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.

 

[alphy]

Hello,

Thank you for your question about transposing a line with known references. Transposing a line, also known as a transformation, involves changing the position, orientation, or size of an object while maintaining its shape. In your case, you are trying to transpose a line segment, represented by bar B, to three different positions.

To calculate the new coordinates of points A1 and A2 at position 2, you will need to use a combination of rotation and translation. Translation involves moving an object in a straight line without changing its orientation, while rotation involves changing the orientation of an object around a fixed point.

In your scenario, bar B is the fixed point for rotation, as it remains in the same position at both positions 1 and 2. The bottom bar, represented by the red bar, is the object that is being translated and rotated. To calculate the new coordinates of points A1 and A2, you will need to use the following steps:

1. Calculate the translation vector: The translation vector represents the distance and direction that the bottom bar has moved from position 1 to position 2. This can be calculated by subtracting the coordinates of the bottom bar at position 1 from its coordinates at position 2.

2. Calculate the rotation angle: The rotation angle represents the amount of rotation that has occurred from position 1 to position 2. This can be calculated using the angle theta that you have mentioned, as well as the length of the bottom bar.

3. Apply the rotation and translation: Once you have calculated the translation vector and rotation angle, you can apply these transformations to points A1 and A2 using the appropriate transformation equations. These equations will depend on the orientation of your coordinate system and the direction of rotation, so it's important to double check your calculations to ensure accuracy.

I hope this explanation helps you in your design work. If you need further assistance, I would recommend consulting with a mathematician or engineer who specializes in transformations. Good luck with your project!