A Kinematic and Dynamic Analysis of Shoveling Snow
by
José Andrés DeFaria
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
Master of Engineering
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Thesis Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
May 2016 (Second Progress Report: March 2016)
i
© Copyright 2016
by
José Andres DeFaria
All Rights Reserved
ii
CONTENTS
A Kinematic and Dynamic Analysis of Shoveling Snow ................................................... i
LIST OF TABLES ............................................................................................................ iv
LIST OF FIGURES ........................................................................................................... v
ACKNOWLEDGMENT .................................................................................................. vi
ABSTRACT .................................................................................................................... vii
1. Introduction.................................................................................................................. 1
2. Background .................................................................................................................. 2
3. Methodology ................................................................................................................ 6
3.1
Initial Phase ........................................................................................................ 7
3.2
Second Step ........................................................................................................ 8
3.3
Third Step ........................................................................................................... 9
3.4
Fourth Step ....................................................................................................... 10
3.5
Fifth, Sixth, and Seventh Step .......................................................................... 10
4. Results........................................................................................................................ 11
5. Discussion .................................................................................................................. 13
6. Conclusions................................................................................................................ 14
7. References.................................................................................................................. 15
8. Appendices ................................................................................................................ 16
8.1
Appendix A - Determination of Body Segment Weights ................................ 16
iii
LIST OF TABLES
Table 1: Errors associated with estimation in step three ................................................... 9
Table 2: Average body heights and lengths [8] ............................................................... 16
Table 3: Average body segment weights [8] ................................................................... 16
Table 4: Average heights and weights for across the adult human population ............... 16
Table 5: Body segment lengths and heights across the human adult population ............ 17
Table 6: Body segment weights across the human adult population ............................... 17
iv
LIST OF FIGURES
Figure 1: A typical straight-shaft shovel and an ergonomic bent-shaft shovel [3] ............ 1
Figure 2: Regular and modified shovel design for dirt used in study [4] .......................... 2
Figure 3: Flexion angle and loads which induce moments in the lower back [5] ............. 3
Figure 4: Dimensions of the snow shovels used in [6] ...................................................... 4
Figure 5: Mean L5/S1 extension moment-time curves (sagittal plane) [6] ....................... 5
Figure 6: Mean upper body flexion-time curves (sagittal plane) [6] ................................. 5
Figure 7: Heaviest and lightest weights for subjects of given heights [7] ......................... 6
Figure 8: Initial positions of upper arm (green) and lower arm (blue) for the Lewinson
Average .............................................................................................................................. 7
Figure 9: Calculation of moment arm ................................................................................ 8
Figure 10: Position of back and arms at the end of the second step for the straight-shaft
(left) and the bent-shaft (right) shovels ............................................................................. 9
v
ACKNOWLEDGMENT
Type the text of your acknowledgment here.
vi
ABSTRACT
Type the text of your abstract here.
Current summary of my progress: (Second Progress Report)
It is now my second progress report and I am pleased to say that things are perfectly
on track! Based on my preliminary schedule from the project proposal, I am supposed to
have completed my model and generated preliminary results. I have succeeded in
meeting this goal and am actually further along with the model than I originally expected
to be.
As discussed with you via email, I decided to switch from Abaqus to Maple for the
software that will run my analysis. Abaqus has a wonderful graphical user interface;
however it is not adequately suited for this type of analysis. To complete a kinematic
analysis in Abaqus, a multitude of points must be drawn and then connected with
connector elements. This is what was done in the Beaman report about throwing a
football. Although Abaqus permits for parameterization of certain geometries, point
cannot be parametrically located. This means that a new model would need to be
constructed for each and every height that I wished to examine.
On the other hand, Maple is a computer algebra system. The height and weight of a
subject can be defined as variables, allowing the results to be recalculated for a subject
of a different height/weight in a matter of seconds. Since everything must be coded into
Maple, it requires a deeper understanding of the geometric motions completed in the
analysis. The model has been simplified into line segments (such as the upper arm,
which has a fixed length and can only rotate at its ends) which means most of this
geometry is limited to three-dimensional trigonometry.
Separate Maple worksheets have been created for the straight shaft and the bent
shaft shovels. Some preliminary data are presented in the Result section, although there
is no discussion about it yet. Although I am confident that the model does not have any
significant sources of error, I am aware of a minor source which, on average, may
misplace some of the positions by about a quarter of an inch. This is not expected
vii
significantly affect the end results, but it will be looked into over the course of the next
month.
Per the MANE6970 Key Deadlines document, the following sections of this report
were expected to have content by today's date: title page, list of tables, symbols,
contents, etc, introduction, methodology, results, discussion, references, and appendices.
As discussed above, most of these sections do have content. The only true exception is
the results and discussion section, which is currently populated by tables and data only.
The data will be further evaluated before the discussion section is written.
Future Work before the next progress report
The next progress report (4/25) is expected to be a complete preliminary final
report. In order to meet this goal, the Maple models will be further examined in an
attempt to reduce some of the known sources of error. Additionally more content will
need to be written to support this document. This is not expected to be an issue since the
primary analytical model is complete, this will permit additional time to focus on the
report writing.
viii
1. Introduction
Snow shoveling is a routine winter task for many Americans, especially those living in
southern New England. Boston and Hartford both receive in excess of 30 inches of
snowfall per winter [1]. While corporations and municipalities rely on plowing or
snowblowers for snow removal, private residences are typically shoveled by the owners
or occupants [5]. Since snow shoveling is not the primary occupation of many of the
participants, they do not receive training as a full-time laborer might. As a result, many
of these residents may incorrectly use the snow shovels they have, such as lifting with
their back, rather than with their knees.
This type of misuse is likely the reason why approximately 11,500 individuals are
treated in US emergency rooms each year due to injuries sustained while shoveling snow
[2]. Many of these injuries occur in the lower back. Ergonomic snow shovels exist which
are purported to reduce stress in the back due to their bent-shaft design, but many
households continue to use straight-shaft shovels.
Figure 1: A typical straight-shaft shovel and an ergonomic bent-shaft shovel [3]
1
2. Background
There have been some previous studies into the impact of ergonomic shovel use. Some
of these studies relied on qualitative surveys to determine the effectiveness of each
shovel design. Other studies used mechanical means in an attempt to measure lifting
forces. A select few studies used data collection equipment to take quantitative
information into the bending of the back during shoveling tasks.
In one of the earlier studies found, a different style of ergonomic shovel was evaluated
[4]. This shovel was designed for dirt rather than snow. Instead of using a bent shaft
design, similar to that depicted in Figure 1, it used a handle mounted to a secondary
shaft, as shown in Figure 2. Only qualitative data was collected via surveying study
participants; however, the results indicated that the modified shovel did reduce perceived
pain in the participants. The authors also noticed that the modified shovel appeared to
reduce the tendency for the participants to stoop. It is these extended periods of bending
that are considered the primary cause of muscle fatigue and back pain or injury. It should
be noted all of the study participants were male, and all were industrial workers who
completed shoveling or digging tasks in their daily work.
Figure 2: Regular and modified shovel design for dirt used in study [4]
In another study, published ten years later, shovels similar to those depicted in Figure 1
were used exclusively for snow [5]. Quantitative data was collected for this study,
including the trunk flexion angle, lateral bending angle, and rotation angle. The results
2
showed usage of the bent shaft shovel significantly reduced the trunk flexion angle. The
average trunk flexion angle was 41.4 degrees with the bent shaft shovel compared to
49.2 degrees for the straight shaft. This difference in bending angle is significant because
it decreases the moment placed on the lower back by the upper body as shown in Figure
3. It should be noted that all study participants were male.
Figure 3: Flexion angle and loads which induce moments in the lower back [5]
Despite the fact that ergonomic shovels are marketed as such, as recent as 2014, no
scientific evidence supported claims that the shovel would reduce mechanical loading on
the lower back [6]. Another study, [6], continued the work from [5], with an attempt to
determine the reaction moment in the lower back, referred to as the L5/S1 extension
moment. L5 and S1 refer to a particular location within the vertebrae, between the
lumbar and the sacrum, essentially the base of the spine.
3
Figure 4: Dimensions of the snow shovels used in [6]
The dimensions of the snow shovels used in [6] are presented in Figure 4. It should be
noted that out of all the previous studies examined, this was the only study which
included women in the sample size, although the results were not broken down by
gender. The study found the L5/S1 peak extension moment was 0.627 N·m/kg·m for the
bent-shaft shovel compared with 0.703 N·m/kg·m for the straight-shaft shovel.
Additionally, the peak upper body flexion for the bent-shaft shovel was 74.3°, reduced
from a value of 84.8° with the straight-shaft shovel. These results indicate that the
ergonomic shovel does reduce mechanical loading on the lower back. Graphs of the
L5/S1 extension moments and the upper body flexion are presented in Figure 5 and
Figure 6, respectively. In an attempt to account for the different body proportions, the
extension moment was divided by the total mass and height of each participant.
4
Figure 5: Mean L5/S1 extension moment-time curves (sagittal plane) [6]
Figure 6: Mean upper body flexion-time curves (sagittal plane) [6]
Although this study did include women in the study, its presentation of the final results
in the form of averages speaks only to the average individual. A female of the 5th
percentile height is fifteen inches shorter than a male of 95th percentile height [7]. A
95th percentile height male who is also in the 95th percentile in weight can weigh more
than three times more than a 5th percentile female in height and weight. These
discrepancies in height should greatly affect the flexion angle and the discrepancies in
weight should greatly affect the extension moment.
5
3. Methodology
This evaluation will expand upon previously completed work in [6]. Will ergonomic
shovels reduce mechanical loading of the lower back across the human adult population?
Figure 7 shows the weight range of North American and European adults within various
height ranges. While the subjects selected in Figure 7 are at the extremes for their
heights, the 5th percentile female is 4 feet, 11 inches tall and weighs on average 113 lbs
(150 cm, 51.26 kg) and the 95th percentile male is 6 feet, 2 inches tall and weighs on
average 246 lbs (188 cm, 111.58 kg) [7].
Figure 7: Heaviest and lightest weights for subjects of given heights [7]
To understand the ergonomic value of the bent-shaft shovel, it must be proven to reduce
the mechanical loading of the lower back in a great proportion of the adult population. A
small female will not need to bend over much to reach the snow. Additionally, her upper
body will weigh significantly less than that of a large male. The extension moment is
theorized to increase with both flexion angle and upper body weight; therefore,
ergonomic advantages gained by use of the bent-shaft shovel may diminish as height and
weight decrease.
6
To evaluate the effectiveness of the ergonomic value across the adult human population,
a kinematic analysis will be completed. This analysis will use Maple (a computer
algebra program) to compute the body joint positions throughout the shoveling motions.
Kinematic analysis will first be accomplished for an adult matching the average height
and weight of the subjects in [6] (1.77 m, 73.5 kg) to reproduce the results shown in
Figure 5 and Figure 6. When this kinematic model is complete, the variables defining the
height and weight can be modified to represent a 5th percentile female and a 95th
percentile male and the results will be compared.
3.1 Initial Phase
Two separate Maple worksheets were created, one each for the standard shovel and the
bent shovel. A global coordinate system is defined with the ground below the base of the
trunk as (0,0,0). The x-direction is the front-to-back direction, the y-direction is the
vertical direction, and the z-direction is the left-to-right direction. The height and weight
of the subject can be input in inches and pounds. Using these values, and the ratios
discussed in Appendix A, the body segment weights and lengths can be computed.
The subject is assumed to stand with their upper arm rotated 10 degrees from
vertical, and their lower arms parallel to the ground. This can be seen in Figure 8.
Knowing these angles permits the calculation of the base of the trunk, the top of the
trunk, both shoulders, both elbows, both hands, the shovel shaft end, and the center of
the shovel blade. The x-, y-, and z-coordinates of these points are calculated. For the
bent shovel, additional points are necessary to define the two vertices which comprise
the bent shaft.
Figure 8: Initial positions of upper arm (green) and lower arm (blue) for the Lewinson Average
7
The total moment on the base by summing the contributions of each item. For
simplicity, the center of mass for the trunk and head was considered to be the
supersternale height. The center of mass for the upper and lower arms was calculated to
be at the center of each arm. The center of mass for the shovel was located at the shaft
termination and the snow load was applied to the blade position. To determine the
contributions each of these items have towards the total moment, the moment arm was
determined using the distance from the base in the x- and z-directions as shown in Figure
9. Only the x-direction contribution is considered for the upper and lower arms as the zdirections are counteracted by the left and right symmetry.
Figure 9: Calculation of moment arm
3.2 Second Step
In the second step, the trunk rotates at a constant angular velocity until the peak trunk
flexion angle (84.8° for the straight shovel, 74.3° for the bent shovel) is reached. The
8
upper arm rotates another 20° with respect to the vertical and the lower arm rotates until
it is perpendicular to the ground. The positions of these arms is shown in Figure 10.
Figure 10: Position of back and arms at the end of the second step for the straight-shaft (left) and
the bent-shaft (right) shovels
3.3 Third Step
During the third step, the left arm lowers while the right arm raises to reduce the blade
height to zero. This is accomplished by estimating what angle the shovel needs to be
rotated to in order to reduce the blade height at the end of the second step to zero. Since
the lower arm remains perpendicular to the ground, this raising and lowering is
accomplished by increasing and decreasing the angle at the shoulder. As a result, the
right arm moves closer to the body and the left arm moves further away, causing a
rotation of the shovel in the x-z plane as well as the y-z plane.
The estimation used in determining these angles is a small source of error in the
overall calculation. Theoretically, the blade height (y-direction) should be zero at the end
of this step. The actual blade heights for the three body types are shown in Table 1.
Table 1: Errors associated with estimation in step three
Straight shovel
Bent shovel
5th percentile female
NEED
-0.04672 in
Lewinson average
NEED
-0.39272 in
9
95th percentile male
NEED
-0.54481 in
3.4 Fourth Step
During the fourth step, the weight of the snow linearly ramps over the time period.
Based on [6], the weight of the snow is assumed to be 6 pounds.
3.5 Fifth, Sixth, and Seventh Step
During the remaining steps, the motions are completed in reverse. This is accomplished
by setting the position values equal to the appropriate position value in the
corresponding step.
10
4. Results
The graphs and tables below are PRELIMINARY. That is why they are not yet
captioned or discussed in great detail.
Moment for the Lewinson Average individual
70000
60000
Momnet (in*lbs)
50000
40000
Straight Shovel
30000
Bent Shovel
20000
10000
0
0
1
2
3
4
5
Time (seconds)
Similar style curves to what is seen in Figure 5.
Peak Moment
Straight shovel
Bent shovel
32.5e3 in*lb
26.7e3 in*lb
5th percentile female (average) 37.1e3 in*lb
31.0e3 in*lb
Lewinson average
57.3e3 in*lb
50.2e3 in*lb
95th percentile male (average)
86.7e3 in*lb
78.0e3 in*lb
95th percentile male (heavy)
101.4e3 in*lb
91.9e3 in*lb
5th percentile female (light)
11
6
Peak Moment, normalized for height and weight using the Lewinson
methodology
Straight shovel
Bent shovel
6.269
5.134
5th percentile female (average) 5.571
4.648
Lewinson average
5.079
4.450
95th percentile male (average)
4.762
4.286
95th percentile male (heavy)
4.615
4.182
5th percentile female (light)
Graph showing Moment over time for all five subjects with both shovels
120000
100000
A1
Momnet (in*lbs)
80000
A2
A3
A4
60000
A5
B1
B2
40000
B3
B4
B5
20000
0
0
1
2
3
4
5
6
Time (seconds)
A= straight shovel, B=bent shovel, 1-5 = the five subjects listed in the order of the
table above.
12
5. Discussion
This is a discussion of the results.
13
6. Conclusions
conclusions will go here.
14
7. References
[1]
National Oceanic and Atmospheric Administration. (2014, February). National
Overview - February 2014, Winter Snowfall Departure from Average. Retrieved
February 23, 2016, from
https://www.ncdc.noaa.gov/sotc/national/2014/2/supplemental/page-4/
[2]
Watson, D. S., Shields, B. J., & Smith, G. A. (2011). Snow shovel-related
injuries and medical emergencies treated in US EDs, 1990 to 2006. American
Journal of Emergency Medicine, 29(1), 11-17.
[3]
Huang, C., & Paquet, V. (2002). Kinematic evaluation of two snow-shovel
designs. International Journal of Industrial Ergonomics, 29(6), 319-330.
[4]
Degani, A., Asfour, S. S., Waly, S. M., & Koshy, J. H. (1993). A comparative
study of two shovel designs. Applied Ergonomics, 24(5), 306-312.
[5]
McGorry, R. W., Dempsey, P. G., & Leamon, T. B. (2003). The effect of
technique and shaft configuration in snow shoveling on physiologic, kinematic,
kinetic and productivity variables. Applied Ergonomics, 34(3), 225-231.
[6]
Lewinson, R. T., Rouhi, G., & Robertson, D. G. E. (2014). Influence of snow
shovel shaft configuration on lumbosacral biomecahnics during a load-lifting
task. Applied Ergonomics, 45(2), 234-238
[7]
Dowell, B., & Gscheidle, G. (2003). The Evolution of Anthropometrics and User
Control: The Science and Research Behind the Mirra 2 Chair. Retrieved
February 21, 2016, from http://hermanmiller.com/research/solution-essays/theevolution-of-anthropometrics-and-user-control.html
[8]
Clauser, C. E., McConville, J. T., & Young, J. W. (1969). Weight, Volume, and
Center of Mass of Segments of the Human Body (Tech. No. AMRL-TR-69-70).
Wright-Patterson AFB, Ohio: USAF Aerospace Medical Research Laboratory.
15
8. Appendices
8.1 Appendix A - Determination of Body Segment Weights
Weights, volumes, and center of masses for the human body and body segments are
presented in [8]. The body mass segments in this study will be used to determine the
mass of each segment as a percentage of the total body weight. Using this percentage,
the body mass segments of any body type can be extrapolated proportionally. Similar
extrapolation can be accomplished for body segment lengths. Table 2 presents body
lengths and heights while Table 3 presents body segment masses.
Table 2: Average body heights and lengths [8]
Total height
Head + trunk
Suprasternale height
Chest breadth
Trunk
Arm
Length (cm)
172.72
81.92
141.05
33.23
57.89
77.45
Percentage of Height
100%
47.43%
81.66%
19.24%
33.52%
44.84%
Table 3: Average body segment weights [8]
Total body
Head + trunk
Total arm
Trunk
Upper arm
Forearm and hand
Mass (kg)
65.606
38.061
3.216
33.312
1.730
1.483
Percentage of Weight
100%
58.01%
4.901%
50.78%
2.64%
2.26%
The weights and heights presented in Table 4 will be used in this study.
Table 4: Average heights and weights for across the adult human population
Body Type
Light 5th percentile female [7]
Average 5th percentile female [7]
Lewinson Average [6]
Average 95th percentile male [7]
16
Height (in)
59.00
59.00
69.69
74.00
Weight (lbs)
88
113
162
246
74.00
297
Heavy 95th percentile male [7]
To calculate the respective heights and lengths across the adult population, the height
from Table 4 will be multiplied by the segment height of length from Table 2 and then
divided by the total height from Table 2. These results are shown in Table 5.
Table 5: Body segment lengths and heights across the human adult population
Total height
Head + trunk
Suprasternale
Chest breadth
Trunk
Arm
Light 5th Average
Lewinson
percentile 5th
Average
female
percentile
female
59.00 in
59.00 in
69.69 in
27.98 in
27.98 in
33.05 in
48.18 in
48.18 in
56.91 in
11.35 in
11.35 in
13.41 in
19.77 in
19.77 in
23.36 in
26.46 in
26.46 in
31.25 in
Average
95th
percentile
male
74.00 in
35.10 in
60.43 in
14.24 in
24.80 in
33.18 in
Heavy
95th
percentile
male
74.00 in
35.10 in
60.43 in
14.24 in
24.80 in
33.18 in
To calculate the respective body segment weights across the adult population, the height
from Table 5 will be multiplied by the segment height of length from Table 3 and then
divided by the total height from Table 3. These results are shown in Table 6.
Table 6: Body segment weights across the human adult population
Total body
Head + trunk
Total arm
Trunk
Upper arm
Forearm + hand
Light 5th Average
Lewinson
percentile 5th
Average
female
percentile
female
88.00 lbs 113.00 lbs 162.00 lbs
51.05 lbs
65.56 lbs
93.98 lbs
4.31 lbs
5.54 lbs
7.94 lbs
44.68 lbs
57.38 lbs
82.26 lbs
2.32 lbs
2.98 lbs
4.27 lbs
1.99 lbs
2.55 lbs
3.66 lbs
17
Average
95th
percentile
male
246.00 lbs
142.72 lbs
12.06 lbs
124.91 lbs
6.49 lbs
5.56 lbs
Heavy
95th
percentile
male
297.00 lbs
172.30 lbs
14.56 lbs
150.80 lbs
7.83 lbs
6.71 lbs