1. The problem is to develop a healthcare telepresence robot with specific design requirements including mobility, safety, autonomy, and integration with hospital systems. 2. The design process involves defining Product Design Specifications (PDS) such as speed, payload, power, autonomy, connectivity, safety, materials, environment, cost, and compliance. 3. Concept generation uses function analysis and morphological charts to explore options for locomotion, sensing, navigation, HMI, payload, power, structure, safety, connectivity, and cybersecurity. 4. Concept selection is done by screening and scoring based on weighted criteria: Safety (0.20), Maneuverability (0.15), Runtime (0.10), HMI (0.10), Cybersecurity (0.15), Integration (0.10), Cost (0.10), Modularity (0.10). 5. Concept A is selected as the best design due to its clinical safety, maneuverability, runtime, and cybersecurity features. 6. Embodiment design includes modular architecture with base, tower, sensor, and payload modules; materials like antimicrobial PC-ABS and aluminum; and machine elements such as BLDC motors, planetary gears, bearings, and battery packs. 7. Kinematics of the differential-drive robot are modeled by: $$\dot{x} = v \cos \phi, \quad \dot{y} = v \sin \phi, \quad \dot{\phi} = \omega = \frac{r}{L}(\omega_R - \omega_L)$$ where $v = \frac{r}{2}(\omega_R + \omega_L)$, $r$ is wheel radius, $L$ is track width, and $\omega_R$, $\omega_L$ are right and left wheel angular speeds. 8. Safety and reliability are ensured by FMEA, watchdog timers, mechanical locks, redundant emergency stops, and soft-limit zones. 9. Virtual prototyping includes 3D CAD modeling, animations for docking, drawer operation, and navigation. 10. The final design is ready for detailed engineering, FEA validation, and clinical testing. This summary covers the first and main problem of designing the telepresence robot as requested.