Engine shaking while accelerating - Renault Cars & Trucks

I would be looking at my drive shaft and any bushes around the engine mounts, particularily any at the back of the engine.

If you check anything you distrubed when you changed the tie rods.

More info on the car would nbe helpful

Mrs Amanda when you said on pushing the gas pedal is shaking do you mean the whilst accelerating with engine running ( reving) you do receive a shake? or when pushing the pedal you do feel on the pedal with engine off a shake? If it is the first check for any spark plug or spark plug HT Lead not working and cause the engine to shake. If is the second cause then check for your pedal connection cable etc.

Tune up spark plugs, wires, check fuel filter, etc... Check distributor, change transmission fluid and coolant. If you need a new distributor I would try looking for a used one online.

Is the check engine light on ? A cylinder miss would cause the shake on acceleration.

Shakes ONLY under acceleration? Goes away when you back off of the throttle? Are you sure?
Please inspect the front and both side engine mounts.The half shafts will cause that sort of a shake(whole car) when they go bad(inboard CV joints).
Aggravated OR caused my a motor mount that has shifted to one side,binding the half shaft.
Common in Chrysler mini vans!!!!!!That is why the front motor mount is adjustable.
Check the engine mount on the short half side first.

How about timing? How about the distributor and rotor? What about the timing chain?

it could be the ignition coils spark plugs or the timing, would have these checked.

no, idle air control valve is literally to control your idle speed.
what happen when you press on gas? car shakes, RPM goes up, or engine just bogs down?

Bring it in so that the check engine light will be off and it will run smoother.