Work in progress paper

Engineering Statics curricula in most institutes do not comprise virtual work (VW), though the subject appears in most standard textbooks.  A possible reason is that it requires a shift in the approach to solve equilibrium problems. The students need to think in terms of work and energy; and derivation of solution is more mathematically intense than the other topics such as force and moment balance.  However, because it introduces the important concept of stability, we decided it is worthwhile to include VW in our Statics course.

Our approach to teach VW, is to introduce a project with an experimental design and discovery.  Students are asked to build a few prototypes of a composite object (a roly-poly) made up of simple geometric primitives (hemisphere, cylinder, cone) with different ratios in the dimensions of the components.  The ratios are chosen to examine whether the composite is stable, unstable or neutral when subject to an external force.  The prototypes can be fabricated using simple materials such as ice, paper, chocolate, play-doh, wood or metal etc. readily available at home, while lathe and machining, 3-D printing, and molding are also allowed.

A horizontal force F acting at the tip, tilts the roly-poly until the axis inclines at an angle q with the vertical.  A homemade force gage using strings, paper, pencil and sand / rice grains is designed and constructed at home.  Students will submit final reports covering the following topics: (i) Free body diagram, (ii) Mechanical equilibrium, (iii) Center of gravity of the composite roly-poly, (iv) Potential energy formulation with and without the external force, (v) Theoretical prediction of F(t) for different dimension ratios using Matlab, (vi) Experimental force and angle measurements, and (vii) Data analysis.  Video clips and photos are required to show the prototypes and force measuring mechanism.  Project assessment is based on mathematical rigor, ingenuity and aesthetics in engineering design, and measurements and analysis.  Interested students are encouraged to rock the roly-poly to perform simple harmonic motion and to measure the oscillation frequency and amplitude, which is a preamble to subsequent courses in dynamics.  The project promotes experiential learning and arts of design and incorporates calculus-based energy method of VW into conventional Statics curriculum.  A forerunner ME 2350 Statics project was implemented in Fall 2020, and an improved version is underway in Fall 2021.