I get what you're saying man but do you mind explaining how you could deduce it using the right hand grip rule? I tried using that and got a result that violated the law of conservation of energy lol.
In this case to deduce it using the right hand *palm rule you cannot consider it at that point.
Here are the two cases:
Ignore the graph for now, and consider the framed diagrams:
LEFT:
LK is moving clockwise, hence when the plane is parellel to the magentic field, it will be moving downwards. To oppose that motion, a current will be generated such to make it move up, and now we use the right hand palm rule to deduce that the current must run from K to L in order to oppose the motion.
RIGHT:
LK is moving anticlockwise, and will also being moving downwards when the plane is parallel. To oppose that motion the current will flow from K to L.
Now even though they are the same in direction at this point, they are still in different half-turn's. So when LK reaches Y (on the right picture), the current will in fact be moving from L to K (using RHP rule).
Consider the graph now:
So in half-turn 'A', they are going different directions, hence one is negative of the other. Hope that makes a little more sense.