To choose the appropriate width for the aluminum extrusions that will make up the frame, an FEA analysis was conducted on the worst-case load scenario. Based on the chosen design, the worst-case scenario would be where the end effector is at the center of the member that is driving the y-axis movement. This member is experiencing the highest load as it is the longest, which will increase the torque arm in the calculations of the torque generated by the weight of the end effector when it is at the center. In addition, the only other members with a load applied in the middle of it are the two members driving the x-axis movement. However, given that the load will be supported on both sides, each member will experience half of the actual load.

Hence, the load scenario where the end effector is at the center of the y-axis member was simulated using varying widths for the aluminum extrusions. The lengths of the members were kept the same for consistency. The material used in the simulation was 6061 aluminum to match the actual material of the extrusions used closely. As the end effector mechanism hadn’t been fully designed at this point, the mass was assumed to be 2 kg. So, with a conservative safety factor of 3.75, a load of 75 N (approximately equivalent to 7.5 kg) was applied. The two ends of the members were fixed to the connecting supporting beams. The following figures show the results of the simulation.

20x20 mm aluminum extrusion, 75 N load, 1.073 mm deflection, mass of 1.7 kg

30x30 mm aluminum extrusion, 75 N load, 0.3012 mm deflection, mass of 2.87 kg

1”x1” (25.4x25.4 mm) aluminum extrusion, 75 N load, 0.439 mm deflection, mass of 2.44 kg

1.5”x1.5” (38.1x38.1 mm) aluminum extrusion, 75 N load, 0.1317 mm deflection, mass of 5 kg

The 1.5” x 1.5” aluminum extrusion has the best results in terms of resisting deflection, but it is also the heaviest (and most expensive) option. The deflection of 1 mm form the 20 mm x 20 mm extrusion was deemed acceptable for our purposes. After the full CAD had been designed, it was found that the z-axis mechanism weighed less than a kilogram, meaning that the simulation had a safety factor of over 7, making the 1 mm deflection even less of a concern. Since the 20 mm x 20 mm extrusion also had the lightest mass, this was chosen to be used on the robot.