Car shudders when in gear and foot off brake


I have changed the ignition coils, spark plugs, and belt tensioner, nothing seems to be making a difference.
When I first put the engine in gear with my foot on the brake no problem the engine doesn’t shake but as soon as I take my foot off the car shudders until I get going with a bit of speed.
I can replicate this issue by putting on the E brake while in gear but like I said when my foot is on the brake no shaking.

My car shudders similarly to your description when the RPMs are too low. This happens in first if the idle is too low, higher gears when I should be in a lower gear. I have a manual transmission: I get to choose my gears; an automatic should make the right choice as long as the idle is set high enough.

stopped, in gear, foot on brake. no vibration
remove foot from brake and not pressing gas and vibration starts?
does car creep forward with foot off brake and no gas pedal?

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Is it possible that the motor mounts are in need of replacement?
I would suggest that the OP have a qualified mechanic check the motor mounts.

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Exactly right and the car does move forward but here is when I get the most shuddering

I had an idea it could be the mounts. However, the engine doesn’t seem to shift a significant amount when I put it in gear.

Mine is automatic, not sure if this would be related? Hopefully, we get some clarity here.

If you could either clamp shut or remove the brake booster vacuum line and plug it, you could determine if the booster is the problem (leaking in air and causing a lean mix). DO NOT DRIVE THE CAR DURING THIS TEST.

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Does it happen only in first gear? Does it stop when you reach a certain speed?

Is the check engine light on? Any diagnostic codes in the computer memory? It does sort of sound like what insightful above is suggesting, the engine is running a little on the lean side at the lower rpms, and misfiring. When you step on the gas enough it causes enough gas to be injected the low rpm lean problem is masked. A small vacuum leak should be considered. Clogged injectors could cause it too. You might try running a bottle or two of injector cleaner through the gas tank. A couple years ago I had a sort of similar problem on my Corolla where it would jerk only in slow speed neighborhood driving. I wouldn’t describe it as shaking, but when I stepped on the gas say after slowing for a corner, arouind 10 mph, instead of smoothly increasing in speed, it would not increase in speed at all at first, then all of a sudden jerk forward. Very annoying Setting the idle speed to spec and an injector cleaner treatment fixed that problem for me.

Happens at low idle just starting out, basically when you just take your foot off the brake and are gently accellerating the. Stops when you get going like 7mph and up.

Sounds reasonable, I will be testing that and will post the results thank you.

Alright, I went through the whole engine bay and checked for vacuum leaks while it was in gear and shuddering. I also pinched off the vacuum lines to the break booster under the same conditions to no avail. This sure is a resiliant issue.

I have ran a full bottle of injector cleaner through previously seems not to make much of a difference, I am with you on injectors except the relationship to the brake is odd. The engine never acts jerky, always just the same shudder at low rpm and in gear.

Still not resolved, please help.

This is exactly the behavior I get with a low idle: did you check the idle?

Have you used a hand-held vacuum pump to verify the brake power booster is holding vacuum to 20 inches hg?

Just ran the codes on the engine here is what I got