Deformation modeling of belt object with angles

A differential geometry based modeling to represent belt object deformation is proposed. Deformation of a belt object such as film circuit boards or flexible circuit boards must be estimated for automatic manipulation and assembly. First, the fishbone model to describe deformation of a rectangular belt object is explained. In this model, the object shape is represented by the curved ldquospine linerdquo and straight ldquorib linesrdquo. We can estimate deformation of the object by minimizing its potential energy under geometric constraints. Next, this model is modified to represent deformation in which the rib line at an endpoint does not coincide with the transverse edge. Moreover, the modified model is applied to a belt object with angles. The deformed shape of an angled object can be derived by separating it into rectangular parts and angled parts and by assuming that each angled part forms a part of a cylindrical surface. Finally, the validity of our proposed model is verified by comparing the computed shape of an L-shaped belt object with its measured shape.