Solution: Types of Robot Coordinate Systems

A robot coordinate system defines how the position and orientation of the robot tool are represented and controlled.

1. Cartesian Coordinate System

Uses three mutually perpendicular linear axes: X, Y and Z.

        Z
        ↑
        |
        |____→ Y
       /
      X

The robot moves the tool along straight X, Y and Z directions. It is commonly used for Cartesian robots and precise linear movements.

2. Cylindrical Coordinate System

Uses:

• radial motion $r$
• rotational motion $\theta$
• vertical motion $z$

       Z ↑
         |
         |  •
         | / 
         |/ r
        O────────→
          θ

It is suitable for robots performing cylindrical-workspace operations.

3. Spherical / Polar Coordinate System

Uses:

• radial distance $r$
• two angular coordinates
• $\theta$ and $\phi$

The tool position is described relative to a fixed origin using distance and angles.

4. Joint / Articulated Coordinate System

Each robot joint is controlled according to its own joint variable, such as $\theta_1,\theta_2,\ldots$.

Base → Joint 1 → Joint 2 → Joint 3 → Wrist → Tool
          θ1        θ2        θ3

This is natural for articulated industrial robots.

5. Tool Coordinate System

The origin is attached to the end-effector/tool. Movements are specified relative to the tool's own axes.

6. World / Base Coordinate System

A fixed coordinate frame attached to the robot base or workcell. It provides a common reference for robot motion and other objects.

Comparison

Coordinate system	Main variables	Typical use
Cartesian	X, Y, Z	Linear positioning
Cylindrical	$r,\theta,z$	Cylindrical workspace
Spherical	$r,\theta,\phi$	Radial/angular motion
Joint	Joint variables	Articulated robots
Tool	Tool-frame axes	End-effector motion
World/Base	Fixed reference axes	Workcell coordination

Conclusion

Different coordinate systems allow robot motion to be programmed conveniently for different applications. Industrial robot programming commonly uses joint, world/base and tool coordinates together.