Transposing a line with known references

[_Bd_]

Hi, I have a question for a desing I am working on. I want to model it in excel and I am having a hard time finding out how to transpose some lines: Let Bar B's position and dimensions be known, and I want bar B to be set in 3 positions, I can however apply joints to anyplace near or at bar B, so that I can get a 4-bar-linkage-system that can move as I desire. so for example point A1(x1,y1) and A2(x2,y2) are the joints that are going to hold on to bar B, how do I calculate the new coordinates of A1 and A2 at position 2 if I only know their relationship to bar B at position 1?

I hope this image helps:
http://img526.imageshack.us/img526/4945/thingoz.png

http://img526.imageshack.us/img526/4945/thingoz.png

At position 1 i know everything

At position 2 I only know the coordinates of the bottom bar (the red bar) I know where its two end points are, I know its angle (theta) with the horizontal and I know its lenght.
points A1 and A2 have not changed their position with respect to the bottom bar, but they have moved in the plane, how do I calculate their new position?

thank you!

NOTE: THERE IS ROTATION AND TRANSLATION! (FROM POS 1 to POS 2)

 

[SteamKing]

If you know the coordinates at Position 1, and you know the translation and rotation to Position 2, the coordinates of the bar at Position 2 can be calculated by means of a transfer matrix.

The following link shows the procedure:
http://ugweb.cs.uAlberta.ca/~c201/F07/resources/Presentations/homogeneous_coords.pdf

 

[_Bd_]

The thing about that is that I get weird values when I use that matrix, because they are not rotating around the origin so it creates weird

 

[SteamKing]

Then you need to translate the coordinates of Position 1 to the origin of rotation, then apply the rotation matrix.