IMO 1962 Problem 3

Consider the cube $ABCDA'B'C'D'$ ( $ABCD$ and $A'B'C'D'$ are the upper and lower bases, repsectively, and edges $AA', BB', CC', DD'$ are parallel). The point $X$ moves at a constant speed along the perimeter of the square $ABCD$ in the direction $ABCDA$ , and the point $Y$ moves at the same rate along the perimiter of the square $B'C'CB$ in the direction $B'C'CBB'$ . Points $X$ and $Y$ begin their motion at the same instant from the starting positions $A$ and $B'$ , respectively. Determine and draw the locus of the midpionts of the segments $XY$ .