You can drag the vertices of the shadow linkage to alter its geometry.
Can you create a linkage which draws a figure 8? How about the letter D? How close to a straight line can you get?
If you like this, you might like my 4 bar linkage clock app.
You can set the lengths of the four bars in your linkage. Then drag point B till you think it encloses the maximum area. Click the button to examine the area.
Click Solution to observe that the solution occurs where all four vertices lie on the same circle.
Here is a design for a 4 bar linkage which opens a door either to the left or to the right. Note the pivot points for the linkage are the circumcenters of the triangles whose vertices are the corresponding ends of the door in the three required positions.