Z axis is up-down. The Z axis zero point is up, at the point where the homing cycle leaves the head. Positive Z coordinates are down. PCB surface level is measured during calibration.
X axis is left-right, Y axis is front-back. X & Y zero point is at front left, where the optical calibration cycle leaves the machine. Positive X coordinates are to the right. positive Y coordinates are to the back, away from operator.
Rotation (A axis) is counter-clockwise. There is no zero point. The A axis zero point is where it happened to be when the machine was powered on. Therefore, please put a mark on the big pulley on the rotation tube and check manually, that it is in a same spot when starting the machine. Although the axis has minimal wobble, this ensures that if there is any, the calibration will work as intended.
Current X & Y position is the down looking camera view center point. The needle position is given by the nominal needle offset (determined during calibration) plus correction factor (measured separately to correct needle variation and rotation misplacements). The exception is the up-looking camera position which is found during calibration. Nominally the camera position is the machine location where the needle, at PCB surface level and without the dynamic correction, is in the middle of view.