In concurrent work, we introduced a novel robotic package delivery system latching intelligent modular mobility system (LIMMS). Each LIMMS end effector requires a small, lightweight latching mechanism for pre-manufactured containers, such as cardboard boxes. In order to effectively process a high volume of packages, aligning the latching mechanism quickly and reliably is critical. Instead of depending on highly accurate controllers for alignment, we propose a novel self-aligning rotational mechanism to increase the system’s tolerance to misalignment. The radial latching design consists of evenly spaced blades that rotate into slots cut into the box. When misaligned, the blades contact the edges of the engagement slots, generating a self-correcting force that passively centers the blades with the slot pattern. This paper introduces a mathematical framework with closed form expressions to quantify error tolerance for these mechanisms. Through our mathematical and optimization analyses, it is shown that a two-blade design can tolerate a maximum misalignment of three times the radius to the blade tips, much larger than commonly used designs with three or more blade-like contacts. Our approach can be generalized for a class of rotational latching mechanisms with any number of blades. Utilizing this theory, a design process is laid out for developing an optimal self-aligning rotational latching mechanism given desired parameters and task constraints. With this methodology, we designed, manufactured, and verified the effectiveness of both two-blade and three-blade self-aligning in practical experiments.