These are 6-axis robots, meaning they have six rotating joints. Each joint, seen below, must rotate some amount in tandem with the others to place the end of the robots arm into a desired location.

Because we want the robot to be able to use multiple tools and work on a variety of surfaces with different orientations, here are 3 coordinate systems that you need to understand in order to work the robots:
It's not as confusing as it sounds.
World Coordinates
The center of a robot's world is located at the center point of the its base - it is the point around which axis A1 rotates.
This is how the robot navigates within its workcell.
TCP or "Tool" Coordinates
Remember that the controller's job is to calculate the 6 angles of rotation that the axes must make to move the end of the robot's arm to a point in relation to the world (0,0,0).
The "end of the robot's arm" is called it's Tool Center Point (TCP).
When there is no tool on the machine, the default location of the TCP is at the center of the faceplate at the front of axis 6. This is (0,0,0) for your tool.
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The TCP is the center of it's own cartesian system.
To Recap:
Therefore:

Whenever you are dealing with multiple coordinate systems, the Right Hand Rule is useful to remember: |