# Mechanical Design of a Bioinspired Compliant Robotic Wrist Rehabilitation Equipment
## 3 Conception of the Rehabilitation Equipment  
### The Bioinspired Character of the Rehabilitation Equipment  
The innovative character of the hand joints rehabilitation equipment is given by the bioinspired concept of the hand support and its actuation. The system supporting the patient's hand within the equipment was conceived consequently to observing the similarity of the stabilizing and propulsion motions of manta ray fins and the flexion/extension motions of the hand (Figure 4).  
The motions of manta ray fins underlaid the formulation of the Fin-Ray effect by [PERSON] in 1999 [23; 24]. The skeleton of the fins of these fish consists of two bones arranged in a V shape with connective tissue in between. Pulling on one side of the V causes the fin to deform [25].  
The Fin-Ray effect is scalable and versatile. A mechanical structure based on this effect consists of two elastic struts mounted at an angle by means of transversal ribs. Thus, several bar mechanisms are series linked in the decreasing order of their size in a reversed pyramid-like structure of V-shape. The connections of the struts to the transversal ribs are  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Joint**} & \multicolumn{1}{c}{**Motion**} & \multicolumn{1}{c}{**Rotation Angle**} & \multicolumn{1}{c}{**Maximal Rotation**} \\  & & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{**Speed [\({}^{\circ}\)/min]**} \\ \hline \multirow{3}{*}{Wrist} & Flexion & 0 to 80 & \multirow{3}{*}{30 to 180} \\  & Extension & 0 to 70 & \\ \hline \multirow{3}{*}{Joints of the fingers} & Metacarpo- & Flexion & 0 to 90 & \multirow{3}{*}{55 to 440} \\  & phalangeal & Extension & 0 to 90 & \\ \cline{1-1}  & Proximal & Flexion & 0 to 120 & \\ \cline{1-1}  & Distal & Flexion & 0 to 90 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Limits of the hand and finger joint motions.  
Figure 4: Emphasizing the similarity of manta ray fins and human palm motions.  
flexible and thus allow relative displacement as well as deformations of the component mechanisms. Upon applying a rotation to one of the joints at the base of the mechanism the entire structure deforms as shown in the schematics of Figure 5. It can be noticed that the top of the structure is displaced in the opposite direction to the rotation, in a similar manner to the manta ray fin.  
Starting from these considerations the construction of the palm support mimics the manta's flexible body, endowing the rehabilitation equipment with unique mobility characteristics. The most important of these is the possibility of simultaneously exercising several joints.  
The designing process of the rehabilitation equipment also took into account the differences between the motions of the hand and those of the fins. In the case of the manta ray fin motions are symmetrical in relation to a horizontal neutral position, while in the case of the hand the flexion angles are greater than the extension ones thus rendering the motion asymmetrical.  
Another bioinspired idea stemming from fish fins relates to the actuators used to generate the motions required by rehabilitation exercising. Both the manta ray and the rehabilitation equipment the structures based on the Fin-Ray effect are mobilized by muscles, biological in case of the former and pneumatic in that of the latter. While in the manta ray the movements are caused by muscles arranged on either side of the skeleton operating antagonistically, the rehabilitation equipment is set into motion by a single pneumatic muscle.  
By biomimetics the working principle of pneumatic muscles copies the operation of the biological ones, meaning that upon being fed compressed air they generate forces and displacements. Like the muscle fibers they imitate, pneumatic muscles have a number of beneficial properties, like to capacity to absorb shocks and shock-resistance, low weight and volume, a high power-to-mass ratio, elasticity, compliance, easy connectivity and safe operation.