The concept of quaternions is fascinating with various applications, but in robotics we care about quaternions mainly as a very efficient parameterization of 3D orientation, primarily that of the robot end-effector. Even though, in industrial robotics, Euler angles are the standard choice for representing orientation in space, there are situations when users must know how to use quaternions. There are dozens of in-depth presentations on quaternions, but none is meant for industrial robot users. To fill the void, we present in this tutorial the strict minimum about quaternions that users of industrial robots should be familiar with. We discuss Euler's rotation theorem, slerp interpolation, and orientation errors, and present the basic formulas for dealing with quaternions.

If you intend to use a six-axis robot arm, you are most probably interested in positioning and orienting the robot’s end-effector in various locations poses. Therefore, you’ll certainly want to know the set of pose that you can reach with a specific end-effector. You’ll probably ask for some kind of diagram showing the working volume, working envelope, or working range of the robot. And, unfortunately, you’ll often be presented with a simplistic schematic like the image on the left, or worse yet, with the so-called reach of the robot. In this tutorial, we describe the actual workspace of a six-axis robot arm, which is a set of several 6D entities. We discuss singularites, configurations and ways to make optimal use of your robot's workspace.

If you intend to use a six-axis robot arm, you will probably need to do more than just position and orient the robot end-effector in various poses. You will likely also need the end-effector to follow prescribed paths as in gluing, or when inserting a pin. If this is the case, then you must learn about robot singularities, because these special configurations will often impede the Cartesian movements of your robot end-effector. You must therefore know how to keep away from robot singularities or how to confront them by properly designing your robot cell and robot paths. In this tutorial, we present everything you need to know about the singularities of a six-axis robot arm.

If you use a six-axis robot arm, you are most probably interested in positioning its end-effector in various orientations. In other words, you need to be able to program your robot to move its end-effector both to a desired position AND a desired orientation (i.e., to a desired pose). Of course, you can always jog your robot’s end-effector to approximately the desired pose, but this so-called online programming method is tedious and imprecise. It is much more efficient to calculate and define your desired pose offline. In industrial robotics, the most common method for describing orientation in space is Euler angles. In this tutorial, we present everything you need to know about Euler angles and their use in industrial robots.