By thinking through previously developed solutions as well as examining the laws of nature, an engineer looks for ways in which present needs can be met. Whether designing a spacecraft, automobile, machine, or computer algorithm, the engineer reaches out into literature, the internet, supplier catalogs, textbooks and other sources, then reaches inward for new combinations and uses of products for purposes not originally intended and finds answers to problems.
I once needed a reasonably low cost way to capture the shape of a human foot arch. Scanners at the time were costly and I needed to capture the foot shape while under partial weight bearing. Read the following excerpt from “Foot Notes” and see how my mind worked through specific problems toward a feasible solution. Then click on the link below to see a video of it’s application at a real company.
“Now, how am I going to measure the position of each pin, quickly?”
He asked one of his team mates if there was a pin mold he could borrow for experimentation and received a small prototype…
Back at his home office, Ken played with the little mold, by pressing various objects against the pins and considering how the shape could be digitally extracted.
“If I take a photograph from the side,” he thought. “I will only be able to see the first row, and perhaps a few other pins that are extending higher than the first row. So that won’t work. If I take a photograph from directly above, I really won’t be able to see how high each pin is standing.”
He rotated the pin mold with his fingers to various angles.
“Suppose I take a picture of the mold at an angle between a front view and a top view, such that I can see the tip of every pin? Can I use this image to get the z-values?”
He sketched the small pin mold and placed coordinate axes x, y, and z on the illustration. He recalled from a math class something named the parametric line formula. “I think it was linear algebra.“ Ken went to a shelf in his closet where he kept a few old textbooks, but it wasn’t there, so he searched online for the basic description of the parametric line formula…
“If I use the fact that each pin has a known, unchanging X and Y value, and that the only thing changing in the image is the Z value, and it only takes two points in space to define a line, I can use the spot, the end of each pin, to determine where each pin is located along it’s pre-defined line in space.”
He grabbed his digital camera and took several images of the pin mold from different angles…
Back at his desk, thinking through the process, he realized the solution. “All I need is two reference points P1 and P2, two known Z values for each pin. I can get that by taking two reference pictures, one when all the pins are retracted or lowered, and another when all the pins are fully extended or at their highest position, making sure the pin mold and the camera stay in the same place for all the pictures. Using these two digital images, the line in space of each pin will be known. Then, I can shape the mold like a foot, take a third picture, measure the relative distance t, from one of the reference pins, multiply by the total distance between the reference pins, and there is the Z value for that pin. Cool!”
Read Engineering Stories, “Foot Notes” for the complete process of developing this foot mold imaging system. But first, click here and see how this technology is used in industry.