Fishbone Model for Belt Object Deformation

A modeling method for representing belt object deformation is proposed. Deformation of belt objects 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. Finally, we explain a procedure to compute the deformed shape of the object and verify the validity of our proposed method by comparing some computational results with experimental results.