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.