For machining a rectangular island represented by coordinates
$$P(0,0), Q(100,0), R(100,50)$$ and $$S(0,50)$$ on a casting using $$CNC$$ milling machine, an end mill with a diameter of $$16$$ $$mm$$ is used. The trajectory of the cutter center to machine the island $$PQRS$$ is

A robot arm $$PQ$$ with end coordinates $$P(0,0)$$ and $$Q(2,5)$$ rotates counter clockwise about $$P$$ in the $$XY$$ plane by $${90^ \circ }$$. The new coordinate pair of the end point $$Q$$ is

A $$CNC$$ vertical milling machine has to cut a straight slot of $$10$$ $$mm$$ width and $$2$$ $$mm$$ depth by a cutter of $$10$$ $$mm$$ diameter between points $$(0, 0)$$ and $$(100, 100)$$ on the $$XY$$ plane (dimensions in $$mm$$). The feed rate used for milling is $$50$$ $$mm/min.$$ Milling time for the slot (in seconds) is

For generating coon's surface we require