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It is a cottered crank. Crank arms themselves don't seem to be bent. It is a non-cartridge style spindle. Any ideas as to why they are not lining up?

Bent cottered cranks

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Gotta agree with diagnosis. Looks like you're going to need a new bottom bracket/spindle and crank arms. –  Amicable Mar 1 '12 at 11:52
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3 Answers

Like you said, they are cottered, what makes them aligned is that pin through a hole, which at the same time tightens the crank arm around the axle.

If you google "cottered crank", you can see the spindle, which has a slot in each side.

My hypothesis would be: or the cottering bold got deformed, or the spindle slot itself got deformed, or both.

A bolder hypothesis would be twisting of the spindle due to deformation or cracking, but most probably the bearings would not spin freely (how are the cranks spinning, by the way?)

The side which appears on your photo looks OK from outside, the other side we cannot tell.

But for sure this is a VERY irregular situation, which demand a full disassembly of the system, and absolutely no use before that.

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Yep, the cotter pin is probably deformed. Likely the crank slot has been rounded over a bit too, due to the cotter being loose. The cotter on the left side should be removed and replaced. (Frankly, cottered cranks suck, and if the current crankset is toasted the thing to do would be to replace with a modern crank cartridge & crank arms ... or replace the bike.) –  Daniel R Hicks Feb 28 '12 at 0:50
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I also think the crank is rather old, and that problem would be more than enough to deserve replacing without remorse. But that depends a lot, for sure. –  heltonbiker Feb 28 '12 at 2:00
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Looking at the photo I notice that the nut is missing,an indication that it has been worked on at some point. With the right side pedal in the 9 o'clock position the nut side of the pin will face up verify that the leftarm pin has the nut on the bottom.Several size pins were used and it is possible that you have two different sizes.I have several cottered cranks and it seems that there is no standard as far as which direction the pin goes on which side but they are always facing in opposite directions.

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That is a point -- there is a taper to the cotter, and if one is installed the wrong way that will cause the pedals to be out of alignment with each other. –  Daniel R Hicks Feb 28 '12 at 1:55
    
If you do not have a proper cotter tool loosen the nut several turns and tap with a soft faced hammer (just has to be softer than steel) the nut will protect the threads.Only a small amount of movement is needed to loosen the cotter.When installing don't use the nut to seat the cotter as the threads will break before it is seated.Put a ratchet socket over the threaded end and press the pin in with a c-clamp.Then tighten the nut. –  mikes Mar 2 '12 at 2:38
    
That works in theory, but when a cotter has been in there for decades without removal then you pretty much gotta beat the living heck out of the thing to get it out. Plan on replacing the cotter. –  Daniel R Hicks Mar 2 '12 at 12:34
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One of the cotter pins is in backwards. I did that once by accident when reassembling. It's easy to fix - take the nut off, tap the pin out with a hammer, then insert it in the opposite direction from what it was before.

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