In this paper, we introduce a family of novel sparse array designs called the augmented ULAs (AULAs) for the localization of non-circular signals (NCS). Accurate direction of arrival (DOA) estimation and the ability to resolve multiple targets are critical in modern wireless communication systems. Most existing sparse arrays are optimized solely for the difference co-array, making them less efficient at utilizing the sum co-array resulting from the non-zero pseudo-covariance of NCS. Meanwhile, state-of-the-art designs for joint optimization of the sum and difference co-arrays remain constrained by a three-way performance trade-off. The proposed AULAs configure single sparse and two dense ULAs alongside two separate elements to achieve a perfect splicing of holes and lags in the difference and sum co-array. This results in a larger virtual aperture and increased DOFs for NCS. Building on this structure, other variants of AULAs are developed, each exhibiting distinct characteristics. The shifted AULAs (SAULAs) judiciously displace the AULAs structure to minimize co-array redundancy and further enhance the DOFs. A transformed SAULAs (TSAULAs) design is proposed, which mitigates mutual coupling effects by converting the dense ULAs of SAULAs into sparse ULAs. By reconfiguring the elements of TSAULAs, the complementary TSAULAs (Co-TSAULAs) design inherits the desirable properties of SAULAs and TSAULAs.All these structures belong to a unified design framework, within which one configuration can be adapted into another during the design phase to meet different performance requirements. Meanwhile, they provide in-built physical locations for convenient extension to a larger aperture. Closed-form expressions for precise element placements, DOFs, and weight functions are derived. Simulation results validate the effectiveness of the proposed approach.