The study presents a novel cable-driven serial robot based on flexible joints and tensegrity structures, which features a rapid response capability in complex dynamic environments. This makes it particularly suitable for human–robot interaction scenarios. Compared to traditional rigid serial robots, the design’s compliance demonstrates significant advantages in addressing complex demands. The study delves into kinematic and dynamic modeling methods and verifies their effectiveness through simulations. The kinematic model transforms the local coordinate system to the global one using general kinematic equations. First, the static and dynamic model of the robot is derived based on the torque balance equation, and then the dynamic model of the robot is constructed. By simplifying the robot model, the relationship between tension values from driving cables and the robot’s workspace is analyzed under the constraints of tensegrity structures and flexible joints. Additionally, trajectory simulations validate the kinematic and dynamic models. The kinetic energy variation curves based on the trajectories confirm the accuracy of the theoretical analysis. This method demonstrates broad applicability and can be applied to other serial robots with flexible structures, offering effective solutions for use in complex dynamic environments.