This section is from the book "Handy Man's Workshop And Laboratory", by A. Russell Bond. Also available from Amazon: Handy Man's Workshop And Laboratory.
Most universal joints on the market have at least a dozen different parts. One which has a big sale at present has no fewer than seventeen distinct parts, not including the shafts or feather keys for adjustment.
The universal joint illustrated in Fig. 90, which was designed on account of the high price asked by some of the standard makers, and which has given every satisfaction for the rough purpose fur which it was intended, has but two jaws, two pins, and one washer or distance piece, shown in plan and elevation on the right.
It will be noticed, however, that this design is imperfect, in that the two pins, which cross each other at right angles, are not in the same plane. To improve upon this, and also to reduce still more the number of parts, the writer designed a joint as shown in Fig. 91. A model was made and so far it seemed successful.

Fig. 90 - A two-pin universal joint.

Fig. 91 - Universal joint with round pin and slot.
The model was shown to a well-known engineer, who, while commending the idea of reducing the number of parts, pointed out the bad feature of the design, in having a round pin wearing on a Hat surface.

Fig. 92 - The square pin universal joint.
The writer tried to rectify this by having a square slotted hole instead of a round one, and a square shaft or pin with a round hole through, for the main pin. This he found would require so much fitting that the cost would bring it up to the standard price.
In Fig. 92 a design is shown which has not been put to a practical test, but is open to criticism. The slotted round hole shown in Fig. 92 has been changed to a slotted square hole.
One end of the pin is the same in diameter as the diagonal of the square body. The other end of the pin is the same in diameter as the side of the square.
There is no reason, however, why the square body of the pin could not be continued to the end. and fitted into a collar or bushing, the inside hole of which is a square tight fit, and the outside a loose round fit, to enable it to revolve as the other end of the pin.
 
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