# Experimental Investigation of Free-Motion Task Implementation on a Serial Metamorphic Manipulator
## 4 Experimental Case Study
### Dynamic Performance Evaluation  
#### 4.4.1 Optimizing Joint Torque to Velocity Output  
The initial segment of the performance analysis was focused on comprehending the overall dynamic performance and efficiency. This involved comparing the supplied joint torques with the resultant joint velocities. The norms of the joint torques and velocities were normalized given the maximum value achieved along the path waypoints and were plotted in the same chart for each of the executed tasks. Figure 11 presents the notable correlation between joint velocities and joint torques. It is observed that larger joint velocities were achieved with smaller joint torques in these optimal performance segments, where the LCI achieved its higher values. Larger values of the LCI reflect higher joint velocities with lower effort. Moreover, the variation in the LCI accurately tracked the changing relation, providing a valuable tool for the offline identification of efficient operating conditions. In Figure 12, the normalized DCI values are presented to compare the index's capability in providing accurate information about the task implementation on the real robot. The DCI only considered the conditioning of the GIM, with no further investigation on robot configuration and task space characteristics. During the time span of \([1.75,6][\mathrm{s}]\), the DCI presented its peak values, suggesting that the robot was closer to an isotropic configuration. However, this information did not offer any useful insights into the overall robot effort and its maximum torque. In contrast, the LCI within the same time span clearly indicated a higher robot effort to achieve the desired joint velocities. For a comprehensive performance analysis during task execution, it is crucial to consider not only the inertia properties of the robot in joint space but also their relationship to the operational space. This approach yields more accurate and relevant information. In Figure 13, two distinct anatomies were compared during the execution of the same circular path, with key numerical results presented in Table 2. Task path 19 corresponded to the LCI-optimized anatomy (ID: 2), while task path 25 was executed with the robot configured in its reference anatomy (ID: 0). Both anatomies exhibited the previously identified behavior, where higher torque peaks were associated with lower LCI values. The LCI-optimized anatomy (ID: 2) demonstrated relatively consistent index values with minor fluctuations, highlighting the effectiveness of the optimization process. The optimized anatomy achieved a substantial reduction in maximum torques produced, maintaining lower torque values for 74% of the task execution time compared to the reference anatomy. Both anatomies demonstrated comparable median velocity norms (0.27 [rad/s] for the optimized anatomy and 0.29 [rad/s] for the reference anatomy). However, the optimized anatomy performed the task with a median torque norm of 2.86 Nm, representing a 41% reduction relative to the 4.86 Nm observed for the reference anatomy. Furthermore, the  
Figure 11: Joint torque to velocity output evaluation for optimized EMI CP anatomy (ID: 1). joint's torque-to-velocity ratio improved by 35%, decreasing from 16.84 to 10.81. This improvement signified a marked enhancement in task execution efficiency through the reduction in the torque-to-velocity ratio. In Figure 13, the most significant difference in the LCI score was observed between the two anatomies during the time interval of approximately \([8,14][\text{s}]\). Within that period, the optimized anatomy demonstrated a substantial reduction in joint effort. Conversely, during the time interval \([1,5.8][\text{s}]\), the reference anatomy exhibited a slightly higher LCI score, with a correspondingly higher torque-to-velocity ratio. This observation indicates that anatomy optimization may result in task segments where suboptimal performance is observed.