In this paper, a modular wire-actuated robotic arm was designed to improve the safety and adaptability of service robots during human-robot interaction. To raise the stiffness adjustment range of the robotic arm, a symmetric variable-stiffness unit was designed based on flexure, which had compact and simple structure, and lowly nonlinear stiffness-force relationship. In this paper, we focused on the research of the symmetric 1-DOF joint module. Based on the kinematics and stiffness analysis, the pose of the joint module could be adjusted by controlling the length of the wires, and the stiffness of the joint module could be adjusted by controlling the tension of the wires. Because of the actuation redundancy, the pose and stiffness of the joint module could be controlled synchronously. Furthermore, a directly method was proposed for the stiffness-oriented wire tension distribution problem of the 1-DOF joint module. A simulation was carried out to verify the proposed method.