The proposed changes, which reduce the rules governing the game to 24 from 34, will be settled in 2018 and take effect on Jan. 1, 2019, the governing bodies said in a statement on Wednesday.
Another change would rely on a player's "reasonable judgement" when estimating or measuring a spot, point, line, area or distance, even if video evidence later shows it to be wrong. And another would impose a limit of 40 seconds for players to play a stroke.
Golfers around the world can offer their feedback on the proposed changes over the next six months.
"Our aim is to make the Rules easier to understand and to apply for all golfers," said David Rickman, executive director for governance at the R&A.
"We have looked at every Rule to try to find ways to make them more intuitive and straightforward and we believe we have identified many significant improvements.
"It is important that the Rules continue to evolve and remain in tune with the way the modern game is played, but we have been careful not to change the game's longstanding principles."
The "ball moved" rule caused controversy at last year's U.S. Open, where Dustin Johnson's victory was threatened by his being docked a shot after the ball moved fractionally when he grounded his putter next to it on the fifth green.
Johnson played the closing holes not knowing whether he would be given a stroke penalty that might have denied him the title on a technicality, although he eventually finished four strokes clear.
In December, the governing bodies introduced a new local rule to eliminate the penalty after the USGA came under fire from Tiger Woods, Rory McIlroy and Jordan Spieth, among others.
(Reporting by Simon Jennings in Bengaluru, editing by Larry King)