The mechanical behavior of fixed-angle bows

We study analytically, numerically, and experimentally the mechanical behavior of a fixed-angle bow, i.e., a slender rod with both ends rotationally fixed, where one end is completely constrained (orientation and displacements), while the other can be translated (only) along the line connecting the two ends of the bow. Understanding the behavior of fixed-angle bows is of importance and direct relevance to the design of diverse engineering applications, such as compliant mechanisms, nonlinear springs, energy absorbers and energy harvesters. The analysis, based on inextensible elastica, accounts for large rotations and large displacements. We find exact analytical solutions for the symmetric case and approximate solutions for the nonsymmetric case. These are validated by comparison with numerical results and experimental measurements. The similarities and differences between fixed-angle bows, fixed-angle circular arcs and rings are also discussed.