Fishbone model for belt object deformation

Abstract

A modeling method for representing belt objectdeformation is proposed. Deformation of belt objects such asfilm circuit boards or flexible circuit boards must be estimatedfor automatic manipulation and assembly. In this paper, weassume that deformation of an inextensible belt object can bedescribed by the shape of its central axis in a longitudinaldirection called "the spine line" and lines with zero curvaturecalled "rib lines". This model is referred to as a "fishbone model"in this paper. First, we describe deformation of a rectangular beltobject using differential geometry. Next, we propose the fishbonemodel considering characteristics of a developable surface, i.e.,a surface without expansion or contraction. Then, we formulatepotential energy of the object and constraints imposed on it.Finally, we explain a procedure to compute the deformed shapeof the object and verify the validity of our proposed method bycomparing some computational results with experimental results.