EXPERIMENTAL DETERMINATION OF AN
OPTIMAL FOOT PEDAL DESIGN
by
DONALD J. TROMBLEY, B.S, in E.E,
A THESIS
IN
INDUSTRIAL ENGINEERING
Submitted to the Graduate Faculty
of Texas Technological College
in Partial Fulfillment of
the Requirements for
the Degree of
MASTER OF SCIENCE
IN
INDUSTRIAL ENGINEERING
AE6.- ^C>M
"805
19a
No. \55
ACKNOWLEDGMENTS
I wish to express my appreciation to Drc Mc Mc
Ayoub for his direction of this thesis and to the other
members of my advisory committee, Dro R« Ao Dudek, Drc
Eo Ro Tichauer, and Dr., Co Go Halcomb, for their helpful
advice and criticismo
I also wish to thank my wife, Helen Ann, for her
assistance in performing the experiment and proofreading
the thesiSo
ii
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS . . . . . . * . . , . . . . . . . . .
LIST OF TABLES
ii
, . . . , . . . .
v
LIST OF ILLUSTRATIONS
I.
vi
INTRODUCTION
1
Purpose and Scope
, ,
History ,
II.
EQUIPMENT
3
,
.
Technical Description of Task Device
III:
...
EXPERIMENTAL DESIGN AND PROCEDURE
13
13
24
Experimental Design
24
Load e c t . e « * * o . .
Foot-Tibia Angle
Fulcrum Location
Ratio e e
Replication
Criteria of Optimality
Experimental Procedure
IV,
1
.
RESULTS AND DISCUSSION
'-
.
25
28
28
29
29
31
32
36
Method of Analysis
36
Results » ,
«
Analysis of Variance
Significant Variables
Reaction Time
Travel Time
36
36
40
40
44
iii
iv
TABLE OF CONTENTS—Continued
Page
Vc
CONCLUSIONS AND RECOMMENDATIONS
Vy o n C X U S J. o n o
o
o
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o
o
o
c
o
o o o c o o =
c
o
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c
o
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5
'
55
Constant Distance of Travel
56
L I S T OF REFERENCES
ST dVi U X ^
o
Constant Angle of Pedal Travel o o o o o
c o c « o o
Recommendations for Further Research
nL
o
5'-^
o
o
o o c
o o o o o o o o o o o o o o o c c
o
o
o
o
o
o
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o
58
59
DU
Significant Contrasts within Factors o o o o o
6l
Significant Means
65
o o o o o o o o o o o o o o
LIST OF TABLES
Table
Page
lo
Work Done by t h e F o o t
2o
Summary of Experimental Factors
0 0 0 0 0 0 0
26
3o
Determination of Expected Mean Squares 0 0 0 c
27
4o
Significant Variables Constant Angle of
Travel--Reaction Time « 0 0 « o 0 o 0 0 c 0
37
Significant Variables Constant Distance of
Travel—Reaction Time e 0 « 0 0 0 0 0 0 o c
37
Significant Variables Constant Angle of
Travel--Travel Time c 0 c c c 0 c c 0 c c c
38
Significant Variables Constant Distance of
Travel—Travel Time c 0 , c 0 c c o 0 0 0 c
38
Significant Orthogonal Contrasts for
F o o t - T i b i a Angle and Load
0 0 0 0 0 0 0 0 c
39
5o
6c
7c
80
0 0 0 0 0 0 0 0 0 0 0 =
19
LIST OF ILLUSTRATIONS
Figure
lo
Page
Pedals Used by Barnes, Hardaway, and
X U U U X S x v y
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
P
2o •Pedals Used by Lauru o o « o o o o o o o o o o
7
3o
Lauru's Experimental Results o » o » o » o o o
8
4o
Pedals Used by Ensdorf o o o o o o o o » o » o
11
5o
Experimental Apparatus o o o o o o o o o o o o
l4
6o
Operator's View of Apparatus » o o o o o o o »
15
7o
Experimental Pedals
o o o o o o o « o o o o »
17
8o
Schematic Diagram of Timing Circuits « o o « o
21
9o
Tendon Attachment on the Foot
30
100
o o o o o o o o
Relationship of Operator's Foot and Leg to
l O O u J r e C l a . X o
O
O
O
O
O
O
O
O
O
O
O
O
llo
Effect of Foot Ratio on Reaction Time
12o
Effect of Foot-Tibia Angle on Reaction
L MlUsS
13o
o
o
o
o
o
o
o
o
o
o
o
o
o
Effect of Load on Reaction Time
o
o
o
0
0
O
0
o o o o
o
o
o
o
« » o » o o «
140 "Effect of Foot Ratio on Travel Time
o o o c o
J D
41
< ^
45
46
15o
Effect of Fulcrum Location on Travel Time
o »
48
l6o
Effect of Foot-Tibia Angle on Travel Time
» »
51
17o
Effect of Load on Travel Time
vi
o o o o o o o o
52
CHAPTER I
INTRODUCTION
Purpose and Scope
This research study hafl as its purpose determination of an optimal design of a foot pedal to be used as a
control device for activation or termination of the operation of a machine or an industrial processo
In an increasingly automated industrial environment, the role of man in the man-machine relationship is
rapidly changingo
The traditional relationship of man as
a prime mover with the machine as a device for increasing
his strength and precision is becoming one in which the
machine is the prime mover and man the controlling element
from a remote locationo
This trend is a result of two primary causeso
First, advances in technology now permit more sophisticated control of machinery than once was thought possiblec
Secondly, the upward spiral of labor costs in the United
States, in fact world wide, has forced management to find
cheaper methods of production to maintain a competitive
position in the international market«
2
In the role of a manipulator of control devices
rather than working directly with machines, man's task has
become, in some respects, more complexo
In many instances
a control task requires a continuous force to be applied
or manipulation of more than two functions to be accomplished almost slmultaneouslyc
It is in cases such as
this that the foot pedal has an increasingly important
functions
Foot controls, rather than hand controls, should
be considered in the following situations:
ac
When a continuous control task is required (if
precision of control positioning is not of primary importance) c
bo
When the application of moderate-to-large
forces (greater than about 20»30 pounds), whether intermittently or continuously, is necessaryo
Co
When the hands are in danger of becoming over-
burdened with control tasks [l]o
This investigation was designed to experimentally
determine an optimal foot pedal for use in situations
where the hands are overburdened with control tasksc
Reaction time to a visual stimulus and the time of travel
to a fixed stop were selected as the criteria of
optlmalityo
The design of the experimental investigation considered the following factors?
lo
The ratio of the distance from the ankle to
the ball of the foot and the distance from the ankle to
the back of the heelo
2o
The location of the fulcrum of the pedal con-
sidering the muscle groups in the leg required to move the
pedal and the physiological limitations of the foot and
ankleo
3o
The size of the load to be moved by the footo
4o
The angular relationship between the foot and
the tibia as well as the angular relationship between the
femur and the tiblao
A detailed description of the equipment used is
given in Chapter II; the experimental design and procedure
are described in Chapter III; the experimental results and
a discussion of the findings are covered in Chapter IV;
and Chapter V contains the conclusions reached from the
investigation and recommendations for further researcho
In the past there have been several investigations
of foot pedals to determine an optimal design based on a
particular criteriono
The following descriptions are a
brief synopsis of these experimentSo
The first efforts to determine an optimal foot
pedal design were made by Barnes, Hardaway, and Podolsky
in 1942 C2]o
The five pedals investigated are shown in
Figure lo
Fifteen subjects, twelve male and three female,
were used in the experimento
The pedals were operated
from a seated position, and each subject was instructed to
assume a position that felt most comfortableo
The subject
/
was given one-half minute to familiarize himself with each
/
pedal; during this period the 'pedal was operated as frequently as possibleo
The one-half minute period was imme-
diately followed by a three minute operations cycle during
which the pedal was operated as many times as possibleo
Travel time-for each pedal stroke was measured, using a
kymograph, for the last half of this three minute cycleo
Each pedal was operated against a tension spring requiring
20'inch-pounds per strokeo
All pedals were operated as a
trip type, such as would be found on a punch press»
The
operators performed the routine twice, the first time using
the pedals in orderi
reverse orders
1, 2, 3, 4, 5 and the second time in
5, 4, 3, 2, lo
Utilizing the mean time
per stroke during the recorded one and one-half minutes,
the following conclusions were reachedo
Pedal 1
least time per stroke
Pedal 2
5^ more time per stroke than Pedal 1
Pedal 3
6% more time per stroke than Pedal 1
Pedal 4
34^ more time per stroke than Pedal 1
Pedal 5
9% more time per stroke than Pedal 1
These conclusions have been frequently cited in other
I
WWWWVSNJ
Pedal 2
Pedal 1
fe^
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Pedal 4
Pedal 3
Pedal 5
Pig.
•Pedals used by Barnes, Hardaway, and Podolsky
publications as the criteria to be considered when selecting foot pedals for industrial applicationso
In 1957 the results of an investigation by Lauru
of the muscular efforts Involved in operating foot pedals
were published [3]<. Utilizing a force platform [4], Lauru
investigated the lateral, vertical, and frontal forces
involved in activating the pedals, from a seated position,
shown in Figure 2o
Figure So
The results obtained are shown in
Pedal 5, fulcrum directly under the ankle joint,
was found to be the best of the pedals investigatedo
In
one respect, Lauru*s results were biased by the fact that,
with the exception of Pedal Number 5, all of the pedals
required muscular effort on the part of the operator to
maintain the position of the foot between activations of
the pedalo
Since the fulcrum of Pedal 5 was in the axis
of the tibia, no muscular efforts were required between
activationso
Lauru's intent was to determine which pedal
was best with respect to muscular effort involved, but he
also stated that as a result of reducing muscular effort
the time required to perform the operation was also
reduced^ although no quantitative value of time reduction
was statedo
A further investigation of foot pedals in terms of
physiological cost to the operator was conducted by
Nichols and Amrine in 1959 [530
Their study used as a
criterion the increase in the operator's heart rate over
Pedal 1
Pedal 2
Pedal 3
Pedal 4
Pedal 5
Figo 2o^—'Pedals used by Lauru
8
Pedal
5 Force
3
lif
70
Kg
0
\yy
t
''^^^^^zfcc^A^yu^
^^^^^^=5=
•VW Vertical
Frontal
\:::7-
Transverse
0
102
149
148
109
Time in 1/100 Second
69
Figo 3c--Lauru*s experimental results
the resting statec
Operators were paced with a metronome
to insure that they all worked at the same speedo
The
pedals used were the same as the ones used by Barnes and
his associates [2] and are shown in Figure 1 (page 5 ) ;
however, the pedals were operated from a standing position
rather than from a sitting positiono
load were used?
Three levels of work
5j 10, and 15 pounds; work in inch^-pounds
was not reportedo
The weights were suspended from a cord
by detachable snapso
The cord was threaded through a
system of pulleys to change the direction of the force,
and each pedal had a separate pulley systemo
The cord was
attached to a metal arm extending from the front of the
pedal, with all pedals using the same size and length
extensions
Friction in the system was balanced by attach-
ing a container of sand that was just heavy enough to hold
the pedal in its normal position under no load conditionso
Based on the criterion of smallest average increase in
heart rate, the rank order of the pedals was found to be
Ij 2, 4^ 5, and 3o
It is interesting to note that Barnes
and his associates [2]^ using the criterion of minimum
time J, ranked the pedals 1, 2, 3, 5, and 4, the choice of
the first two pedals being the sameo
The analysis of
variance showed that the main effect of pedals was significant at the 10^ levelo
A Newman-Keuls multiple contrasts
test indicated pedals 1 and 2 were not significantly different from each other,, but were significantly different
10
from the other three pedals=
The variance due to work
load was found highly significant, indicating that the
measured variable was indicative of task difficultyo
The two-factor interaction of pedals and work load
was found non-significant, indicating that the choice
of a pedal is not dependent on the force the pedal
must movec The operator effect was highly significant, but was attributed to the individual differences among the operators. [5]
Another source of research on this topic was an
unpublished master's thesis by Ensdorf [6]c
used are shown in Figure 4c
The pedals
The object of this thesis
was to incorporate in one design several factors previously
investigated individually by other Investigators and to
eliminate deficiencies in other studies.
Included in the
design were accuracy of movement and dimensions of the
subjects* feeto
An attempt was made to make all the pedals
have the same mechanical advantage to provide a basis for
comparisonc
However^ the adjustments made provided a cor-
rection only for the dimensions of the subject's foot and
not for differences in mechanical advantageo
The most sig-
nificant conclusion reached, that had not been postulated
by other investigators, was that travel time for pedal
activation increases as the fulcrum position is moved from
the heel toward the ball of the footc
Ensdorf's study
included accuracy of positioning as a task variable rather
than movement to a fixed stop; therefore, only limited
comparisons could be made with this studyo
11
Pedal 2
Pedal 3
Pedal 4
a = distance from the ankle joint to ball of the foot
All pedals were 30 degrees above horizontal
Figc 4c=='Pedals used by Ensdorf
12
Attempts at comparison were further complicated by
the fact that Ensdorf used a foot ratio of the distance
from the ankle to the ball of the foot and the distance
from the ankle to the bottom of the foot, while in this
study the foot ratio used was the distance from the amkle
to the ball of the foot and the ankle to the back of the
heelo
A study related to this research was conducted by
Reijs at the Harvard School of Public Health in 1953 [7].
In his study Reijs found that maximum power of the foot,
for downward motion, is generated when the initial included
angle between the foot and tibia is 78 degreeso
This find-
ing was based on a horizontal attitude for the femur and
an included angle of 114 degrees for the femur and tibiae
The results and conclusions of the above studies
are compared with the results and conclusions of this
experimental investigation in Chapters IV and V,
CHAPTER II
EQUIPMENT
The equipment in this investigation was fabricated
to provide the means for measuring the reaction time and
travel time of a subject operating a foot pedal under a
variety of predetermined conditionsc
Technical Description of Task Device
Photographs of the equipment used are shown in
Figures 5 and 60
All parts were constructed of wood and
were securely fastened to provide the necessary rigidity
to the apparatus 0
The fulcrum of the foot pedal was attached to a
hinged section to allow adjustment of the pedal to obtain
four different foot-tibia angles, 78, 84, 90, and 96
degreesc
The proper angles were achieved by using a com-
bination of a nylon strap with a metal grommet at the
proper length and a block of wood with the top beveled at
the correct anglec
This technique established a positive
and rapid check of the desired angular relationships0
Instead of having a movable fulcrum on the pedal, a movable heel stop was utilized to move the foot in relation
to the fulcrumo
This stop was adjustable in one-quarter
13
14
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15
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- ^waMinns'f--.-y^i-.;':r.. xa.^^i^^^.itiiLX'-Jtiii'' •
16
inch increments
The point of load attachment was made
adjustable in one-quarter inch increments so that there
would be no difference in mechanical advantage between
pedals.
To avoid excessively complex apparatus all pedals
had a mechanical advantage of zero.
used are shown in Figure 7o
The fulcrum positions
The following calculations
were used to determine the point of load attachment and
are based on equilibrium^
M = moments about the fulcrum
a = distance from the ankle to the ball of the foot
b = distance from the ankle to the back of the heel
c = distance from the fulcrum to point of load
attachment
W = weight of the load, normal to the plane of the
pedal
F = force applied by the ball of the foot
Pedal 1
zn = (a+b)F « cW = 0
let F = W
then c = a+b
Pedal 2 2
ZM == (a+b-l)F - cW = 0
let F = W
then c = a+b-1
Pedal 3t
J^M = aF - cW = 0
let F = W
then c = a
Pedal 4?
i^ = (2/3)(a)F - cW = 0
let F = W
then c = (2/3)a
17
Pedal 1
Pedal 2
Pedal 3
Pedal 4
a = distance from ankle to ball of foot
b = distance from ankle to back of heel
c = distance from fulcrum to point of load attachment
Figo 7c—^Experimental pedals
18
The beam on the top of the apparatus was adjustable so
that the pull of the load would be normal to the plane of
the pedal for any point of load attachment:
This normality
existed only before the pedal was moved by the footThe size of the load to be moved by the foot, 8,
12, 16, or 20 pounds, was varied by changing weights in
the metal bucket which is shown at the right of Figure 5
(page 14)e
Work in inch-pounds, based on the distance
moved by the ball of the foot for constant angle and constant distance of pedal travel, is shown in Table Ic
Friction in the system was balanced by the weight of the
bucket^
The subjects were seated in a dental chair to
facilitate the vertical adjustments necessary to maintain
the femur in a horizontal attitude.
The femur-tibia
relationship of 114 degrees, prior to movement of the
pedal, and the horizontal attutude of the femur were
checked^ with a wooden frame assembled with an included
angle of 114 degreesc
A bubble level was attached to the
frame to Insure that the femur was horizontalc
A schematic diagram of the electrical circuity
used to measure reaction time and travel time is shown in
Figure 8.
An electronic counter was used in conjunction
with an oscillator to obtain a measure of reaction time to
the nearest one-thousandth of a seconds
The oscillator
frequency of 1 Kc was calibrated, using the counter, prior
19
TABLE 1
WORK DONE BY THE FOOT
Constant Angle (12 degrees)
Pedal
Foot Ratio
Work (inch-lbs)
13c64
20c46
27c28
34cl0
13c4l
20cll
26c82
33c52
14
21
28
35
09
13
18
22
lo58
8
12
16
20
11.98
17c96
23o95
29c94
1=67
8
12
16
20
llo74
17c6l
23c49
29c36
lo95
8
12
16
20
12.42
I8c64
24c85
31c06
r
- \
8
12
16
20
8c40
12c60
I6c80
21c00
lc67
8
12
16
20
8o38
12c58
I6c77
20c96
lo95
8
12
16
20
9c30
13o94
I8c59
23c24
lc58
1
' te=irr:ym::r.
20
TABLE 1—Continued
Pedal
Foot Ratio
Load (lbs)
Work (inch-lbs)
lc58
8
12
16
20
5o6l
8o4l
llc22
I4o02
lo67
8
12
16
20
5o59
9o39
10o5^
13c98
lc95
8
12
16
20
6o20
9c30
12e40
15c50
Constant Distance (Q°7^ In)
Foot Ratio
Load (lbs)
8
Ic =
Work (inch-lbs)
I
6
58
12
1. 67
Ic
95
16
12
20
15
21
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SWITCH NO. 4
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SWITCH NO. 1
SWITCH NO. 2
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SWITCHES:
NO. 1
NO. 2
NO, 3
NO. 4
NO. 5
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REACTION TIME
CONSTANT' DISTANCE IHAVKL TIME
CONSTAOT AN3LE TRAVEL TIME
AC POWER
SELECT ANGLE OR DISTANCE
SWITCH
STOP
r~UJUuuLU"
SWITCH NO
STOP TIMER
TIMIRt
1 and 2 - MOTOR
1 and 4 - RESET
3 and 6 - CLUTCH
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5
SWITCH NO. 3
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Fig. 8.—Schematic diagram of timing circuits
22
to each subject's use of the apparatuso
The face of the
counter was covered with the exception of a predetermined
number, and the illumination of that number was used as
the stimulus for the subject to operate the pedalc
light was of a reddish orange color.
The
To preclude the sub-
ject's anticipating the stimulus, the counter was started
with a hand-operated switch that could not be seen or
heardc
The counter was stopped by a micro switch located
at the back of the pedalo
This micro switch stopped the
counter as soon as the pedal began to move, thereby giving
an accurate measure of reaction timco
This switch simul-
taneously stopped the counter and started the travel timer
which measured time in hundredths of a seconds
The travel
time was stopped by one of two other micro switcheso
The
first switch stopped the timer after an angular travel of
12 degrees by the pedal, and the second switch stopped the
timer after the ball of the foot had traveled a distance
of Oc75 incheso
The switch for measuring the time of
angular travel was fixed at the front of the pedal, while
the second switch was movable so that it could be placed
directly under the ball of the footo
travel was restricted by a rigid stopo
In both cases pedal
Due to equipment
limitations, it was necessary for the subjects to hold the
pedal in a fully depressed position until the time on the
travel timer could be recordedo
23
The experimental procedure using this equipment is
discussed in Chapter IIIo
,-X
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CHAPTER III
EXPERIMENTAL DESIGN AND PROCEDURE
Experimental Design
This experiment was designed as a five factor
mixed model,
The levels of the fixed factors of ratio
of the distance from the ankle to the ball of the foot and
the ankle to the back of the heel (3 levels), fulcrum
location (4 levels), foot-tibia angle (4 levels) j, load (4
levels), and replications (5 levels for each foot ratio)
were selected prior to the start of the experiment:
The right foot of volunteer male subjects was then
measured to determine their foot ratio-
Five subjects
were selected for each of the three levels of foot ratio
to be investigated, giving a total of fifteen subjects for
the experiment:
Although each of the subjects was
selected on the basis of a particular ratio of the distance from the ankle to the ball of the foot and the
distance from ankle to the back of the heel, they represented a random selection of male subjects with that right
foot ratiOc
Reaction time to a stimulus of light and the
travel time required to move the pedal to a fixed stop
24
25
were selected as the criteria of optimality for this study
Reaction time and travel time were recorded for each level
of the fixed factors for each subject for both constant
angle and constant distance of pedal travelc
To eliminate
bias of the results due to the sequence of performance,
each subject performed the experiment in a random sequence.
A different random sequence was used for each subject
An air-conditioned area was used for the experiment
in an effort to eliminate the possible effects of changing
environmental conditions-.
The experiment was performed
approximately 3300 feet above mean sea level.
A summary of the experimental factors is shown in
Table 2e
The determination of the expected mean squares
(EMS) for the analysis of variance is shown in Table 3 [8].
The following is a brief discussion of each of the
factors investigated and its relationship to the design
Load
Previous investigators have found that load is a
significant task variable in the operation of a foot pedal
The smallest value of load was selected to be of sufficient magnitude to insure that the subject had to apply a
downward pressure of the foot, greater than the weight of
the foot and leg^ to activate the pedal.
Four equally
spaced levels of weight, 8, 12, 16, and 20 pounds, were
used so that a definitive measure of the trend in time.
26
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CtJ
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cd
cc;
cd
0
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27
TABLE 3
DETERMINATION OF EXPECTED MEAN SQUARES
3
F
1
F
j
Ri
0
4
PJ
3
0
Model
F
k
4
4
F
m
5
R
q
EMS
4
5
ol + 320a^
1
2
4
5
ale + 240a^
P
1
3
1
df
i
i
RPij
0 1
1
0
4
4
5
^e ^ SOa^p
Ak
3
4
0
4
5
of
e + 240a^
A
3
RAlk
0
4
0
4
5
"e * 80a2^
6
PAjk
3
0
0
4
5
"e + ^O-'PA
9
1 0
0
0
4
5
"e -^ 20app^
18
3
4
4
0
5
ol2 + 320a22
3
4
0
5
RPAljk
Lm
6
i
RLim
4
0
6
1
•
PLjm
3
0
4
0
5
"e * ^O-'PL
9
RPLljm
0
0
4
0
5
"e + 20o2p^
18
ALkm
3
4
0
0
5
RALikm
0
4
0
0
5
PALjkm
3
0
0
0
5
RPALljkm
0
0
0
0
5
"e
2
"e
2
"e
2
1
eq(ijkm)
_i.l
i
^
—
•
* 6°°AL
2
-^ 20ap^L
2
* ^5op^L
X c 2
9
18
27
54
i
1
- ^
768
1
....•••
'
'
28
with change in load, required to activate the pedal would
be obtained,
Foot-tibia anglg^
The angles were selected so that the required
movement of the foot would be within the physiological
capabilities of the subject and not require movement of
body members other than the foot and lege
One limit of
the included angle between the foot and tibia was selected
as 78 degreesc
This was done for two reasonsc
First,
based on Reijs* finding that maximum power was generated
at this angle, it was anticipated that this angle would
also result in minimum time of operation.
Secondly,
smaller included angles produce discomfort in the lower
lego
The other limit of an included angle of 96 degrees
was selected because with a pedal travel of 12 degrees the
limit of downward movement of the foot, without involving
body members other than the foot and leg, is closely
approachedc.
The other two angles investigated, 84 and 90
degrees, were included to obtain a definitive measure of
the trend in time with changes in the foot-tibia relationship.
Fulcrum location
T>leU»^i»r.?«j I'Mra.'f iat=«g::a«eOBg:3aaw?»eT»M
Fulcrum locations were selected to include the two
natural pivots of the foot:
the spur of the heel bone
located approximately one inch from the back of the heel
29
and directly under the ankle joint.
The back of the heel
and one-third of the distance from the ankle to the ball
of the foot were included as fulcrum locations to determine the trend in time as the fulcrum is moved from the
back of the heel toward the ball of the footc
All motions
required downward movement of the foot, because this type
of motion uses the largest muscles of the leg and in a
repetitive task these muscles would be less subject to
fatigue C9]c
Ratio
As can be seen in Figure 9 the foot is a compound
lever with the fulcrum at the ankle^
The major muscles
used in the extension of the foot work through the tendon
at the heel while the lesser muscles work through the
tendons attached toward the front of the footc
For this
reason the ratio of the distance from the ankle to the
ball of the foot and the distance from the ankle to the
back of the heel was Included as a factor to determine its
effect, if any, on reaction time and travel timec
For
convenience the ratios are referred to as lower, middle,
or upper third although the actual ratios were 1.58, lc67,
and 1-95--
To avoid any confounding of results, each subject
performed the experiment only once*
The sequence of
30
Ratio = a/b
I^lg^ 90—Tendon Attachment on the Foot
31
performance followed by each subject was obtained by numbering each of the 128 tasks to be performed and determining the sequence from a table of random numbers.
The
randomization was accomplished prior to the experimentation.
Use of five subjects in each ratio category pro-
duced a total of 960 observations for each factor of
reaction time and travel time for both constant distance
and constant angle of pedal travel.
Criteria of opjtljnali^y
Reaction time and travel time were selected as the
criteria of optimality because of their relationship to
labor costs.
By reducing the time required to perform a
task, an increase in productivity can be anticipated with
a resultant decrease in per unit labor cost^
Additionally
there are tasks where the fastest possible performance is
essential from other than a cost point of view,
The time
was separated into its component parts, reaction time and
travel time, to determine the effects of the factors on the
component parts of the total time of operation of the foot
pedalr
Reaction time was defined as the period from illumination of the visible numeral on the face of the electronic counter to the start of downward motion of the foot.
Travel time, for all fulcrum locations, was defined from the start of downward motion of the pedal to
32
the completion of the motion against a fixed stop after a
movement of 12 degrees by the foot for constant angle of
travel or 0,75 Inches by the ball of the foot for constant
distance of travele
Experimental Procedure
Subjects were scheduled to perform the experiment
in a single session requiring approximately two hours and
fifteen minuteso
Each subject reported to the experimental
area at his scheduled timec
Prior to any experimentation
the apparatus and experimental routine were explained to
the subject and any questions by the subject were answeredo
The apparatus was then adjusted to place the femur, tibia,
and foot in a direct line with the center line of the foot
pedal as shown in Figure 10c
The subject was then seated in the dental chair
which was adjusted vertically to establish an Included
angle of 114 degrees between the femur and tibiae
This
angle was selected based on the findings of Reijs [7]c
Each subject was then given a five minute familiarization period to operate the foot pedal, so that data
would not be taken while the subject was still learning
the taskc
The subject was instructed to depress the pedal
as rapidly as possible as soon as the number in the aperture on the face of the electronic counter (see Figure 6,
page 15) was llluminatedc
Foot Pedal
•Foot
4^
Tibia
Femur
Fig: 10c —Ralationship of operator's foot and leg to
the foot pedal.
Following the practice period the experimental
routine was startedc
This consisted of the data taker
reading aloud the particular combination of the factors
required for the next observation in the random sequence
for the subject.
The desired foot-tibia angle was
achieved by changing the beveled block of wood and strap
discussed in Chapter lie
The heel stop was moved to
achieve the proper fulcrum location, and the point of load
attachment was changed to insure that all pedals provided
the same mechanical advantage to each operator.
of the load was changed by the data taker.
The size
The correct
micro switch for constant angle or constant distance of
pedal travel was then selectedo
Because of the movable
micro switch for constant angle of pedal travel the subject was aware, in advance, of whether the movement was to
be constant angle or constant distancec
After all adjust-
ments had been made and the subject was ready, the electronic counter was started with the hand-operated push
buttonr
Since the subject was not aware of when the
counter was activated, the illumination of the number in
the aperture could not be anticipatedr
The subject then
held the pedal in a full down position while the travel
timer was read to the data taker.
After this value was
recorded the pedal was allowed to return to its original
position, and the subject then opened the cover on the
electronic counter and read the reaction time to the data
35
taker..
The same routine was followed for each of the 128
observations required for each subject.
The adjustments
on the apparatus between each observation consumed
slightly more than one minute, allowing the operator a
rest period which minimized the effect of fatigue.
The
operators were allowed to get out of the chair to stretch
any time they desired; howevei'j none of the operators
reported discomfort from being seated in one position for
the time requiredc
Results of the experiment are discussed in the
next chapter.
CHAPTER IV
RESULTS AND DISCUSSION
Method of Analysis
All data were analyzed on an IBM 1620 Model I
computer using the IBM object program for completely generalized analysis of variance, ANOVA 6c0c090o
analyses were required?
Four
reaction time-constant angle of
travel, travel time-constant angle of travel, reaction
time-constant distance of travel, and travel time-constant
distance of travele
computer time-
Each analysis required 26 minutes of
F ratios were calculated, using the
expected mean squares of Table 3 (page 27), for all main
effects and interactions with a Friden desk calculatorc
Results
Analysis of variance
Tables 4, 5, 6, and 7 list the significant effects
determined in the analysis of variancec
Only main effects
were found to be significant in the analysisc
Table 8 shows
the significant orthogonal contrasts for foot-tibia angle
and load, the only equally spaced independent variablesc
Contrasts between levels within each of the factors are
36
37
TABLE 4
SIGNIFICANT VARIABLES CONSTANT ANGLE
OF TRAVEL—REACTION TIME
Source
T
df
SS
MS
F-Ratio
a
R
2
02806573
01403287
I60O3
.01
A
3
01949296
00649765
7c42
.01
L
3
04255877
01418626
16.21
.01
768
67213040
00087517
Error
I IIIMMMII
Total
Legend:
959
R
I
I
I • H I II H I B I I I I I
•
89810398
Ratio
A
Foot-Tibia Angle
L
Load
TABLE 5
SIGNIFICANT VARIABLES CONSTANT DISTANCE
OF TRAVEL—REACTION TIME
MS
SS
df
Source
F-Ratlo
a
•
R
2
c0248l764
.01240882
I4c80
.01
A
3
c02461686
c00820562
9c80
.01
L
3
CO5165292
.01721764
20.60
.01
Error
768
.64294440
c00083717
Total
959
c88917217
Legend:
R
Ratio
A
Foot-Tibia Angle
L
Load
38
TABLE 6
SIGNIFICANT VARIABLES CONSTANT ANGLE
OF TRAVEL—TRAVEL TIME
Source
df
SS
MS
F-Ratio
a
R
2
0OI8508
.009254
10cl6
.01
P
3
0032763
0OIO92I
12c00
cOl
A
3
.012875
.004292
4.71
.01
L
3
c059928
c019976
21c90
eOl
768
.699640
Error
»g|II.I..III.IIM. I.JMIIIMIM.M
Total
Legend:
959
R
A
c901285
.000911
II.. II. ll«|
1 ill
^
Ratio
Foot-Tibia Angle
. ii*.-?^o*^ vr.'t..,rr=Tr!irr;irT:r
111
•
-
'
P
L
^
'
Fulcrum Location
Load
•rw"^•»•---js^.'wffe,-.'«iicij«ji'.r 111 i w TB ~i II iiw 1
mi
mM
TABLE 7
SIGNIFICANT VARIABLES CONSTANT DISTANCE
OF TRAVEL—TRAVEL TIME
Rr5=>'°^rsi55sar,ig=g=T5Effgiirt?!rg^
Source
df
\
' '
1
MS
F Ratio
a
R
2
c023540
.011770
25c27
.01
P
3
.029530
c009843
21.12
.01
3
c004585
c001528
3.28
.05
3
.006723
.002241
4c8l
cOl
Error
768
c357720
c000466
Total
959
o466725
A
1
L
Legend:
R
A
Ratio
Foot-Tibia Angle
P
L
Fulcrum Location
Load
39
TABLE 8
SIGNIFICANT ORTHOGONAL CONTRASTS
FOR FOOT-TIBIA ANGLE AND LOAD
Reaction Time—Constant Angle of Travel
UJJtt.:-.gr-.--3L-.j
u t » » - A r :ac6'::3Jr_?aK: '^.aLDrjfcSjjrerJS
-04255877
.00413623
768
Error
.01418626
00413623
.67213040
- --:tcr.'. J- -.'^—z^::xi:.T,^
16.21
4.73
.01
.05
,00087517
^,i_';-'r_'
M^-ia^
•K^'ssc .wr -,•«£_-w—a^.3«r/.CKJt;
Reaction Time—Constant Distance of Travel
•--z:--.nl r - r - w a - . ^ - vtar—c--^-1^,,• - T
L-T«-.-.-«g/—M-'t-^z-T^jp-y •
3
c0246l686
.02382712
00820562
c02382712
9c80
28.46
cOl
.01
3
.05165292
=05148300
01721764
.05148300
20c60
6lc50
cOl
.01
T,
T,
L
Error
-.| •fn ^ y — j
J
1
64294440
^SLIJ-SX..' . ; d ~ = ; r jyiL-j
00083717
.•-•3iu.».':."=v. jsu.. .-^, -•:::;
u-oL •3!0eKm:'am^mvjmrmmjmK.vaa::i;sr:.M.mu::tmm
Travel Time—Constant Angle of Travel
,, -CK ,';5Kr_«_ ^awr
A
3 T
'^L
L
T^L
Error
.•.-i.;3'_f;:j..>.
1
.'::£:.ss..ux..iar;ii
012875
.012288
.004292
.012288
4c71
13.49
01
01
.059928
j
.058464
.019976
.058464
21e90
64.18
01
01
768
c699640
c000911
Travel Tlme--Constant Distance of Travel
I3
1
T.
? 768
Legends
001528
.002881
004585
002881
A
T.
A
002241
.005962
I .006723
i
.005962
355270
1
i
3=28
6.18
05
01
4.81
01
01
12.79
000466
.. • J X , - J L
'J.V, 1.
•.rj^i-:-:
Foot-Tibia Ann;le
Load
Lineal- contrast- , quadratic and cubic contrasts
i.-er-c not ,.'ouiid to be significant.
40
tabulated in Appendix I, and significant means are shown
in Appendix IIo
Significant Variables
Reaction time
lo
Ratio (R)
The effect of the ratio of the distance from the
ankle to the ball of the foot and the distance from the
ankle to the back of the heel is shown in Figure lie
The
effect of this foot ratio had not been investigated in
earlier studies of foot pedals, although Ensdorf [6]
investigated the ratio of the distance from the ankle
joint to the bottom of the foot and the length of the foot.
As can be seen in Figure 11 the lower third group had significantly lower reaction time than the middle third and
upper third groupso
Statistically there was no difference
between the middle third and upper thirds
Based on these
results, operators on whom the distance from the ankle to
the ball of the foot is more nearly equal to the distance
from the ankle to the back of the heel should be used,
because they have a shorter reaction time when using the
extensor muscles of the lower lego
It is conceivable that
this effect is due to the fact that there were only five
subjects in each of the ratios investigated, and this
relationship would not hold true if a larger sample of the
41
Constant Angle
—©
Constant Distance
270--
265--
CO
T>
C
O
O
0
CO
260--
0
B
•H
255"-
.250--
245--
lo58
1 68
lc78
Ratio
1.88
1.98
Figc 11 -^^Effect of foot ratio on reaction time
42
population at each ratio were investigated^
However, the
results were almost identical for both constant distance
and constant angle of pedal travel, and in fact the
results of the contrasts for the two cases were identical.
2.
Foot-tibia angle (A)
The effect of the foot-tibia angles investigated
on reaction time is shown in Figure 12e
The foot-tibia
angles used in this experiment had not been studied by
previous researchers in terms of time.
On the basis of
the orthogonal contrasts. Table 8 (page 39), reaction time
increases linearly, for both constant angle and constant
distance of pedal travel, as the foot-tibia angle is
Increased from 78 to 96 degreeso
Angles smaller than 78
degrees were not Included in the experimental design as
this value is very close to the physiological limit of
foot flexionc
Slightly greater flexion of the foot
causes severe discomfort and could cause physical damage.
In fact, all subjects reported minor discomfort in the
calf of the leg at 78 degrees.
Values larger than 96
degrees were not used because, for the angle and distance
of travel investigated, larger foot-tibia angle would have
required movement of body members other than the foot and
lego
The finding that 78 degrees produced the lowest
reaction time is consistent with Reijs* [7] findings that
maximum foot power is generated at this angle, since
43
Constant Angle
&
•
Constant Distance A-
-A
265--
CO
TJ
260--
O
o
CO
0
6
c255"
EH
250--
245"
78
V
8
90
t
Foot-Tibia Angle
(degrees)
Figo 12o«-Effect of foot-tibia angle on reaction time
44
reaction time in this experiment measured the time
required to generate a force of sufficient magnitude to
Just move the pedalo
It is reasonable to conclude that
the foot-tibia angle that generates maximum power would
also generate sufficient force to move the pedal in the
shortest timeo
This is supported by the results for the
effect of foot-tibia angle on travel timeo
3o
Load (L)
Figure 13 shows the effect of load on the reaction
time for constant angle and constant distance of pedal
travelo
The orthogonal contrasts. Table 7 (page 38), show
the increase in reaction time to be linear with increase
in load from 8 to 20 poundso
Because of the way reaction
time was defined for this experiment, time required to
generate a specific force, it appears that for this range
of required forces the muscles of the leg generate
increases in force linearly with respect to timeo
Consid-
ering the findings of Nichols and Amrine [5] that minimum
increase in heart rate occurs with the smallest load, the
optimal value would be 8 poundso
Travel time
lo
Ratio (R)
Figure l4 shows the effect of ratio on travel time
for constant angle and constant distance of pedal movement
45
C o n s t a n t Angle
e-
Constant Distance A-
265-
CO
c
o
260-
o
0
CO
0
5
o255r
EH
250--
o245"
8
12
16
Load
(lbs)
20
Figo 13o—Effect of load on reaction time
-A
46
Constant Angle
^
-A
Constant Distance A-
105--
095--
CO
c
O
O
0
CO
085"-
ii
u
TT
0
• m
11
22
B
075"
II
O65--
055"
lo58
TTb 8
lo78
Ratio
Tj8
Figo 14o—Effect of ratio on travel time
lc98
47
From the contrasts in Appendix I it can be seen that for
both constant angle and constant distance of travel the
lower and upper thirds were not significantly different,
but the middle third was significantly different from both
the upper and lower thirdso
As can be seen in Figure 14
the effect was the same for both constant angle and constant distance of travel with the middle third requiring
significantly less time to move the pedal to a stopo
As
previously mentioned, this difference could be due to the
number of subjects used for each ratio, and any definite
conclusions should be based on further study of the effect
of ratio on travel timeo
2o
Fulcrum location (P)
The effect on travel time of fulcrum location for
constant angle and constant distance of pedal travel is
shown in Figure 15o
Values of travel time are plotted
against the mean locations of the fulcrum for all subjects<
The locations are measured with the back of the heel as
the origin and Increase as the fulcrum position is moved
toward the ball of the footo
3o01, and 4o75 incheso
The mean values were Oj, 1,
For constant angle of pedal travel
the time required to move the pedal to a fixed stop
decreased as the fulcrum was moved toward the ball of the
footo
This is a result of decreasing the distance the
ball of the foot must travel to move the pedal through the
48
Constant Angle
Constant Distance A-
105:r
09^CO
TJ
O
o
0
CO
08
i
I
f f
0
B
r r
•H
&H
i
I
07
I r
065--
055--
0
1
2
3
4
Fulcrum Location
(measured from back of the heel)
(Inches)
Figo 15o—Effect of fulcrum location on travel time
49
prescribed arc of 12 degrees.
Earlier studies did not
investigate constant angle of pedal travel.
For constant distance of pedal travel, time
increases as the fulcrum is moved from the heel toward the
ball of the footo
This is a result of the fact that
although the distance the ball of the foot must move is
constant the foot must move through a greater arc each
time the fulcrum is moved toward the ball of the foot.
This result agrees with Ensdorf»s conclusion [6].
It is
also in agreement with Barnes and his associates [2] concerning which pedal is best, since all his pedals apparently moved through a constant distance to maintain a
work load of 30 inch-pounds for each pedals
Also, for
constant distance of travel the heel was found to be the
best fulcrum location in terms of increased heart rate by
Nichols and Amrine [5].
It is difficult to make any comparison with
Lauru*s results [3] on fulcrum location because his pedals
required muscular effort to maintain the pedal in position
prior to its operation, while in this study loads were of
sufficient magnitude to support the weight of the foot and
leg on the pedal without muscular effort on the part of
the operatoro
< U A 3 TECHNOLOGICAL COLtEQl
LUBBOCK. TEXAS
LIBRARY
50
3r
Foot-tibia angle (A)
Figure 16 shows the effect of foot-tibia angle on
travel time for constant angle and constant distance of
pedal travelc
The orthogonal contrasts. Table 8 (page 39),
show travel time to Increase linearly with an increase in
foot-tibia angle from 78 to 96 degrees.
Minimum travel time
with a foot-tibia angle of 78 degrees is consistent with
Reijs* finding [7] and it is logical to conclude that the
angle for maximum power would also be the angle which
would produce minimum timec
However, because of the
reported discomfort, this angle cannot be considered optimal for two reasonso
First, it is quite possible the
operators would develop physiological problems, such as
Inflammation of the tendons or some type of muscular problems, with protracted use of a foot pedal with a foottibia angle of 78 degreeSc
Secondly^ very decided psycho-
logical problems would be generated because of the discomfort experienced by the operator.
A foot-tibia angle of
84 degrees would therefore be more desirable, even though
a slight increase in both travel time and reaction time
would resultc
4.
Load (L)
The effect of load on travel time for constant
angle and constant distance of travel is shown in Figure
17o
The orthogonal contrasts. Table 8 (page 39), show a
51
Constant Angle
&•
Constant Distance A-
105
,095—
CO
C
o
o
0
CO
Z
c085-
0
B
•H
E^
075--
065-^
c055--
78
t
+
90
Foot-Tibia Angle
(degrees)
96
Fig. 16.—Effect of foot-tibia angle on travel time
^
52
©"
-0
Constant Distance A-
-A
Constant Angle
105--
c095"
CO
TJ
c
O
o
0
CQ
c085--
0
B
•H
EH
075—
c065--
055--
8
12
16
Load
(lbs)
20
Figo 17.—Effect of load on travel time
53
linear increase in travel time with increase in load from
8 to 20 pounds0
In terms of the travel time required and
the findings of Nichols and Amrine [5], the 8 pound load
would be considered optimalo
CHAPTER V
C O N C L U S I O N S AND
RECOMMENDATIONS
T h i s study was an i n v e s t i g a t i o n of the effect of
foot d i m e n s i o n s J f u l c r u m l o c a t i o n , foot-tibia a n g l e , and
load on the t i m e r e q u i r e d to operate a foot p e d a l .
The
c r i t e r i a for o p t i m a l i t y in the experiment were reaction
time to a v i s u a l stimulus and travel time to a fixed stop
for constant angle and constant distance of t r a v e l .
Fif-
teen s u b j e c t s w e r e used in the experiment giving five
r e p l i c a t i o n s at e a c h of the three levels of foot d i m e n sions I n v e s t l g a t e d c
S e p a r a t e a n a l y s e s of variance were conducted for
each of the
criteriao
pQ-P-gl-^g-j-QJilg.
In the interest of clarity the conclusions w i l l
be d i s c u s s e d in two s e p a r a t e areas?
a foot p e d a l that
m o v e s t h r o u g h a constant arc of 12 degrees and a foot
p e d a l that r e q u i r e s the b a l l of the foot to move a c o n stant distancec
Only limited comparisons w i t h e a r l i e r
s t u d i e s can be m a d e in the first case as this type of
m o t i o n had not been studied p r e v i o u s l y .
In the second
c a s e , c o m p a r i s o n s can be m a d e on a b r o a d e r basis since
54
55
several other Investigators have explored this areao
For
both types of motion the experiment was based on all fulcrum locations having the same mechanical advantageo
The
selection of the optimal combination of factors is based
on the foot pedal being used in a repetitious task in
which the hands are already occupied and where the time of
performance is of importanceo
All conclusions are subject to the limitations of
the experimento
Constant angle of pedal
travel
An optimal foot pedal design for a constant angle
of travel of 12 degrees would use the following combination
of factors 0
lo
Foot RatiOo
Operators should be selected that
have a foot ratio between lo58 and lo67 because these two
foot ratios result in minimum total time of operation,
reaction time plus travel timeo
These ratios also require
fewer inch-pounds of work by the operator for all fulcrum
locations (see Table 1, page 19)o
2o
Fulcrum Positiono
The optimal fulcrum posi-
tion is forward of the ankleg one-third of the distance
between the ankle and the ball of the footo
This position
is based on travel time only since this factor had no
significant effect on reaction timeo
56
3o
Foot-Tibia Angleo
The optimal foot-tibia
angle would be 78 degrees; however, for the reasons discussed in Chapter IV, an angle of 84 degrees would be more
desirableo
This angle is predicated on the femur being
horizontal, to reduce the constriction of blood flow to
the leg by the edge of the operator's chair, and a femurtibia angle of 114 degreeso
4o
Loado
A load of 8 pounds resulted in a minimum
/
for both reaction time and travel time in this experimento
A more precise definition of optimal load would be that
the load should be of just sufficient magnitude to support
the weight of the foot and leg without muscular effort on
the part of the operatoro
This definition is based on the
findings of this study as well as the finding of Nichols
and Amrine [5] that the increase in heart rate is smallest
with the smallest load and an extrapolation of the finding
of Lauru [3] that minimum force is required when the operator does not have to exert muscular effort to prevent
undesired activation of the foot pedalc
Cpnstant^dj^jtance^of travel
An optimal design of a foot pedal in which the
ball of the foot must move through a fixed distance would
use the following combination of factorso
lo
Foot RatiOo
The experimental results were
identical for constant angle and constant distance of
57
pedal travelo
Therefore, operators should be selected with
a foot ratio between lo58 and I067 for the same reasons
discussed under constant angle of travelo
However, for
constant distance of travel there is no difference in work
by the operator as in constant angle of travelo
2o
Fulcrum Positiono
The optimal position for
the fulcrum, with the load attached at the ball of the
foot J, is at the heel because it results in minimum time of
motiono
This result is in agreement with the findings of
Barnes and his associates [2] and with Ensdorf"s conclusions [6]o
It also results in the same choice of fulcrum
location as was made by Nichols and Amrine [5], using a
criterion of increase in heart rateo
3o
Foot«Tibia Angleo
A foot-tibia angle of 84
degrees should be used for the reasons discussed under
constant angle of travelo
4o
Loado
The optimal load for constant distance
of travel would be the same as for constant angle of
travel, as small as possible while supporting the weight
of the foot and lego
In the design of a foot pedal the decision whether
to use a pedal that travels through a constant arc or a
constant distance must be predicated on the task to be
performed by the pedalo
However, if time of performance
is the most important criterion^ then a constant distance
of pedal travel would be the best choiceo
58
Recommendations for Further Research
^rr.T.^lPKn^Ju,
The most productive area for further research in
foot pedal design would be in terms of physiological cost
to the operator, using the same experimental designo
Because of the short duration of the task, a force platform would probably be the best method of measuring the
effort required of the operatoro
A second possibility for additional research is
the inclusion of accuracy as a task variable to determine
its relationship to travel and reaction timeo
LIST OF REFERENCES
(1)
Morgan, Co To, Cook, Jo So, Chapanis, Ao^ and Lund,
Mo Wo, Human Engineering Guide to Equ
Equipment Design^
m
i
l
BooK
Coo,
1963,
^65o
^^^•-^»-——-^^
McGraw
(2)
Barnes, Ralph Mog Hardaway, Henry, and Podolsky, Odif,
"Which Pedal Is Best?", Factory Management and
Maintenance Magazine^ McGraw-Hill Book COo, Janu-
ary, 19^2, 9^^9To
(3)
Lauru, Lucien, "Physiological Study of Motions," The
Advanced Management Magazine, March, 1957* 23°
(4)
Greene, James Ho, and Morris, Wo Ho Mo, "The Force
Platforms An Industrial Engineering Tool," The
Journal of Industrjjil Engineerlnga 1958, IX, 12813^0
(5)
Nichols, Do Ec, and Amrine^ Ho To, "A Physiological
Appraisal of Selected Principles of Motion Economy," The Journ^^_of_Industrial Engineering, 1959,
X, 5, 376-377c
(6)
Ensdorf, John, "An Optimal Design for a Foot Activated
Lever Mechanism," Unpublished Master's thesis,
Texas Technological College^ May, 1964o
(7)
Reijs, Jo Ho Ooj, "Human Body Size and Capabilities in
the Design of Vehicular Equipment," Harvard Sghoo 1^
of Public Health, Boston, Mass., 1953j 3^^TC
(8)
Hicks, Charles Ro , Fundamental Concepts in ^he^Desj^gn
of Experiments a Holt, Rinehart, and Winston, Inco,
February g 1965 s, 153-155c
(9)
Steindler, Ac, Kinesiology of .the^,H}maj7. B o ^ unde^
Normal and PathblQ^gl^u7?"Q^^^^-^-» ^° ^° "^^Q^^^s*
Springfield, Illo, l9b^o
59
APPENDIX
lo
IIo
Significant Contrasts within Factors
Significant Means
60
APPENDIX I
SIGNIFICANT CONTRASTS WITHIN FACTORS
KEY:
Rl = Lower Third, R2 = Middle Third, R3 = Upper Third
PI = Back of Heel, P2 = 1 inch from Back of Heel,
P3 = Directly under the Ankle, P4 = 1/3 of
Distance from Ankle to Ball of Foot
Al
78 degrees, A2 = 84 degrees, A3 = 90 degrees,
A 4 = 96 degrees
LI = 8 lbs, L2 = 12 lbs, L3 = 16 lbs, L4 = 20 lbs
Constant A n g l e — R e a c t i o n Time
e « O0OOO87517, df = 768
Contrast
SS
020142
Rl - R2
E
Ratio
Level of Significance
23c02
cOl
Rl
R3
1
0O219OO
23o01
oOl
Al
A3
1
c008855
IO0I2
oOl
Al
A4
1
cOl6511
I8c87
cOl
A2
A4
1
0OO7930
9c06
cOl
LI - L3
c010990
12 c 56
oOl
LI - L4
0O370OO
42o28
oOl
L2 - L3
o004360
4o98
0O5
L2 - L4
o023580
26o94
cOl
L3 - L 4
c007660
8o75
oOl
61
62
APPENDIX I—Continued
Constant Distance—Reaction Time
e = 0OOO83717, df = 768
Contrast
df
SS
F-Ratio
Level of Significance
Rl - R2
1
0OI5148
I80O9
oOl
Rl - R3
1
0O21492
25o67
oOl
Al - A3
1
0OIIO36
13ol8
oOl
Al - A4
1
0OI896I
22o65
cOl
A2 - A3
1
0OO563I
60 72
oOl
A2 -
A4
1
0OII596
13o85
oOl
LI - L2
1
0OO583O
6o96
oOl
LI - L3
1
0OI857O
22ol8
oOl
o048048
57o39
oOl
1
0OO395I
4o29
0O5
1
0O20405
24o37
oOl
1
0OO6877
8o21
oOl
LI —
L4
'
L2 - L3
L2 -
L4
L3 - L4
1
»»#.-».»«
-^
— —
•••-••
•».-^«iil"' —
"'».«' ••• - 1 - ^
WP--P-
—
-'ig •--!•
•••---r—
63
APPENDIX I—Continued
Constant Angle—Travel Time
e = 0OOO9II, df = 768
Contrast
df
SS
F-Ratio
Level of Significance
im.»r M i - m = » = ? i
Rl - R2
1
001128
12o38
oOl
R2 - R3
1
001632
17o91
oOl
PI - P2
1
000432
4o74
0O5
PI - P3
1 1 001532
16082
oOl
PI - P4
1
002920
32o05
oOl
P2 - P4
1
001105
12ol3
oOl
Al - A3
1
000675
7o4l
oOl
Al - A4
1
000972
IO067
oOl
A2 -
A4
1
000507
5o57
0O5
LI - L3
1
001875
20o58
oOl
LI -
L4
1
004994
54o82
oOl
L2 - L3
1
000888
9c74
oOl
L2 - L4
1
003267
35o86
oOl
1
000479
5o26
0O5
L3 - L4
;
64
APPENDIX I—Continued
Constant Distance—Travel Time
e = o000466, df = 768
Contrast
df
SS
F-Ratio
Level of Significance
Rl - R2
1
0OI6OO
34o33
oOl
R2 - R3
1
0OI936
4lo55
oOl
PI - P3
1
0OII29
24o23
oOl
PI - P4
1
0OI997
42o83
oOl
P2 - P3
1
0OO929
19o94
oOl
P2 -
P4
1
0OI728
37o08
oOl
Al - A3
1
0OO265
5o69
0O5
A2 - A3
1
0OO30O
6o44
0O5
LI - L3
1
0OO222
4o76
0O5
LI - L4
1
0OO432
9o27
oOl
L2 - L3
1
0OO222
4o76
0O5
L2 -
1
c00432
9o27
cOl
L4
APPENDIX II
SIGNIFICANT MEANS
(All Values in Seconds)
Reaction Time
Constant
An^le
Constant
Distance
Ratio
Lower Third
Middle Third
0o246
0o257
0o258
Upper Third
0o246
0o256
0o258
Foot--Tibia Ang
78 degrees
84 degrees
90 degrees
0o248
0o252
0o256
0o247
0o250
0o256
96 degrees
0o260
0o259
8 lbs
0o246
12 lbs
16 lbs
0o250
0o256
0o264
0o243
0o250
0o256
Load;
1
20 lbs
0o263
Travel Time
Constant
Angle
Constant
Distance
Ratios
O0O98
Lower Third
Middle Third
Upper Third
O0O89
OclOO
65
O0O65
O0O55
O0O66
66
APPENDIX II—Continued
Travel Time (Continued)
Constant
Angle
Constant
Distance
Fulcrum Locations
Back of Heel
1 inch from Back
of Heel
Directly under Ankle
1/3 of Distance from
Ankle to Ball of
Foot
00104
00056
00098
00057
0,093
o°o^^
00088
00069
Oo 091
Oo 060
Oo 093
Oc 060
Oo,098
Oc,065
Oc,100
Oc.063
0..086
0,.059
0,3O9O
0,.059
0 olOO
0,o064
0 0IO7
00065
Foot-Tibia Angles
78
84
90
96
degrees
degrees
degrees
degrees
>
1
8
12
16
20
lbs
lbs
lbs
lbs