By John Bryant
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Additional info for How Round Is Your Circle?: Where Engineering and Mathematics Meet
The top is exaggerated and the bottom uses the same horizontal and vertical scales. Whether you can perceive a diﬀerence between the bottom two lines will depend to a large extent on the quality of the printing used to create this page! There appears to be no connection between Chebyshev’s linkage and the arrangement of links shown in plate 2. 12. Chebyshev’s approximate straight line. we shall now show that the two arrangements produce identical curves, and we will show that the path of the second form can be calculated more easily and directly.
There are two possible approaches we could use. The ﬁrst is to saw out a slightly oversized piece and sand down to the outer edge of the lines. The second is to saw down the centres of the lines. Since we can only saw down the two diagonals along their centres it is this second method that is needed for all cuts, otherwise there will be noticeable changes in sizes between the parts where they meet. e. width of cut, is twice the thickness of veneer, available in handicraft shops, is ideal. Once all the sawn edges are covered with veneer the original shape will be restored, and they will consequently ﬁt together well in both conﬁgurations.
In very early beam engines, such as that shown, the steam in the cylinder condensed as the valve at E was opened to let in cold water. This created a vacuum in the cylinder and it was the force of atmospheric pressure that pushed the piston down. It was only later that the direct expansion of steam created the force which drove the piston. In any case, the piston rod is designed only to take axial loads, that is to say a push or pull. Its generally slender form is not designed to resist sideways loading forces and so it must HOW TO DRAW A STRAIGHT LINE 19 somehow be constrained to move in a straight line.