All you have to do to open an umbrella is to press a button on the handle that releases a hollow shaft, held against a catch. A compressed spring between the hollow shaft and the base shaft causes the hollow shaft to move up. The movement of the hollow shaft is restricted by another catch on the base shaft. Amidst all this the umbrella does not open up. This is to ensure that you don't get hurt by the spokes of the main framework. After the hollow shaft gets engaged, the relative motion between this shaft and main spring responsible for the opening mechanism is allowed. Now this spring applies an upward force on linkages attached to it which results in the opening of the umbrella.