We discuss the precise cooperative motion of a dual manipulator. In the inverse kinematics of cooperative redundant manipulators, a hierarchical method using null space and an optimization method prioritizing the end-effectors relative position in the objective function have been proposed. However, there is no guarantee that the relative position will be maintained in regions subject to joint limits and task-space reachability constraints. As a result, unacceptable errors may occur, and some tasks cannot be accomplished. We propose designing the maximum permissible errors in advance by expressing the target relative position as inequality constraints in the Quadratic Programming (QP) problem. By extending its description to include a virtual spring, we have also achieved subtle force application by two cooperated manipulators. The proposed method was verified by simulation and experiments.