The hardest thing for me working on these things is that they are all riveted together and come apart as a couple assemblys. The month linkages on the left end of the roller are permanently attached to the frame and unless you break a rivet it has to be cleaned and repaired on the frame.
These calendars give you the day, the date, and the month. Sounds simple enough until you throw in the fact that they self correct for different length months and also for leap years ! That's pretty good for something well over a hundred years old and a bit crude looking.
Most of the calender clocks you see on the schoolhouse and kitchen style clocks simply advance the date by one each day leaving you to correct for the odd number months.
Here's a pic with the month roller removed from the shaft. It's the heart of the calendar.
This is the day wheel. A combination of the cams on the end of the wooden roller and the stepped piece being pointed to is what controls the different lengths of the months.