More manufacturing yapping.

Locus of points is a way of showing geometric data, among other things. For instance:

What is the locus of points of all the points 5 inches from 0,0? That would be a circle, 10″ in diameter. What is the locus of points of the center of a 4″ dia circle travelling around a 10″ square, remaining in contact with the square at all times?

Here’s an illustration. Click to embiggenate.

You can see the original black square. On the right, the blue represents the circle, the green is the locus of points of that center. On the left in pink you can see how the circle drags that center along as it moves, and the orange shows how it brings the center with it as it rolls around the corner.

all machining depends on understanding this. A lot of people never get it, but to many it is intuitive. Most cutting tools are circular, and knowing what they have to cut (In this place, the black square) and what their radius is, it is a simple matter to program a path (The green line) that is the path that must be taken to machine the part that size and shape.

it gets a lot more complex than this, but you have to understand this first. This- and the sort of relative processes that take place in robots, are what my very smart cousin call “N Dimension Geometers” The explanation he gave went mostly in every direction but my skull but I gather that it means the size and shape of things in relation to their location and how they are represented in 1, 2, 3, 4,… n dimensions. I just know there are simple rules to follow and so long as you do, you can bend all this equipment to your will. If you don’t get it, be a barber. There’s no shame in not understanding this, it’s not easy.