In dimensional measurement it isn’t unusual to measure feature locations relative to reference edges. How one measures an edge depends on how we define it. So what exactly is an edge?
Basic edges
Back when people thought the world was flat, they feared that explorers who ventured out to sea might fall off the edge of the earth. That edge was where the “flat earth” ended. The edge was a transition or departure from the two-dimensional plane of the earth where you would fall into the abyss.
If you could look down on that flat earth from above, the edge would be easily visible. Assuming the edge formed the boundary of a circular (not spherical) earth, it would be theoretically possible to measure any feature on that flat earth from the edge (we’ll ignore tangents and vectors).
Visualize the flat earth as the top of a can. The edge is where the plane of the flat surface intersects with the vertical walls of the cylinder (and the oceans run down the sides).
It’s easy to think of an edge as a boundary, the place where a surface ends. Think of a knife or a razor. But there are other types of edges. Consider a page half-printed solid black. The boundary between the black and white areas is an edge. In this case, the edge isn’t formed by the intersection of two surfaces. This edge lies entirely in one surface.
When you consider types of edges, it’s easy to understand that measuring them may require different kinds of tools. That’s where measurement matters.
Edges as intersections
Let’s start with a simple case and discuss different measurement technologies. By definition, all the edges of a cube are the same length and intersect other edges at right angles. To measure one of these edges with a CMM or other single-point probing technology, you would measure at least three points in the plane of one of the surfaces, and then repeat for a perpendicular surface. Then you mathematically fit a plane to each surface and extend those planes until they intersect. That intersection is the edge.
Because each face of the cube is a plane, and by definition an edge is where those planes intersect, you could think that you had measured that edge. Although you determined an edge, you didn’t actually measure it. How about measuring the edge without measuring any of the planes?
Of course, all kinds of surfaces can be intersected. Plane-to-plane is easiest to visualize, but there is plane-to-sphere, plane-to-cone, and plane-to-cylinder. Those are the simple cases. Intersecting conic sections of any kind create edges where they meet.
Measuring edges directly
Vision/video measurement excels at measuring edges. In the case of the cube you would focus on an edge and measure points along it. In this case the edge is the boundary where the contrast changes in the image of the part. Then, rather than fit those points to a plane as in the previous example, you fit them to a line. Measure enough points along the line and you’ve measured that edge. In this example, you have no information about the angular relationship between the sides of the cube that intersect to form that edge, but you know where that edge is accurately enough to measure the distance to an edge parallel to it, or the angle of an intersecting edge at the periphery of the same plane.
This example shows how an edge of a cube could be measured indirectly by calculating the intersection of two measured surfaces, or directly by measuring changes in edge contrast. Not all edges can be measured in two ways. By measuring edges from changes in image contrast, it’s possible to measure edges that cannot be measured by another method.
My earlier example of the half-black sheet of paper shows how a change in the image contrast between the black and white areas can be accurately determined and treated as a boundary or edge. In this case, touch probing the white and black areas, fitting them to planes, and intersecting them won’t yield the edge between the two colors, because all the points lie in the same plane. There’s no physical difference between the two areas (ignoring any measure of the thickness of the black ink versus the blank page). Such edges need not be so black and white, however. Differences in image contrast occur from color changes, from changes in texture/roughness, and where differing materials are joined together.
Sensors and 3-D
Some people think that vision technologies are only suitable for 2-D (planar) measurements. Obviously they can only measure surfaces they can image. Think back to the cube example. Vision technology can measure a surface presented to its optical system, but not one that’s perpendicular to it, unless the optics or part are moved (as might be done if the part were on a rotary table). Consider a part with important surfaces at different heights relative to the base of the part. The system could focus on each of those surfaces and use Z scale/encoder information to know where those surfaces are relative to one another. Each is a plane measurement, and the planes lie in different elevations. Three-dimensional software can then display and quantify those relationships.
Practical matters
You may be wondering about actual measurements of physical and visual edges. Consider the importance of a printed pattern relative to the physical edge of a part, or the deposition of a chrome layer on a glass substrate. Such parts are often used as measurement standards, so edge spacing can be critical.
There are edges in flat parts. Sheet metal parts can have intricate punched or etched features with edges that must be in specific locations. Those edges need to be measured optically. A touch probe can’t do this job.
These differences in the types of edges and the different ways of measuring them point out the value of multisensor metrology systems. Because manufactured parts can have physical and “visual” edges, the ability to use tactile probes to measure surfaces and optical technologies to measure edges in a single system in a single part setup can be a significant timesaver. Combine the measurement data from the different sensors within a single graphical software application to verify that parts meet design criteria.
Get the edge
A rose may be a rose may be a rose (apologies to Gertrude Stein), but an edge can be different things. There are practical considerations involved in how to measure them.
Yes, measurement matters!
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