A method is proposed to predict the shape of a paper model of a three piece brassiere cup, which consists of several cloth and wire parts. Currently, the shape of each part is determined by creating a paper model and then refining the model. This process is repeated until the desired shape is achieved. However, predicting the 3D shape with a simulation would improve design efficiency. As a model is made of paper, each part is assumed to be inextensible and its surface is represented as combination of developable surfaces. The potential energy of a cup and geometric constraints imposed on the cup are formulated by use of the normal curvature and the direction of a generatrix of each developable surface. Minimizing the potential energy under geometric constraints derives a stable shape of the cup model. The computed and measured cup shapes coincided qualitatively.

A method to generate an appropriate path for manipulation of a belt object is proposed. It is important for automatic manipulation of a belt object such as a film/flexible circuit board to generate an appropriate path for a manipulator because such object is flexible in a certain direction but fragile in another direction and an inappropriate path which causes deformation in the fragile direction may lead to wiring disconnection. First, deformation of a rectangular belt object is modeled considering its bending and torsional deformation under the force of gravity. Next, a method to generate a path for belt object manipulation with quasi-static and non-excessive deformation is proposed. After that, deformation and loaded condition in the path generated by our proposed method and those in a common path based on linear interpolation are compared. Finally, the validity of our proposed method is verified by measuring the deformed shape of a polyethylene sheet during manipulation with the generated path.

A differential geometry based modeling of a belt object to represent its deformation path is proposed. Adequate deformation path of a belt object such as film circuit boards or flexible circuit boards must be generated for automatic manipulation and assembly. First, deformation of a belt object is described using the curvature of its central axis, torsion around the central axis and the curvature in the transverse direction. Second, a method to derive an adequate transition of the object shape from the initial state to the final state is proposed. It can be derived by minimizing the maximum of the local potential energy in the belt object during its manipulation. This is because locally excessive potential energy often leads to the excessive stress that makes fractures in the belt object. Finally, the validity of our proposed deformation path is verified by estimating the maximum local potential energy in a belt object.

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.