Context. Origin and evolution of blue stragglers in globular clusters is still a matter of debate. Aims. The aim of the present investigation is to reproduce the evolutionary history of four binary blue stragglers in four different clusters, for which precise values of global parameters are known. Methods. Using the model for cool close binary evolution, developed by one of us (KS), progenitors of all investigated binaries were found and their parameters evolved into the presently observed values. Results. The results show that the progenitors of the binary blue stragglers are cool close binaries with period of a few days, which transform into stragglers by rejuvenation of the initially less massive component by mass transfer from its more massive companion overflowing the inner critical Roche surface. The parameters of V209 from omega Cen indicate that the binary is substantially enriched in helium. This is an independent and strong evidence for the existence of the helium rich subpopulation in this cluster.
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