What are the types of coordinate system of robot? Explain with neat sketch.

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Accepted Answer

# 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**.

```text
        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 $	heta$
- vertical motion $z$

```text
       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
- $	heta$ 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 $	heta_1,	heta_2,\ldots$.

```text
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 | $r,	heta,z$ | Cylindrical workspace |
| Spherical | $r,	heta,\phi$ | 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.

Solution: Types of Robot Coordinate Systems

1. Cartesian Coordinate System

2. Cylindrical Coordinate System

3. Spherical / Polar Coordinate System

4. Joint / Articulated Coordinate System

5. Tool Coordinate System

6. World / Base Coordinate System

Comparison

Conclusion

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