I want specific gear movement analysis by force
As for the force direction, the gear is in contact with the rack, because the tooth profile curve of the rack is straight, so the force direction coincides with the normal curve of the tooth profile of the rack at the contact point between the gear and the rack. The direction of the force is opposite to the direction of movement, and the direction of the force acting on the follower is the same as the direction of motion.
Separate analysis can easily solve the problem. The motion direction of the rack is only linear reciprocating. The direction of motion of a gear should be the direction of motion of a point, because the gear is rotated so that the direction of motion of a point is, of course, perpendicular to the diameter.
The analysis of motion force is nothing more than analyzing the direction of motion and the direction of force.