Bio-inspiration can be used in the development of novel dextrous and energy-efficient manipulators. This paper focuses on planar manipulators inspired by the bird neck, built upon stacking a series of tensegrity X-joints. The manipulators are actuated with four tendons and have different numbers of modules, with or without offsets. The objective of this work is to study the influence of offsets, number of modules, geometry of the joints, configuration at rest of the manipulators, and actuation scheme on the size of the tension-feasible workspace (TFW). The spring constants of the X-joints are determined so that the configuration at rest features a desired end-effector (EE) pose with minimal stiffness to ensure stability. Our study demonstrates that increasing the number of modules results in a larger TFW, although the number of active tendons is fixed. We find that the TFW can be maximized with appropriate modification of the joint geometry. Additionally, we explore the influence of bio-inspired approaches on the manipulator configuration at rest and actuation scheme in relation to the TFW. In addition, we conduct an analysis of the EE pose stiffness, revealing that offsets decrease this stiffness, while an optimal number of modules exists to achieve maximum stiffness. We observed that increasing the width of the manipulator generally enhances stiffness, while the configuration at rest and the actuation have little effects. Furthermore, experiments were conducted to validate the methodologies.