In version 10.1, try this:
Manipulate[
TimelinePlot[
{Interval[{ToString[a]ToString[myBegin], ToString[b]ToString[myEnd]}] -> "My range"},
PlotRange -> {DateObject[{1940}], DateObject[{2020}]},
Ticks -> All
{DateRange["1940", "2020", Quantity[5, "Years"]]}
],
{{amyBegin, 1950, "Begin"}, 1950, 2014, 1},
{{bmyEnd, 1960, "End"}, amyBegin, 2015, 1}]