vo Rinkel won the 1945 Dutch championship singles title. Partnered with Huib Wilton and Hans van Swol he won six national doubles titles between 1945 and 1950 as well as mixed doubles titles in 1946 and 1950. Rinkel participated in six Wimbledon Championships between 1946 and 1952. With Van Swol he reached the quarterfinals of the men's doubles competition in 1948. His best result in the singles competition came in 1946 when he reached the third round in which he lost to Frenchman Pierre Pellizza.
In 1947, he won the triple crown at the British Covered Court Championships played at the Queen's Club in London. In the singles final he defeated Ernest Wittman in three sets. Together with R.E. Carter he won the men's doubles title defeating H. Billington and Ignacy Tłoczyński in the final. In the mixed doubles he was partnered with Mrs. P.J. Halford and in the final they proved too strong for John Olliff and Mrs. E.W. Dawson–Scott. Between 1946 and 1952 he played in ten ties for the Dutch Davis Cup team comprising a record of seven wins and five losses.
After his active sports career Rinkel became captain of the Netherlands Davis Cup team.
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