This paper completes the proposal of a new adaptive reaction torque/force observer (RTOB/RFOB) design method. In the first paper, a new adaptive RTOB/RFOB design method is proposed when environmental impedance is considered as pure damping or stiffness. The proposed method can be used in several motion control applications, e.g., stiff model of environmental impedance is widely used in industrial applications. However, the exact adaptive RTOB/RFOB design method, in which environmental impedance is modeled by using damping and stiffness, has not been proposed yet. In this paper, a new adaptive RTOB/RFOB design method is proposed when damping and stiffness are considered in the model of environmental impedance. In the proposed method, not only the force control gain, but also the bandwidths of a disturbance observer (DOB) and a RTOB/RFOB and the ratios between uncertain and nominal inertias are adjusted automatically to improve the stability and performance of the robust force control system. Environmental impedance is modeled by using lumped parameters, and they are estimated by using an online recursive least-mean-square error algorithm. The validity of the proposal is verified by simulation and experimental results.