What is a Work Envelope?

A robot’s end effector is constrained to move within a specific volume. This volume is known as the work envelope of a robot – a volume in which the robot’s end effector can reach and operate. Work envelope is an important consideration in designing and programming robotic systems for specific tasks. 

My Simple Method to determine the Work Envelope

To find out the work envelope, I took an example of one of the most popular industrial robots – KUKA KR-1000. It’s an articulated robot with 6 degrees of freedom. 

KR 1000 Titan
Fig 1 : Rotational animation on KUKA KR-1000

I downloaded a Blender model of this robot and gave rotational animation to all the 6 arms. I ran this animation for more than 20000 frames and the trick is that at every frame the robot ejected a small ball from its end effector and the ball would just remain there in space. After running for more than 20000 frames this is the image Blender produced. It is clear that the tiny balls are not able to reach many volume pockets. 

Rotational animation on KUKA KR-1000
Fig 2 : Rotational animation on KUKA KR-1000

Work Envelope of a KUKA Robot

Now the task is easy. Just create a smooth surface around all these tiny balls. Look at the image below. This is the work envelope of KUKA KR-1000. I compared this with the official documentation from KUKA website and it matched perfectly. 

work envelope of KUKA KR-1000
Fig 3 : Work envelope of KUKA KR-1000

More Details of Work Envelope

Next, I took the cross section of the volume above in three different directions. From the 2D shape of the volume cross section you will get more idea about the shape of the work envelope.

Fig 4 : Cross section of the volume

Why is the Work Envelope not a Perfect Sphere?

The work envelope is not perfectly spherical mostly due to the structural design of the robot’s body. It restricts the specific arm movement. For example a robot’s arm can retract only upto its body and not beyond that. Therefore when the body design of the robot is in such a way that it won’t allow any further movement of the arms and it creates limitations in angle movement and eventually the work envelope assumes a shape which is a little complicated.

I hope you now have a better understanding of work of envelope. Thanks for reading the article.