基于卡氏第二定理,推导出椭圆型弹性球铰链柔度、精度的解析表达式.提出弹性球铰链柔度精度比的概念,并以此为性能指标对铰链的设计进行了优化.结果表明:铰链应选用弹性模量大、切变模量小的材料;在保证强度的前提下,应尽量减小椭圆广角、椭圆长短半轴之比以及铰链最小厚度与椭圆短半轴之比.指出在设计弹性铰链时不能仅追求转动性能,还需要考虑其疲劳强度,进而推导出弹性球铰链疲劳强度的校验公式.%Based on the Castigliano's second theorem, the equations were formulated for the compliance and precision of an elliptical flexure spherical hinge. A new concept of compliance accuracy ratio of flexure spherical hinge was proposed, which was used as the performance index of hinges. Optimization was done, and the results show that materials of hinges should be with high elastic modulus and low shear modulus; all of the wide-angle, the ratio of long half axis to short half axis and the ratio of the minimum thickness to short half axis of ellipse should be as little as possible on the premise of ensuring strength. A view point was proposed,that fatigue strength must also be considered except for improving performance while designing the flexure hinges, and the check formula of fatigue strength was derived.
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