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.

我们通过分析、数值和实验研究固定角度弓的机械行为，即两端旋转固定的细长杆，其中一端完全受约束（方向和位移），而另一端可以平移（仅）沿着连接弓两端的线。了解固定角度弓的行为对于各种工程应用的设计非常重要且直接相关，例如柔顺机构、非线性弹簧、能量吸收器和能量收集器。该分析基于不可扩展的弹性，考虑了大旋转和大位移。我们找到对称情况的精确解析解和非对称情况的近似解。这些通过与数值结果和实验测量的比较得到验证。