Universal Robots Forum

How Calculate the Max COG(center of gravity) offset?


We are SAMWON FA, Located in South Korea,
and We are UR’s Korea Distributor.

I studied hard and looked it up, but I don’t know.

How can I Calculate the Max CoG offset?
What formula should I use?

and I upload the UR’s CoG offset data and Rainbow robots CoG data.
Please refer it.


The max CoG offset is dependent on the mass attached to the tool end. A high mass will limit you to a short offset, while a low mass will allow you to have a larger offset. Use the graph below to check that your payload and offset are within the shaded region. This offset should be analyzed in the x, y, and z direction relative to the tool flange.

If you need to calculate the values by hand, most scenarios on a robot will be 2 body systems: a gripper assembly, and an item to be gripped. This can be calculated with the following formula:


So let’s say you have a 2kg gripper with CoG in mm of [0,0,50] relative to the tool flange, and you pick up a 3kg object with CoG of [0,0,150] relative to the tool flange. That leaves you with the following calculation:

CoGz = ((2kg * 50mm) + (3kg * 150mm)) / (2kg + 3kg) = 110mm

So your total payload on the robot would be 5kg with a CoG of [0,0,110] which falls safely in the shaded area on the graph above.

If you need to offset the payload beyond the 800mm max on the graph, please reach back out, and we can further analyze your application.


I always upvote hyperphysics anywhere I see it.



Sorry to Jump on this, but I’m also confused.

I recently got told by a UR rep that if I keep the tool flange/ load parallel to the ground, I only need to take into consideration the Z offset. but all the information I’ve seen in UR manuals/tech notes seems to say the opposite,

Looking in this application guide it seems to only take the Y offset,
(Universal Robots - How to design for higher payloads)

could you please confirm? is it that we only need to consider the offset that is perpendicular to gravity as the linked guide suggests?


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You’ll want to take into account offsets in all directions. This is outlined in sections 2.2 and 3.1.2. You can see both a Y and Z offset for CoG are entered.

As a reminder, when looking at the tool flange face with the tool port oriented up, Z is coming out of the tool flange towards you, Y is pointing down (opposite the tool port), and X is pointing left based on the right-hand-rule. CoG always references this tool coordinate system, and does not reference TCP.

That being said, if you have a Z CoG value that is outside the graph in section 3.2, you can keep the application mechanically safe by restricting tool motion. That is what is being outlined in sections 3.2 and 3.2.1.

Hopefully this clears things up a bit. Let me know if you have other questions.

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