# Adjustable Stiffness-Based Supination-Pronation Forearm Physical Rehabilitation
## 3 Adjustable Stiffness Rehabilitation Device  
Figure 2 is a photograph of the developed experimental platform of the adjustable stiffness medical device reported in this paper. The main element is the handle that, automatically, reproduces the required supination-pronation angular motion. In Figure 2, a right forearm-hand is driven by the handle of the system through the pulley (in blue) that receives four non-elastic cables (in red) that are connected to two linear electric actuators (not visible in the photo). The aluminum frame provides structural stability and serves as a support for the handle and for a set of redirection small pulleys (in white) that can be observed thanks to the change of direction of the cables from horizontal to vertical. This set of small pulleys serves to redirect the cables through the frame. An auxiliary monitor that is used during the active-assisted phase of the rehabilitation protocol displays the desired trajectory to be followed. Figure 3 illustrates the way cables interact with the handle and how they are connected to the actuators. The combined actions of four forces \(F_{1},F_{2},F_{3}\), and \(F_{4}\) acting, respectively, through four cables \(l_{1}\) (in green), \(l_{2}\), \(l_{3}\), and \(l_{4}\) (in blue) generate the angular motion defined by \(\theta\). As it is illustrated in Figure 3, cables \(l_{1}\) and \(l_{3}\) are driven by actuator 1 while cables \(l_{2}\) and \(l_{4}\) are driven by actuator 2. Figure 2: Experimental platform. In addition, Figure 3 illustrates the way each cable is attached to the handle pulley by highlighting that cable \(l_{1}\) (in green) is connected to this pulley at point \(P_{c}\) after winding \(270^{\circ}\) on its surface. The four cables are tangent to the handle pulley with radius \(r_{p}\). Cable \(l_{1}\) changes its direction several times thanks to the aforementioned set of small pulleys, proceeding through the aluminum frame (dotted green line) to finish at point \(P_{1}\) where cable \(l_{3}\) arrives too. A spring and a load cell are placed between point \(P_{1}\) and the end of the rod of linear actuator 1. Cables \(l_{2}\) and \(l_{4}\) are connected in a similar manner to linear actuator 2. Each spring allows adjusting the stiffness of the medical device, through the control strategy described in Section 5. The motion of the rehabilitation system is performed on the \(xy\) plane. Then, torque \(\tau\) generating the desired angular motion is always parallel to the \(z\)-axis. In Figure 3, the handle is vertical at the initial (neutral) condition \(\theta_{0}=0\) (solid lines). If the handle rotates clockwise, \(\theta<0\) (dashed lines). Otherwise, \(\theta>0\). Figure 4 illustrates, in a more detailed manner, how cables are driven by actuators. A first connector (in blue) is placed between each actuator rod and a load cell. A second connector (in blue) is placed between that load cell and a spring that receives the respective pair of cables (in red). The double-headed arrow illustrates the displacement that each linear actuator can produce, resulting in a change in the tension of the respective pair of cables. It is highlighted that cables \(l_{1}\) and \(l_{3}\) are rigidly attached to a first spring in the same manner that cables \(l_{2}\) and \(l_{4}\) are attached to a second spring. The two springs have the same stiffness value (\(185.39\) N/m).