The derailment broke on my cruiser. I had to remove it and the cable was cut too. It has 7 speeds with a hand brakes and shift control. I have this bright idea to shorten the chain, make it a single speed and keep the hand controlled brakes. I suppose this is too simplistic as the rear sprocket has 7 gears not just one. Is it doable or just replace the derailer and shift cable?
Personally I'd recommend fixing it. Even if you only choose to ride in one gear in the future.
Parts definitely needed:
- A new right-hand shifter for the handlebars. You need a 7 speed shifter, and it can be a twist like your existing one, or a trigger / pod shifter. I find twist shifters like your old one to be mostly terrible.
- An inner gear cable
Parts maybe needed:
- Gear outer cable/sheathe - depending on the state of the existing outers.
- Rear derailleur - depends what broke and why you had to remove it. This also needs to be 7 speed but 6 and 8 speed should also work fine. The 10mm mounting bolt is part of the derailleur mechanism.
Probably serviceable as is:
- Rear hanger - this is the tang of metal poking down on the right hand side of the bike, just aft of the rear axle. It looks fine in the photo, but may need straightening or chasing.
- Chain and Cassette/Freewheel - they look rusty but are probably serviceable.
To repair the bike:
- remove the right hand grip, and disconnect the old shifter.
- fit new shifter and reinstall grip.
- feed inner cable through shifter, then down through all the outers toward rear of bike.
- bolt derailleur in place on bike and roughly set limit screws by eye
- break chain and feed through derailleur and over cogs. Mind the routing.
- with shifter set to 1, set the chain on the second smallest cog, then feed inner cable into pinch bolt on the derailleur and clamp it down. This should give a reasonable starting point for fine adjustment with barrel adjusters.
If you feel this is too much, check locally for a bike cooperative who can help. Sometimes its a matter of having someone to provide moral support.
Never try to ride a bicycle designed to use a rear derailleur without a rear derailleur. The chain will not stay in place. And that can be dangerous.
Again: you can not safely run a rear-derailleur-equipped bicycle without a derailleur. Something is needed in place of the derailleur to guide the chain and keep it on the correct cog.
Multi-gear bicycles with rear derailleurs and multiple cogs/gears on the rear are specifically designed to make the chain easy to move from cog-to-cog when you shift. Without a derailleur or similar to guide the chain, the chain will shift up and down the cogs by itself as random motions cause the chain to move side-to-side.
And since the derailleur also does the important job of taking up the slack in the chain as necessary, without that the chain will either go slack if it shifts to a smaller cog, or it will attempt to shift to a larger cog, where if it's set to be with proper tension on the original cog, it will be too short to fit on the larger cog it's trying to shift to.
And that also means it will go slack, too: because something broke.
Things breaking on a bicycle while you're riding it can be dangerous. If you're lucky, the only thing that will happen is your chain will snap.
You need to find a replacement rear derailleur to guide the chain and take up chain slack. Both of those functions are necessary. You can set up the derailleur without a shift cable to hold the chain on a specific cog if you like, but you need a derailleur.
In an effort to make my answer clearer for the luddites, I will explain the possible configurations more fully.
What you are proposing is possible but may not be worthwhile. Riding singlespeed is fun and can be a good challenge but you'll almost certainly miss the gears sometimes.
The easy answer: If you have horizontal dropouts.
If this is the case, you can select the middle of your sprockets and slide the wheel back in the dropout until you have sufficient tension on your shortened chain to take up any slack. The straight chainline and the zero-slack mean that the chain will not move off this sprocket unexpectedly. It can't, as it needs slack to change up or down! Once the chain tension is in place, you adjust your brake alignment and away you go.
The not-so easy answer: If you have vertical dropouts.
If you have vertical dropouts, it's almost impossible to get a good chain tension. If the chain is too slack, it could shift gear out of your chosen sprocket and at the very least, this is irritating. By chance, there are "magic" combinations that work and it's also possible to buy a half-link for the chain (which is as expensive as a whole chain) to fine tune the length, but it is more likely that you would need another device to give the chain the tension it needs to stay in place.
While these work just fine, if you have to buy one, you'll find they are more expensive than a new derailleur of the type fitted to your bike and therefore you may as well keep the gears.
Keeping the gears: option 3
The gear shifter on your bike is the SRAM gripshift type and these are very reliable, very simple, but a pig to replace the cable in. It's easiest to take the shifter off the handlebar and pull it into two parts to thread the cable through if you need to. The cheapest Shimano derailleur that fits your frame will do the job for you and is probably no more effort to fit than your singlespeed conversion and likely cheaper if you had to buy a tensioning device anyway.