John Oldham Describes His Gears and Toothed Wheels

Original Communications.

PART. I.  ON TOOTHED WHEELS.

To the Editor of the London Journal of Arts and Sciences.

SIR, I have latterly been engaged in putting up some wheel gearing that required great accuracy, so as to enable them to run as smooth as possible; and I consider that I have succeeded in so doing; the plan adopted, I believe possesses some originality, and I therefore send it to you for publication, if worth your notice. This ground is so well treated by various authorities I have read, that little is to be expected of novelty. I have tried various curves for the teeth of wheels, but find none to answer so well as the epicycloid. The Technical Repository, published 1822, (Vol. I.) contains some very valuable information on this subject.

VOL. VIII.-SECOND SERIES.                          Original Communications.                                                  Page     34

In the wheels made for me on a late occasion, there was no allowance for clearance. The cogs and spaces being equal, except at the tops and bottoms of the teeth, and only so much that light was barely visible; in a very few revolutions the wheels run as smooth almost as belt or band. To milan

To obtain truth, and with but little trouble of calculating for odd members required, I availed myself of the following geometrical construction, for finding the circumference of a circle from its diameter, and which will be found to contain no error beyond 00000,1, of the latter to the former, and that I consider never could be discovered in workmanship of the most exquisite finish.

Take the diameter of any wheel or circle with com- passes and step it from A, to B, and to D, (see the diagram in Plate III, at figure 17), on a horizontal or base line, upon which raise a perpendicular, and again step upon it the same distance from A, to M, N, K; again scribe, and intersect the arcs made from B, D, meeting in E; from E, and D, do the same, with the same distance, meeting in cross arcs at F; upon D, raise a line parallel to A, K, intersecting the line B, F, in c, and upon this describe the circle G, H, O, P,-C, K, will be the circumference of a circle, of which G, c, is the diameter: the error being something less than one hundred-thousandth part of the distance G, c. It follows therefore, that if c, be the centre or joint of a sector, a proportional com- pass or callipers, the opening of either will express or point out the circumference and diameter of whatever circle or wheel may be required at one and the same time.

If it be required to have an odd number of teeth in a wheel, say 67, one inch pitch, for tooth and space, lay off a straight line equal to 67X2-134 divisions, stretch the sector to this line K, L, and it will be the diameter-o, P,

On improved Castors.  35

of the proportional compasses or callipers, will be the same of course. all vol botafusins How If it be required to cut a wheel from a solid blank circle of metal, to have, say 43 teeth of inch pitch, and that the proportion of teeth be also given as to the thickness and height, each shall have, viz. 4-5ths or 3-4ths of its height to be the thickness, reduce either proportions to a decimal, and divide this decimal into 3,1416,-the quotient resulting therefrom will be the number of spaces to be added to the line K, L, for the tops of teeth, or deducted therefrom for the circle that bounds the bottoms of the teeth; polygons of prime numbers may readily be found out by this means. You will observe the compass to be used with this geometrical problem is never to be altered from first to last in forming its construction.

I think if this subject had the attention of some of the mathematical instrument makers directed to it, something practically useful to wheel makers might result.

I remain, yours very truly,

                           JOHN OLDHAM.                         Bank of Ireland, Dublin.                

P. S.-I know not whether you may consider there is any material novelty in the construction of the castor described here by sketch. I had several sizes made for myself and others, for sofas, beds, and tables, which have performed much better than any I have yet seen. The spindle A, is a fixture in the boot socket c, and rests upon its point in The friction by this arrangement is spindle socket B. considerably reduced.

PLATE  III

• Gibs's Boiler
• Ferrabees Dressing Machine
• Charlesworth's & Mellors Gig Mill
• Profsers Imp. Tacks
• Oldham on Toothed Wheels