A gear with $$84$$ teeth is to be machined using a milling process with indexing. The index plate has the following four hole circles: $$36,38, 42., 48.$$ The change gear ratio required is

A cup is to be drawn to a diameter of $$70mm$$ with $$35mm$$ depth from a $$0.5mm$$ thick sheet metal. The cup is drawn in one operation. Assume $${\sigma _u} = 430\,\,MPa.$$

The maximum drawing force is

A cup is to be drawn to a diameter of $$70mm$$ with $$35mm$$ depth from a $$0.5mm$$ thick sheet metal. The cup is drawn in one operation. Assume $${\sigma _u} = 430\,\,MPa.$$

The required blank diameter is

It is required to punch a hole of diameter $$10mm$$ on a sheet of thickness $$3mm.$$ The shear strength of the work material is $$420MPa.$$ The required punch force is