By Simon Cambers
NEW YORK (Reuters) - Serena Williams has been here before.
Twelve months after her bid for the coveted calendar-year grand slam ended with a shock defeat to Roberta Vinci of Italy in the U.S. Open semi-finals, the world number one is back, chasing another piece of history.
Victory at this year's U.S. Open would give the American, who begins her quest on Tuesday versus Ekaterina Makarova, a 23rd grand slam singles title and break the professional era record she shares with Germany's Steffi Graf.
A year on, despite a niggling injury to her right shoulder and in danger of losing her world number one ranking, Williams claims things are easier to handle.
"At this point, I'm taking it a day at a time," said Williams. "(But) I think I just am more relaxed, for sure."
Williams will need to be at her best during her first-round match against Makarova, a Russian now ranked 29th but as high as eighth last year and who has beaten the American once in their five meetings.
"I'm OK with it," Williams said. "I try to look at it like we always have tough matches. I played her I think in the semis before. I know she's a good player. I've just got to do the best I can."
In other Day Two action, Agnieszka Radwanska, one of three women who could replace Williams atop the world rankings this fortnight, plays American Jessica Pegula while sixth seed Venus Williams opens against Kateryna Kozlova of Ukraine.
In the men's event, second seed Andy Murray begins his title bid with a first-round match against Czech Lukas Rosol.
Murray is bidding to complete a golden summer having added the Olympic title to his Wimbledon crown.
“He's a tough, tough opponent,” Murray said. “Big, strong guy, goes for his shots; takes a lot of risks.”
Former U.S. Open champion Juan Martin del Potro, back for the first time in three years after three operations on his left wrist, plays fellow Argentine Diego Schwartzman in round one.
(Editing by Frank Pingue)