Aha, quivering before me in the mist, The Sacred Trihedron, emblematic of the one point in hyper space that has no coordinates. Now, after a yearlong quest, my avatar had only to reach out, ever so softly, and cradle it. The incomparable prize would be mine.

It was just then that the phone rang. I flinched and The Sacred Trihedron warped off to an alternate universe—Whoosh. I boldly mustered my professional decorum and answered the phone.

"E. M. Sleuth here."

On the other end of the line I heard the nearly breathless voice of Wily Jones, Vice President of Marketing for BTI (aka Bodypart Technologies Inc.).

"You've got to help," he gasped. "We are about to lose our multi-million dollar custom kneecap program because our costs are out of control. We have to measure and certify every one we make. Now manufacturing is telling me they can't measure a custom kneecap on our CMM without a matching fixture that doubles our manufacturing costs. Can you help me?"

(Can I help???? Good grief, I thought. If I could find The Sacred Trihedron, I think I might solve an earthly alignment problem . . . Some people can be so clueless.) "Certainly. Assemble your team and I'll be over first thing in the morning."

The next morning, there was quite a crowd assembled around the conference table. There was Wily Jones, an executive VP, and managers from engineering, manufacturing, and quality assurance. There was also Skeeter, the CMM operator. In the middle of the table was a beautiful proprietary thermoplastic and titanium composite kneecap, looking very much like a miniature modern art sculpture.

"They've been working at it for weeks now and say it can't be measured without a fixture," sneered Wily Jones.

The engineering manager was more enlightening. "The CAD model of the part was reverse engineered using data captured from a male patient," he volunteered. Gives new meaning to body coordinates, I thought. "To measure the free-form kneecap, the part must first be aligned to the CAD model. To complicate matters, the origin of the complex curves that define the part in the model is out in space, not on the part itself," I mused.

"Actually we have been able to measure it without a new fixture," he said, giving the Marketing Manager a crushing look out of the corner of his eyes. "Just not very well." He then summarized the various ways his team had attempted to measure the part.

1. Engineering volunteered to align the part to the CAD model taking manual measurements and doing complex trigonometric equations but thought better of it once they saw how long it was taking.

2. Skeeter thought he could create a makeshift fixture by softly wedging the part into a cylinder and then aligning the cylinder's coordinates to the CAD model. It might work, but the FDA would never buy it.

3. Actually, the part does have a small flat ground surface and a couple other discrete points related to it that might be used for a conventional hard alignment. This would not be kosher since those features are among the ones that need to be certified.

4. The custom kneecap prototype is very similar to the ones Bodypart Technologies mass-produces for female patients. So they tried using that fixture. The measurement results were off; so they didn't know if there were problems with the part, the CAD model, or the fixture itself.

"We just can't afford to make a new measurement fixture every time we make a custom kneecap," the engineering manager pleaded. "Is there any way you can help?"

"If you will let me borrow your prototype part, the CMM, and Skeeter, I think we can straighten this one out before lunch. Skeeter and I will meet you in the executive dining room at noon."

When lunchtime arrived, I savored delectable morsels of medium rare filet mignon while I let Skeeter explain how we solved the freeform part alignment conundrum. He was quite eloquent.

"It took Sleuth about a half an hour to set up and measure the kneecap using something called Iterative Alignment. He told me that almost all CMM software has something like it. It used to be called '3 -2– 1 alignment' because you had to measure a plane, a line, and a point and then the software jiggles the part in its memory until it lines up with the CAD coordinates. If the CMM can't do it on the first try, it will ask you to measure some more points. And it never asks for additional points more than two times.

Figure 1: Simple Rules for Iterative (3-2-1) Alignment Need a minimum of 6 point features for a "classic" case. All points and vectors must accurately reflect the CAD theoretical model. ■  3 points (for "leveling") must use vectors which are reasonably identical, although they need not be co-planar ■ 2 points (for "rotation") must use vectors which are reasonably identical, but relatively normal to the first three ■  1 point (the "origin") must have a vector which is reasonably normal to both of the first two sets

"Today, you don't even need a plane, a line and a point. With best fit algorithms in the software, you can measure any six points within about a half an inch of where you think they are." (Yes, "best fit" helps kneecaps fit best, I mused.)

"It works on any part, any time," Skeeter continued, "as long as you follow some simple rules. (See figure 1.) What you wind up with is a 'virtual fixture' that exists in software but works like hardware, and you don't have to buy hard fixtures all the time. Sleuth showed me how to do it and let me practice by relocating the kneecap on the CMM table and having me align the part and measure it three more times. The results were all repeatable to within the specification each time."

The problem was solved, and the team concluded that a little CMM operator training in Iterative Alignment along with the right software tools could save Bodypart Technologies big bucks. Most lingered over lunch asking me to explain how this built-in CMM software feature might be used to replace some preproduction measurement fixtures and hard gages.

They clung to my every word. All but Wiley Jones, who, not being much concerned with details, made himself disappear like a Trihedron into the mist.

EM Sleuth is a feature developed by Wilcox Associates Inc., (www.pcdmis-ems.com) part of the Hexagon Metrology Group and makers of PC-DMIS measurement software. Contributors to this case were Don Ruggieri, Senior Applications Engineer, Wilcox Associates Inc., Doug Sjogren, Software Support Manager, Hexagon Metrology, Inc., and Joel Cassola, freelance Writer.