DoF - a Robotiq Community
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@George1969 the simple answer is yes, if you can create a parametric formula for a trajectory path it is possible to make the robot follow it.

What I wrote above is the code for making a parametric circle work on a UR3, you would need to understand the UR scripting language to be able to make this work on your robot.  You can find more information on UR Script

@ehte to make the base the center of the circle, you just need to find the current position of the robot and rotate the Rz portion by 6.28 radians and then go to that point, that should be the easiest way to make the robot the center of a circle