Robot arm kinematics is slightly different compared to robot base kinematics. You would need to move five different actuators to five different positions to move the robot arm's tooltip to a required position. The mathematical modeling follows the Denavit-Hartenberg (DH) method of computing kinematics. Explaining the DH method is out of our scope, so we shall look at the kinematics equation directly.

The arm kinematics equation is defined by a 4 x 4 homogeneous transformation matrix that connects all of the five links with respect to the robot base coordinate system, as shown here:

Here, we have the following:

,

This represents trigonometric equations; is the angle between the normal to rotation axis (usually represented as ) and the rotation axis (usually represented as ), and is the same for  and , respectively. is the distance from the rotation axis () to the origin (i-1) system of axis, and is the shortest distance between two consecutive rotation axes.

From the preceding homogeneous transform, the first 3 x 3 element indicates the rotation of the gripper or tool, the bottom row defines the scale factor, and the tool's pose is given by the remaining elements:

Now, let's look at the software parameters.