Metrology study on the effects 3D printing processes.

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Utilizing Measurement Tools to Develop a Shrink Rule for the 3-D Printing Process
Author: Casey J. Jones
Construction Project Engineer
Directorate of Public Works
Camp Atterbury JMTC
Bldg. 232 Eggleston St.
Edinburgh, IN 46124
Telephone: (812)526-1499 ext 62778
Fax: (812)526-1314
casey.j.jones22.nfg@mail.mil
Author: M. Austin Creasy, Ph.D.
Assistant Professor
Mechanical Engineering Technology
Purdue Polytechnic Columbus
Advanced Manufacturing Center of Excellence
4444 Kelly Street
Columbus, IN 47203-1749
Telephone: (812)348-2030
Fax: (812)348-2016
mcreasy@purdue.edu
Speaker/Author: Joseph P. Fuehne, Ph.D., P.E.
Director and Maha Associate Professor
Mechanical Engineering Technology
Purdue College of Technology
Advanced Manufacturing Center of Excellence
4444 Kelly Street
Columbus, IN 47203-1749
Telephone: (812)348-2040
Fax: (812)348-2016
jfuehne@purdue.edu
Abstract
Rapid prototyping, in particular 3-D printing, has quickly grown to be a critical part of the
design, inspect, and evaluate process involved in product design. Parts of moderate size may be
3-D printed using various plastic materials like Acrylonitrile Butadiene Styrene (ABS) and
nylon, which have quickly replaced the powder-based 3-D printers. These plastic processes
utilize relatively inexpensive printers and materials and their popularity has soared as a result.
The Purdue Polytechnic campus in Columbus, Indiana, now employs five 3-D printers to
supplement its mechanical design, inspection, and validation instruction by also using the tools
and resources of an environmentally-controlled metrology lab. The objective of this study is to
design, print, and measure various part geometries to determine how closely the 3D printed part
dimensions are to the original design. 3D printed parts do shrink as they cool following the

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printing process. In essence, this is very similar to shrinkage that occurs during the metal casting
process and so the goal is identify and create a “shrink rule” for 3D printed plastic parts. There
are multiple variables involved in the process including material, nozzle speed of the 3D printer,
resolution of the printer, and size of the part among others. These different variables are explored
in this study to determine the optimal process for accurate and repeatable 3D printing. A Zeiss
Duramax coordinate measuring machine is utilized to perform the dimensional measurements of
the parts. Various part orientations on the CMM are also investigated to determine any
sensitivity to the measurement process. Results will demonstrate that parts need to be scaled up
by 1.1% to 1.3% to accurately account for shrinkage of the material.
Introduction
Rapid prototyping gives companies the ability to produce a working model without the
preparation and supply procurement necessary for a large manufacturing run. In order for a
prototype to be beneficial, it must match desired specifications as closely as possible. The 3D
printers used to create these prototypes have many settings and can be manipulated to make parts
more or less accurate. This study intends to determine the accuracy and precision of a rapid
prototype machine while exploring linear relationships and error correction through
experimentation. For this study, a MakerBot replicator was used to print several parts of various
sizes of a defined geometry and a Zeiss coordinate measurement machine (CMM) was used to
measure the geometry of the printed parts. The part size and resolution have a large impact on
part accuracy and repeatability. Printed parts shrink after cooling and this deviation must be
accounted for in the design process in order to produce a more accurate part. This study
concluded that when producing parts through 3D printing, extra attention must be given to the
manufacturing process in order to prevent parts from having incorrect geometries.
The American tool manufacturing market encountered challenges in the 1980’s when they found
a need to turn drawings and files in to a physical product. In order to remain competitive within
the international market, agencies including NASA, the Department of Energy, and the
Department of Defense, among others collaborated to help develop a set of processes known as
solid freeform fabrication. Today these processes are known as rapid prototyping. Rapid
prototyping gives companies the ability to produce a working model without the preparation and
supply procurement necessary for a large manufacturing run. The prototype is generally made
through 3D printing or some other method of additive layer manufacturing. 3D printing is ideal
for small batch runs resulting in little waste and less use of raw materials. Products can be made
in an economical way with the highest levels of quality and precision [1]. The question remains,
however, exactly how precise are these 3D printing machines? Precision was mandatory for a
organization like NASA, for example, when they recently proved that a spacecraft’s 3D printer
could print replacement parts for itself while in orbit [2]. The objective of this study is to
determine the accuracy and precision of a MakerBot rapid prototype machine through
experimentation. A study by Ogden [3] compared the dimensional accuracy of a 3D printed
vertebra with direct measurements made on a dissected specimen used to produce the working
model. His findings not only proved that 3D printed anatomical structures can be powerful tools
for surgical planning and analysis but that it is possible to produce 3D printed anatomy with an
accuracy that is comparable to measurements made in a rendered version. In his experiment,
Sanchez [4] examined three control factors in open source additive manufacturing: layer
thickness, extrusion width, and nozzle speed. His results showed that the only significant control
factor was the nozzle speed. He also found that the dimensional accuracy in the XY plane is poor

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relative to other planes. Based on these findings, further experimentation is needed to determine
whether the results are specific to open source printers or if it could be generalized to the
Cartesian family of printers.
Strategy and Hypothesis
The purpose of this study was to determine the accuracy and precision of a MakerBot rapid
prototype 3D printer while exploring linear relationships and error correction through
experimentation. A prediction was made that the error would follow a proportional linear trend
in comparison to size so that the larger the block, the larger the error. After a test print of six
variously sized blue prototypes, the printed parts were consistent in material and material color
in order to eliminate these as variables. Black ABS (Acrylonitrile Butadiene Styrene)
thermoplastic polymer was extruded to create square blocks containing a centered through hole
that each had a diameter measuring half of its width. Five different sizes of blocks were used for
this experiment: 12.5 mm, 25 mm, 37.5 mm, 50 mm, and 75 mm with all having a through hole
diameter of half the size. The hypothesis of this study was that the printed parts would shrink
during cooling making the final geometry less than intended and that this would be a consistent
trend amongst sizes.
Materials and Equipment
For this project, a MakerBot Replicator 2X is used as the rapid prototype 3D printer. While the
institution has two of these printers, only one is used to manufacture the specimens. Similarly,
only a single material, ABS, is used throughout the project. Since the material is available in
different colors, the two colors chosen for this work are black and blue. While it is not expected
that the color of the material would influence the dimensions of final product, these two were
chosen to allow for that possibility.
For the measurement part of the project, a Zeiss DuraMax CMM, shown in Figure 1, is utilized
to perform the measurements. The CMM is calibrated and the Zeiss Calypso software is used to
develop and execute the measurement plan for each specimen. Additionally, Autodesk Inventor
is employed as the Computer Aided Drafting (CAD) program to create three-dimensional solid
models of the parts and then export those parts to a stereolithography file for printing on the 3D
printer.
Experimental Procedures
One hundred and fourteen parts were printed in multiple sets over the course of several weeks.
All printed parts followed the same procedure unless otherwise noted. Parts were designed using
Autodesk Inventor before print settings were assigned in MakerWare, which has the option of
printing at low, medium, and high resolution. Low resolution provides faster printing but has the
worst layer height resolution and surface quality of the three. High resolution takes longer to
print but the surface quality and dimensional accuracy are much better. Prototypes were printed
in both high and low resolution to test the extremes of the printer options. To determine the most
optimum size range for the parts, six test parts were printed with blue ABS ranging in size from
25 mm to 150 mm. The parts exceeding 75 mm took too long to print and were not reliable as
they warped due to inconsistent build plate temperatures. Also, printing multiple parts at the
same time proved to be unsuccessful so all future parts were printed one at a time in the center of
the build plate to eliminate location on the build plate as a variable. After examining the test
parts, it was decided that the experimental parts would measure 12.5 mm, 25 mm, 37.5 mm, 50

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mm, and 75 mm. Each part was square with a height of 15 mm and contained a through hole
with a diameter measuring half that of its width. Initially, it was decided that with the exception
of the initial parts, each experimental part would be printed 24 times, 12 times in low resolution
and 12 times in high resolution. After each set of parts was printed, the CAD model was
imported into Calypso to create a measurement plan for the CMM. All data collection by the
CMM was done in an environmentally controlled metrology lab in which temperature is 20°C
±0.5°C and the relative humidity is kept below 50% and is typically around 32%. Size
deviations illustrated on a report by the CMM were recorded and analyzed in Excel for each part.
Initial Parts
Twelve 25 mm square blocks with a 12 mm diameter column were designed and printed at low
resolution. The model in Figure 2 shows the appearance of the part. The CMM has the option of
collecting data points at many different speeds. In order to determine which speed is preferred,
the parts were measured three times at low, three times at medium, and three times at high speed
to eliminate this as a variable. Data showed that the deviation was the worst at high speed, but
that low and medium speeds yielded similar deviations. Due to the layered surface finish of the
prototypes, all future parts were measured at medium speed so the measuring probe could move
across the layers slowly without producing errors. After examining the data recorded during the
Figure 1. The Zeiss Duramax CMM utilized in this project.

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medium speed measurements, it was found that the deviations were consistent enough to only
measure each block one time. The procedure determined by this set of parts established the
measurement style for the rest of the experimental parts.
Initial Parts Result
Once all deviations from the initial parts were input in Excel, it was clear that the data was
inconsistent among each axis. When the parts came out of the printer, the origin was not marked
since it was assumed that the parts were square. Upon further review, knowing the location of
the x and y axis from the printer orientation proved to be very important and was also the cause
of the inconsistencies. The data from these parts was not fit for use but all future prints would
have the origin marked straight from the printer to prevent further problems. At this point, it was
also clear that the extruded column was not of much use as the z axis was not being explored in
this study. The column used more material and therefore took longer to print. All future parts
were designed to contain a through hole centered in the part which would still allow for a
diameter and roundness measurement.
Twenty five millimeter parts, Set 2
The blocks in this set were 25 mm x 25 mm x 15 mm high with a centered 12.5 mm diameter
through hole. The column was eliminated to conserve time and material while still allowing for
a second feature to be measured. Figure 3 shows the appearance of the part. The parts were
printed at both high and low resolution and were then measured with the CMM at medium speed.
The CMM was programmed to measure the roundness and diameter deviations from nominal of
Figure 2. Example of the 12 initial parts.

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the through hole along with the geometry deviations from nominal of the 25 mm x 25 mm
square. This process yielded 2 values for the parallel sides of the x axis and 2 values for the
parallel sides of the y axis. An example of the CMM report can be seen in Figure 4. Although a
new measurement plan had to be written for each different sized part, the features and
characteristics that the CMM measured remained consistent throughout the blocks.
Fifty millimeter parts, Set 3
This set of blocks was designed to compare the geometry deviations in this set against the
geometry deviations of the blocks in set 2. The blocks in this set were 50 mm x 50 mm x 15 mm
high with a centered 25 mm diameter through hole. Figure 5 shows the appearance of the part.
Again, the parts were printed at both high and low resolution. After being measured by the
CMM, the range from set 2 and set 3 was calculated for each axis and averaged. Data from set 2
Figure 3. An example of the part from set 2.
Figure 4. A sample CMM report.

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was compared with data from set 3 and it was determined that larger parts were needed to further
investigate whether a linear trend was present or if one axis was more accurate.
Seventy five millimeter parts, Set 4
The blocks in this set were designed to a geometry of 75 mm x 75 mm x 15 mm high with a
centered 37.5 mm diameter through hole. This set followed the same procedure as sets 2 and 3
except the printer nozzle was cleaned and the build plate tape was replaced before set 4 began
printing. To prevent the parts from becoming detached from the build plate, a mixture of ABS
and acetone (slurry) was added to the Kapton tape where the part would be printed. Data proved
that the precision of the printed blocks in sets 2 and 3 was very high, eliminating a need to print
so many (24) parts. After printing 6 parts at low resolution, the roll of black ABS was replaced
on the printer. Once the ABS was fully loaded, the remaining 6 parts were printed at high
resolution. Figure 5 shows the appearance of the part. The deviations from the blocks in set 2,
3, and 4 were compared on two separate Excel graphs. One graph compared deviations for all
parts printed in low resolution and the other compared deviations for all parts printed in high
resolution. The goal was still to find a linear trend in terms of size. In order to create these
graphs, each deviation was normalized by dividing by the part size.
Figure 5. An example part from set 3 (50 mm square).

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Thirty sevenand one half millimeter parts, Set 5
After anazlying the data from the previous sets it was found that more blocks had to be printed.
The blocks in set 5 were designed to a geometry of 37.5 mm x 37.5 mm x 15 mm high with a
centered 18.75 mm diameter through hole. Figure 7 shows the appearance of the part. The tape
was replaced on the build plate and slurry was applied before set 5 was printed. Six parts were
printed in high resolution and 6 parts were printed in low resolution. The data from this set was
added to the graphs mentioned in section 3.4 before being analyzed. After reviewing the data, it
was decided that more parts were needed and at this point the data proved to be unstable unless
the parts were in high resolution. From this point moving forward, parts were only printed in
high resolution.
Figure 6. An example part from set 4 (75 mm square).
Figure 7. An example part from set 5 (37.5 mm square).

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Twelve and one half millimeter parts, Set 6
Blocks in this set were 12.5 mm x 12.5 mm x 15 mm high with a centered 6.25 mm diameter
through hole. Six parts were printed at high resolution. Every part thus far was printed from the
right nozzle to eliminate the nozzle as a variable. For experimental purposes, two additional
parts of the same geometry were printed from the left nozzle to make sure that the right nozzle
was still stable. After this, the right nozzle was cleaned and 2 additional parts of the same
geometry were printed from the right nozzle. Figure 8 shows the appearance of the part. Data
from the two separate nozzles was compared to look for discrepencies. After looking at all data
collected up to this point, it was decided to design parts and compensate for any error caused by
printing.
Correction Factor Determination
To correct the error due to shrinking, the deviations from the parts ranging in size from 37.5 mm
to 75 mm were averaged and a percentage was found. Original CAD files were loaded to
MakerWare and scaled up to print at 101.13% of the original size. Six of the corrected 50 mm
parts were then printed at high resolution from the left nozzle. After these parts were measured
by the CMM using the previous measurement plan for that size, 6 corrected 50 mm parts were
printed from the right nozzle. These 6 parts were printed with a freshly cleaned extruder and
measured by the CMM using the same measurement plan. All data was then analyzed to
examine if any variance was a result of different extruders being used. These parts intended to
find out if the correction factor was successful.
Now that a correction factor had been found for the right extruder, it was time to examine the left
extruder. Since the right extruder was linear in terms of size, it was assumed that the left would
be also. Due to this, only one size was examined during this phase of the experiment. A
Figure 8. An example part from set 6 (12.5 mm square).

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MakerWare file was created for the 37.5 mm block from set 5 and set up to print from the left
extruder. Six parts were printed, measured with the previously written CMM plan, and all data
was recorded in Excel. Deviations from these parts were averaged and a percentage was found.
Since the parts from the right extruder were linear, a percentage change was found between the
37.5 mm part printed with the right extruder and the final correction factor of 1.13%. The value
obtained was applied to the percent found from the 37.5 mm part printed with the left extruder,
yielding a new percent correction. Ideally, this new value would also work to correct the larger
parts. The original CAD file was loaded to MakerWare and scaled up to print at 101.29 % of the
original size. Two of the corrected 37.5 mm parts from set 5 were then printed at high resolution
from the left nozzle. These parts were measured with the previously written CMM plan, and all
data was recorded in Excel and examined to determined if the correction factor was successful.
Results
Findings from the first set of parts will be covered briefly, along with deviation information from
the remaining sets including the parts printed with the correction factor.
Twenty five millimeter parts, Set 2
Once all deviations from the high and low resolution prints were input in Excel, that data values
were used to create a plot to analyze the results visually. The graph shows that high resolution
prints had a smaller range among deviations. The range of the low resolution prints was
approximately 0.5 mm while the range of the high resolution prints was approximately 0.2 mm.
Figure 8 shows the relationship between resolutions and it can also be seen that the diameter
printed more accurately in high resolution. The data also shows that the roundness of the
through hole was a little worse in high resolution even though the diameter was better.
Figure 8. Excel data comparing low vs. high resolution prints from set 2.

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Fifty millimeter parts, Set 3
The deviation values from the 24 parts printed in this set were used to create a graph in Excel.
The range was better in this set for low resolution and high resolution. When comparing the data
from set 3 with the data from set 2, it was clear that larger parts were needed to determine if one
axis was more accurate than the other. At this point, the expected linear trend was visible in the
plot. The roundness deviation remained unchanged from the previous set and hovered around
0.2 mm from nominal. Data from set 2 and 3 proved to be consistent enough to only print 6 parts
at each resolution for the next set.
Seventy five millimeter parts, Set 4
This set of parts made it clear that cleaning the extruder nozzles, replacing the build plate tape,
and replacing the roll of ABS had no visible impact on part deviations. Data was consistent and
followed the expected linear trend. Deviation values from set 2, 3, and 4 were organized in one
Excel graph. Figure 9 shows the relationship between the sets printed in low resolution. Figure
10 shows the relationship between the sets printed in high resolution. Both graphs show that the
data follows a proportional linear trend in terms of part size. The parts are all consistently
shrinking after being cooled and all deviations are below nominal. The results show that the
larger the block, the larger the error. The difference between the two resolutions is apparent,
showing that the high resolution is more stable and more precise. The roundness remains
unchanged throughout part sizes and the range is much smaller when printed in high resolution.
After reviewing the data contained in the high resolution graph, it was found that there was a
decent gap in deviation between set 2 and 3. At this point more parts were needed to see if the
linear trend would be apparent in the middle of these two sizes.
Figure 9. Excel data comparing set 2, 3, and 4 in low resolution.

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Figure 10. Excel data comparing set 2, 3, and 4 in high resolution.
Thirty sevenand one half millimeter parts, Set 5
The parts in this set fit right in line with what was expected. The data follows the predicted
linear trend and was begging the question, what is the smallest size that the parts become less
linear? Figure 11 shows this relationship and shows that the roundness still remains unchanged.
After analyzing the data up to this point, it was found that examination of parts smaller than 25
mm was needed to determine if smaller parts would also fit this linear trend. Only parts printed
in high resolution would be focused on for the next set.
Figure 11. Excel data comparing set 2, 3, 4, and 5 in high resolution.

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Twelve and one half millimeter parts, Set 6
The parts in this set were not at all in line with the previous results. Figure 12 shows that the
range is much worse for the smaller parts and the roundness worsened by approximately 0.2 mm.
For this set to be in line with what was expected, the range would have fallen between 0 and -0.2
mm deviation from nominal. The graph shows a range of approximately 0.8 mm proving that
parts this small are not at all reliable and will not be accurate. Data from the graph also shows
that the change in nozzles used did not change the deviation much and cleaning the right nozzle
did not impact the results either. Since this small of a size is not reliable overall, the data
regarding the different nozzles was most likely not reliable either.
Figure 12. Excel data comparing right and left nozzle in set 6.
Corrected Results
Figure 13 shows a comparison of the corrected set 3 parts from the right and left nozzle. The
graph shows that the axis deviations remain rather consistent among nozzles, however, the
diameter is more accurate for the parts printed from the right nozzle. The deviations have a
range of less than 0.05 mm which is equal to 50 microns. To put that data in to perspective, this
shows that the parts were corrected to be accurate within the diameter of a human hair. The
graph also shows that the roundness does not change significantly with correction.
Figure 14 shows the deviation values from the corrected set 5 parts. The graph shows that the
roundness and diameter values remained consistent with the values from the corrected parts in
set 3. The difference with the corrected parts printed from the left nozzle is the x-axis is more
accurate than the y-axis. The data in Figure 13 does not show the type of separation between
axes that Figure 14 shows. Initially, it was suspected that the different axes would exhibit
different deviations although the results have not been definitive. Further investigation is needed
to determine if the deviation would remain this way for the left extruder if more parts were

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printed. The correction factor that was made for the left nozzle did work well and made the
deviation less than 0.1 mm. This correction factor was successful enough that it would work to
correct the parts in set 3 and 4 as well.
Figure 13. Excel data comparing right and left nozzle for the corrected set 3.
Discussion
Overall, the results of this study show that the part size and resolution have a large impact on
part accuracy and repeatability. The results show that the printer is very precise for parts
measuring 50 mm and larger at high resolution, exhibiting a range of less than 0.1 mm. Printed
parts shrink after cooling and this deviation must be accounted for in the design process in order
to produce a highly accurate prototype. Figure 11 proves that the larger the part the larger the
error and the data does show a linear trend with respect to size as predicted. Printing at low and
medium resolution is not as reliable or stable as printing at a high resolution. High resolution
printing takes more time but the part comes out more accurate. The printer has many settings
and they proved to be very influential. The build plate temperature and the presence of a raft
were also considered as variables. If the build plate temperature was too low, the parts did not
stay on the plate and the parts warped. Parts also warped when the raft was omitted and when
multiple parts were printed at once. Through the use of an infrared thermometer, it was found
that the build plate did not heat evenly which is why all parts were printed in the same location in
the center of the build plate. The CMM also has many settings that can change how data is
recorded. When measuring parts with a layered surface finish such as ABS, the CMM needs to
collect data at low to medium speed to prevent errors. The CMM measured inaccurately when

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Figure 14. Excel data for the corrected set 5.
ran at a high speed. Another important detail was part orientation in the printer. To gather
accurate measurements of repeated parts the origin must be marked and known throughout the
measurement process since the x and y axis were not consistent. Several different sized parts
were printed and it can be said with certainty that small parts, specifically those smaller than 25
mm, are not accurate and do not print with a consistent size. The very large parts, specifically
those larger than 75 mm, do not print as evenly due to inconsistent build plate temperatures.
They also take longer to print and sit on the hot plate for a longer amount of time which causes
the corners to warp. The extruder and nozzle being used is also important. Switching back and
forth between right and left nozzles during a multiple part run is not recommended if part
precision is important. Experimentation proved that cleaning the extruder and nozzle, changing
the Kapton tape, and replacing the roll of ABS had little to no effect on the accuracy of printed
parts.
Finding an error correction value is possible but it is believed to be on an extruder-to-extruder
basis. The parts corrected in this study turned out to have a very low deviation from nominal and
the correction values found for each extruder could be used in the future to compensate for the
error caused by shrinking. This study was based off only one of the two printers that were
available. If given more time, it would be interesting to see if the second printer follows the
same pattern of error percentage and deviation between axes or if these deviations are different
among printers entirely. The ABS comes in many colors and the black that was used during this
study worked very well. During the initial part of the study it was found that blue also prints
well but yellow and red have printing issues and cause the machine to clog. That being said,
there are many more variables that could be explored when using these printers. In the future, if
new nozzles and extruders are acquired for these printers, a run of parts ranging in size from 37.5

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mm to 75 mm should be printed to find an average deviation. This data can give a value of error
correction to allow future parts to be scaled up to make the geometry more accurate.
Conclusion
In conclusion, when producing prototypes with a 3D printer, extra attention should be given to
the manufacturing process including the settings of all equipment. If parts are printed in a high
resolution at the center of the build plate with an average geometry of 50 mm then they will be
accurate within approximately 1.13% - 1.29%. Since all printed parts shrink, if they are scaled
up within a range of 101.13% - 101.29% before printing, then the accuracy will be within 50
microns of nominal. Due to the many variables that were found throughout this study, a second
study based off multiple printers and extruders that further examines the variables is suggested
for future work.
References
1. The Benefits of Rapid Prototyping - Excello Tool | Machine Shop | CNC | Milling | Rapid
Prototyping. (2015, January 28). Retrieved February 10, 2015.
2. Hubscher, B. (2014, November 25). Open for Business: 3-D Printer Creates First Object
in Space on International Space Station. Retrieved February 10, 2015.
3. Ogden, K. (2014). Dimensional Accuracy of 3D Printed Vertebra. Retrieved June 23,
2015.
4. Sanchez, F. (2014). Towards a Standard Experimental Protocol for Open Source Additive
Manufacturing, Virtual and Physical Prototyping, 9:3, 151-167. Retrieved June 23, 2015
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Center for Manufacturing Excellence “Learning Lab”, Proceedings of the NCSL
International Workshop and Symposium, Sacramento, CA, 2012.
6. Fuehne, J., “Developing an Integrated Curriculum in Metrology for a Mechanical
Engineering Technology Program”, Proceedings of the NCSL International Workshop
and Symposium, Nashville, TN, 2013.
7. Oberg, E., Jones, F., Horton, H., and Ryffel, H., Machinery’s Handbook, 28th Edition,
Industrial Press, New York, 2008.