Toward simpler models of bending sheet joints

Sheet hinges, thin flexures that are rigid in the plane but which can bend freely, are common in stamped and lithographically manufactured devices. The behavior of these machine elements as joints in a robot is difficult to model because they are two-dimensional continuum elastic bodies that admit three-dimensional motion and twisting. This paper presents a parametric modeling technique that can be used to accurately predict elastic behavior of sheet hinges in three dimensions. Parameterized backbone curves can be used to represent ruled surface bending in a fashion that implicitly accounts for some of the complex boundary conditions imposed on typical sheet hinges. Approximate methods of integrating the non-commutative equations defining the sheet hinge backbone curves will be discussed, demonstrating acceptable trade-offs between accuracy and representational simplicity in overall model performance.