In this research, we explore the computational and experimental optimization of compliant constant-torque mechanisms (CTMs) fabricated via injection molding using polymeric materials. We investigate how geometric variations influence the torsional strength of CTMs through numerical simulation, experimental validation, and artificial neural network (ANN) modeling. Four different geometries with the same overall dimensions were designed and analyzed to quantify their mechanical performance. The results reveal that the geometric configuration significantly affected the torsional behavior of the CTMs, with circular cross-sections demonstrating superior strength. Moreover, the ANN model exhibited a high prediction accuracy and minimal relative errors, closely aligning with the experimental outcomes. Despite this, discrepancies between our numerical and experimental results suggest that further refinements in material modeling and manufacturing processes are warranted. In this paper, we emphasize the importance of integrating computational (CAE), artificial neural networks (ANNs) and experimental techniques for optimizing polymer-based CTMs. CAE simulations for Model 4 showed a constant-torque section from 23–44 degrees with 0.142 N·m torque, while experimental and ANN results indicated a longer range (20–45/46 degrees) with higher torque values (0.164 N·m). Experimental and ANN predictions for Model 4 showed an approximate 97% similarity. While these findings represent a foundational step, the characteristics of polymer CTMs suggest potential relevance for advancing applications in precision engineering, biomedical devices, and soft robotics, pending further application-specific validation.