Tuesday, October 28, 2014

Painting a Carousel

I've been listening to Car Talk for a few years now. The hosts Tom and Ray kept me company on my 2,000 mile trip from Iowa to California. Their mix of sarcasm and loving judgment reminds me of the times I’ve rooted around to fix things. Every week they post a puzzler. The problem statement for this week asks listeners to determine the area between two concentric circles given the length of a chord tangent to the inner circle.

Since I'm an engineer, I had to sketch it out:

D, diameter of the outer circle
R, radius of the outer circle
d, diameter of the inner circle
r, radius of the inner circle
C, length of chord tangent to the inner circle
C = 70 ft
Examining Figure 1, we see that r intersects C at its midpoint. Therefore,makes up one leg of a right triangle with r and R. The Pythagorean Theorem relates the three sides of a right triangle as

Substituting in our variables yields

Which can be rearranged as

Now we have one equation but two unknown variables. Let’s establish some relationships for area. The generalized equation for the area of a circle is

In terms of the outer circle

In terms of the inner circle

To solve the problem, we must find the area between the circles:

Recall from our Pythagorean relationship that we (rather fortunately) know the value of (R2-r2).

Ed, Biff, and Skip need enough paint to cover 3,846.5 square feet.

Tuesday, March 11, 2014

ASCE Concrete Frisbee

ASCE Concrete Frisbee was part of a multi-university Civil Engineering Student Conference.  My project’s vision was to try different mold and construction techniques.  I decided on liquid Polyurethane casting to accomplish detailed form work.  I also experimented with color pigments, stains, dyes, and a variety of lightweight aggregates and property-modifying admixtures.

The final product, dubbed "1738" in honor of Bernoulli's Hydrodynamica
I used Inventor to CAD the formwork before starting construction.  This was an important step in justifying the procurement of pricey Polyurethane rubber.  It helped everyone understand the process.

Expanded view of the male mold, plastic form, female mold, and foam pre-form
The following images illustrate the process of making a Polyurethane mold from liquid urethane rubber.

Carved a void in a block of Styrofoam
Lined the pre-form with an impervious layer
Mounted the plastic cast into the Styrofoam case
Batched the rubber and hardening agent
Poured in to the form work then let cure for 72 hours
The structural concrete mix consisted of Type I Portland Cement with expanded slate as the primary aggregate.  Primary reinforcement was a net of alkali resistant glass (ARG).  Secondary ARG chopped strands were dispersed into the mix to reduce shrinkage cracking.  Metal oxide pigments were blended in for aesthetic purposes.  Water reducing and superplasticizing admixtures were batched with the wet components.  The final mix was laid by hand between the male and female molds.

Durability tests were heuristic.  I flexed the disc by hand and applied lateral pressure to visually detect flexure.  A coating of orange marking chalk amplified any imperfections in the discs.  Before competition, I attempted to FEM a point load (to simulate a lateral collision).

Finite Element Analysis of 1738
At competition, aesthetics judging went exceedingly well.  The judges seemed impressed by the product’s form, color, and quality.  The accuracy competition involved throwing the disc as close as possible to a fixed cone.  My team’s best attempt was still 8 feet out.  The best distance throw achieved stable flight and went 153 feet before striking the side of a building.
After the building collision
Primary and secondary reinforcement maintained the integrity of the disc.  With the broken pieces still attached, the durability score was not horribly affected.

Although a rubber mold yielded impressive results, the technique was expensive and sensitive to environmental factors while curing.  Nevertheless, this project proved that a Concrete Frisbee could be a real Frisbee.  In a future iteration, I would introduce more lightweight concrete aggregates and put more care in to the coloration of the final product.

As part of a larger conglomerate of student engineering projects (including Concrete Canoe), Frisbee served as a testing ground for new methods.  The smaller scale of the project allowed for more liberal application of unproven ideas and methods.

2nd place for Concrete Frisbee at the 2008 PSWRC

Monday, March 10, 2014

AMHS Robotics MkII Drivetrain

I designed this chassis while participating in the FIRST Robotics Competition.  Key considerations were standardization of parts and manufacturing simplicity.  3D CAD, CAM, and 2D drawings were key to making the design come alive.

The chassis served as a platform to move around a field the size of a basketball court.  Coupled with an extending arm designed by the rest of my team, our machine joined up with other schools on the field to stack tetrahedral game pieces on to scoring racks.

Machined components assembled with some of the drive electronics
3D model of one of the wheel assemblies

Shop drawing for one of the aluminum rims
Two rims fit back-to-back to form a wider wheel, and were assembled with sprockets and spacers to interface with the electric drive system.  The front wheels were raised slightly off the ground to reduce the effective turning radius (but still present to support the machine if it tipped forward).

3D rendering of a complete drive side

Test run of MkII with the upper arm mounted to the chassis
The machine performed well for its first trial.  It was stable, as expected, but the exceptionally low profile made maneuvering around obstacles somewhat awkward.  Future iterations would raise the ground clearance.