Brinkmann came from Harburg, Hamburg, West Germany. At the age of 16 he first solved a Rubik's Cube which belonged to his maths teacher: the teacher had given-up, but Brinkmann solved it overnight. On 6-13 March 1981 a Guinness Book of Records speedcubing tournament took place at the Olympia Shopping Centre, Munich. Brinkmann was joint winner (with Jury Fröschl) with a best time of 38 seconds. He also achieved 29 seconds on German TV and before the end of 1981 reached 24 seconds.
He won the first West Germany Championship in 1982 with a winning time of 19 seconds. This has sometimes been reported as a world record time. If so, it was broken by March 1983, when Robert Pergl won the 2nd Czechoslovakian Championship with a best time of 17.04 seconds.
The World Rubik's Cube Championship 1982 took place on June 5. Brinkmann was, according to Guus Razoux Schultz, the favourite to win. However, the tournament used stiff cubes which favoured those using more efficient methods. Brinkmann ultimately finished in 14th place with a best time of 30.59 seconds. According to David Singmaster, Brinkmann used two methods: one was a Corners first technique (DC, UC, U & D E, ME); the other was DC, 3DE, 4UC, rest.