Robot Modeling for Physical Rehabilitation The ankle associated to hip, the knee, and the foot motion allows the foot to take up any position in space and to adapt to any irregularities of the ground. The upper limb displays a certain similar- ity: the joints of the wrist, assisted by pronation and supination, allow the hand to assume any position in space but the mobility of the hand is much greater than that of the foot. The joints of the foot are many and complex. In addition to flexion and extension, which occur at the ankle, the foot can move about the vertical axis of the leg and about its own horizontal and longitudinal axis. Adduction movement occurs when the tips of the toes move towards the plane of symmetry of the body and face inwards. Abduction movement occurs when the tips of the toes move away from plane of symmetry and point outwards. The plantar vault acts as a shock absorber, which is essential for flexibility of the gait and helps support the body on the ground for running, walking and the maintenance of the erect posture. lateralization in the coronal plane and, rotation in the longitudinal plane (Kapandji, 2008). MECHANICAL SYSTEMS FOR REHABILITATION The science of rehabilitation shows that repeated movements of human limbs can to help the patient regain the function of the injured limb. Mechanical systems under automatic control can be more efficient in performing these exercises than humans because they can perform the nec- essary rehabilitation movement as well as record information like position, trajectory, force, and velocity, maximizing motor performance during active movements, and guiding the movement of a patient's limb attached to it. All trajectory data can be archived and then compared to check the progress of patients in therapy. Different mechanical systems have been developed and applied for rehabilitation. These mechanical systems can be divided in robots, exoskeletons, and cable-based manipulators. Spine The spine is a complex remarkable mechanical structure. The primary function of a spine con- sists of musculoskeletal support and mechanics. It provides the longitudinal stiffness of a human body, by allowing movement between its parts. Secondly, it constitutes a firm support of adja- cent anatomical structures such as the ribs and abdominal muscles by allowing the maintenance of body cavities with shape and size relatively constant. Another function of the spine is to allow the spinal cord to gain access to distant parts of the trunk and limbs. The spine consists of discrete bony elements called vertebrae, which are joined by passive ligament restraints. They are kept separated by intervertebral discs and articulating joints, and they are dynamically controlled by muscular activation. The motions of the human spine are character- ized by the actuation planes as follows: flexion and extension in the sagittal plane; right and left Rehabilitation Robots Although specific mechanical systems, called robots, have been developed for rehabilitation of human limbs, based on IFToMM definition of a robot (Ionescu, 2003), an industrial robot used for rehabilitation can also be considered a rehabilitation robot. Industrial robots have big advantages because they provide a three-dimensional workspace with multiple Degrees of Freedom (DOF), enabling good flexibility to carry out different trajecto- ries, which are useful for motion rehabilitation, and its technology is well known, enabling a force-feedback control in a three-dimensional workspace. These industrial robots have serial architecture, in which it is attached to the human limb with a special device, in order to execute the programmed motion. 159