You can find and display the coordinates of the center of gravity (CG/COG) of a closed region or solid with the AutoCAD command MASSPROP. But if you want to draw the center of gravity as an entity, use the utility CADstudio Centroid.
The LISP application Centroid calculates and creates (as a POINT or SPHERE object) the center of gravity (centroid) of any closed polyline (pline), 2D region or 3D solid. Optionally you can draw XYZ labels, volume or surface area labels.
Load it with APPLOAD and run the CENTROID or CENTROIDS command.
The free utility Centroid can be downloaded from Download
See:
You use the LISP variables to preset Centroid options: (setq _centroidmarkertype "sphere"), (setq _centroidxyztype "yes"), (setq _centroidproptype "volume"), (setq _centroidsize 10.0).
Since AutoCAD 2016 you can also use the osnap mode "geometric center" to snap to the center of gravity of an object - e.g. in the POINT command.
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Please use these tips at your own risk. Arkance Systems is not responsible for possible problems that may occur as a result of using any of these tips.