Vic Braden, who mixed psychology, biomechanics and a rapier wit to become an immensely influential teacher of tennis, spreading his cheerful gospel through camps, clinics, books and national television appearances, died Monday at his home in Coto de Caza, California, in Orange County. He was 85.

His daughter Kristen Paul said the cause appeared to be a heart attack.

Jack Kramer, a professional tennis star of the 1940s and ’50s, called Braden “the No. 1 tennis coach in the world.” An instructional show Braden hosted on PBS in the early 1980s was carried by 238 stations. Some said he did for tennis what Julia Child’s PBS show had done for cooking.

He also appeared on NBC, wrote eight books, made instructional videos and taught thousands at his traveling tennis college in the United States, Germany, Spain, Switzerland and China. He lectured in all 50 states. In 1976, Sports Illustrated called him the highest-paid tennis coach in the world.

He trained champions, including Tracy Austin, to whom he claimed to have rolled tennis balls in her crib, and who, in a Twitter message after his death, called him “a pioneer, innovator and true legend in our sport.”

Typifying his meld of humor and wisdom, Braden once said, “My theory is that if you buy an ice cream cone and make it hit your mouth, you can learn to play tennis. If you stick it on your forehead, your chances aren’t as good.”

He helped pioneer the use of high-speed cameras and computers to dissect the minutiae of the sport. He determined that a ball touched the court for 3 milliseconds and that it actually stayed on the racket for a full 6 inches of a swing. He said that even top professional stars had strokes only a tenth as good as what he expected the next generation of champions to possess.

But Braden’s forte was psychology, which he thought could nearly work miracles. He told Sports Illustrated that if he were given eight good 13-year-old players — “I don’t mean great athletes,” he specified — he could have all of them in the Wimbledon quarterfinals at 18.

Braden was often called altruistic and optimistic. He taught people in wheelchairs to play tennis effectively, and blind people to enjoy trying. He shouted out code numbers as a clue to where the ball was. He often did not charge children for lessons.

Victor Kenneth Braden Jr. was born Aug. 2, 1929, in Monroe, Michigan, one of eight children. Just 5 feet 6 inches tall, he played football, basketball and baseball in high school.

When he was 13, he was caught stealing tennis balls from the municipal court by the recreation director and offered a choice: He could go to jail or learn to play tennis. He chose tennis, and it fascinated him so much that he soon hitchhiked to Detroit to observe how the tennis great Don Budge hit his backhand.

In addition to his daughter Kristen, he is survived by his wife, the former Melody Watts; another daughter, Kory Braden-Hittleman; two sons, Troy Davis and Shawn Davis; and six granddaughters.

For all his expertise in tennis, Braden readily admitted he did not know everything.

“Why do people choke?” he wondered aloud in an interview with The Los Angeles Times in 1986. “Be nice to know that.”