## 3 End Effector-Based Devices for Gait and Balance Rehabilitation
### Review of End effectors
#### 3.2.2 Non-Commercially Available End Effectors
(2014) is an example of the application of this strategy. With respect to the end effectors driven by PKMs for balance rehabilitation, all of them consist of a unique platform that can provide at least two rotations around the two horizontal axes (mediolateral and anterior-posterior rotations). The amplitudes of the rehabilitation movements required for balance training are not as big as the ones for gait rehabilitation, and hence the workspace limitation of a PKM does not affect them. Despite this advantage, the number of end effectors driven by PKMs for balance rehabilitation is fewer than those for gait recovery. Among different PKMs for gait rehabilitation, two Stewart platforms, one for each foot of the patient, are used. The main advantage of using Stewart platforms is that they provide 6 DOFs to each foot of the patient and thus they can introduce perturbations in any direction of the space. Overall, two kinds of Gough-Stewart platforms are examined in the literature: 6-UPS and 6-UCU, where U, C, and S, stand for universal, cylindrical, and spherical joints, respectively. As an example, the prototype presented by [PERSON] et al. for walking simulation \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Authors** & **Ref** & **Topology** & **DOFs** & **Objective** & **Training Mode** \\ \hline
2023, [PERSON] et al. & [131] & 2-PRR & (2T) \(\times\) 2 & Gait & Passive \\
2021, [PERSON] et al. & [132] & P-P-RFRR & (1 TIR + T) \(\times\) 2 & Gait & Passive \\
2020, [PERSON] et al. & [133] & 2-PSS-(2-PRR-PRR) & (1T2R) \(\times\) 2 & Gait & Passive \\
2019, [PERSON] et al. & [134] & E-2-PSS-(2-BRR-PRR) & (1T2R + T) \(\times\) 2 & Gait & Passive \\
2018, [PERSON] et al. & [135] & 3-PRR & (2T1R) \(\times\) 2 & Gait & Passive \\
2018, [PERSON] et al. & [136] & 2-PRR & (2T1R) \(\times\)2 & Gait & Passive \\
2017, [PERSON] et al. & [137] & P-3-UPS-PS & (1T3R + T) \(\times\) 2 & Gait & Passive \\
2016, [PERSON] et al. & [138] & 6-UCU ([PERSON]) & (3T3R) \(\times\) 2 & Gait & Passive \\
2016, [PERSON] et al. & [139] & 6-UPS ([PERSON]) & (3T3R) \(\times\) 2 & Gait & Passive \\
2015, [PERSON] & [140] & 6-UPS ([PERSON]) & (3T3R) \(\times\) 2 & Gait & Passive \\
2013, [PERSON] et al. & [141] & E-6-UCU ([PERSON]) & (3T3R + T) \(\times\) 2 & Gait & Passive \\
2010, [PERSON] et al. & [142] & P-(PR-PRP) & (1T1R + T) \(\times\) 2 & Gait & Hybrid \\
2006, [PERSON] et al. & [143] & 3-RRR + (PSPP + PRP) & (2T1R + 1T2R) \(\times\) 2 & Gait & Hybrid \\
2004, [PERSON] et al. & [144] & 6-UCU (Stewart) & (3T3R) \(\times\) 2 & Gait & Passive \\
2003, [PERSON] et al. & [145] & 3-RRR + (2-RR-2-RP) & (2T1R + 1T3R) \(\times\) 2+ R & Gait & Passive \\
2003, [PERSON] et al. & [146] & 2-RRR & (2T) \(\times\) 2 & Gait & Passive \\
2000, [PERSON] et al. & [147] & R-(3-UCU-PPP)-R & (2T2R) \(\times\) 2 & Gait & Active \\
2019, [PERSON] et al. & [148] & E-6-UCU (Stewart) & 3T3R + R & Both & Passive \\
2023\_[PERSON] et al. & [149] & 3-PRS & 1T2R & Balance & Passive \\
2023, [PERSON] et al. & [150] & 3-RPS & 1T2R & Balance & Hybrid \\
2022, [PERSON] et al. & [151] & 4-RCU/U & 2R & Balance & Passive \\
2021, [PERSON] et al. & [152] & 2-RSSU & 2R & Balance & Hybrid \\
2020, [PERSON] et al. & [153] & 2-RSS/U & 2R & Balance & Passive \\
2011, [PERSON] et al. & [154] & 3-PSS/S & 3R & Balance & Passive \\ \hline \hline \end{tabular}  
* Topology column represents the nature of the parallel kinematic manipulator’s chains, where P, R, S, U, and C stand for prismatic, revolute, spherical, universal, and cylindrical joints, respectively. Underlined letters indicate the actuated kinematic joints. R\({}_{\text{P}}\) stands for a shared revolute joint in a pantograph. DOFs column indicates the number and type of each degree of freedom: translation (T) and rotation (R).  
\end{table} 
Table 2: PKM-driven end effectors for gait and balance rehabilitation. consists of two 6-UCU platforms [144], whereas the one proposed by [PERSON] et al. consists of two 6-UPS platforms [140].