# Dorna Coordinate System

In this post, I will review the Dorna coordinate system. You will become familiar with how Dorna knows where it is and how it moves in space. Dorna is a five-axis robotic arm, with five rotary joints J0 through J4. Each joint has a predefined positive (+) and negative (-) rotary direction, see Figure 1. As you can see, the blue curved arrows define the positive rotary direction for the associated joint. Figure 1. Five joints and their positive rotary directions.

So, at any moment the position of the robot and its geometry can be uniquely identified by the values of the five joints: (J0, J1, J2, J3, J4). We can also define the XYZ Cartesian coordinate system for the robot. In this scenario the origin (X=0, Y=0, Z=0) is the center of the bottom plane of the robot (base), where robot touches the ground. After fixing the origin, we set X,Y axis in a manner that they form the bottom plane, while Z axis forms the height, see Figure 2. Figure 2. X, Y and Z axis from a side view. (X=0, Y=0, Z=0) is where all three axis intersect.

### Coordinate Systems

We describe Dorna\\’s position as the location of the tip of it\\’s toolhead. The location of the toolhead can be described by two separate coordinate systems:

• Cartesian
• Joint

The coordinate system you choose to work in will depend on your needs.

#### Cartesian Coordinate System

In this system, X, Y, and Z represent the position of the head of the robot in the Cartesian coordinate system, see Figure 3:

• A is the angle between the tool head and the XY plane (A = J1+J2+J3)
• B is exactly equal to J4 (B = J4) Figure 3. Toolhead location in Cartesian space.

#### Joint Coordinate System

As we mentioned earlier given the values of the five joints as a tuple we can uniquely identify the position of the head of the robot. To be more precise (see Figure 4, 5):

• J0 is the angle between the second arm (L1) and X axis in the XY plane (the rotation of the robot around the Z axis).
• J1 is the angle between L1 and X axis in the XZ plane.
• J2 is the angle between L1 and third axis (L2).
• J3 is the angle between L2 and fourth axis (L3).
• J4 is the rotation of the fifth axis. Figure 4. J1, J2, J3, J4 and A from side view.

For more information, you can refer to the Dorna Wiki. You can also watch our Youtube video on the subject here.