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The “Back To The Future” Experience Of Graphical Analysis

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2006 Annual Conference & Exposition


Chicago, Illinois

Publication Date

June 18, 2006

Start Date

June 18, 2006

End Date

June 21, 2006



Conference Session

Back to Basics in Mechanics

Tagged Division


Page Count


Page Numbers

11.1338.1 - 11.1338.11



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Paper Authors


Thomas Malmgren University of Pittsburgh-Johnstown

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Thomas Malmgren, P.E.
Associate Professor of Mechanical Engineering Technology at the University of Pittsburgh at Johnstown. B.S. Mechanical Engineering from Pennsylvania State University, M.S. Industrial Engineering from University of Pittsburgh. Registered professional engineer in Pennsylvania. Interests include CAD, design, thermodynamics, enjoying the outdoors (swimming, hiking, hunting, fishing, kayaking) and my family. Worked as a journeyman machinist for General Electric, U.S. Navy Machinery Repairman, and methods engineer for Elliott Company (manufacturer of turbo-machinery) prior to teaching Mechanical Engineering Technology.

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NOTE: The first page of text has been automatically extracted and included below in lieu of an abstract


Graphical analysis has always been an integral part of the medley of techniques to solve engineering problems. In the past, the accuracy of the graphical analysis solution was limited by the precision of the instruments associated with producing it. Rudimentary tools such as pencils, scales, protractors, T-squares, planimeters, slide rules, etc., provided a solution within acceptable limits of error. However, the precision, accuracy, and flexibility available now with computers antiquated the hand-drawn graphical analyses methods for solving engineering problems.

The advent of computer-aided drafting (CAD), re-engineered the old concept of graphical analysis. CAD brought it out of the past and into the future with a renewed respect, appreciation, precision, and applicability to a wide variety of engineering problems. Thus, graphical analysis has become a champion of faculty seeking to provide solutions to problems and offer an entirely new perspective to engineering problem solutions. “Graphical thinking” provides a tremendous tool to engineers seeking to develop an extensive conceptual knowledge base via greater visualization capabilities.

Vector solutions provide an excellent example of the versatility of graphical analysis. The types of vectors commonly encountered in engineering problem-solving include displacement, velocity, acceleration, force and moments. Using “graphical thinking”, one can visualize vector components and vector manipulations such as vector addition, subtraction, vector dot and cross products. A graphical picture of the vector solutions makes problems easier to conceptualize, providing an intuition check on the correctness of the vector solutions that one does not readily get from utilizing matrix solution techniques or even vector component manipulation analyses.

The application of common CAD software to a multitude of engineering problems significantly enhances the students’ ability to solve an endless variety of engineering problems. Requiring students to use a CAD-based graphical solution in place of or in addition to a traditional analysis provides students with a greater understanding of the solution to the problems on which they are working. Stressing a CAD-based graphical solution in the courses of Engineering Statics, Dynamics, and Mechanics of Material provides a strong foundation for using “graphical thinking” to solve upper level course problems as well as have a positive impact on engineering design coursework. This paper will emphasis and focus on the application of CAD-based graphical solutions to Statics, Dynamics, and Mechanics of Material courses taken by the majority of engineering and engineering technology students.


Times have certainly changed for undergraduates in engineering and engineering technology programs. We have gone from using slide rules to calculators to computers for computations. Engineering graphics were a major part of the curriculum and involved T-squares, triangles, protractors and a variety of scales. Unfortunately, some of the basic concepts from the “old days” have been lost despite an increase in the level of sophistication in engineering analysis methods. Graphical analysis techniques were routinely used in many courses such as Statics,

Malmgren, T. (2006, June), The “Back To The Future” Experience Of Graphical Analysis Paper presented at 2006 Annual Conference & Exposition, Chicago, Illinois. 10.18260/1-2--929

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