On a pizza delivery car with a rectangular signboard on its roof, how should the signboard be aligned, parallel to the direction of the car or perpendicular?
It should be aligned parallel because in this case a thin film boundary layer is formed along the signboard. But the drag force imparted the the vehicle due to this thin film is very small compared to the resistance force that occurs when the wind is hitting the board perpendicularly. Hence a monetary savings of around 40% can be achieved by aligning the signboard properly after the calculations.
What happens when a robotic manipulator's "gets stuck" in an orientation. How is this related to a Gimbal Lock?
When the robot reaches a 'singularity configuration', it loses a degree of freedom as the torque required at this configuration is infinite. It generally happens when the outermost link is completely outstretched. A gimbal lock is also an example of losing one degree of freedom in particular configuration in three gimbal mechanism. This happens when two of the three gimbals are in a parallel configuration. Great care is taken to avoid singularity configurations as the undesirable loss of DOF causes severe loss of dexterity.
Which casting method is employed in making complicated difficult to machine shapes which require a very high amount of precision and why?
Investment or Lost Wax casting method is used as practically any shape can be cast using this method. The defects in this type of casting is vary less and a extremely high amount of precision can be obtained. The only con is that it is an expensive process and the rate of production is relatively slow.