Reckoning the Ball

By definition the Gage Ball does not work - “in the field”.

PROOF: Point Marker Adapters, cutting them “out” of the program and literally cutting them “off”!

How a little misunderstanding goes a long, long way! Ever since the invention of CMMs and robotic manipulators the presence of spherical targets for measurement have become popularized. Within the design, build, development, and calibration of CMMs and robotic manipulators the spherical targets are easily justified. Once any given CMM or robot is sold and deployed as a reliably accurate and repeatable machine the spherical targets should stay behind – stay in-house with the manufacturer of the CMM or robot.

Without getting deep into the mathematics, kinematics, and linear algebra of CMMs, robotics, and metrology a few baseline facts need to be brought to the forefront. First, a point in space. Well, how many decimal places should we use until every person accepts “the point”? Needless to say, the size of “the point” is an infinitely small number. The probe point on a CMM arm could easily become a lethal weapon as it becomes smaller than a needle point. However, a simple mathematical solution solves the probe point. The probe point more generically is the Tool Center Point. To protect the delicate tiny point and to protect people from the point, a 2 mm vector is added to the TCP which is easily processed though linear algebra so the CMM or robot still knows where the TCP is located. When the 2 mm vector is rotated in every direction around the TCP it creates a sphere – a ball. So, we do not have to argue how small a point has to be for it to be a “good point”.

Now for the meat-and-potatoes – the Gage Ball. Put yourself in the shoes of a designer, technician, engineer, mathematician, or software coder and you are part of a team creating CMMs and robots. There are massive headaches in the creation of these machines but no one cares about anything except one basic concept – can the machine locate any point within its operating zone repeatedly from any approach angle. The word accuracy was left out intentionally because it would be redundant since the word point was used.

Every CMM and robot consists of mechanical arms, gears, actuators, and other hardware. The majority of the mechanical devices have clearances to allow for lubrication and freedom of movement. The required clearances in turn become a massive nuisance since the clearances introduce deflection and backlash. Jumping ahead – while a CMM or robot may contact a point in space repeatedly within an acceptable tolerance this may only occur from a specific approach path (vector). The same CMM or robot may be off location by grossly unacceptable amounts simply by approaching the same point from a different approach vector. The difference is attributable to the backlash and deflection differences that are unique to every orientation of a CMM or robot arm even at one common point in space. To this end, the development team described above will invest tens of thousands of labor hours in trial runs to have a CMM or robot approach hundreds of points from hundreds of arm orientations. The ONLY economical way to do this amount of testing is to position points in space that are rigid, reliable, and acceptable as being a tiny enough point – well, not really. Remember the story from above about the TCP ball? The points in space can also be defined as the center of a sphere. For easy linear algebra – a 10 mm vector from the surface of a sphere can define the center point of a 20 mm diameter steel ball. In development, CMMs and robots can be programmed to contact a ball in space from any orientation (except the very small pin or rod that holds the ball in place). This nearly unrestricted point in space is critically important for the development of a CMM or robot as a product. Repeating the last phrase: “as a product”. CMMs and robots are manufactured, validated, and sold as products. What would you think if each CMM or robot came with the following WARNINGS:

WARNING #1 - This machine is only accurate when targets are APPROACHED

from left to right (+X), front to back (+Y), and bottom to top (+Z).

WARNING #2 - This machine’s accuracy is +/- 5.0 mm

unless WARNING #1 is followed.

The ridiculous warnings above do not exist because of tireless engineering efforts to eliminate or even compensate for deficiencies such as backlash in gear boxes and deflections in the long reach of an extended arm. Standards such as ISO-10360 clearly define how CMMs (and robots) are to be validated at a multitude of points in space from “any” orientation. Basically, a qualified CMM or robot must be able to locate each defined point in space from ANY ORIENTATION – ANY APPROACH PATH (vector). Could ISO-10360 testing occur with multiple needle points mounted in space – yes. Would 20-plus rigidly mounted needle points in a test envelope be dangerous – yes. Would the same 20-plus needles be susceptible to damage – yes. The solution: Simply use the mathematical center point of a strong, stable, and safe 10mm radiused ball.

The usefulness of an unrestricted point in space or “gage ball” on an inspection gage has NO value. There is NO added value in measuring the same point on your company’s product from 12 different orientations of a robot with 6-axis of motion. Can you imagine doing a “Gage R &R” where every point had to be measured with 12 different orientations? That is what a SPHERICAL point would allow! That is what CMMs and robots have to do before they are sold.

Tangible points, lines, and planes on physical gages are not only intuitive but also easily managed, validated, more economical, and tolerated by non-contact machine vision / light inspection devices. The usage of the ISO-10360 standard and gage balls is for CMMs and robots to leave THEIR factory. Putting a CMM or robot to work in your factory ensures that you can get your company’s product out the door without the quagmire of gage balls.