors in endpoints.
If the CNS does not use a specific ending arm configuration in space, other
mechanisms are possible. Soechting et al. (1995) calculated the minimum work needed to
move the arm from a specific starting location to an end point and found that it generally
predicted the final arm configuration of the subject’s movements. This implies that the
brain prioritizes the path of least resistance for arm movements, and thus produces
different ending configurations for the arm for different starting orientations. However,
Nishikawa et al. (1999) found that movement speed had no systematic effect on ending
configuration of the arm. Indeed, Soechting et al. (1995) stated that there are most likely
a multitude of constraints which factor into how the upper limb is controlled. Kistemaker
et al. (2010) found this concession to be accurate, stating that movements controlled by
the CNS did not minimize work or metabolic energy during movements. They argued
that control of effort, stability, and minimizing variance due to signal-dependent noise
play a large role in adaptive control.
Donders’ law has significant implications not only for final arm configuration, but
also how the arm executes a movement. As a movement theory describes how the arm
moves through space, the final arm configuration would be calculated by considering the
endpoint of the desired movement. If Donders’ law was found to hold in upper limb
movement then any theory that would predict different final arm configurations based on
starting arm configuration would be proven wrong.
4
Many mechanisms for control of arm motion have been investigated, most bound
by the idea that the CNS is working to optimize some parameter. The minimum jerk
hypothesis proposed by Hogan and Flash (1987) assumes Donders’ law does not hold for
upper limb movement. This theory states that in upper limb movement the rate of change
of acceleration, or jerk, of the hand is minimized. Another prediction of this theory is
that the average hand speed for any movement distance or duration is constant,
specifically around 1.88 m/s (Hogan and Flash 1987). Minimizing jerk is associated with
the hand moving in a straight line from the starting point to the end location with a
smooth, unimodal, bell shaped velocity profile. Soechting et al. (1995) criticized this
approach by pointing out that this model does not take into account jerk produced at the
joints proximal to the hand. That is, minimizing jerk of hand motion does not ensure
maximum smoothness of shoulder and elbow angular motions.
Other potential control mechanisms for planning upper limb movements have
been considered, including minimization of torque changes (Uno et al. 1989), minimizing
absolute work (Berret et al. 2008), and requiring the least amount of muscular effort
(Biess et al. 2007). Berret et al. (2011) hypothesized that the human brain takes multiple
control mechanisms into consideration. Using an inverse optimal control approach they
adjusted a weighted coefficient on different theories of movement and fit the predictions
to reaching movements performed to touch a bar. Because this experiment was not
concerned with a specific final end point in space, various trajectories predicted by
different models would become more distinct, as subjects could reach to any position
along the bar to complete the task and each model would predict a different ending
location along the target. Berret et al. (2011) found a hybrid model best described
movements of the CNS, primarily focusing on mechanical energy cost minimization
followed by angle acceleration minimization with small contributing factors from hand
and angle jerks and geodesic costs. Notably, minimizing torque, torque changes and
effort costs were not involved.
5
There may in fact not be a universal function used by the CNS to plan upper limb
movements for all tasks (Desmurget et al. 1998a). Soechting et al. (1995) stated that if
energy were minimized then different factors would dominate at different movement
speeds to minimize joint peak angular velocities and energy expenditure. Related to this
idea, Papaxanthis et al. (2002) found that gravitational and inertial forces play an
important role in movements that vary in direction and speed. At lower speeds the CNS
used gravity to assist movement in the upper limb, whereas for high speed movements,
gravity was no longer sufficient to produce high acceleration and increased muscle
activity was required.
Helms Tillery et al. (1995), Soechting and Flanders (1993), Desmurget et al.
(1998b), and Schot et al. (2010) investigated Donders’ law with respect to arm
configuration at the end of a reach to grasp task. Object configuration in space was
suspected by Soechting and Flanders (1993) to be the primary reason why Donders’ law
failed in grasping tasks, concluding that Donders’ law may still hold when precise hand
orientation was not required. In support of this idea, Schot et al. (2010) found that when
subjects moved the hand to grasp a sphere, starting position played a minimal role in final
arm configuration, the target’s location was considerably more important. Moreover,
within deviations of a few degrees, Donders’ law was obeyed for these movements.
Specifically the axes of rotation found experimentally only varied from the predicted axes
by a few degrees.
The aim of the present study was to test whether Donders’ law fails to hold in
unconstrained movements to a target from multiple initial positions in different reaching
tasks. Specifically, we hypothesized that comfortable speed pointing movements from
different starting locations to place the tip of the index finger over a target will exhibit
low variability in upper limb orientation at the endpoint. Fast pointing movements are
expected to exhibit larger variations in upper limb orientation for different hand starting
locations than slow movements due to greater variability of index fingertip position at
6
endpoint. Comfortable speed reaching movements from different starting locations to
grasp and lift a target are hypothesized to exhibit low variability in final upper limb
orientation at the endpoint because of consistency in hand orientation used to grasp the
target. We also tested whether the transport phase of reach to grasp movements is
controlled similarly to pointing movements by comparing the final upper limb
orientations of pointing and reach to grasp movements. Demonstrating that these different
classes of arm movements all exhibit low variability of final arm configuration at
endpoint for movements from a wide range of starting positions to targets in commonly
experienced locations would show that the CNS uses a simple mechanism to control such
arm movements.
7
MATERIALS AND METHODS
Subjects
Eleven right handed subjects (6 males) with an average age of 25.25 ± 4.37 (mean
± S.D.) years with no history of neuromuscular disorders participated in these
experiments. All subjects signed informed consent documents sanctioned by the
University of Iowa Institutional Review Board before participation. These subjects were
naive to the purpose of the study. Right handedness was verified by the revised
Edinburgh Handedness Inventory. Subjects received compensation for participation.
Experimental Setup
Each subject’s biacromial width and right arm length (from the most distal end of
the index finger to the acromion) was measured. This measurement allowed the
experimenter to control for sizes of different subjects by adjusting target locations and the
subject’s distance from the table where the target was located. The subject sat naturally in
front of a table which was a distance of 60% of the arm length to the xiphoid process
(Figure 1). Subjects were asked to remove any metal objects from their upper limbs
because such objects may interfere with the devices used to record arm position and
motion.
The initial four subjects used five position sensors recorded by an electromagnetic
system (Ascension Technologies minibird system, Burlington, VT, USA) using Skill
Technologies (Phoenix, AZ) 6DResearch software. These sensors were attached to the
subjects on the distal phalanx of the index finger, the halfway point on the third
metacarpal in the hand, the styloid process of the ulna, the lateral epicondyle of the
humerus, and the acromion process of the scapula. Attachment was done using doublesided tape under the sensor and single-sided tape to attach the wires to the skin to
minimize strain on the sensors, tangling of wires, and to ensure the subject had a full
unhindered range of motion at the shoulder elbow, wrist, and finger joint. The transmitter
8
rested on the left side of the table. Each sensor’s X, Y, Z, azimuth, elevation, and rotation
in space were recorded at 74 Hz using Skill Technologies software and then transferred to
Datapac 2k2 (Run Technologies, Laguna Hills, CA, USA) for data analysis.
Seven subjects used four Trakstar magnetic sensors (Ascension Technology
Corporation, Burlington, VT, USA). These sensors were applied to the finger, wrist,
elbow, and shoulder as described above. The magnetic transmitter for the Trakstar system
was placed, centered, 10.2 cm from the front of the table to ensure the greatest workspace
range would be captured because the sensors must be within 36 inches of the transmitter.
The limited scope was a problem for three larger subjects. The acromion sensor was
located outside of the maximum sensor range such that their data could not be fully
analyzed because an accurate location for the shoulder could not be obtained. A
MATLAB (Mathworks, Natic, MA, USA) program captured and recorded all six degrees
of freedom for each sensor: X, Y, Z, azimuth, elevation, and rotation for a span of five
seconds at a sampling rate of 200 Hz.
9
15.2 cm
1
Shelf
10.2 cm
38.1 cm
19.7
cm
Table
7
76.8
cm
23.5
cm
5
100 degrees
53.3
cm
TABLE + SHELF:
FRONT
2
4
48.3
cm
60% of Tip of
CHA
Index Finger-Acromion
Distance
IR: SIDE
TABLE + SHELF:
SIDE
Figure 1: Experimental setup with dimensions. Top Left: Subject’s view of table setup
from the front. Top Right: Specific dimensions of experimental setup from the
side. The top shelf was 15.2 cm in depth, 19.7 cm in height, and targets were
placed 10.2 cm away from the edge of the table or on the removable shelf.
Bottom: The distance the subject is from the table is a function of the subject’s
acromion to fingertip length.
10
Experimental Protocol
After the subjects were familiarized with the experimental setup, they were asked
to perform two to four practice trials to various targets until he or she felt comfortable
with the protocol. During this time, subjects were familiarized with the five or seven
starting positions (Figure 2). The target was a piece of tape marking the middle of a
cylinder (Figure 3).
Once comfortable, subjects executed four blocks of trials from which they would
start from one of five or seven locations, and would end the movement positioning the
index finger just above the center of a cylinder at one of the six target locations. Targets
B and E were placed in the midline, resting 30.5 cm from the edges of the table sides.
The distance between target location A and C, and D and F was set a distance apart equal
to the subject’s biacromial breadth (Figure 4). The table was marked with a small colored
dot sticker representing the correct target location to eliminate the need for measurement
after each trial.
Four subjects were tested with five hand starting locations and seven subjects
were tested with seven hand starting locations (Figure 2). Starting position one had the
subject rest the right hand on the right thigh. In starting position two, the subject rested
the right hand on the abdomen. Position three the right hand was rested on the left thigh.
In position four, the subject abducted the arm 90o from the torso and flexed the elbow 90o
such that the right hand was pointing upward. To reach starting position five, the subject
horizontally adducted the arm as much was comfortable, flexed the elbow 90o such that
the right hand was pointing upwards. In starting position six the subject abducted the arm
90o to the right so that the hand was pointing to the right. In starting position seven the
subject horizontally adducted the arm as far as was comfortable, and then flexed the
elbow so that the right hand was pointing to the left.
There were two blocks of 42 trials where the subject was instructed to reach at a
comfortable speed (CR) and two blocks of 42 trials in which the subject was told to
11
complete the movement quickly (QR) by positioning the right index finger just above the
center of the target. These blocks were performed in a random order for each subject.
Starting position of the hand and target locations were randomized within blocks as well.
After these four blocks were completed the subject was instructed to grasp the cylinder
with the first three digits (thumb, index finger, and long finger) with the palm of the hand
directly above the target, and then pause before carrying it two inches forward past a
string embedded in the table and then back to the initial target location. Between each
two block set subjects were given the opportunity to rest for one to two minutes as
desired.
Subjects produced movements in an unconstrained three dimensional environment
for all movement conditions. Torso and wrist movements were unrestricted to allow
maximum degrees of freedom in the upper limb. This freedom allowed for the greatest
possible variability in final arm postures and more closely approximates movements in
everyday environments than in many previous experiments (Cruse 1986, Uno et al. 1989,
Straumann et al. 1991, Hore et al. 1992, Gielen et al. 1997, Papaxanthis et al. 2002,
Kistemaker 2010).
For each block, the subject performed movements to a particular target from five
(the first four subjects) or seven (the last seven subjects) starting positions in random
order before the target was relocated to a new position on the table or shelf. Verbal
instruction was provided about the starting location before the movement; subjects were
allowed time to put the arm in this position. Subjects were instructed to move by a verbal
command “go” or “reach” given by the experimenter. The subject would complete the
movement and maintain the end position until prompted by the experimenter.
12
Figure 2: View of the seven starting hand locations from anterior perspective. The subject
would start with his or her hand in one of the seven locations before a
movement as described in detail within the protocol. The initial four subjects
only used starting positions 1-5.
13
5.1 cm
3.5 cm
4.4 cm
Figure 3: Schematic of the cylinder used for experiments. The silver mark on the top
represents tape that was used to indicate the target over which the index finger
was placed in CR and QR experiments. The cylinder weighed 340 grams.
14
Figure 4: Target cylinder locations. A, B, and C were upper targets placed on a
removable shelf. D, E, and F were lower targets placed on the table itself. The
removable shelf was not present for trials when the subjects were reaching for
the lower targets.
Data Analysis
Data were transferred directly into Datapac 2k2 as text files from Skill
Technologies or MATLAB software for analysis. A low pass Butterworth filter was
applied to the motion of each sensor with a cutoff of 10 Hz. Each movement was visually
analyzed, marking a display of index tip X, Y, and Z position and velocity versus time to
15
mark the index tip sensor’s initial and final positions (Figure 5). This process was done
visually instead of using a velocity criterion for movement onset and endpoint to reduce
errors due to small tremors in arm starting and ending locations. Data for the index
fingertip motion was used to mark movement onset and end because largest movement
occurs at the distal point of the upper limb. The starting position was marked a few
milliseconds before movement was initiated and was marked as complete when the
positions were constant (Figure 5). Once these data were marked, start and endpoint
locations and orientations for all sensors were exported to Microsoft Excel for further
analysis using a macro to calculate arm angles. Movements that were not fully captured
within the five second recording period were removed from the analysis.
The Excel macro calculated the yaw, elevation and roll for the arm and the
forearm segments as a series of ordered rotations from a standard upper limb
configuration in which the arm was pointing straight forward from the subject (Figure 6).
Yaw was defined as a rotation of the segment about the vertical axis with 0o being
directly forward from the subject and 90o being directly to the left of the subject (positive
Y axis). The second rotation was about a horizontal axis (medial to lateral in the standard
configuration) and defined elevation of the segment, which was measured as the angle of
the segment from the vertical Z axis. 0o indicates that the arm segment is pointing straight
down and 90o corresponds that the segment is confined to the XY plane. The third
rotation, at the shoulder only, was about the long axis of the humerus to define arm roll.
This angle was calculated by defining a new coordinate system, X’, Y’, Z’, with the X’
axis running through the arm and the Y’ axis parallel to the initial Y axis. The forearm
vector’s angle from the Z’ axis in the Y’Z’ plane was defined as the arm roll, 0o being no
internal or external arm rotation; a positive angle indicates internal rotation, and a
negative angle represents external rotation.
16
Elbow extension, φ, was calculated using the law of cosines (Equation 1), where a
is the length of the arm, b is the length of the forearm, and c is the magnitude of the
vector between the wrist and the shoulder. 180o describes full extension at the elbow.
φ = cos-1([a2+b2-c2]/2*a*b)
(1)
The angle of inclination of the plane of the upper limb (ν), defined by the 3dimensional location of the acromion, elbow, and wrist, was computed by Equation 2,
where θ is arm elevation and ζ is humeral roll.
Sin(ν) = sin(θ)*sin(ζ)
(2)
Angle of inclination of the plane of the upper limb defines the configuration of
the arm in three dimensions by finding the vector, p, the cross product of the arm and
forearm vectors which is perpendicular to the plane of the arm, then finding the vector’s
angle from the XY plane (Figure 6). This convention is the same as the one used by
Soechting et al (1995) and provides a simple measurement of upper limb configuration,
because for a given index fingertip location the inclination angle will be constant if arm
and forearm yaw and elevation angle are the same, assuming that the wrist and finger
have a minimal contribution to the overall movement.
The variability of angles of inclination for each subject’s movements to a target
from the different starting positions within a condition was computed as the standard
deviation of these angles. High variability in these inclination angles indicates that the
arm and forearm segments assume different orientations at the end of the movement for
that target. Because this study allowed for unconstrained movement and variations in
wrist and finger joint orientations, it is possible that angle of inclination does not
correspond with precisely one end configuration. Previous studies, however, have found
that wrist movement produced minimal variation in end point posture of the arm and
forearm compared to the shoulder (Cruse 1986; Miller et al. 1992; Wang 1999; Schot et
al. 2010). Low standard deviation in the angle of inclination of the plane of the upper
17
limb for movements from different starting positions to the same target indicates a similar
ending configuration regardless of starting position.
The variability of end point location for the fingertip was calculated as the volume
of an ellipsoid with radii equal to the standard deviations in X, Y, and Z (σx, σy, and σz)
location of the index tip sensor at the end of the motion (Equation 3).
Endpoint Error Volume = (4/3)*π*σx*σy*σz
(3)
We tested whether the endpoint error volume was correlated with the standard
deviation in the angle of inclination for movements in different starting positions in order
to determine whether variability in angle of inclination at endpoint was due to variations
in endpoint finger positions. A high correlation would indicate that variability in the
angle of inclination was caused by subjects not reaching to the exact same location in
space, possibly due to endpoint drift through trials in pointing conditions or target
location slightly changing in the grasping condition when subjects had to move the target
away and then back to the starting position.
A 6 X 3 repeated measure ANOVA using general linear models was used to test
within subject effects of target location (A-F) and conditions (comfortable reach, quick
reach, and grasp) on variability (standard deviation) of final arm orientations (upper limb
inclination angles) for movements from different starting positions to test whether
variability differed for different targets and conditions. A similar repeated measures
ANOVA was used to test whether mean final arm orientation for the different targets
differed for the different conditions. Mauchly’s test was used to check for sphericity and
Huynh-Feldt corrections were applied when necessary. Post-hoc Tukey’s HSD tests were
used to assess differences among individual targets and conditions if main or interaction
effects were statistically significant.
18
Figure 5: Example of raw data for a subject 5 start position 3 to target F. The fingertip X
(green line), Y (black line), and Z (horizontal red line) data are displayed here.
The red vertical line marks the initiation of the movement while the blue line
signifies the completion. Y axis is cm demarcated by 25.4 cm blocks for the
top two position graphs and 49.53 cm/s blocks for the bottom velocity graphs.
X axis is in seconds, with each line representing 0.5 seconds. Top Left: Quick
reach position. Top Right: Comfortable reach position. Bottom Left: Quick
reach velocity. Bottom Right: Comfortable reach velocity.
19
Y
Figure 6: Angles defining the posture of the arm. Three angles are required to define the
motion at the shoulder (η, θ, and ζ). The yaw angle (η) represents a rotation of
the arm about the vertical Z axis, measured relative to the positive X direction.
The elevation angle (θ) represents the angle between the arm and the negative
Z axis, measured in a vertical plane. θ is 90o when the upper arm is in the
horizontal (XY) plane. The humeral rotation is defined by ζ, ζ being 0o when
the plane of the arm is vertical. φ corresponds to elbow extension. The vector
p, perpendicular to the plane of the arm, provides a succinct description of the
arm’s posture. Angle of inclination, ν, the acute angle between p and the
horizontal plane.
20
RESULTS
Upper Limb Angles and Paths of the Index Finger
Although the angle of inclination of the plane of the upper limb provides a
succinct way to characterize the upper limb in space, arm and forearm yaw, elevation,
and roll along with elbow extension angles were also assessed to more fully describe arm
and forearm orientation. Forearm yaw angles were similar for the different reaching
tasks; although quick reaches usually had the lowest forearm yaw angles with grasp
yielding the highest (Figure 7). The high targets had higher arm elevation angles (Figure
8) and smaller arm roll angles (Figure 9) as expected. The left targets on average were
associated with the largest elbow extensions (Figure 10), as expected. The angle of
inclination was computed from the arm angles found by Equation 2 (Figure 11). The
angle of inclination of the upper limb succinctly describes the configuration of the arm in
three dimensions by finding the vector, p, angle in respect to perpendicular plane.
Movement of the index fingertip to a target from different starting positions often
did not follow a straight path (Figure 12). This suggests that the movements were not as
would be predicted from a minimum jerk model. However, this model predicts minimum
jerk for hand motion, not for motion of the tip of the index finger. As shown in Figure 5,
fast movements were usually associated with bell shaped velocity of index tip motion as
would be expected for a minimum jerk model, but comfortable speed movements were
often associated with skewed, rather than bell-shaped, velocity profiles.
21
Figure 7: Subject 6 forearm yaw angles at endpoint for two of each condition in degrees,
for targets A-F from the seven different starting positions. Each plotted point is
the final forearm yaw angle for one movement to a target. Yaw calculated in
the XY plane, with 0o being straight forward from the subject and 90o being
directly to the subjects left, along the positive Y axis.
22
Figure 8: Arm elevation at endpoint under each condition for subject 6 in degrees for
targets A-F from the seven different starting positions. Each plotted point is the
final arm elevation angle for one movement to a specific target under a specific
condition. Elevation is measured from the negative Z axis, here 0o corresponds
with the arm pointing straight down and at 90o would be with the arm
horizontal.
23
Figure 9: Arm roll at endpoint under each condition for subject 6 in degrees for targets AF from the seven different starting positions. Each plotted point is the final arm
roll angle for one movement to a specific target under a specific condition. 0o
corresponds to no internal, positive angle, or external rotation, negative angle,
at the shoulder joint.
24
Figure 10: Elbow flexion at endpoint under each condition for subject 6 in degrees for
targets A-F from the seven different starting positions. Each plotted point is
the final elbow angle for one movement to specific target under a specific
condition.
25
Figure 11: Angle of inclination of the plane for the upper limb for subject 6 under each
condition in degrees for targets 1-6 A-F from the seven starting locations.
Each plotted point describes the final angle of inclination for one movement
to the target. Angle of inclination describes the configuration of the arm in
three dimensions by finding the vector, p, angle in respect to the XY plane.
26
Figure 12: An example set of paths of the index fingertip from the seven different starting
positions moving to target E in CR first block of subject 6. The numbers
within the green dots indicate the starting position used. The points trace out
the index fingertip path through the movement from each starting position to
target E (lower middle target), the red dot.
27
Profile of Quick Reaches Compared to Comfortable
Reaches
In the anterior, X, movement direction, subjects moved with a peak index
fingertip speed of 0.46 ± 0.19 (mean ± S.D.) m/s for comfortable reach, while quick
reaches were over twice as fast with a peak speed of 1.13 ± 0.54 (mean ± S.D.) m/s.
These data are only from a subset of the subjects in whom we had clean recordings of
peak velocity. The initial set up used for the first four subjects created artifacts if the
subject reached passed the transmitter. The artifacts in no way affected the measured start
or end locations, but affected calculations of movement velocity. This was not a problem
with the second protocol (7 starting positions) in which a different transmitter (Trakstar
system) was placed in a different location.
Index Fingertip Endpoint Error Volume and Variability of
Angle of Inclination
Variability of inclination angles of the plane of the upper limb at endpoint was not
related to variability of index tip position at endpoint. We examined this association in
individual subjects for the six targets and three conditions. There were no significant
correlations between index fingertip endpoint variability and variability of inclination of
the plane of the upper limb at endpoint for movements from different starting positions
for any subject (range of correlation coefficients across all subjects: -0.24 to 0.34, p >
0.392) or conditions (Mean R across subjects: CR = 0.12, QR = -0.21, Grasp = -0.11)
(Figure 13). These data show that variations in ending angle of inclination of the plane of
the upper limb are unrelated to variations in accuracy of subjects’ movements to the
target from different starting positions and under different reaching conditions.
28
Figure 13: Scatterplot of variability (standard deviations) of angles of inclinations of the
plane of the upper limb at endpoint versus endpoint variability of the tip of
the index finger across all targets and conditions. Each plotted point is the
standard deviation of the angles of inclination of the upper limb for all
movements by one subject to a single target in a single condition
(comfortable reach [♦], quick reach [-], grasp [x]).
29
Mean Angles of Inclination of the Upper Limb in Different
Reaching Conditions
The mean angle of inclination of the plane of the upper limb did not depend on
target location (F5, 35 = 2.49, p = 0.14) but there was a strong trend for dependence on
reaching condition (F2, 14 = 3.88, p = 0.08) and a significant condition X target interaction
was discovered (F10, 70 = 4.11, p = 0.002) (Figure 14). Mean inclination angles of the
plane of the upper limb were significantly lower for reaches to grasp than for comfortable
and quick reaches to point at targets A (p < 0.001), B (p < 0.0003), and C (p < 0.0002) as
well as to target E in quick reach only (p < 0.0005). Post-hoc testing was also applied to
test for differences among the three reaching conditions because of the strong trend for
differences among conditions (p= 0.08). The mean inclination angles of the plane of the
upper limb were similar for comfortable and quick reaches (p = 0.830). However reaches
to grasp the target differed from quick reaches (p = 0.047), but not from comfortable
reaches (p = 0.134). Thus, mechanisms for controlling end positions of comfortable
reaches are the same for faster movements, or at least produce a similar final upper limb
configuration, but the upper limb adopted a slightly different configuration for the upper
targets in the grasping condition (Figure 14).
30
Figure 14: Mean angle of inclination of the plane of the upper limb for different targets.
Top: Each plotted point is the mean angle of inclination across all subjects to a
specific target (A-F) under a specific condition (comfortable reach, quick
reach, or grasp). Vertical bars denote ± 1 standard error. Bottom: Each plotted
point is the individual subjects’ mean angle of inclination to a specific target
(A-F) under a specific condition (comfortable reach, quick reach, or grasp).
31
Variability in Angles of Inclination of the Upper Limb
Variability in inclination angles of the plane of the upper limb for movements
from different starting positions was affected by target locations (Figure 15, F5, 35 = 4.42,
p = 0.0057). Variability of inclination angles of the plane of the upper limb were smaller
for targets on the left side (below 3.5 degrees on average), while the middle targets, along
with the lower right target, all had slightly larger variation (all above 4.0 degrees on
average). These findings are consistent with previous observations (Soechting et al. 1995,
Desmurget et al. 1998b).
Variability in inclination angles of the plane of the upper limb for movements
from different starting positions showed a strong trend for differences among reaching
conditions (F2, 14 = 3.36, p = 0.098) (Figure 16) but there was no target X condition
interaction (F10, 70 = 0.75, p = 0.65). The size of the average standard deviation and the
mean values of the angle of inclination for quick reach was comparable to comfortable
reach (Figure 16 and Figure 17). These data show lower variability of angles of
inclination than observed by Soechting et al. (1995). Although reaches to grasp an object
tended to exhibit lower variability than reaching to point to an object there were no
statistical differences. Post-hoc Tukey’s tests of differences among conditions showed no
difference between comfortable speed reaching and reach to grasp movements (p =
0.490) but variability of final inclination angles trended to be higher for quick reaches
than for reaches to grasp (p = 0.053). These data indicate similar variability of inclination
angles of the upper limb plane at end point configuration for reaching to point at and for
reaches to grasp the targets.
32
Figure 15: Variability of angle of inclination of the upper for targets A-F. Each bar is the
average of standard deviations of the inclination angles of the plane of the
upper limb for movements from different starting positions to a single target
across all subjects and across all conditions. Error bars represent ± 1 S.D. *
and ^ denote significant differences between standard deviations of the angle
of inclination of the plane of the upper limb for targets A, D, and E.
33
Figure 16: Variability of angle of inclination of the upper limb for all three conditions,
comfortable reach, quick reach, and grasp. Each plotted point is one subject’s
standard deviation in the angle of inclination to a specific target under a
specific condition.
34
Figure 17: Aggregate data showing the mean variability of the angle of inclination for six
targets A-F (1-6) for the three conditions, comfortable reach, quick reach,
and grasp. Top: Each plotted point is the mean variability in the angle of
inclination for a specific target under a specific condition. Vertical bars
denote ± standard errors. Bottom: Each plotted point is the individual
subjects’ standard deviation in the angle of inclination for a specific target
(A-F) under a specific condition (comfortable reach, quick reach, or grasp).
35
DISCUSSION
Comfortable Speed Movements
Data from this study provides support to the idea that Donders’ law does hold for
comfortable speed reaching movements to targets located in commonly encountered
locations. Previous studies have shown that Donders’ law is obeyed by the upper arm to
within a few degrees as Hore et al. (1992), Gielen et al. (1997), and Schot et al. (2010)
found that the axis of rotation’s standard deviation was only 3-4o from the expected axis
that conform to Donders’ law. The present study allowed for full movements of the
finger, wrist, elbow, shoulder, and torso. Donders’ law was previously found to be
closely adhered to when constraining movements by limiting degrees of freedom,
specifically limiting motion to the shoulder (Hore et al. 1992). Miller et al. (1992), Wang
(1999), and Schot et al. (2010) found that variations in wrist orientation did not
significantly contribute to variations in endpoint configurations of the arm and forearm
segments. In the present study, subjects sat 60% of arm length away from the table on
which targets were located in order to minimize the need for torso movements. Even
under these conditions, it is possible for unconstrained upper limb movements to exhibit
high variability in final upper limb configurations for a given target location in pointing
or grasping tasks. For example, the same index fingertip location can be maintained while
varying humeral rotation substantially, which greatly alters arm and forearm elevation
and yaw. Our data shows that even with these increased degrees of freedom Donders’ law
appears to hold, with relatively small variations within a subject, for comfortable speed
reaching tasks. Soechting et al. (1995) found that variations in the angle of inclination of
the plane of the upper limb for movements from different starting positions were
relatively large (i.e. range of 30o or more) except for a few targets. In contrast, the range
of upper limb plane inclination angles for movements from a wide range of starting
positions to the six targets studied here was less than 22o in all subjects for both
36
comfortable and quick reaches to point to the target and was less than 15o for most
subjects. Thus, the ending configuration of the upper limb for comfortable reaching
movements is similar regardless of starting position.
Another point to consider is the threshold at which Donders’ law fails to hold,
how much variance is needed to prove a violation? Variability in rotation vectors during
the vestibuloocular reflex is considered sufficient to violate Donders’ law (~15 ± 3.7o,
Misslisch et al. 1994b). Whereas the head varied by ~2o (Misslisch et al. 1994a) and the
eye only varies by approximately 1o in pursuit movements, both of which are considered
to follow Donders’ law (Tweed and Vilis 1987, 1990; Misslisch et al. 1994b). The
variability found in the angle of inclination of the plane of the upper limb was similar to
the variability of rotation vectors from a curved surface found by Gielen et al. (1997) (i.e.
~3-4o). Gielen et al. (1997) argues that this variability is sufficient to conclude a violation
of Donders’ law, however, Schot et al. (2010) reason that this variability is not adequate
to declare a violation.
Some variation is expected because sensors mounted on the skin can move
relative to bony landmarks. Also, biological noise plays a factor causing different end
configurations for the same target (Harris and Wolpert 1998) in both planning and
execution of movements (Darling and Cooke 1987a; Churchland et al. 2006; Apker et al.
2010). Measurement of this noise may reveal a significant contribution to endpoint
configuration variance. If this were the case, it would present a strong argument that the
CNS attempts to reach a point in space by associating it with predicted feedback of
muscle lengths, creating a universal joint configuration for that target.
Soechting et al. (1995) found that middle targets, particularly at shoulder level,
had the most variation, while the lower left target (53 cm from the right shoulder, -32.5x,
32.5y, -26.5z cm relative to the shoulder) had the smallest variation of inclination angles
of the plane of the upper limb for movements from a variety of starting positions.
Similarly, in the present study, the left side targets had the smallest amount of variation.
37
In general, the same is also true when compared to the Desmurget et al. (1998b)
experiment, the farthest target, located 80% of the upper limb length away from the
shoulder directly in front of the subjects shoulder and 20 cm to the right, produced the
least variance, while the closest target located 10 cm to the right and 80% of the upper
arm length minus 17.5 cm ahead of the right shoulder produced the most variance. This
may be due to the far targets requiring greater elbow extension; elbow extension angle
was 117.7 ± 11.8o (mean ± S.D.) and 123.1 ± 10.2o to targets A and D respectively in the
present work. The next highest elbow extension angle was for targets E and F, with an
average 110.3 ± 11.3o and 109.6 ± 12.4o. As shown by Hore et al. (1992), movements
with an extended elbow tend to be invariant in terms of final arm configuration, which is
defined completely by shoulder orientation, thereby obeying Donders’ law more closely
than unconstrained movements involving elbow flexion/extension.
As Soechting et al (1995) stated, the elbow extension angle depends only on the
distance of the target from the shoulder, assuming minimal hand and finger involvement.
Elbow extension angle data (Figure 10) qualitatively shows the most variance where the
least was expected (i.e. for the lower left target). Possible explanations include torso and
shoulder girdle movement in reaching to farther targets. Another explanation is that
subjects adjusted their posture between some trials, leading to different locations of the
shoulder in space. However, neither shoulder movement during reaches (R2 = 0.04) nor
shoulder movement between trials (R2 = 0.0007) correlated with elbow extension angles
for subject 6. Even with this variability in elbow extension angles, inclination angles of
the plane of the upper arm exhibited low levels variability.
Quick Reaching Movements
As movement speed increases, Soechting et al. (1995) proposed that different end
configurations might be used because the CNS may modify arm movement trajectories to
minimize joint peak angular velocities and energy expenditure. This proposition was not
38
supported in the present investigation as no significant differences in mean or variability
(S.D.) of end point upper limb configurations between comfortable reaching and quick
reaching were observed (Figure 16 and Figure 17). Thus, endpoint configurations appear
to be controlled similarly for comfortable speed and quick reaches.
The present results agree with the recent suggestion from Kistemaker et al. (2010)
that energy expenditure is not greatly considered by the CNS in controlling reach
movements as subjects did not adapt the most energy efficient path in an applied force
field. In contrast, Berret et al. (2011) found that for casual reaching mechanical energy
expenditure and joint-level smoothness play a larger role as indicated by their inverse
optimal control approach. However, it is possible that movements at extreme speeds,
much less than 0.46m/s or much greater than 1.13 m/s in the X direction, use different
final limb configurations.
Another possibility is that the CNS uses the same ending configuration for a
target in space, but alters the strategy used to get there. Different limb segments could
reach maximum velocity, acceleration, or jerk at different points in the movement.
However, Gottlieb et al. (1996) have shown invariance in joint torque profiles in different
speeds of reaching. If the CNS does use different movement strategies for different
speeds of reaching, they only seem to affect movement trajectory as endpoint arm
configuration appear to be relatively invariant.
Quick reaches exhibited somewhat greater variability in angle of inclination of the
plane of the upper limb at endpoint when compared to comfortable reaches and reaches to
grasp the target at all target locations except targets A and D in the comfortable reach
condition (Figure 17). Greater variability in faster movement is consistent with previous
studies (Fitts 1954) and may be due to lack of time to adjust the movement based on
sensory feedback (Gordon et al. 1995) or error within the CNS (Apker et al. 2010). For
targets A and D there could be a different mechanism at play. These far targets can be
expected to have lower variation of angle of inclination because the far targets reduce
39
available range of motion of the joints because the arm is close to full extension. Close
targets provide the greatest variety of usable endpoint upper limb configurations
(Desmurget et al. 1998b). However, there were no statistical differences in variability of
final arm configuration for the different targets between quick and comfortable reaches.
A possible reason why quick reaches had variations in index fingertip endpoint
positions than comfortable reaches for targets A and D could be because the CNS stores
an internal memory of arm configuration in joint space, as the eye has been shown to do
(Tweed and Villis 1987). The CNS could execute a movement in joint space as fast as
possible instead of relying on a minimizing effort, energy, or hand jerk, as Berret et al.
2011 found in slower reaches. Using this internal joint space configuration would lead the
arm to the same endpoint regardless of starting position as expected from Donders’ law.
Slower movements may exhibit larger deviations from Donders’ law due to less strict
minimization of factors affecting end positions or by greater online feedback corrections.
Simply put, greater use of feedback to correct comfortable reaches may play a larger role
in the variability of final upper limb configuration at endpoint (Crossman and Goodeve
1983), while motor output error (noisy motor commands) may dominate variability for
quick reach movements (Wisleder and Dounskaia 2007).
Reaches to Grasp an Object
Reaching movements to grasp the target object showed a different mean final arm
posture compared to comfortable and quick reaching movements for the three higher
targets (Figure 14). The grasping condition also provided the lowest mean variation in
angles of inclination of the plane of the upper limb for all target locations except for
target C in comfortable reach (Figure 17). Precision required for grasping could influence
the CNS to adopt a strategy to reduce error, perhaps by reducing degrees of freedom,
leading to more similar endpoint arm configurations for reaches to grasp the targets.
Another explanation for the reduction in variance of reaches to grasp is that the subjects
40
actually made physical contact with the target, possibly providing feedback concerning
endpoint that could be used to reduce variability in subsequent reaches from different
starting locations.
Assigning the reduction in variance to the fact that the target provides a physical
anchor point in space is questionable. The Grasping condition had the highest average
endpoint error volume (3.49 cm3), while CR and QR were 1.63 cm3 and 0.98 cm3
respectively. A possible reason for this high volume is due to the fact that the subject did
not accurately replace the target after each trial, possibly creating drift in endpoint
locations. However, any such changes in target location did not correlate with changes in
inclination angles of the upper limb which exhibited quite low variability.
The lack of association between index fingertip endpoint error volume and
variance in arm inclination angles can easily be explained. Endpoint error volume only
considered final fingertip locations, for CR and QR this was controlled for by a 9.62 cm2
target circle located on top of the cylinder. Grasp had no imposed goal for placement of
the digits on the cylinder, and could be grasped anywhere along the exterior surface,
theoretically providing a 70.49 cm2 target surface. Making the assumption that subjects
do not grasp more than a fourth of the available area with the index finger to avoid
extreme wrist joint angles brings the target surface down to 17.62 cm2, almost double that
of the pointing movements. The lack of a positive correlation between endpoint index
fingertip volume and variability of upper limb plane inclination angle could also be
explained by movement in the wrist and finger joints creating variations in grasp location,
while the general configuration of the arm and forearm in space would remain the same.
That is to say, the arm and forearm reach the same final configuration (providing a low
variability in the angle of inclination) while adjustments for fine motor tasks are made in
the hand and fingers (creating a large endpoint error volume).
Another explanation for reduction in variability of upper limb plane inclination
angles is a learning effect. Subjects always performed the grasping blocks last, after two
41
blocks of CR and QR each. Variability in muscle activation has been shown to recede
with practice (Darling and Cooke 1987b). It is likely that some subjects had a learning
effect after completion of the pointing trials. This effect, however, was not enough to
produce a statistically significant reduction in variability of the inclination angle of the
plane of the upper limb at endpoint in grasping movements compared to pointing
movements. Average velocity in the X direction in the comfortable condition was 0.46
m/s and 1.13 m/s in the quick reach. Grasping average X fingertip velocity averaged 0.91
m/s, almost twice that of comfortable speed reaches to point to the target. Darling and
Cooke (1987b) showed that with practice movement velocity increased while accuracy
was maintained. The higher speed of comfortable reaches to grasp than comfortable
reaches to point at the target may be evidence of a learning effect on reaching to grasp the
targets from previously performing reaches to point at the targets. The decrease in
accuracy, the larger endpoint error volume, in the grasping condition suggests that there
is no learning effect. However, the increased error volume may be due to the task
conditions (e.g. larger target area) as explained previously and not due to increased
variability that arises from faster movements.
Previous studies have shown that grasping movements do not obey Donders’ law
(Helms Tillery et al. 1995; Soechting and Flanders 1993; Desmurget et al. 1998b). In
contrast to the present work, the orientation of the target object was varied in these
previous studies. Schot et al. (2010) conducted a grasping experiment using a sphere as
the target object, thereby negating effects of orientation of the object on the upper limb
configuration for positioning the arm to grasp with the fingers. They found that reaches to
grasp targets had similar variability of endpoint configurations for movements from
different starting positions. Our data supports this theory and suggests that Donders’ law
is largely followed for upper limb movements to grasp objects with the same orientation.
42
Future Directions
One important issue to pursue is whether upper limb configuration at the end of a
reach to grasp movement is modified in relation to object properties such as size, weight,
and the task to be performed using the object. It is likely that the arm would be positioned
differently for light objects depending on whether the object will be lifted and moved in a
particular direction. The present study used a 340 gram cylinder, if weight increased two,
three, or ten times would the arm still use a consistent ending configuration?
This study found that mean ending configurations for quick reaches and
comfortable reaches were similar. However, we did not investigate joint velocities or
paths of the hand during the movements from different starting positions. It is possible
that comfortable movements differ from quick movements in their execution even if they
end in the same configuration. If significantly different velocity profiles were found
between reaching speeds an argument could be made in favor of a control mechanism for
reaching based on minimization of certain variables (e.g. work, effort) at least during fast
movements. Studies of planar movements have suggested that the elbow and shoulder
joints have the same velocity profile for different speed reaching movements (Gottlieb et
al. 1997). Nishikawa et al. (1999) found similar movement profiles of the angle of
inclination of the plane of the upper limb under different speeds but did not directly
measure specific joint profiles. More investigation, however, of the effects of movement
speed are needed. Similarly, moving the arm with different weights in the hand at
different speeds may influence hand paths and joint velocity profiles, perhaps providing
additional clues to elucidate the control mechanisms for upper limb movement under
different conditions.
Summary
This study sought to assess whether unconstrained movements to targets located
in common locations (on a table and shelf in front of the subjects with targets within
43
arm’s reach) to see if Donders’ law holds in three different reaching task conditions. For
comfortable reach, large variations in initial position had little effect on variations in final
upper limb orientation. The mean of standard deviations of the angle of inclination of the
plane of the upper limb for comfortable reaches to a variety of targets was 3.83o. These
results imply that upper limb ending configuration does not vary as much as reported by
Soechting et al. (1995), at least for commonly encountered targets. These small
variations may be caused by noise in the motor commands for movement (Apker et al.
2010) with some contribution by noise due to motion of sensors on the skin. These
relatively small deviations are consistent with results found by Gielen et al. (1997) and
Schot et al. (2010) using a different measurement approach (i.e. deviations of the axis of
upper limb rotation from those predicted by Donders’ law).
Quick reaches were expected to deviate from Donders’ law due to their higher
variability (Fitts 1954; Elliot et al. 2009) and possibly a change in movement strategy by
the CNS, favoring minimizing of energy used and maximizing movement smoothness
(Hogan and Flash 1987; Soechting et al. 1995). However, even though quick reaches
produced somewhat more variability in arm configurations at endpoint (despite
unexpected lower variability in final index fingertip locations), this variability was not
significantly different from variability of comfortable reaches (p = 0.36). If a shift in
strategies by the CNS occurs when speed of reaching increases, it is not evident in final
arm configurations. Surprisingly, lower variability in endpoints of the index fingertip
were observed in faster movements, despite slightly higher variability in final upper limb
configurations. This low variability in index fingertip endpoints may be due to online
feedback corrections using wrist and finger joint motions to more accurately position the
index finger. The higher variability in final arm configurations may be due to increases in
the noise in the CNS during generation of faster movements which requires greater
activation of larger populations of neurons in the brain and spinal cord (Harris and
Wolpert 1998; Apker et al. 2010).
44
Reaches to grasp the targets were found to have different mean ending arm
configurations than reaches to point at the high targets, but not the low targets. Also,
grasping provided slightly lower variance in final upper limb configurations, 3.53o on
average, compared to the other conditions (CR averaged 3.83o, QR averaged 4.20o).
Thus, although reaches to grasp targets may use slightly different mean final
configuration of the upper limb than reaching to point at targets, they do conform to
Donders’ law as variability in final arm configurations for movement from different
starting locations to a target is quite low. Indeed, it appeared that final arm and forearm
orientations for reaching to grasp the lower targets were controlled almost identically to
reaching to point at these targets, suggesting that the transport phase of reach to grasp is
controlled similarly to that for reaching to point at the target.
45
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