Understanding Robots

https://www.solisplc.com/tutorials/robot-coordinate-frames-and-points

Reverse Kinematics:

These robots have 6 axes. That is sometimes called "six degrees of freedom".

Figure 1. The six axes.

The machine has an origin point (0,0,0 in the world coordinate system) at the center of axis 1 and an end of arm point (0,0,0 in the tool coordinate system) at the center of axis 6.

The axes are loosely equivalent to our shoulder, elbow and wrist (with separate axes for rotation in vertical space and horizontal space).

When computing how to rotate the joints in order to place the tool tip at a specified location, there are always 4 possible configurations. Some may not be reachable by the machine, but there are almost always at least two, and the robot must decide which to choose. Kuka robots receive a code that weights each axis to choose in favor of a positive or a negative number, which helps the machine decide how to move.