# Design and Implementation of Adam: A Humanoid Robotic Head with Social Interaction Capabilities
## 3 Mechanical Design and Implementation
### Kinematics and Stress Analysis  
As shown above, three independent mechanisms control the head movement: the eye mechanism, the jaw mechanism, and the neck mechanism, all of which are adaptations of a four-bar linkage. The head weighs 1.05 kg and is solely supported by the neck and, hence, is the most crucial structural component. This section provides the kinematic and structural analysis of the neck mechanism.  
The pitching motion is driven by two synchronized servo motors actuating a set of parallel four-bar linkages with identical input, but moving in the opposite direction.  
Figure 7 shows a simplified kinematic diagram of the linkages; O4B is the crank, which is actuated by the servo motor, AB is the coupler link, and O2A is the output link, which is a part of the internal frame of the head. The rotation of the output link results in the pitching motion of the head. The folded-in configuration of the crank-coupler is selected as it delivers a good overall transmission angle and keeps the neck compact. A kinematic motion study is performed using the SolidWorks motion analysis package by simulating the crank rotation for one complete cycle of operation. The transmission angle is the angle between the coupler and the rocker and it is an important parameter indicating the efficiency of force transfer between the links. The motion analysis results show that the transmission angle varies from 47\({}^{\circ}\) to 95\({}^{\circ}\), as shown in Figure 8, ensuring an efficient and smooth motion.  
The head's center of mass is offset from the neck pivot by a radial distance of 70 mm and can create unbalanced forces of varying magnitudes depending on the angle of the head. This off-balance mass also results in inertial forces, especially when there is a sudden change in direction as in a nodding motion. A dynamic force analysis is, hence, found suitable for capturing the internal forces in the system. The nodding motion is simulated in SolidWorks by applying two virtual motors as the servomotor with a pitching angle of 60\({}^{\circ}\) to match the range of motion of the actual robot. These motors are then set to oscillate at  
Figure 5: Neck movement mechanisms; 3D design.  
Figure 6: (**i,ii**) Pitch and (**iii,iv**) yaw movements.  
1 Hz around the horizontal plane to simulate the nodding motion. The results show a peak motor torque of 325 N-mm (see Figure 9). This occurs when the head changes direction from a downward to an upward motion. At this position, the center of gravity of the head is furthest from the neck pivot, which creates a high unbalanced force. The structural analysis presented in the following section is performed in this critical position with the highest internal forces. The two notches observed in the chart around 0.2 s and 0.8 s correspond to the position where the head is perfectly upright and the center of mass is vertically above the neck pivot. At this position, the head is perfectly balanced and, hence, very little motor torque is required to support the head.  
Stress analysis performed on the important load-bearing members of the neck is depicted in Figure 10. The dynamic forces applied to each of the members are obtained directly from the SolidWorks motion study. These are applied as remote loads in the  
Figure 8: Transmission angle.  
Figure 7: (**a**) Side view of the neck pitching mechanism with the kinematic chain highlighted in orange; (**b**) kinematic diagram of the pitching mechanism showing the transmission angle \(\gamma\).  
Figure 9: Motor torque for pitching.  
simulation and are shown in the figure using pink lines; the region of maximum stress is highlighted and the corresponding values are displayed.  
All the analyzed critical components show stresses below the yield strength and the corresponding values are recorded in Table 2.