190 



REMARKS UPON THE TEETH OR COGS OF WHEELS. 



The parts of the teeth that are in con- 

 tact respectively, when in operation, I 

 name the faces or acting sides of the 

 teeth. 



The parts that join the base, end, and 

 faces, I call the edqes of the teeth. 



The concentric convex circle at the 

 base of the spur-cogs, I call the periphery 

 or circumference of the wheel. 



The straio;ht lines meeting the peri- 

 phery and the centre, are named rudii. 



The straight lines that intersect the 

 periphery and radii, and at right angels 

 to the latter, are called tangents. 



A curve where all the radii are so ma- 

 ny tangents to a circle developed, and are 

 also all respectively perpendicular to the 

 several points of the curve described, 

 (which has for its greatest radius a line 

 equal to the periphery of the circle evolv- 

 ed,) is named an involute. 



The diameter of the wheel is a straight 

 line passing through the centre of the 

 wheel from the peripher}' on opposite 

 sides of the centre, or axis. 



The interior surface of the wheel is 

 called the concave surface. 



Where the acting faces of the teeth 

 extend beyond a straight line from the 

 base to the end of the tooth, they are 

 called convex faces. And where the 

 parts between the base and end do not 

 extend so far as to meet a straight line, 

 the term concave face is used. 



Where the ends of all the teeth of a 

 wheel are equidistant from the centre, 

 and where the base of each, is connected 

 with the periphery of a cylinder, it is 

 called a spur-wtieel. When the base of 

 the teeth are connected with the frustum 

 of a cone it is called a bevil-wheel, and 

 when the cone, from the base to the apex 

 is at an angle of forty-five degrees from 

 the centre it is called a mitre-iv/ieel. 



When the base and end of each tooth 

 is equidistant from the centre or axle of 

 the wheel, it is denominated a face- 

 ivheel. 



Where all parts of the teeth are in 

 straight lines, and are intended to move 

 in that direction to and fro, the term rack 

 is given. When the motion is intended 

 to be to and fro. and not in straight lines, 

 I use the term circular rack. 



The circle upon which the divisions 



between the respective teeth, and the 

 spaces between them, are laid off, is call- 

 ed the pitcfi circle or line, and the points 

 thus laid off for the respective acting 

 faces of the teeth is called the pitch of 

 the wheel. 



Now let us suppose a wheel or pattern 

 on which we wish to form teeth for a 

 spur-wheel: the periphery of the wheel 

 and the part for the ends of the cogs be- 

 ing concenti'ic, and the former extending 

 the fourth of an inch beyond the parts 

 which are to form the edges of the teeth, 

 so that a wire or string can be wound or 

 wrapped round the periphery at the base 

 of the teeth. The parts for the edges of 

 the teeth, also, dressed to perfect planes 

 at riglit angles to the axle of the wheel.. 

 The planes thus prepared, are to be 

 covered with varnish, or otherwise pre- 

 pared to receive a fine true mark or scribe 

 with a pointed instrument, as hereafter 

 described. 



1. Prepare an extremely fine wire, 

 the length of which should be a little 

 more than the circumference of the 

 wheel with the thickness of one tooth at 

 the base added: paint the wire of a light 

 color, and let it become dry, — reduce the 

 heads of two small needles, each to a 

 point as near the eye as possible consis- 

 tent with the necessary strength, when 

 they are used as scribes, to trace lines 

 on the edges of the teeth; pass a needle 

 upon each end of the wire and confine 

 them upon it at a distance asunder, equal 

 to the thickness of a tooth at the base, 

 added to tlie circumference of the wheel: 

 by riveting the ends or in any other con- 

 venient manner. Decide upon the thick- 

 ness of each tooth and space between 

 each respectively at the base, and mark 

 with black ink the divisions on the wire, 

 ^vith a fine pen, (this should be done 

 with perfect uniformity if possible.) 

 Then wrap the wire round the circumfe- 

 rence of the wheel, and let the needles 

 pass each other equal to the thickness of 

 a tooth; confine one of them by sticking 

 the point into the wood, (at the angle 

 between the wheel and tooth.) parallel 

 with the axis of the wheel; then with the 

 point of the other needle, while the needle 

 itself is kept parallel with the axis of the 

 wheel, trace a line from the base of the 



