It's a little difficult to draw, but essentially we are just left with a disc, like a solid circle. We've prevented positions where the arm would intersect either itself or the ground, so along one circle in the parameter space we'll restrict to nearly half (the base joint). The second parameter is then restricted more or less depending on the position of the first joint. When the first limb extends vertically, the second can swivel almost 360 degrees around, but when the first limb is extended horizontally the second limb has less than 180 degrees to turn.

Now if we're asked to put the arm from one position to another, we merely calculate the shortest path in the area that has not been blocked out, in our configuration space. ("merely" indeed! but we have programs that can do this).

More about Linkages

One of the earlier problems in linkage design was the problem of turning rotary motion (motion along a circle) into linear motion (motion along a line). Can you think of examples where this would be useful?