Because the Players Championship is the tour’s signature event, dubbed golf’s fifth major by many, it attracts a loaded field, enticed by purse ($9.5 million) and prestige. The best players want to play their best at the best tournaments.

On this particular Friday, golf’s biggest names and highest-ranked players were all scrambling to make the cut, flirting with the projected number throughout the second round. Some - Tiger Woods, Luke Donald, Lee Westwood, Phil Mickelson, Keegan Bradley - succeeded. Some - Rory McIlroy, Hunter Mahan, Steve Stricker, Webb Simpson - did not.

There is a trio at the top, because Zach Johnson (66), Kevin Na (69), and Matt Kuchar (68) share the lead at 8 under par. But at least for one day, keeping tabs on who might be leaving TPC Sawgrass early trumped who was leading.

The day’s musical chair feel focused mostly on Woods and McIlroy. Woods was trying to prevent missing consecutive cuts for the first time in his PGA Tour career, while McIlroy wanted to finally figure out a course that had already beguiled him twice.

“I just need to try and get the hang of this golf course somehow,’’ said McIlroy, the top-ranked player in the world, who shot 72-76 to miss the Players cut for the third time in three tries, never breaking par now in six rounds at the Stadium Course. “Something about this place I just can’t get to grips with.’’

The same player who lost in a playoff last week said he hit it the same this week, yet is going home prematurely. His disdain for Pete Dye’s design kept him away from the Players in 2011. Despite another missed cut, he vowed to be back next year.

“I promise,’’ McIlroy said. “Hopefully, I’m coming back for another 20 years. If I don’t figure it out by my 20th go, there’s something wrong.’’

McIlroy was smiling when he spoke after his round. So was Woods, who began the day tied for 100th and carrying a streak of eight rounds without breaking 70, dating to a second-round 65 at Bay Hill two months ago, the only PGA Tour event he’s won since September 2009.

He punched his weekend ticket with solid play on Friday: six birdies, two bogeys in a 4-under-par 68, which left him tied for 30th at 2 under, six shots behind the leaders.

“Very consistent, nothing spectacular, just real solid golf,’’ said Woods, who made four consecutive birdies, starting on the difficult par-3 eighth. “Sixty-six was my [target] number today. But I’m still with a good chance.’’

Woods will be paired in the third round with Bradley, who was 2 over par and two strokes above the cut line when he made the turn. The Hopkinton (Mass.) High graduate and reigning PGA champion responded to the personal challenge he set, making four birdies on the inward nine, including Nos. 17-18. He shot 70, ending a stretch of two straight missed cuts.

“I was really sweating it out. I’d missed two cuts in a row, things weren’t going my way even when I hit good shots or good putts. It was a scary time, but I really hung in there,’’ Bradley said. “It felt good to be rewarded for good shots. I didn’t miss a shot coming in, from the 14th hole on.’’

He had an internal chat with himself on the lengthy walk from the 16th green to the 17th tee, knowing he needed to make three solid swings: the shot to the island green, then a drive and approach to No. 18, with round-wrecking water hugging the entire left side. Two birdies later, Bradley’s talking-to had the desired effect.

“Walking to 17 I said, ‘Two years ago I would have killed to be in this position. I’m just a bum from Vermont, so enjoy it, love it.’ It seems like when there’s a little more pressure, I hit really good shots, which is a good sign,’’ he said.

Donald, the No. 2-ranked player in the world, had two eagles (Nos. 2 and 16) and shot 69, getting to 3 under. He’ll be paired in the third round with Westwood, ranked No. 3. Westwood shot 70 to also reach 3 under. Mickelson had another 71 and is 2 under.

They’ll all be looking for upward moves on the weekend. Stricker, ranked No. 6, gets a rare weekend off. His 76-74 ended 49 consecutive cuts made, which had been the tour’s longest active streak. Mahan is the only two-time tour winner this year and ranked fifth in the world. He tied for sixth here last year, but after 74-76, will have to wait a year to improve on that.

Now the focus can return to the leaders. Na and a pair of Sea Island, Ga., residents (Johnson and Kuchar) have positioned themselves for a possible run at winning the Players.

Woods, Bradley, McIlroy, and the others who tap-danced along Friday’s fine line know all too well what comes first, though. Without making the cut, winning the tournament remains but a dream.

Michael Whitmer can be reached at mwhitmer@globe.com. Follow him on Twitter @GlobeWhitmer.