an optimal design for a foot activated a thesis
TRANSCRIPT
AN OPTIMAL DESIGN FOR A FOOT ACTIVATED
LEVER MECHANISM
by
JOHl ENSDORPF, B.S.
A THESIS
IN
INDUSTRIAL ENGINEERING
Submitted to the Graduate Faculty of Texas Technological College
In Partial Pulfillraent of the Requirements for
the Degree of
MASTER OP SCIENCE IN
INDUSTRIAL ENGINEERING
Approved
Accepted
May, 1 9 ^
75
l\Eh^73H
ACKN0WLEDGr4ENTS
I am deeply indebted to Professor Morris Schneider
for his over-all guidance in this thesis work and to Dr«
Richard A. Dudek, Dr. Robert Keller White, and Mr. Richard
Carmon for their advice and helpful comments. In addi
tion, I wish to express appreciation to the subjects
utilized in this research project for their willingness
and enthusiasm in cooperating with me throughout the study.
ii
TABLE OP CONTENTS
Page
ACKNOWLEDGMENTS ii
LIST OP TABLES v
LIST OP ILLUSTRATIONS vi
Chapter
I. INTRODUCTION . 1
Purpose and Scope . . • • • 1
History • • . . . • • • • . • • 2
I I . EQUIPMENT 8
Description of Equipment . 8
Use of Equipment 12
III. DESIGN OP THE EXPERIMENT l4
Discussion of Variable Factors . . . . . . 14
Schedule of Subjects 20
Experimental Procedure . . . . . . . . . . 23
Recording Data 24
IV. ANALYSIS OP DATA AND CONCLUSIONS 25
Computer Processing • • . . . • 27
Analysis and Interpretation 27
Conclusions • • . • . . . . . . • 35
Recommendations for Further Study . . . . . 37
BIBLIOGRAPHY ^2
iii
APPENDIX 63
A. Sketches of Important Components of the Experimental Device 64
B. Preliminary Study of Foot-Ratio Correlation 67
iv
LI3T OF tkBlMS
T^f^^U Pag«
1« 3ett«ioii Se^di iU ri»r 3iiSiJ««t« with
ChNlttr 0t fll»i« A t t i t u d e t « * * « * * * « 21
2 , Ideatif leAtion Teiile » « » • » • • 26
3« 3«irea«l*ftetor AaftVA Antlirfie « « * • • • » • « 28
LIST OP ILLUSTRATIONS
Figure Page
1. Barnes's Experimental Pedals . . 39
2. Lauru*s Experimental Pedals 40
3» Force-Load Relationships • . • • • 41
4. Pedal Assembly . • • . . . . • . . 42
5* Side View of Frame Assembly 43
6. Front of Frame Assembly 44
7* Pedal Linkage • • . • . 45
8. Electrical Equipment . . . . . . . 46
9. Electrical Schematic 47
10. Foot Dimension Ratio Study 48
11. Sample Data Sheet . 49
12. Fulcrum - Composite Score Main Effect . . . . 50
13. Resistance - Composite Score Main Effect . . 51
14. Ratio - Composite Score Main Effect . . . . . 52
15. Fulcrum - Resistance - Composite Score Interaction . • • . • • . . . 53
16. Resistance - Ratio - Composite Score
Interaction 54
17. Fulcrum - Type Score Main Effect . . . . . . 55
18. Resistance - Type Score Main Effect 56
19. Fulcrum - Resistance - Type Score Interaction • • . . 57
vi
20. Ratio - Type Score Interaction 58
21. Resistance - Ratio - Type Score Interaction , , 59
22. Fulcrum - Resistance - Ratio Type Score Interaction 60
23. Optimal Pedal Arrangements . . . . . . . . . 61
vii
CHAPTER I
INTRODUCTION
Purpose and Scope
Ralph M. Barnes (1) states that
although the foot pedal is one of the most common devices for freeing the hands for productive work^ most pedals are poorly designed.
Pedals might be classified as those requiring considerable effort for manipulation and those requiring little effort. The first class is well illustrated by the garment press and by certain foot-operated punch presses and shears. The second class is illustrated by the trip on a power punch press or the control on an electrical sewing machine.
This research study had as its purpose the investi
gation of the leg and the foot and their functional per
formance with a foot pedal under multivariant environmental
conditions.
For optimal design of a foot pedal mechanism a
number of factors must be considered which directly affect
output of energy and over-all performance. These factors
aret
!• Fulcrum position in relation to the foot.
2. Resistance or load imposed against pedal
movement.
3* Foot dimension.
/
4. Relation of application points of force exerted
by foot and linkage point of attachment on pedal.
5. Angular attitude of operator's tibia to plane
of the floor.
These factors are considered independent to over-all
performance of a foot pedal mechanism. The dependent
output can be measured in terms of operator's reaction
time to some stimulus, time to accomplish a specific task,
and by a measure of accuracy. For this research these
factors were measured in terms of2
1. Reaction time.
2. Travel time.
3* Accuracy.
All of the variables were considered significant
areas for study in the attempt to determine significant
design characteristics of a foot pedal mechanism.
History
Research of available publications concerning design
of foot pedal mechanisms indicates that comparatively
little work has been done in the area.
In 1941, Ralph M. Barnes, Henry Hardaway and Odif
Podolsky (2) of the College of Engineering at the State
University of Iowa conducted an experiment involving five
different types of pedals. The object of their study was
to determine the relative effectiveness of the five diffe3>-
ent pedals. Each pedal had a different arrangement of the
fulcrum, which brought into use different muscles of the
body and required different body movements. The five
pedal arrangements used are shown in Figure 1.
Each pedal was depressed against a tension spring
requiring twenty inch-pounds for one complete stroke. For
example, one of the pedals had the fulcrum point installed
under the heel, the ball of the foot moving through a
distance of two inches against a resistance of ten pounds.
Copper contacts connected in series to solenoid-
operated pencils on a kymograph were used to time all
movements. Time to accomplish task was the only depend
ent variable analysed.
In this study, fifteen experimental operators were
used, twelve male and three female. The operators were
all given similar instructions in the manipulation of the
pedals. The subjects came to the laboratory twice during
the experimental period. The first time they ran the
series of pedals in one order, i.e., 1-2-3-4-5. Then on
the second day the subjects operated the pedals in the
reverse order, 5-4-3-2-1. Before an operator was tested,
he was told to adjust his position and his chair so that
he would be comfortable. Each pedal was operated by the
right foot for a period of three minutes, and the opera
tors were told to work as fast as they could. After
one and one-half minutes of work, the kymograph was set
into operation for approximately seventy-five cycles.
After approximately a three-minute work period, the opera
tor had a three-minute rest which was followed by a prac
tice period of one-half minute on the next pedal and
another rest period of one-half minute. At the end of
this half-minute rest the operator began another three-
minute work period* This procedure was carried through
for all operators and on all pedals.
Data were taken from the paper tape which passed
under the solenoid pencils of the kymograph. The average
values of both orderlngs (from 1 to 5 and 5 to 1) of the
pedals were taken. The data for the fifteen operators
were averaged and analysed.
Considering the five pedals studied and the condi
tions under which the study was made, the following con
clusions were made:
1. Pedal 1 required the least amount of time per
stroke.
2. Pedal 2 required 5% more time per stroke than
Pedal 1.
3. Pedal 3 required 6% more time per stroke than
Pedal 1. ,
4. Pedal 4 required 3^% nore time per stroke than
Pedal 1.
5* Pedal 5 required 9% more time per stroke than
Pedal 1*
Lueien Lauru (4) analyzed various foot pedal ful
crum arrangements utilizing the force platform to collect
the dependent variable data. The pedals tested in his
experimental procedure activated a cutting and stamping
press. Both the standing and sitting positions were
analyzed in his experimental work, but only a detailed
analysis was made of the sitting position. Again, as in
the Barnes experiment, five pedal arrangements were used.
The arrangements are shown in Figure 2.
Force measurement with Lauru's force platform indi
cated that Pedal 5 fulcrum arrangement was by far the
best model.
Two related experimental works concerning levers
were performed in 1952 and 1953 by A. A. A. Caminada (3)
and R. E. Peale (5), respectively, at Purdue University.
These levers, however, were hand-operated. The 1952
project investigated the effect of size of a lever upon
the time required to operate it. The 1953 study was a
follow-up project in which the physical elements of the
experimental equipment duplicated the equipment of the
previous year.
The latter study attempted to determine an optional
value of a lever length at a given torque.
General conclusions reached in the 1952 experiment
were:
1. When the torque increases and the lever size
is kept constant, the time required to operate it in
creases proportionately to the torque.
2. The time required to operate a lever is nearly
proportional to the distance the hand has to travel.
3* The path that the hand has to travel is, proba
bly, the predominant factor in determining the time for
operation.
Conclusions reached in the 1953 experiment, using
the same torque values of the previous year, were:
1. For a given torque the cycle time to operate a
lever decreases as the length is decreased up to an opti
mal point. As the lever length decreases beyond this
optimal length, the cycle time increases. Optimal lever
length was found to be nine inches.
2. In general, as the torque was increased the
curve of lever length vs. cycle time tended to "flatten
out" and approach a straight line; therefore, the optimal
lever length became less definite.
Historically, experimental designs concerning the
foot pedal were confined to a single-factor design or, at
most, to a two-factor design.
The importance of the present study lies in the
fact that nearly all of the variables incorporated in
previous research, as well as a nuB^er of other important
variables, were incorporated into one single study.
A description of the equipment and its use will
be discussed in Chapter II. Chapter III will discuss in
detail the experimental design and the control of various
factors during experimentation. Chapter IV will be de
voted to an analysis of interrelationship of all the
variables introduced and their apparent effect, one upon
the other. Appendix A will be devoted to drawings of
specific components of the experimental device, and Appen-
dix B will reflect the results of a preliminary study.
CHAPTER II
EQUIPMENT
The discussion of the experimental device used in
this study will be divided into two sections. The first
section will provide a description of the equipment in
general terms. The second section will relate to the use
of the device during experimentation.
Description of the Equipment
The experimental device used in this study was
electrical and mechcuiical in nature with the structural
portion built of wood.
For definitive purposes a few terms are described
in order to differentiate terminology used throughout the
remainder of the text.
1. Task is the amount of deflection (tensile) of
a helical spring upon depression of the pedal. The task
distance remained constant throughout all experimental
sessions. The task deflection was 7*5 centimeters.
2. Load will be defined as the force in inch-
pounds necessary to deflect a specific spring the distance
of 7.5 centimeters.
8
3« Force is defined as the amount of pressure
exerted by the subject on the pedal.
With the experimental conditions a basic static re
lationship Qb«Wa was adhered to where:
Q « effort expended in inch-pounds;
W « spring arm load in inch-pounds
for a 7.5 centimeter deflection;
a » perpendicular distance from the pivot
or lever arm fulcrum to the line of
force in the spring arm;
b " distance from the lever fulcrum point
to point of force application by sub
ject's foot (ball).
Figure 3 portrays these relationships.
The foot pedal assembly. Figure 4, was constructed
entirely of wood and was adjustable to the appropriate
fulcrum point and allowed linkage adjustment for control
of mechanical advantage. The pedal component of the
assembly was eig hteen inches long and five inches wide
with a formed heel stop attached to the rear of the unit.
The dimensions of the pedal unit allowed positive contact
with the pedal for the entire surface of shoe sole and
heel for all subjects. Pedal action was accomplished by
use of a hinge attached to the underside of the pedal and
10
a base pedestal. The entire pedal assembly was mounted
on a plywood base for the purpose of positioning and
rigid support of the pedal unit itself.
The entire frame. Figure 5, supporting some instru
mentation, wiring terminal strips and linkage, took the
shape of an inverted "U." The frame was forty-eight
Inches in height and thirty inches in width. The front
of the frame. Figure 6, served as the subject's indica
tor panel. This panel was cut to a height twenty inches
from the floor and two feet in width to allow for pedal
positioning and freedom of leg movement during experimenta
tion.
Paz*t of the linkage between the pedal and the re
sistance. Figure 7» was accomplished by use of a non-
stretching Dacz*on cord. This portion of the linkage made
contact with the pulley system. For stability in indi
cator movement the portion of the linkage attached
directly to the spring resistance was one-fourth inch brass
tubing. The indicator assembly was attached directly to
this portion of the linkage. The tubing also offered a
rigid surface for braking pedal movement. This linkage
design functioned smoothly and with negligible friction.
The electrical portion of the equipment. Figure 8,
was designed to measure output of pedal movement auto
matically. In a single depression of the pedal, accuracy
or control, reaction time, and travel time were measured.
11
Figure 9 offers a schematic diagram of the electrical
circuity designed to achieve automatic measuring of the
dependent variables and automatic braking of the pedal.
The electrical timing devices used, measured time
in units of 1/100 of a second. Two were used: one to
measure reaction time, the other travel time. Reaction
time is defined as the time taken by subject from receipt
of visual stimulus to start of pedal depression. Travel
time is defined as the time taken from first movement of
the pedal until movement was braked.
A light stimulus was utilised to initiate action
by the subject. This light was mounted on the indicator
panel.
The sequence of events for the subject to perform
a single pedal depression was as follows:
1. Light switched on.
2. Pedal depressed by subject €md upward motion
of indicator with goal being task line (7*5 centimeter
task deflection of spring).
3. Braking occurred when the subject made his
Initial decision to stop pedal movement.
The proper electrical sequencing of these actions
by the subject was controlled by four relays and two micro-
switches. The microswltches were attached to either side
of the pedal, and the relays were mounted on the frame
and table. The release of a simple contact on the pedal
12
assembly stopped the reaction timer after switching of
visual stimulus. The travel timer started measurement
when reaction timer stopped. The travel timer stopped
when pedal movement stopped.
Pedal movement was detected by an astatic cartridge
arm attached to the linkage. The cartridge movement on a
thin aluminum surface generated sound which, in turn, was
amplified to detect the slightest pedal activation. When
movement stopped, sound detection ceased and braking action
occurred.
The braking component of the electrical system was
a solenoid unit which, with extensions of metal strapping
material, enclosed the rigid tubing portion of the link
age. Rubber-surfaced wooden blocks mounted within the
solenoid extensions clamped on the tubing when motion
stopped. This action offered positive braking action.
Proper electrical balance for the entire electri
cal circuit was accomplished before each experimental
session by adjusting voltage.
Attitude of each subject's tibia in relation to the
plane of the floor was indexed by simple angular devices
constructed of wood.
Use of the Equipment
All sessions were accomplished with the subject in
a seated position. The chair used offered a formed
13
back rest, «md all subjects were required to sit in a pos
ture position so that the subject's back contacted the
chair back. The subject was then strapped to the chair
with a seat belt.
Tibia angle was indexed and chair raised or lowered
to minimize visual parallax with the panel. The upper leg
was checked for horizontal attitude, and proper axis align
ment of the right leg and pedal were assured.
Each pedal depression and subsequent braking action
dictated that the accuracy measurement be read first on
the scale attached adjacent to the indicator track. Then
the travel time and reaction time were read and recorded.
Since four tibia attitudes were assigned to each experi
mental session, the subject was required to move to a new
position after the prescribed number of trials at a par
ticular tibia attitude.
Chapter III will discuss the experimental design
and the scheduling of variable factors for the research
study undertaken with this equipment.
CHAPTER III
DESIGN OP THE EXPERIMENT
Discussion of Variable Factors
The independent variables included in this ex
perimental project were carefully chosen to fit a real
life range of conditions confronted by operators of
pedal-activated mechanisms. Due to the fact that a num
ber of variables were being investigated, some thought
was given to limiting the number of variables that were
introduced. For this reason all subjects assumed only a
seated position, and only male subjects were used.
Four fulcrum points were selected for study. These
were:
1. Directly underneath the ball of the foot.
2. Midway between the ball of the foot and each
subject's ankle joint.
3. Directly underneath the ankle joint.
4. Underneath the extreme rear (heel) of foot.
Fulcrum points forward of the ball of the foot were not in
vestigated in this study due to the fact that previous
pedal studies have shown that pedals with this type of ful
crum are not as effective as those included in this study.
14
15
Resistances to pedal depression were introduced by
four helical springs. Each spring was carefully cali
brated prior to experimentation in order to determine ten
sile pressure in inch-pounds necessary to deflect each
spring 7.5 centimeters (2.86 inches).^ Calibration of
springs resulted in the following tensile forces necessary
to deflect the spring 7 5 centimeters:
Spring A - 12.8 inch-pounds
Spring B - 16.5 inch-pounds
Spring C - 21.3 inch-pounds
Spring D - 25#6 inch-pounds
The range of tensile forces adequately encompassed the
constant twenty inch-pounds resistance utilized by Barnes
(2).
Tibia or shinbone attitudes were introduced into
the design of the experiment in order to determine their
effect upon over-all pedal design. Tibia angles were
varied while the angular position of the pedal was held
constant at 30^. Pour tibia attitudes were incorporated
into the experimental design beginning with 90^. The
others were 100**, 110® and 120**. This chosen range of
attitude values includes that angle of the tibia required
7*5 centimeter deflection remained constant for all subjects for all experimental sessions.
16
for maximum power to be exerted by the foot as shown by
Reijs (6). Converted to angular attitude, this maximum
power angle is 108*, His findings, measured by a dyna
mometer, indicated that when the foot and tibia are at an
angle of 78* maximum power can be exerted by the foot in
a downward movement.
The trfiuismission of power through foot movement
created interest in the use of foot dimension as a vari
able factor. In the movement of a human foot upon a
device such as a pedal, the ankle joint will function
differently depending upon fulcrum position. For example,
when the fulcrum point is located forward in relation to
the ankle joint, the joint will rotate during the depres
sion of a pedal in the manner of a floating pivot.
Thus, a preliminary study was made of particular
male foot dimensions. Figure 10 illustrates the segments
of foot dimensions that were measured. All measurements
were taken of male subjects wearing Oxford-type footwear.
A device constructed in a shape similar to a com
mon woodworker's square was used to take the measure
ments. Plastic scales were attached to the appropriate
edge of the device, and measurement could be accomplished
directly and rapidly.
S«unples of twenty subjects were measured for the
dimensions a and d and for the dimensions a and c, and
17
thirty subjects were measured for the dimensions a and
b.
Nearly all of the twenty subjects (a-d sample) were
contained in all three samples. A correlation coefficient
was calculated for the three samples with the following
results:
a-d 58 20 samples
a-c 65 20 samples
a-b • .88 30 samples
The high degree of correlation evident in the a-b dimen
sions justified the fact that these dimensions, converted
to a ratio (a/b) and defined as the foot-ratio, were in
troduced into the experiment as a variable factor. Note
that both the a and b dimensions have a common point of
reference, the ankle joint. The correlation result in
creased the interest in the function of the ankle joint
in pedal movement. Identification of subjects with a par
ticular a-b ratio was a comparatively easy matter due to
notation during the correlation study.
The total range of foot-ratio values noted during
the sample correlation studies extended from .80 to 1.13*
In order to achieve some balance in the experimental sched«
uling, four foot-ratio categories were established. Each
category was limited to a particular range. Within each
18
category two subjects were identified. This procedure in
grouping subjects allowed the introduction of another vari
able factor, that of replication within ratio category.
The replication factor was introduced specifically for the
purpose of attempting to determine if significance could
be detected with subjects within a particular category.
The grouping of subjects as described limited the number
of male subjects to eight. The limits established for
each foot-ratio category were:
.80 - .85
.86 - .93
.94 -1.00
1.01 -1.07
Each experimental combination was limited to five
trials, the trial being the last independent variable in
troduced into the design.
The dependent variables were certain measures of
performance by each subject as he proceeded through the
sessions. Each pedal depression produced three experi
mental values: reaction time, travel time, and a measure
of accuracy foot control. The type score, then, was the
dependent variable factor of the experimental design.
A number of factors were strictly controlled during
all experimental sessions. Mechanical advantage as
19
impaired by each subject's foot during pedal depression
was an important consideration in the design of the physi
cal components and experimental procedure. Obviously,
mechanical advantage will vary for each subject depending
on foot length. For this reason, the linkage point was
constructed to be adjustable, and through proper adjust
ment no subject had a mechanical advantage over any other,
regardless of size of foot. The resistance arm was ad
justed to six and one-half inches for all subjects at the
beginning of all sessions. This distance was measured
from point of pressure (ball of foot) to the linkage point.
Parallax in visual reference to indicator panel was
controlled by appropriate elevation or lowering of ad
justable chair base. Each subject, regardless of stature,
had no visual difficulties in tracking the indicator to
the task line.
Since reaction time was a measure of subject per
formance, bias due to subject age was minimized by estab
lishing an age limit for experimental subjects. Subjects
utilized were restricted to an age range from twenty to
thirty-five years. This age range was selected in order
to have people with comparable reactions. All subjects
were Industrial engineering graduate students, with one
exception. Seven were Air Force Officers.
20
The task was controlled by keeping it constant
throughout all sessions.
Environmental conditions for subject comfort during
sessions were controlled by the use of an air-conditioned
room.
Fatigue was controlled by assuring adequate rest
periods between sessions and holding each session to no
more than twenty minutes' duration.
Each subject was afforded the opportunity to "learn"
to use the pedal device before actual experimentation
began. This was done to assure that learning factor bias
was eliminated. All eight subjects performed twenty trials
at each of the four attitudes during the learning period.
Variable combinations of fulcrum point and resistance were
introduced at this time. Data were taken during the learn
ing sessions for review and notation of stabilization in
each subject's performance. No subject experienced any
appreciable difficulties in learning to use the device.
Schedule of Subjects
Table 1 illustrates the schedule of subjects and the
combination of variable factors that they experienced dur
ing a total of sixteen separate sessions.
21
J .. •-'s.
••*•
I
• \ >
•- -
.'- n r r • • • T -
': • 1
•• - I
.-•1 ;
' I
;.;>. A t V
0C
I '
• I
> I "S -. r.
* I
- \ I
.. < . »
! i > C*
I I .
f " ' .
( • '
I
I »
1.. . -oi;:^s
TABLE 1—Continued
22
? Ad 90® 100 no 120
Cc 100® no 120 90
Ac no® 120 90 100
Ba 120® 90 100 no Da 90® 100 no 120
Ab 100® no 120 90
Bb no® 120 90 100
Bo 120® 90 100 no
10 Db 100® no 120 90
Dd no® 120 90 100
Cb 120® 90 100 no Bd 90® 100 no 120
DC 100® no 120 90
Ca no® 120 90 100
Ad 120® 90 100 no Bb 90® 100 no 120
11 12 Bd no® 120 90 100
Ab 120® 90 100 no Da 90® 100 no 120
Db 100® no 120 90
Bb no® 120 90 100
Cb 120® 90 100 no Dd 90®
100 no 120
Ad 100® no 120 90
DC 120® 90 100 no Ac 90® 100 no 120
Bd 100® no 120 90
Cc no® 120 90 100
Ad 120® 90 100 no Dd 90® 100 no 120
Da 100® no 120 90
Ba no® 120 90 100
13 Da 90® 100 no 120
Ca 100® no 120 90
Ab no® 120 90 100
Aa 120® 90 100 no Db 90® 100 no 120
Ba 100® no 120 90
Be no® 120 90 100
Cc 120® 90 100
14 Ab 100® no 120 90
Cd no® 120 90 100
Cc 120® 90 100 no
Dd 90® 100 no 120
Cb 100® no 120 90
Aa no® 120 90 100
Ac 120® 90 100 no DC 90® 100 no
15 Cd no® 120 90 100
Bd 120® 90 100 no Ad 90® 100 no 120
Da 100® no 120 90
Aa no® 120 90 100
Be 120® 90 100 no Cb 90® 100 no 120 Ab 100® no 120
no 1 120 I 90
16 Bb 120® 90 100 no Aa 90® 100 no 120 Cd 100® no 120 90
Ab no® 120 90 100
Cd 120® 90 100 no
Da 90® 100 no 120 Ba 100® no 120 90 Dd 110® 120 90 100
Legend ^m^
Fulcrum Position
A r'x _ ^ •*
A - Ball B - Midpoint (be-
•1 1 • ! tween ankle joint and ball)
C - Ankle Joint D - Rear of Heel
Resistance (for 7.5 centimeter deflection)
a - 12.8 inch-pounds
b - 16.5 inch-pounds
c - 21.3 inch-pounds
d - 25.6 inch-pounds
1 1 t HI
23
Each subject was confronted with a completely ran
domized schedule of fulcrum point-resistance combinations.
The sixteen possible combinations of these factors dic
tated the number of sessions that were to be held for each
subject. In any one session, however, the schedule was
designed to prevent a repetition of any one combination
during the same session. No more than two sessions were
held for any one person on any particular day.
The attitude factor was counterbalanced in effect
throughout the schedule. No subject assumed the same
tibia position at the start of testing until four sessions
had been completed. Only two subjects assumed the same
tibia attitude in any one session. This schedule design
minimized any systematic scheduling effect.
Experimental Procedure
Each experimental session, as scheduled, consumed
on the average approximately fifteen minutes of time. All
necessary adjustments in equipment were made prior to the
subject*8 arrival for his experimental session, except for
the mechanical advantage adjustment. After subject posi
tioning, the mechanical advantage adjustment was made.
Trials were Initiated by means of a precompiled random
time list. The values of 1,2,...,5 seconds were random
ized in order to provide random activation of the stimulus
24
Recording Data
Figure 11 illustrates the format of the data sheet
used during this study. After each pedal depression the
accuracy measurement, travel time, and reaction time were
noted in that order.
The accuracy measurement was converted to a numeric
system adaptable to computer progreimmlng. A constant
value of 2.0 was added to each accuracy value for this
purpose. Accuracy was measured in tenths of centimeters
above or below the 7.5 centimeter task line. If, for ex
ample, the subject stopped the indicator .2 of a centi
meter above the task line, the value was recorded as <f.2.
Thus, the value recorded was 2.2. The value of 2.0 would
Indicate perfeet control or accuracy. All accuracy values
were noted algebraically on the data sheets but converted,
as stated above, before punching the data on IBM cards.
Reaction and travel time were noted directly as read.
The analysis and interpretation of results will be
discussed in Chapter IV.
CHAPTER IV
ANALYSIS OF DATA AND CONCLUSIONS
The analysis of variance technique was utilized to
determine main effects and higher order interactions of
variables introduced into this study. To do this, the ex
perimental data was punched on IBM cards for IBM computer
processing.
The 6.0.090 60K Anova Program was used. This pro
gram will handle up to eighteen factors with a maximum of
999 levels per factor. With this program the data field
may be of any size, located in any position on the detail
card, with the only restriction being that the total un
corrected sums of squares may not exceed thiirty-four
digits. In addition, the computer operator has the option
of picking up extra decimals in the calculations of the
sums of squares and means for additional accuracy where
desired.
Table 2 Illustrates the identification for sort
order, factors, levels, and codes used in IBM card pro
cessing.
The design of the experiment generated 7680 experi
mental values. Of this total, there were 2560 values each
25
26
for reaction time, travel time, and accuracy. Each value
represented one punched card with appropriate coding and
experimental data.
TABLE 2
IDENTIFICATION TABLE
Field
5
10
15
20
25
30
35
40-41
Factor
Fulcrum Point
Resistance
Ratio
Attitude
Replication
Type Score
Trial
Observation
Level
Heel Ankle Mid-Point Ball
Light Light-Medium Medium Heavy
.80- .85
.86- .93
.94-1.00 1.01-1.07
90® 100® no® 120®
1 2
Reaction Time Travel Time Accuracy
1 - 5
Code
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3 4
1 2 3
Sort Order 1 2 3 4 5
A
B
C
D
E
P
G
i 1 H5
•I
Hi
27
Computer Processing
The entire lot of experimental data was processed
through the computer on the initial pass with the appropri
ate seven-factor sums of squares control cards. Table 3
represents the results of the Seven-Factor Anova Analysis.
In Table 3 It can be seen that three main effects, eight
first-order interactions, ten second-order interactions,
three third-order interactions, and one fourth-order
interaction were significant at the 1% and 5% level.
Mean values were then obtained by further computer
processing for the above significant main effects and
interactions. Since the computer memory storage was ex
ceeded on seven- and six-factor processing for the appro-
priate means, the two variables of replication and atti- 5
tude were dropped from the design in order to obtain the
means for the main effect and interactions of the five
remaining variables.
Analysis and Interpretation
The results of this design will be discussed under
the following topics but not specifically in the order
listed!
1. Fulcrum Main Effect - Composite Score
2. Resistance Main Effect - Composite Score
3. Foot-Ratio Main Effect - Composite Score
28
S &4
04
O •H ^ 00 K
fCt
CO
£ OS 3 O* CO
c ti 0) s:
10 0)
(d 3 o* CO
^ O
tt
CO
%-« •d
«> o ^ O CO
CO 2:
O QO
•
o\ ON 00 O
#
r^^* IVCT\ rHVO b-csi
• •
t^cn
<*^ o ^m^
1 n C "P o 0) O «H 0) a> ^p
44 A « « d moo
OO H rH i H
e
•sr t*. Jar
•
* r
<x C O «H *> Cd o •H i H
a « m
<<«> i^
w w o s.^s,^
« » - ^
i n i H U M f M n i n c o i A c o w u M n f - i H i n m O O O O O O Z 0 5 5 5 K O O O O O O
. . . . . . • . . . . . .
« i « t 4 e « » m m m m m m m m m m
t ^ H - B T t ^ O O i V D i n a\oo JBT CVi -ar o o>vo r-|j«* ovcNj t«-oo m « r o IACTNOO i n ON ON i n rHONCN|VO-*OOHt»-mOCN|OOCNI-=rOH XT CM moo voifN<NicMJW-b-.irNmt-uMnc\j
. . . . . . . . . • . . . • • • OO co-«r o ro-=r <M t n H »H <N| rH iH OO iH i n H OO fH
rHCNI vo H
ONOO H « • vo •*»• en t ^ JT vo 00 (NJ 00 ON«r <\J t*-VO CntncSO COfHVO ^ - m f ^ O O O O h - r - l t * -
a\Hfsllnl- cMl- rHooor^oovo -o j o o o o o o o o o o o o o i n o
H rH OO
Hr^rninorHvocTNCNiO coinmawoooov ONonoe^ONt*-ocoot-oj ONVooooo cvirvi t-ONino ONvo mrotnvo coo tnmcocNjvo OOOOOeNJxriHVOOHOOCMOOCVJVOrH-sr
ON fOVO O vo CNJ rH
ruoofncjNO>cyNt**rr)a\ONONb-t«-t*-iHCNjvo r^ CNJ CM <M CNIOO vo
.'"^ " Q) 0) O - ^ lU
«^ C 0) O S 01 T) O p + i d CO %i m -P O -H -H 0)
CO rH m 4^ O* t 43 a 9» +> ^ >» C O t k i K < ^ ^ ^ Q ^ ^ 4><^s^ O v - f Q Q Q O v ^
wH ::! » CO
29
•a
4»
o
I CQ
0U F Ratio
Mean Squares
Sums of Squares
4-4
Source
intnininLnBOUMninrHinrHrHiHcococococococococococococo o o o o o a o o o o o o o o S 2 : 2 : 2 : 2 : S 5 2 5 2 : s : 5 2 : 2 ; 2 2 5 2 ;
. . . . . . . . . . . . . m m m m m « * « i | l « l « l « l « I I I 4 I til
OOt- . rHmrv|J8rJ9'OJOOiHCNifHONrHUfNCNJONr*-HVO<VJrH Cr>0O 00 fvl-a* vo o H«r 00 <7\vo b-ONCNiLncM.«-^fnoN<Ni COJ^OOVO O O ininvo t^ invo-sroooo c\jt*-or>ooNCOONina\CNi<nLfNrH awooo c?Nino ooo cvi rHONC7Nt*-ininrHrHinrotMcocN»cuQO ocofocM mvo-sr-^ ^-^-vo vo
C7\ rH en 00 CM rH vo CM i n H ^ - rH rH rH H r-{ f^ H
t«»OrHooc\jcoinaN»HrHa\rH-^vo<M onoo h-vo ONinmcnvovo rncvj vo»HO*rooi*- iHOoo t«-vo b-voNO-cr inrHvovofvirr><Nic\icofOcnro j s r v O C M ^ T r H O C r N H C M O m O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
cno rooo ONOJ »H inrH cr>t~t^vovooo J * O IH t*-vo a^^-^r>r^ ONt*-co OVO ovovo H f-mt-in-ar-ss- t*-a\vo cncsi o ONOO I I * -O foovo t*--sr 00 vo (M O rOJer VOONrHCOVOOO-srvOrHVOCXjOO ^-VO CVI ONOO nr> b- CM rH CMfOfHOOCMiHinrHtn COVO C n c O O O O O O O O O O O H r H r H r H
rH iH iH
vovovoooaoaoaocOj:r .9-co«r- :4 'CM«r CMCMCMCM-st-covovovo^rvovo rH H rH PH rH i n i n iH i n invo r^ r^ M r^ <M rOCOCOCMCOCO
(0 H (d •H
fk* p:;* PC4 |lk« Q £-4 0 PK. (fc. 1^ Ik, fk, 0 Q pi« Q Q 0 ^ 0 0 0 0 0 0 0
C Q O Q < ^ C Q C Q O « < < « < < C Q ^ O < C Q O O < | k , ^ < < : ^ C Q c £ |
30
c •H 4^ c o o I I
CO
CQ <
0^
o <H
Rat
Vti
n 0} ^ flO 3 CJ*
CO
Mea
n Q> SM «d 3 C3*
CO
o (0
CO
4H TJ
a> o u d o CO
cocococococoHcococococoeococococococo s;a2;ZS:Zoa5S5S:»S5;z:2:2!S52;2:s :
41 « m m
C n i n o t * - t» -sr vo CMVOOOrHOOCMJa-OOVOVOCM-sr JsrCMONrHrHOOVOOOVO ^ - f O i n o O ON ONOO OO OO ON OO t^-W" rH rH t*-VOaO VO O^^TOOOCMOVOVOOOCM b-roinja'-sr ovo invovooo t - i n i n i n i n t n i n m
rH H
O OVCO rA r-i \C\ ir\ O J9' rH OOVO O t-VO ON ON o ^-•>ar rH CM CM CM inoo cororo jT rorocMCMCvjCMmcM o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
vo o o incoJT CO in o <M rH CM o cr\oo o av^a- CM CM o o * r iH iH-sr inoo moNrHoo CM IH mint>^^a-- s r j * o i n i n f o o c M v o cninvo H ONVO CM CM i n C-r H r H C M r H O r H C V l C O C n CnJBT CM CM rH invO VO VO t -
H
VOCMOjCM.arJO'-srCOOOOOOOCMCVlCMVOVOVOvOOO f n t * . t « - t > - . C M C M C M O O O O t ^ t ^ t * - r H r H r H H J O -
rHr-irHr-i CM CM CM CM VO
O O O O O P
O O O O O O O O O O f c f e f c f c Q 0 ( ^ f e f e O O O U Q Q Q P ^ P c 4 p ^ O O Q O O QCQOQ| i :< |k ,P :4CQCQOOOQQCQQQOOCQ O 5 2 < < O Q O Q 5 < < J O Q O Q C Q O 5 ^ < O Q < C
rH i n o o
vo a\ CM i n
CA »H
vo en 0 0 en
.*-s >
CM VO <?\ i n
o H CM
ON t*-VO t*-
H cU 4:>
o &^
31
M. Interactions - Composite Score
5. Fulcrum Main Effect - Type Score
6. Resistance Main Effect - Type Score
?• Foot-Ratio Main Effect - Type Score
8. Interactions - Type Score
In the analysis using composite score, a review
must be made of its content. Three type scores or de
pendent variables were simultaneously recorded on each
trial of this study. For definition a listing follows:
1. Reaction time - the time a subject took to
begin pedal depression after receipt of visual stimulus.
2. Travel time - the time taken in pedal de
pression to task line position, when braking occurred.
3. Accuracy - degree of departure, high or low,
if any, of indicator from task line.
Each of these scores measured an independent aspect
of performance of each subject on each trial. However,
while the primary interest in this study is in the joint
effects of each of the Independent variables and their
combined effect upon these three dependent variables, we
shall first consider the Independent variation upon the
composite score.
While the reader may find it unusual to add apples
and pears or, in this case, travel time, reaction time,
and accuracy, it is very important to know if the inde
pendent variables do have the same effects upon the
32
three scores. The composite score considers this rela
tionship.
In Table 3 composite scores are observed to be sig
nificant. In Figures 12 through 22 the mean effects of
the independent variables are charted.
In Figure 12 the effect of fulcrum position upon
the composite score can be observed. This effect shows
that the value of the composite score increases directly
as the fulcrum position moves from the heel out to the n
ball of the foot. ^
In Figure 13 the effect of resistance upon the com-i
posite score may be seen. Here, the effect is curvilinear I •I
rather than the linear effect of Figure 12. ;;
Figure 14 shows the foot-ratio effect. This effect J
is more curvilinear than in Figure 13. t
Figure 15 portrays the joint effect of fulcrum
point and resistance on the composite score. This effect
begins to get somewhat complicated. While the linear com
ponent of fulcrum. Figure 12, is still observable, it
becomes highly erratic in trend when the curvilinear effect
of Figure 13 is superimposed.
Figure 16 shows the effect of superimposing the
mildly curvilinear effect of resistance to the highly cur
vilinear effect of foot-ratio. Here, it can be noted that
while each Independent variable has a curvilinear effect
33
separately, their joint effect is much more extreme as one
progresses to the highest resistance-ratio combinations.
Now, as to the significance of this effect, care
must be taken. The final evaluation of this effect can
be made only when this relationship is broken down in the
subsequent higher order interactions.
More specific meaning of the preceding phenomenon
may be more readily determined through analysis of the
interactions involving the type score factor.
Figure 17 shows the significant fulcrum point by
each type score interaction. Figure 17 definitely shows
the first concrete indication that travel time steadily
increased as the fulcrum point was positioned forward
from the rear of the pedal. Negative correlation between
travel time and reaction time appears as the fulcrum moves
from the point at rear of pedal to ankle point.
Accuracy, though consistently below task line, does
not depict appreciable variation, regardless of travel
time and fulcrum position.
Figure 18 charts resistance-type score interaction.
It shows that resistance has little effect on travel time;
in fact, during the course of this study travel time de
creased when the heaviest resistance was imposed upon the
subjects. Note that reaction appears negatively corre
lated to travel time. Accuracy was not appreciably af
fected by the four levels of resistance.
34
The second-order interaction of fulcrum point-
resistance-score interaction, charted in Figure 19, magni
fies the relationships portrayed in Figures 17 and 18.
All foot-ratio subjects produced the shortest travel time
with the light spring but were affected by slower reac
tion times. The subjects in foot-ratio 4 performed with
a decided decrease in travel time but with sharp increase
in reaction time as well. All resistance-ratio combina
tions indicated little effect on accuracy, regardless of n
travel time. !i
Figure 20 notes the effect of foot-ratio upon type
score. Also, in comparison with Figure 14, the highly !
curvilinear effect was not primarily the result of travel
time. Here, the combined effects of reaction time and i.
accuracy had greater effect in degree of curvature. Fig- "
ure 20 indicates that subjects in the foot-ratio 1 cate
gory appear to have the best control or accuracy, although
not to an appreciable degree.
The resistance-ratio-score interaction. Figure 21,
depicts further information concerning the graphic dis
plays shown in Figures 18 and 20. Reaction time and re
sistance appear positively correlated, while travel time
and accuracy appear negatively correlated.
Figure 22 shows the third-order interaction of
fulcrum point, resistance, foot-ratio, and type score
35
Interaction. It offers the highest degree of interaction
and graphic magnification for the main factors in the
analysis. General upward trend in travel time is again
noted as fulcrum position is moved toward the ball of the
foot. Erratic variations in reaction time are noted for
all subjects with resistances cmd fulcrum position at
rear of pedal. Reaction time is significantly of longer
duration than with other resistance-fulcrum combinations.
Least variation in accuracy measurement appears with ful
crum position under ankle joint. \
Conclusions
In discussing appropriate conclusions generated by
this research, one must put the issues in proper perspec
tive. There are certainly a number of possible issues.
For example, one might ask, what is the optimum combina
tion of these independent variables for a general pedal
design? Second, what is the optimum pedal design for ob
taining accuracy under specific load? Third, what is the
optimum combination for total response time, reaction and
travel time, or for reaction time or for travel time
alone? The most significant result of this study is that
the answer to each of these questions cannot be the same.
However, an answer to each of these questions can be
specified; then, a detailed analysis of a graphic
n
36
relationship, as shown in Figure 22, can assist in making
a determination.
In general, this study has shown that:
1. Travel time increases for pedal activation as
the fulcrum position is moved from heel toward the ball
of the foot.
2. Accuracy or control is not necessarily a re
sult of speed of pedal movement.
3. Reaction to a stimulus appears slower when
lighter resistances are confronted by operator.
Specifically, analysis of Figure 22 will produce
the answers to the questions posed above depending upon
the condition specified. For example, what combination
produces the quickest pedal travel for subjects in foot-
ratio category 2? By analysis, foot-ratio 2 subjects can
manipulate pedals with fulcrum point at rear of heel and
heavier resistances more quickly.
For accuracy, a fulcrum position under the ankle
joint appears to give more consistent control of foot in
depression.
For reaction, subjects in foot-ratio 2 portray the
same rapid response throughout many combinations.
Figure 23 Illustrates some pedal arrangements for
optimum performance as specified. Arrangements are based
on data obtained from this study. It must be understood
37
that the most significant finding of this study is that
optimization is dependent upon job specification and indi
vidual operator. The variations in performance, shown by
subjects under experimental conditions with all combina
tions, prove this point. We need to know how a specific
pedal mechanism will be utilized by an operator or opera
tors. For example, will only one operator specifically
assigned to the machine activate the same pedal for ex
tended periods of time, or will a particular machine be
pedal-activated by a number of different operators? The
arrangements, shown in Figure 23, take this into account
showing, first, a general pedal and, second, a pedal
which would be adjustable for an individual operator.
Recommendations for Further Study
This study has generated a number of questions con
cerning various relationships. A portion of these could
be considered technical, another portion psychological.
However, confining ourselves to the original purpose, the
following recommendations for further study are made.
Reaction time, travel time, and accuracy data can
be processed separately for determining significance to
all other variable factors and graphic portrayals analyzed
in a manner similar to this study.
A further study should be undertaken, eliminating
the accuracy score. This could be done with the same
38
design and experimental device. Task line would remain as
the goal, but subjects would depress pedal until task line
was reached or exceeded. This study would then determine
the relationships between reaction time and travel time
with no accuracy requirement. Another variation would be
the inclusion of a stop in physical component design which
would limit pedal travel. Comparisons of these two stud
ies would be beneficial.
It is also recommended that an identical experiment
and design be repeated with the use of a force platform.
A study of this nature would explore the degree of ex
penditure of effort as each subject was confronted with
the various experimental combinations.
The experimental design used in this study could
explore the standing position during pedal activation.
This independent variable could be incorporated into all
the studies mentioned above.
Finally, with a minimum of modification of the ex
perimental device, vehicular braking studies could be
undertaken with all the variable factors utilized in this
research project.
(9
TTTTTrTTr,
yy////.
- < ^
I ' ' i r ' : , 1 . - - l U - j r ; i r r; • r; f ' .xp'M'1 ni^.n t r, [ I V d n ] . " ,
' t ' I
/ . - - ^
> ^ I r . P . — L n u r i A ' n i .xpor -1 mont,,-) ]. (^ I i a l
Ankle Joirit
Qb Wo
F i r . . 3 . - - • • ' " r c o - i i O n d l^•'1 n t, 1 o i i nh 1 pr.
42
Pig. 4,—Pedal Assembly
13
Fig. 5,—Side View of Frame Assembly
44
Pig. 6.—Front of Frame Assembly
15
I Fig. ?•—Pedal Linkage
46
n
Pig . 8 , - - .E lec t r ica l Equipment
in
^ \ > 'v/ V / V> I
n . - J
[:
M
r >
, « f ;
- I I > ' • )
<"•) . t h i I •
'J-:
r^riv\iQ Jo»r<>
F],:, l t ) . - - F o f ) l Dimrnr. Ion iint. lo :\\.\i'i\'
^9
SUBJECTS NAME
AGE
A / B DIMENSION' A
RATIO
POSITION
ATTITUDE
FULCRUM POINT
DATA SHEET
DATE
B.
CODE
SPRING RESISTANCE IN-LBS IN-LBS IN -LBS. IN-LBS.
TRIALS:
RANDOM TIME REACTION TIME TRAVEL TIME ACCURACY
Fig. 11.—Sample Data Sheet
^HXA. T...NO.^U^..CAU CDUU
.32"
50
8 -3" C/)
<D
(/> O O. E o o
.30-
.29-
.28 Heei Ankle Mid-point Bail
Fulcrum Position Fulcrum Main Effect
Fig. 12.—Fulcrum - Composite Score Main Effect
51
.31 -a» o o
CO
r 30 w O Q. e o U
,29 1
.28 I 2
Light Light-Med. 3
Med. 4
Heavy
Resistance -Main Effect
Fig. 13.—Resistance - Composite Score Main Effect
.31 -o o
CO
.•—
O .30 E o a
.29
52
.28 1 2 3 4
.80-85 .86-93 .94-1.00 I.0I-I.07
Ratio Main Effect Fig. 14.—Ratio - Composite Score Main Effect
53
31 -
o o en
o 30 -
CO o o. E (3 29
28 -
27
Legend - order (Fulcrum - Resistance) Fulcrum Point Resistance
Hee l - I Light - I Ankle - 2 Llght-Med-2
Mid-point - 3 Medium -3 Ball - 4 Heavy - 4
H (- H 1- H 1 H
— c v j r o ^ — < \ j r o ^ — c M r o ^ — cvjro^ij. I I I I I I I I I I i I • I * •
— — cvJCMCsJcvJrorOrOro^^^'^f
Fulcrum-Resistance Interaction Fig. 15.—Fulcrum - Resistance - Composite Score Interaction
5'*
.32
.31 " O
o
in
i . 30 E o o
.29
.28
Legend-order (Resistance-Ratio) Resistance Ratio
Light-I . 8 0 - . 8 5 - I Light Med.-2 . 8 6 - . 9 3 - 2
Medium-3 .94-1.00-3 Heavy-4 101 -1.07-4
— cvjrosr — cviro^ —cMro^ — cvJrO' I I I I I I I I I I I I • I I I
cvicvicMcsJrorororosr^^^
Resistance - Ratio Interaction Fig. 16.—Resistance - Ratio - Composite Score Interaction
55
o D k . 3 O O
< ^»^
0> V) 10)
<D E
H
.55
.50
.45
40
35
.30*
.25 -
. 2 0 "
Legend Reaction time Travel time
X—Accuracy
Accurocy Tosk Line l.lcm.
•f Heel Ankle Mid-point Bali
^Accuracy task line indexed at .30 for clarity.
Fulcrum-Type Score Interaction
Fig. 17.—Fulcrum - Type Score Main Effect
56
o o
O o
<
^^.50 o •^.45 E F .40
.35
. 30 « -
, 2 5 -
2 0 -
.1 5
Legend Reaction time ^Travel time
—X—Accuracy
Accurocy Tosk Line l.lcm
Light Light-med. Med. Heavy ^Accuracy task line indexed at .30 for clarity.
Resistance-Type Score Interaction
Fig, 18.—Resistance - Type Score Nain Effect
57
o s §.55
<
-6-50 W
Q.45 + 0)
E.40
.35-
.30-
.25
.20
.15 I
Legend order (Fulc.um-Resistance) Fulcrum Heel - I "n'-'^ - 2
Mid-point-3 Ball- 4
Re^btG/.cs Lic^hv - I
Light med.-2 ^!odium-3 K^avy- 4
Accuracy Task Line l.lcm.
_, 1—I 1—I > i — I — I — I — I — » — I — I — - X .
Pig. 19.—Fulcrum - Resistance - Type Score Interaction
58
o V .
3
0.55 -<
05.50 o ^ 4 5 + cu
E P.40 -
.35 -f
.30*
.25 -
.20 -
.15 -
Legend Reaction time Travel time
—X—Accuracy
Accurocy Tosk Line - . I cm.
.80-85 .86-93 .94-1.00 I.0I-I.07 ^Accuracy task line indexed at .30 for clarity.
Ratio-Type Score Interaction
Fig. 20.—Ratio - Type Score Interaction
59
> » o o k. O O
<
'g.50 C/)
O -^.45 E P .40
.35 +
.30
.25-
. 2 0 -
.15--
Legend-order (Resistance-Ratio) Resistance Light-I
Light Med.-2 Medium-3 Heavy - 4
Ratio .80-85-1 .86-93-2 .93-1.00-3 1.01-1.07-4
Travel Time
Accurocy Tosk Line l.lcm.
Reaction Time
H 1 h H 1 f- H 1 - c v j r o ^ - c v j r o < r - c v i r o ^ y c v i r o ^ J L J - — J - c v J C V J C v i c v i r o r o r O K ) ^ ^ ^ ^
^Accuracy task line indexed at .30 for clarity
Resistance - Ratio- Type Interaction Fig. 21.—Resistance - Ratio - Type Score Interaction
60
e o
V* u o ^ ^ "c
0) w o u CO
0) a. >% h-
1
o • —
o a: 1
d> u c o M
'w 0)
QC 1
€ 3
3 l i I X .
5 'jp,
o cc 1
o c o "w *w 0)
Q:
rum
-ul
c
u.
k .
a> TO
k .
o
end
CJ>
— M 1 1
lo ro 00 0) 1 1
O <D 00 00
• "
— CM
•«• ^ 1
igh me
- J ^
Ii — CVJ
« «
K) ^ i 1
O N Q 9
1 1
^ 7Z <X> O
' —^
ro 5r E >. .2 > xj a a> 0) 2 X
ro ^
-Poi
nt
Ba
li
• o <u
_ J
(A
O C !o E o o
(oas|0)aui!i g lO in
o — » — •n o
—t— LO
ro
— t — O ro
(O cvf
— t — O CJ
£-> Z-^ 1-^
> •£•
£-£ 2-£ I £ * - - ^ -£-2
i-z > • I £- I-2 -I I -I-
*--^-
^ - f -
£-C-Z-£-/-£-it-Z-£-Z-
z-z -i-z-^ - / -f - / Z- I -I -I -
£-^ • Z-^-l-t^-
^ -£-£-£ -Z £ I -£-
^ -z-£-Z zz-I z •
^-1-£- I -Z - I I -I -^-^ -£-t^ -Z-tf -/ - ^ -^-£-£-£ -Z-£ -t-£ ->-Z -£-Z -Z-Z -l-Z-
p, - I -£- I Z- I -I - I -
- >
•A
£ •£ £ £ £ £ £ £ £ £ £ £ £ £ £ £ Z Z z z z z z z z z z z z z z z
c o •H
o CtJ
SH
c
M
OJ o o
CO 0) C-> : EH
o •H 4^ c6
DC
O c CtJ
- P CO
• H CO <D (X
I
o
I I •
•H
in
61
Optimal Pedal Arrangements Based On Researcti Data
\
Ankle joint-V
Fulcrum point
Specification: (Various number of operators on some pedal) Reaction, Speed and accuracy Resistance 12.80-16.50 inch-pounds Mectianlcal Advantage Constant For All Operators,
Ankle joint \
Fulcrunr) point
Specification: (One operator on some pedal Jong duration Reaction, speed and accuracy Adjustable for a specific foot ratio in regard to resistance, (see Figure 22) Mechanical advantage predetermined
Fig. 23.—Optimal Pedal Arrangements
BIBLIOGRAPHY
(1) Barnes, Ralph M. Motion and Time Study, New York: John Wiley & Sonsl j"anuary, 1961, p, 286.
(2) Barnes, Ralph M.; Hardaway, Henry; and Podolsky, Odif, "Which Pedal Is Best?" Factory Management and Maintenance Magazine. New York: McGraw-Hill Book Co, January, 1942, pp. 98-99»
(3) Caminada, A. A. A. Master's Thesis, Purdue University, 1952.
(4) Lauru, Lueien. "Physiological Study of Motions." The Advanced Management Magazine. Published by the Society for Advanced Management. Vol. 22, No. 2, pp. 17-24.
(5) Peale, R. E. Master's Thesis, Purdue University, 1953.
(6) ReiJs, J. H. 0. "Human Body Size and Capabilities in the Design of Vehicular Equipment." Harvard School of Public Health, Boston, Mass., 1953, pp, 38-40.
62
APPMDIX
A. Sketches of Important Components of the Experimental Device
B. Preliminary Study of Foot-Ratio Correlation
63
APPENDIX A: SKETCHES OF IMPORTANT COMPONENTS OF THE EXPERIMENTAL DEVICE
Dacron Cord ^ Linkage —^
• < . . .
Half Sections Wood Clamped to Cord
Cartridge
Alunninunr) Strip
Astatic Cartridge Assembly
64
65
rV ^
Heavy Gauge''^ Copper Wire
i
r Brass LinKage Section
:S
V Front Panel
= osition
Indicotor Assembly
66
Solenoid Unit
r
^
>
Brass Linkage
/, Wooden Block K / Broke Shoes
/_ Rubber Surfaced
O O O GO o
\
• < ^
Movement of Solenoid Arm on Activation
Broke Assembly
APPENDIX B: PRELIMINARY STUDY OF POOT-RATIO CORRELATION
The following listing of actual (a-b) measurements
taken prior to experimentation resulted in a correlation
coefficient of .88. The coefficient was calculated by
the relationship
^ ngxy -^xgy
[n£x^-(^x)^3[n£xy^-(£y)^]
Subject Number
1
2
3
i|
5
6
7
6
9
10
11
12
13
IM
a Dimension
4.625
4.000
5.375
4.000
4.625
4.250
4.875
4.250
4.625
4.750
4.500
4.375
4.500
5.250
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
b Dimension
4.750
3.375
4.750
4.000
4.250
4.250
5.000
4.308
4.750
5.000
4.500
4.500
4.375
4.750
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
Inches
67
68
Subject Number
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
a Dimension
4.125
4.625
5.000
4.625
4.875
4.500
4.625
4.500
4.750
4.000
4.750
4.500
4.500
4.750
4.250
4.250
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
b Dimension
4.250
4.625
5.125
5.125
5.000
4.500
4.875
4.500
5.250
4.250
5.000
4.500
4.500
4.625
4.250
4.500
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
inches
