The Roller Rotary differs from a chuck rotary since it provides rotation by surface contact.  A chuck rotary is locked into a degree of rotation of the chuck is a degree of rotation of the object and generally do no have adjustment for surface angle (Some used on Fiber lasers are single ended and do have angle adjustment)

A advantage of a surface style rotary is the ability to do glassware easily(avoiding breakage) and to be able to laser on odd shaped cups\items that need their engraving surface to leveled to the laser head.

Roller diameter is ~59mm for all rotaries except the low roller used in the Nova 24 which is ~41mm.

The contact diameter effect:

The cup acts like a chuck rotary in the sense that angular rotation at the contact location results in the same angular rotation at the engraving area. The gear in effect is between the contact location and rotary roller and is based on the diameter ratio of the contact area vs the engraving area.

Setting up in LightBurn:

In lightburn you can draw your graphics using T1 and T2 layers to model the cup. Draw a rectangle the height (circumference of the engraving area) and width (height of engraving area on cup) on the orange T1 layer.

Center your graphics (if doing a double sided cup, draw two rectangles, half the height each and align top to bottom as shown in the picture below) to the T1 orange Rectangle.

Set up your Rotary Settings to match the output from the excel spreadsheet based on your measurements.

Set up your origin to your needs (user origin, middle center, left center, right center etc) and assign the origin. Send the job to the controller, load the file and frame, confirm and BURN!

Note that 2 sided burns can be difficult to dial in for a single pass. You have to have your settings just right to get it done evenly. Two setups using known centers can yield consistent results.