Exemplary embodiments provide a rotary misalignment-compensation bushing connection system that may be used in large-scale operations where several components are mounted in alignment on a single pin. For example, the misalignment-compensation system may be used in preloaded connection of a male lug rotatably mounted between a first lug and a second lug, on heavy equipment, for example, oil field exploration and production equipment. The misalignment-compensation system includes tapered cone bushings and surrounding counter-tapered cup bushings that expand in diameter and align the connection system as it is torqued together assembling the components to the pin.