fig.1
fig.2a
fig.2b
fig.2c
fig.2d
fig.3a
fig.3b
fig.3c
fig.4
Mathematicians call a cone with the tip cut off a frustum. The following figures show how to make a six-sided (hexagonal) and an eight-sided (octagonal) twisted frustum for the conecrusher nutcracker. The choice of using the six- or eight-sided twisted frustum is up to the builder but currently it is assumed a six-sided inner frustum and an eight-sided outer frustum would be best. For smaller nuts just eight-sided frustums could be used. Perhaps 12-sides would be even better but I haven't tried making one.
Fig 1 shows a side view of a frustum with the top, bottom, side and height labelled T, B, S and H respectively. Figs 2a-d show the steps in getting the measurements for a hexagonal twisted frustum. First (see fig 2a) using a set of compasses draw a semicircle of diameter B, the bottom of the frustum and without changing the setting of the compasses mark off the distance from each bottom corner of the semicircle along the arc. Then (fig2b) draw a line joining the points to divide the semicircle into three equal segments. As shown in fig 2c draw another semicircle equal to the top of the cone T and draw lines from the centre of the semicircles through the points on the inner semicircle to cut the outer semicircle into three equal segments. Label the outer and inner segments P and Q as shown in fig 2d. Those are the measurements that will be used in making the twisted frustum. Figs 3a-c shows how to get the corresponding measurements for an eight-sided twisted frustum. Fig 3a shows drawing a semicircle of diameter B, the bottom of the frustum. Without changing the setting of the compasses small arcs are drawn crossing each other above the semicircle from the bottom corner and the top centre of the semicircles shown in fig 3b. A line is drawn between where the small arcs cross to the centre dividing the half arc in half, i.e. quarter arcs. Lines are draw from the top and bottom corners to where the line from the centre crosses the semicircle. These lines are quarter segments. Fig 3c shows the addition of a semicircle equal in diameter to the top of the frustum, T with the lines extended from the centre to cross this semicircle, and lines between the crossings being quarter segments. These lines, labelled P and Q are the lengths to use in the next step.
The six-sided twisted frustum is made of six flat panels joined along the edges, and the eight-sided twisted frustum is made of eight panels. The panels are using the P and Q measurements from the previous steps. Fig 4 shows how the panels are made. Two horizontal lines are drawn a distance S apart (the side of the frustum in Fig 1). The length of the top line is P and it is centered on the vertical line S (dashed in the diagram). The length of the bottom line is Q (dashed in the diagram) and it starts at the bottom end of S and extends to the left. The rightmost ends of P and Q are joined by a new line R. Another line of length R is drawn through the leftmost ends of P and Q. This line extends a bit below the leftmost end of Q. A final line joins the bottom ends of the two side lines, R. This odd shaped panel is used to make the twisted polygonal frustum. The last panel should be extended a bit on the left to have a tab for fasteners. Draw the correct number (six or eight) adjoining panels on the sheet of material for the frustum, cut out in one piece, bend along the edges, and fasten along the tab.
fig.1 | fig.2a | fig.2b |
fig.2c | fig.2d | fig.3a |
fig.3b | fig.3c | fig.4 |