A displacement sensor (a dial indicator) measures the lateral displacement of a mandrel on the taper hole inside a drill spindle. The mandrel axis is an extension of the drill spindle taper hole axis and the protruding portion of the mandrel surface is perfectly cylindrical. Measurement are recorded as $${R_x} = $$ maximum deflection minus minimum deflection, corresponding to sensor position at $$X$$, over one rotation.

If $${R_p} = {R_Q} > 0,$$ which one of the following would be consistent with the observation?

In the deep drawing of cups, blanks show a tendency to wrinkle up around the periphery (flange). The most likely cause and remedy of the phenomenon are respectively,

The figure shows an incomplete schematic of a conventional lathe to be used for cutting threads with different pitches. The speed gear box $${U_v}$$ is shown and the feed gear box $${U_s}$$ is to be placed. $$P,Q,R$$ and $$S$$ denote locations and have no other significance. Changes in $${U_v}$$ should $$NOT$$ affect the pitch of thread being cut and changes in $${U_s}$$ should NOT affect the cutting speed.

The correct connections and the correct placement of $${U_s}$$ are given below

Internal gear cutting operation can be performed by