What could cause a light vibration in an old manual transmission car as you accelerate in any gear along with a loud 'clank' as if something hit the undercarriage?

go get a free brake inspection at a local brake shop, and while they have it in the air, ask if they see anything unsafe or worth noting... also ...everyone should have a manual for their vehicle(parts store or dealer), and a local library should have professional shop manuals available in the REFERENCE section for free...make copies of the appropriate sections...read up and good luck :) When you say it's an "old" manual transmission car, is it rear wheel drive by chance? Often a faulty "U-Joint" can cause some occasional "clanking" and if they're getting bad enough they can certainly cause some vibration. Some of the rear wheel drive vehicles also have what's called a "center carrier bearing" which supports the driveshaft. If neither of those seem to be the problem, start checking the suspension parts. Be aware that if it IS the carrier bearing or U-Joints, they can fail in a serious way, causing the driveshaft to fall out while you're going at highway speed. Not a plesant experience.