"you are trying to move the end of the blue part from its initial position at A to its final position at B using the enforced displacement applied to the end of the blue part at A. Thus causing the blue part (with properties similar to copper) to push the block along the surface against friction?" Yes.
But the thing has been interrupted before because the blue part did not move correctly. So I only studied the movement of the blu part.
I tried to move the blue part into three manners:
1) enforcing angular displacement
The most obvious thing to do but it doesn't work and I don't know why.
2) enforcing horizontal displacement
if the part has a pin at the top, it has only 1 dof; so a singular X or Y displacement might work. No, it doesn't work
3) enforcing horizontal and vertical displacement
even if I think it is not correct, I tried...
In all this three cases the hole of the pin on the blue part deforms.
I've always tried with LDA thinking it was correct given the large displacements of the parts in the model. Now I'm trying as Charles suggested without LDA.