## 7 Conclusions  
Hand\(-\)tracking systems are widely adopted as control interfaces for telemanipulating ARHs. The human thumb is the most complex digit of the hand due to the CMC joint, which plays a significant role in grasping. As such, tracking the CMC joint is critical for  
Figure 11: Time\(-\)lapse images of Volunteer 1 thumb poses followed by the thumb of the ARH to grasp a cylinder.  
Figure 12: Trajectories of the evaluated robot thumb joint angles to grasp a cylinder based on the thumb motion of Volunteer 1 captured by the thumb tracking device and the flex glove.  
Figure 10: Telemanipulation of the ARH by Volunteer 1. (**a,b**) CMC joint pure flexion and extension poses. (**c,d**) Thumb opposition with index and middle fingers. (**e**–**h**) Grasps for different objects (cylinder, cuboid, marker, and sphere) using the developed system.  
the telemanipulation of fully actuated four\(-\)DOF ARH thumbs to grasp and manipulate objects. Existing hand\(-\)tracking systems either fail to track the CMC joint motion or rely on expensive hardware and setups. The developed CMC joint thumb tracking device is inexpensive, affordable, 3D\(-\)printable, and personalizable to different thumb sizes. The tracked human thumb motion requires suitable mapping to telemanipulate a robot thumb with kinematic differences. Accordingly, a hybrid mapping approach, utilizing the RPA for CMC joint mapping, has been proposed and implemented within the framework. Based on the device operation and personalization tests, the CMC tracking device demonstrated its ability to be personalized and calibrated to volunteers with different thumb dimensions and captured the FE and AA motions of their CMC joint. During thumb cirucumduction, it was observed that the RPA mapped the CMC joint motion of \(H_{\textit{Cmc}}\) to the entire \(R_{\textit{Cmc}}\) range of motion. The ability of the proposed framework to integrate system components to telemanipulate the ARH was confirmed during the framework verification test. This test also demonstrated the ability of the tracking device to be used along with the flex glove to telemanipulate the whole ARH and grasp objects. The results from the evaluations of the tracking device, mapping algorithm, and telemanipulation framework provide confidence to expand and employ this system as a research platform to investigate HRI in assistive, manufacturing, or other applicable domains. The CMC tracking device with the flex glove can be a valuable tool to teach and train robotic hands, both in a physical or virtual environment, to effectively and reliably grasp objects of regular or irregular shapes or evaluate grasping performance.  
Conceptualization, P.S.S. and A.H.A.R.; methodology, P.S.S. and A.H.A.R.; software, A.H.A.R.; formal analysis, P.S.S. and A.H.A.R.; investigation, P.S.S. and A.H.A.R.; resources, P.S.S.; writing\(-\)original draft preparation, A.H.A.R.; writing\(-\)review and editing, P.S.S.; visualization, A.H.A.R.; supervision, P.S.S.; project administration, P.S.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The data presented in this study is contained within the article.  
The authors would like to thank the two volunteers who participated in the evaluation of the proposed tracking device and framework on their own accord and without any compensation. The authors would also like the anonymous reviewers whose comments improved the paper from its original form.  
The authors declare no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} ARH & Anthropomorphic Robotic Hand \\ CMC & Carpometacarpal Joint \\ MCP & Metacarpophalangeal Joint \\ IP & Interphalangeal Joint \\ AA & Abduction/Adduction \\ FE & Flexion/Extension \\ DOF & Degree(s) of Freedom \\ RPA & Radial Projection Algorithm \\ \end{tabular}