  It is a crucial problem in robotics field to cage an object using robots like
multifingered hand. However the problem what is the caging for general
geometrical objects and robots has not been well-described in mathematics
though there were many rigorous studies on the methods how to cage an object by
certain robots. In this article, we investigate the caging problem more
mathematically and describe the problem in terms of recursion of the simple
euclidean moves. Using the description, we show that the caging has the degree
of difficulty which is closely related to a combinatorial problem and a wire
puzzle. It implies that in order to capture an object by caging, from a
practical viewpoint the difficulty plays an important role.
