First, set the point A to A 1 point, and the time taken is ts. According to the meaning of the question, we can get AB=2cm, AA 1=2tcm, A 1B= 1cm, BB 1=tcm, and then we can get the answers by analyzing and solving the four cases of internal cutting and external cutting respectively.

Solution: Let point A reach point A 1, and the time taken is ts.

According to the meaning of the question, AB=2cm, AA 1=2tcm, A 1B= 1cm, BB 1=tcm,

Circumscribed at this time: 2t+ 1+t=2,

∴t= 1/3；

Engraved at this time: 2t+t- 1 = 2,

∴t= 1, when two circles coincide and are discarded;

Engraved at this time: 2t-t+ 1 = 2,

∴t= 1, when two circles coincide and are discarded;

At this time, the circumscribed: 2t-t- 1 = 2,

∴t=3.

∴ The translation time from point A to point A 1 is 1/3 or 3s.

So the answer is: 1/3 or 3.