The English word “bead” originally meant “prayer.” The association of beads with prayer seems universal.
Nor is it a matter of using beads to keep track of how many prayers you have said; properly, one should not count prayers, but pray ceaselessly.
Rather, there seems to be something important about the tactile sensation of fingering the beads.
In Greece, there is a secular version, “worry beads,” which are supposed to function as the name implies. Fingering beads reduces anxiety. Chinese baoding balls, dating from the Ming Dynasty, are used similarly.
Those who suffer from anxiety would probably be well advised to get themselves a rosary or something similar, and keep it with them.
The Virgin Mary presents the rosary to St. Dominic.
Prayer beads around the world.
Buddhist prayer beads. 
Muslim prayer beads. Note that they are symbolically declared to be proof against the effects of envy, the “evil eye.” 
Catholic rosary. 
Orthodox prayer rope. 
Baoding balls 
The proper use of worry beads.
Japan 
Europe
The making as well as the using of prayer beads is understood everywhere to be a devotional practice, a form of meditation.
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The Chivalric Order of St. Gerebernus and St. Dymphna 