rotary axis scaling not making sense

Not that it should really matter for this discussion, are we discussing a tinyG or G2core machine here? I ask because tinyG does not support $_mi=16, but you are not using $_mi=16 either.
Also, I will assume you are using the onboard tinyG drivers, or a Gshield/DUE hardware setup. If Gshield, the microstepping pins are all open, thus $_mi=8

Also assuming from what you show that $3ma=3, mapping motor 3 to A axis

Can you verify assumptions so far, or describe what is different?

Can you provide all the motor 3 and all the A axis parameters?
That would be results of $3 command and $a command
Or, Dump all parameters $$ , copy them to a Cloud drive and provide a URL for viewing.

OOps, the link you posted points to this thread, not your Parameters dump

To be honest, first person I have seen using rotary axis limits.
This Link https://github.com/synthetos/TinyG/wiki/TinyG-Configuration-for-Firmware-Version-0.97#xtn-xtm—travel-minimum-travel-maximum says setting min and max to same value means “no limits, which may explain behavior in your other post

You have both motor 3 and motor 4 mapped to A axis and enabled.
Is this really true?. I’m not sure it would make a difference if M4 were not connected to anything.

You have Motor 3 mapped to A axis and A axis in radius mode, Radius = 0.1989 deg, which is interpreted as move 1/.1989 degrees when G1 A1 is sent. Re-read how $3tr =2 is interpreted for a rotary axis.
https://github.com/synthetos/TinyG/wiki/TinyG-Configuration-for-Firmware-Version-0.97#1tr—travel-per-revolution
I am not 100% clear if your movement described is rotary stepper or rotary output after gear reduction

When I read

When I send the command G1 F100 A1 it moves more than 360 degrees instead of one degree.

I sort of think you should be in $aam=1, so that G1 A1 means 1 degree of movement requested.

• This reply was modified 7 years, 1 month ago by cmcgrath5035.

A axis parameters are displayed, in cli mode, with $a command.

I don’t understand your comment

“The rotary stage should be in mode 2 and act simply like the linear stages.”

Axis modes are defined here: https://github.com/synthetos/TinyG/wiki/TinyG-Configuration-for-Firmware-Version-0.97#xam—axis-mode

Gcode movements for rotational axes are in degrees, G1 A3 is a 3 degree movement in standard mode. $aam=1. Use $3tr (in your case, if A axis stepper is connected to motor 3) to implement gearing ratio from stepper to output shaft.
The Gcode specifies movement of the output shaft.

If you prefer to create a custom Gcode stream that specifies linear movement, e.g. G1 A5 to move the A axis 5mm , then you can set $aam=3 (radius mode) and parameter $ara is set based on this definition https://github.com/synthetos/TinyG/wiki/TinyG-Configuration-for-Firmware-Version-0.97#ara—radius-value

I don’t know of any ‘standard’ tool chain that would generate that Gcode for you