Straight Line Mechanism

[snowJT]

I've calculated a straight line mechanism for a 15cm straight line...

39% straightness over the cycle...

lengths came out to

L1 = 10.35cm
L2 = 4.14cm
L3 = 13.445 = L4

these values should give a 15cm line... so I went to go build the thing.. all the distances from each hole on each link are exactly those numbers I worked out... but the length of the straight line came out to 20cm.

the formulas are:

15cm/L2 = 3.623
L3/L2 = 3.25
L1/L2 = 2.5

Any idea why my model didn't work out to what it should of been...

 

[Integral]

I have no idea what you are doing. Could you post more details, you might get better help.

 

[snowJT]

sure.. here is a simulation of the model I built.. you see the line that it follows, that line there is exactly 15 centimeters. It should follow exactly that line and end at that line and go up... but it goes about 2 cm before and after the line.

this is a video of me just playing with a simulation I built in solidworks.

http://youtube.com/watch?v=PtnvXDwMmgQ

 

[Integral]

LOL!
Based on your first post, You wanted help with that!

Where did you get your relationships? Could you share with us how you derived them?

 

[snowJT]

Well its a lot of steps to archive calculations on predicting the path of a linkage system, however, you can figure it out with a compass, protractor, and ruler. I drew in all those lines there to show the predicted path of certain linkages, and bisected some of them ect... the two final lines that go up are as a result of what I figured out by bisecting lines, then drew a line that met in between them. That line is 15cm long, which is what is expected... and it travels exactly along the path that it needs to, but it goes a bit beyond and before the line. (Those lines I left in is the step process on figuring it out, if someone wanted me to show them my work, that's what I would show them)

Hardly any math is required to figure it out, really only someone with experience in designing linkages could clear up my question really. I'm confident with my process of figuring it out because everything makes sense to me, but I have never designed one in real life, so I was wondering if the exact distance before and after the predicted path is not 100% straight.

 

[Integral]

There is a discrepancy between your posted link length and the animation. You say L3=L4, but none of the links shown are the same length.

 

[snowJT]

Ah, I'll make it more clear... there are two of L3, a link is defined in linkage design basically defined as the distance between the 2 holes, in each plate shown here

 

[Integral]

Ahhh! I see, thank you!

I am not going to promise anything quick, but my goal is to find an expression for the position of the tip of L3 as a function of the angle of L2. That seems very obtainable and may cast an interesting light on the motion of L3.

 

[AlephZero]

It looks like one of these, except the OP's dimensions are different:
http://en.wikipedia.org/wiki/Chebyshev_linkage

 

[snowJT]

Ahhh! I see, thank you!

I am not going to promise anything quick, but my goal is to find an expression for the position of the tip of L3 as a function of the angle of L2. That seems very obtainable and may cast an interesting light on the motion of L3.

You know what.. I would be very impressed if you did. And I am excited to see it and see if I can understand it. Do you want the lengths of the links?

 

[Koonism]

How is the mechanism used and what for? A Lawyer is a thief in a Suit.

 

[snowJT]

it actually has no purpose at all, it was just a revolutionary turning point in linkage design. The logic behind creating a mechanism such as this which can go around and do a straight line was quite a feet back in its time. I'm on reading week nothing to do.. why not re create some history to understand it better.