Locating with six points and no more
Kinematic location, and why extra contact makes things worse.
A rigid part has exactly six ways it can move in space, three directions it can slide and three it can tip or spin, and touching it at exactly six carefully placed points removes every one of those movements with no contact left over, which is why kinematic location uses precisely six points and treats any point beyond the sixth as a problem.
Three legs never wobble
A three-legged stool never wobbles, even on an uneven floor, because three points always define a single flat plane, so all three legs are guaranteed to touch at once however bumpy the ground under any one of them. A four-legged stool wobbles on anything less than a dead flat floor, because its fourth leg asks the floor to pass through the exact plane the other three already defined. Any real floor that fails to cooperate leaves one leg hovering fractionally clear, and the stool rocks the moment weight shifts toward it. Six-point location is built on the lesson a wobbly stool teaches for free. Contact beyond the minimum needed to define a position asks the world to be more perfectly consistent than it is, and something has to give whenever it is not.
Six movements, six contacts
A solid object floating freely can move in exactly six independent ways: sliding along any of three directions at right angles to each other, and rotating about any of those same three directions. The count holds whatever the part's size, shape or material, which makes six the exact number of restraints a fully located part needs, with every point beyond it either redundant or fighting the six that came before.
Each single point of contact against a suitably oriented surface removes exactly one of those movements, provided it is aimed correctly and does not repeat a restraint an earlier point already provided. Three points pressed against one broad face remove three at once: sliding straight into that face, and tipping in either of two directions across it, since three points fix a plane completely. Two further points against a second face, angled away from the first, remove two more. A final single point against a third face removes the last one. That makes six points for six possible movements, with nothing left unrestrained and nothing restrained twice.
The arrangement is often called three-two-one, after the number of points on each face. The order matters as well as the count. The three-point face is the one the part is pressed against first, and it should be the largest and most stable face available, because it sets the part's tilt. The two-point face then sets its rotation within that plane, and the pair of points should be spaced as far apart as the face allows, since a pair close together controls rotation poorly. The single last point only has to stop the part sliding along the one remaining direction, so it can sit on the smallest of the three faces.
What a seventh point does to the part
A seventh point of contact on a part already located by six sounds as if it should only help, offering extra support in case the other six are not quite enough. It can only touch the part usefully if the part and the fixture are both made so precisely that the seventh point arrives exactly where the other six already predicted it would. Any real manufacturing variation, in either the part or the fixture, means it does not. Forcing contact there anyway means bending or squeezing the part slightly until it does, which is exactly the clamp-induced distortion the first article in this set was built around avoiding.
A seventh contact can also quietly take over from one of the original six once the part is squeezed against it. The part then sits in a different position from the one the first six points defined, lifted slightly off one of them or rotated a fraction about another, and a quick look at the fixture would never reveal it, since every point still appears to be touching. The result is a part that is both bent and mislocated, with nothing visible to show either.
The same logic on the drawing
The three-two-one arrangement is also the logic behind a formal datum reference system on an engineering drawing. There, a primary, secondary and tertiary datum are established in that order so that a part's position and orientation are each defined once and only once. The primary datum plays the role of the three-point face, the secondary the two-point face, and the tertiary the single point.
A fixture built around six kinematic points and a drawing built around a three-datum reference frame describe the same idea from two directions. One physically restrains the six movements, and the other declares which surfaces are responsible for constraining which of them. A fixture that ignores the drawing's datum scheme can locate the part perfectly well in a fixturing sense while still cutting features in the wrong place relative to what the drawing meant. The fixture designer's first job is therefore to read which faces the drawing names as datums, and to put the three, two and one points on those same faces in the same order.
A fixture designed around exactly six points treats every additional contact as a flaw to be found and removed. Reviewing a workholding design by counting its actual points of contact against the six the part needs is a fast, reliable way to catch a fixture working against the part it is meant to protect. The next article in this set follows what happens once a seventh or eighth point is left in place on a part too delicate to absorb the extra squeeze, and a fixture meant only to hold the part gently ends up pressing on it the whole time it is supposed to be supporting it.