No. A wrench is used for undoing or tightening nuts and bolts. A pulley is a wheel with a V groove in it, usually set in a holder that can be bolted through the centre or hung. The pulley's task is to guide a derive belt or a rope to haul things up.
On the fan pulley...
Use a strap wrench or chain wrench on the pulley to hold it secure.
use a thin wrench or if possible just remove the pulley
Use a strap wrench on the pulley to hold it still, or a pipe wrench on the shaft.
To remove the idler pulley on a Peugeot 107, first ensure the engine is off and cool. Begin by releasing the tension on the serpentine belt using a wrench to rotate the tensioner pulley, then slide the belt off the idler pulley. Next, unbolt the idler pulley from its mounting bracket using the appropriate socket or wrench. Finally, remove the pulley and replace it with the new one, reversing the steps to reassemble.
Use an impact wrench to remove center bolt and pulley should slide off
You have to unscrew the hex nut that is attaching the pulley to the motor. It can be relatively difficult so get a torque wrench.
You need to line up you belt with the pulley except for the tensioner pulley according to the picture in your engine bay. You will need to put a wrench on your tensioner pulley and twist it to relieve the tension then slip the belt on and let off the wrench to return the tension.
its easier to put the pulley on first, then thread the belt up to the pulley then use a wrench to pull against the spring on the pulley, then slide the belt in. using a 15mm wrench on the bolt or an Allen will give you all the leverage you need for an easy install
To replace the idler pulley on a 1998 Mercury Villager, first, disconnect the negative battery terminal to ensure safety. Next, remove the serpentine belt by loosening the tensioner pulley with a wrench, then slide the belt off the idler pulley. Unbolt the old idler pulley using a socket wrench, and install the new pulley in its place. Finally, reattach the serpentine belt and reconnect the battery terminal.
This is normally done with an impact wrench... a type of air tool. The impact wrench can tighten the pulley without turning the crank. You can probably rent a compressor and an impact wrench with sockets from your local tool rental company.
Impact gun/wrench and a puller