The end point of this discussion is the robot, and how it moves. TO understand this you have to have a comprehension of the cartesian coordinates. This is a triad.

This is one given away as a teaching tool by Fanuc. You can see the X Y and Z axis, and you can also see the A, B, and C rotary axis.

it is a common trap to get into to think that each axis is a line, and the triad can add to that confusion; just looking at the X axis, think of it as not a line of motion but a direction. Anything anywhere moving parallel to the X axis is moving in an X direction. The triad shows the positive direction, but if you pick up a jack, you will find it’s almost the same piece.

The Jack has six “Directions” corresponding to the six sides of a cube, and those six directions are x,y,z positive, and x,y,z negative.

What the triad does represent is Origin. The X, Y, and Z axis all originate in the same spot, and the triad helps you to visualize that. Think of the corner of a box represnting the origin, while the edges of the box represnt X, Y, and Z.

But a robot doesn’t have straight axis, or any mechanical way to move in a straight line. Witness:

The robot has six axis, and each axis is a rotary and not a linear axis. So it can’t move in a straight line. Right? Wrong. Comp[lex algorithms allow the robot to move according to a cartesian coordinate system. Imagine that the triad above was at the center of the base of the robot. The robot can easily and accurately move in a straight line, moving all the axis to do so. It can move in X, Y, and Z as easily as jogging a machine tool, and it can do so within very nearly machining tolerances.

This is where it gets weird. The robot also has some kind of an end effector- a gripper, maybe, or a welding torch. That gripper might be double ended, it might even have three grippers all at 120 degrees to each other. Jogging this gripper into position using the basic “Triad” at the base of the robot gets you back to etch-a-sketch type moves again.

Except.

Except the robot has the math in it, to put a ‘Virtual” triad in the center of every gripper, so that you can switch from the robot base triad to the gripper triad to move the robot based on the orientation of the gripper or welding torch.

Now let’s think about what the robot is working on. It’s almost impossible to have the robots base triad lined up perfectly with the table of a machine, or the conveyor bringing parts into the cell, so there are OTHER virtual triads that you can place literally on every component in the system. And you can use vision to change those tiads (Called “Frames”) in real time. And you can manipulate those frames either by using sensory apparatus in the system, or by simply calculating and moving numbers into the frame.

A classic example of this is a process called ‘Through Arc Seam Tracking” or “Tast”. Through arc monitors the amp draw of the robot as it weaves around a weld, and when it “Wobbles” the torch back and forth, if the current on one side of the “Wobble” is bigger than the current of the other side of the “Wobble”, it will modify the path of the weld in real time to make sure the weld metal is deposited in exactly the correct location. And this is only a hint at what the programming is capable of doing. More on that later.