Algodoo

I'm not an M.E. but I always get some enjoyment watching mechanical assemblies and linkages in motion that are relatively simple in complexity, but they produce a unique or unexpected motion. This assembly falls into that category.

Nicely done, s_noonan.

Thanks. I found this linkage very interesting from a mathematical standpoint. The first thing I noticed, is that for a first order approximation (dx = r*(1-cos(a)) ≈ r*a^2/2), dx of the orange link equals the dx of the blue link.

If a = angle, r = radius, r1 = radius of blue link, r2 = radius of orange link, and r2 = 0.25*r1 then:
dx = r1*(0.75+0.25*cos(2*a1)-cos(a1))
If we use the first three terms of a Taylor series approximation for cosine then:
dx ≈< 0.125*r1*a1^4

For r1=4 and a1=0.5:
dx = 0.029972
dx ≈< 0.03125

You said: "dx of the orange link equals the dx of the blue link."

Would that be true only during the linear portion of the movement? (I'm not the math wiz that you are, so please excuse my question if it is a dumb one!)

Q: Would that be true only during the linear portion of the movement?
A: Yes, I was referring only to the vertical almost straight line motion. The cosine approximation is considered a small angle approximation. There are (2) other flat spots on the tracer curve that are most likely just as straight.