I have a problem, that im sure will be quite common but i would like some assistance with.
My right pedal and the cogs wobble both when cycling and staying still, however the left pedal does not. it is annoying as when the cog moves, the chain catches on the front deraileur and changes gear. the cogs are securly attached to the pedal arm and it also sometimes squeeks when being turned.
The bike is a Dawes Ultra Galaxy, (from around 1970s / 80s)
'08 Fuji Roubaix RC; '07 Schwinn Le Tour GS; '92 Diamond Back Ascent EX
Sounds like the crank arm bolt (nut) is loose. There is probably a dust cap at the center of the crank spider (the thing the chain rings are bolted to). Remove that and there will be a bolt or nut that has worked loose. The problem is, once you've ridden it loose, you've probably damaged the interface between the shaft and the crankset. Try tightening it (put a lot of force on it) and see if it stays.
The front gear rings are chainrings. The cogs are the gears in back.
Your description sounds like the drive-side crank arm is loose and wobbling on the bottom bracket spindle. The aluminium crank interface will quickly wear out of square against the harder steel spindle. Once worn enough, the crank arm won't fit securely again, and replacement will be necessary. If yours moves enough to cause the chain to derail, I suspect it's beyond hope.