Modeling of Flexible Belt Objects toward Their Manipulation

A modeling method of flexible belt objects is proposed. Deformation of a belt object such as film circuit boards or flexible circuit boards must be estimated for automatic manipulation and assembly. In this paper, we assume that deformation of an inextensible belt object can be described by the shape of its central axis in a longitudinal direction called "the spine line" and lines with zero curvature called "rib lines". This model is referred to as a "fishbone model" in this paper. First, we describe deformation of a rectangular belt object using differential geometry. Next, we propose the fishbone model considering characteristics of a developable surface, i.e., a surface without expansion or contraction. Then, we formulate potential energy of the object and constraints imposed on it. Moreover, this model is applied to a bent belt object. Finally, we explain a procedure to compute the deformed shape of straight and bent objects and compare their shape with measured shape to demonstrate the validity of our proposed method.