In this paper we present two new designs of spherical flexure joints, which are the compliant equivalent of a traditional ball-and-socket joint. The designs are formed by tetrahedron-shaped elements, each composed of three blade flexures with a trapezoidal shape, that are connected in series without intermediate bodies. This is new with respect to the designs currently found in literature and helps to increase the range of motion. We also present two planar (x-y-${\theta }_z$) flexure joint designs which were derived as special versions of the spherical designs. In these designs the tetrahedron elements have degenerated to a triangular prisms. For detailed investigation we developed equivalent representations of the tetrahedron and triangular prism elements and proved that three of the four constraint stiffness terms depend solely on the properties of the main blade flexure. Furthermore, we derived equations for these stiffness terms which are compared to finite-element simulations, showing a good correspondence for the prism element with a Normalized Mean Absolute Error (NMAE) of 1.9%. For the tetrahedron element, the equations showed to only capture the qualitative behaviour with a NMAE of 34.9%. Also, we derived an equation for the optimal width of the prism element regarding rotational stiffness.

在本文中，我们提出了两种新的球形挠性接头设计，它们与传统的球窝接头相当。设计由四面体形的元素形成，每个元素由三个具有梯形形状的叶片挠性件组成，这些叶片挠性件无中间体地串联连接。这相对于文献中当前发现的设计是新的，并且有助于增加运动范围。我们还提出两个平面（X - Ÿ -${\theta }_{ž}$）挠性接头设计，这是球形设计的特殊版本。在这些设计中，四面体元素已退化为三棱柱。为了进行详细研究，我们开发了四面体和三角棱镜元素的等效表示形式，并证明了四个约束刚度项中的三个仅取决于主叶片挠性的特性。此外，我们导出了这些刚度项的方程式，并与有限元模拟进行了比较，结果表明该棱镜元件的归一化平均绝对误差（NMAE）为1.9％，具有良好的对应性。对于四面体元素，方程式显示仅捕获了34.9％的NMAE的定性行为。同样，我们得出了关于旋转刚度的棱镜元件最佳宽度的方程式。