In a numerical control $$(NC)$$ machine positioning system, the measures of precision are expressed by considering a single axis as shown in the Figure.

If $$\sigma $$ is standard deviation of the error distribution, the $$L$$, $$M$$ and $$N$$ are

A single axis $$CNC$$ table is driven by a $$DC$$ servo motor that is directly coupled to a lead screw of $$5$$ $$mm$$ pitch. The circular encoder attached to the lead screw generates $$1000$$ voltage pulses per revolution of the lead screw. The table moves at a constant speed of $$6$$ $$m/min.$$ The corresponding frequency (in $$kHz$$) of the voltage pulses generated by the circular encoder is __________________.

In a Flexible manufacturing system, the Automated Guided Vehicles $$(AGV)$$ move at a speed of $$50$$ $$m/min,$$ cover an average distance of $$150$$ $$m$$ to deliver and $$100$$ $$m$$ for return. If the time required for pick-up and drop is $$30$$ $$s$$ each, neglecting idle times, then the number of $$AGV$$$$s$$ required to meet the demand of $$50$$ delivers per hour is ____________.

Match the linear transformation matrices listed in the first column to their interpretations in the second column.