Deformation path planning for manipulation of flexible circuit boards

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.