rockers on shaft moving fore/aft

geminimotors said

Is some amount of lateral movement or offset from the valve stem necessary in regards to wear, lubrication, or valve rotation? Just curious.

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“Necessary?” No. There is some room as delivered from the factory that grows over time, AKA, miles. It’s not a harmful thing to have a little bit. It’ll live another 1,000,000 miles or 50 years before anything remotely happens.