Chap. XI.

MECHANICS.

989

Fig. 1453.

¥

Tl

b -

h ^

jiiuiir.

m

-

9 "

i

e

Fig. 1459.

Let an, be be a system of toothed wheels, whose dia-meters are in the ratio of the numbers 2 I, 2 4. Leta'V be a rule, whose extremity a is successively fixed at thepoints 0, 1, and 2 of the wheel a, and subject at the same timeto touch one of the points ac of the wheel «, and 0 and 1 ofthe line b. These points being placed in such a manner thatthey may be found in the same direction in one position ofthe system, each point of the rule a'b' will draw one curve inspace, and another on the surfaces of revolution, which arebelow it.

To draw a cylindrical spiral in space, or what is the samething, to draw’ the helix of a screw’, at is a fixed axle towhich is attached the cylinder c, on the surface ofwhich a helix is to be drawn, and the toothed wheel d.mlkn is a frame turning round the axle ab in its branches;

Imkn is an axle fy, which revolves on its own axis, and isfurnished with a toothed wheel e , which engages d, and acylinder, hi, cut into a screw with the nut p, which at oneend carries the rod op, whose extremity o enters a vertical g,going from one side to the other of the frame, and the othercarries a pencil or tool.

Let a be the radius of the wheel e; b the radius of the wheel d, and d the thread of thescrew’ on the surface of the cylinder hi; if we make the frame Imkn perform a revolutionround the axis ab, the wheel e , and consequently the cylinder hi will have made a portion

of a revolution — round their axes, anda

the tool will have gone over a space

equal to which will be the threada

of the screw, drawn on the cylinder c.

To this quantity any value may begiven, by changing the ratio of a to b,or that of d, by the substitution ofanother guide h i.

fy is the cylinder which directs therectilinear motion, and communicatesit to the tool, by means of its nut p. Itturns on its axle, and its position is de-termined by the collars h and i; e is atoothed wheel fixed to the directing

cylinder, c the cylinder required to be cut into a screw; it ismounted on a lathe, and furnished with a toothed wheel d;the two cylinders c and/V? should be placed in such a mannerthat their axes are quite parallel : a is a third wheel, whichserves as an intermediary to engage two wheels d and e ; itmay be elevated and balanced in order to suit itself to all thechanges which circumstances may require in the wheel d tochange the ratio of the radii d and e. If the proportion is sogreat that the invariable space of the machine between thedistance of the axes of the two cylinders does not permit usto obtain it by the two wheels d and e, and that it is not possibleto change the directing cylinder, we may avoid this difficultyby substituting for the wheel a another wheel and pinion.

We may substitute for the direction screw a rack whoserectilinear motion may be engendered by that of the cylinderwhich we wish to cut into a screw ; the result will be the same,but perhaps the machine does not combine the same advan-tages as that just described.

A small machine for drawing an ellipsis. A circularplate of wood a, and of a greater or less diameter, has itssurface ploughed by two grooves m, n; in these grooves moveeasily two pieces b and C; in the middle of each of thesepieces a small cylinder or point rises; these points enter cir-cular orifices pierced in the rule bd, one at its extremity b,the other at a greater or less distance from it; we place thepencil at any point of the rule cd, and turn it round its two

Fig. 1460.

Fig. 1461.

Fig. 1462.