In this study, we introduce a novel hybrid wrist joint that seamlessly integrates rigid, flexible, and soft components, aiming to optimize the flexibility in robotic systems. This joint features a complexly shaped compliant unit, which forms the basis of flexible limbs with distinct kinematic properties, essential for advanced wrist joint mechanisms. We introduce an innovative fabric chamber-based pneumatic soft actuation system, designed as a lightweight and mechanically simplified alternative to conventional motor-driven actuators, aligning with sustainable development goals by offering a more environmentally friendly solution. Through detailed analysis of the compliance characteristics of these components, we established an equivalent mechanism, enabling us to construct a comprehensive kinetostatic model for both the flexible support chains and the overall wrist joint. Validations are conducted through rigorous mathematical experiments and simulations, confirming that our hybrid wrist joint achieves three rotational spherical motion. This capability ensures it meets the diverse functional requirements of wrist articulation in advanced robotic applications.