Full text: The collected mathematical papers of Arthur Cayley, Sc.D., F.R.S., late sadlerian professor of pure mathematics in the University of Cambridge (Vol. 8)

210 
ON A BICYCLIC CHUCK. 
[513 
and it includes also the remaining two sides (11) of the handle-frame, and, let into 
the same so as to be flush therewith on the upper surface, two slips (12) completing, 
in this plane, the handle-frame. 
We have thus on a level the sides (11), (12) of the handle-frame and the holes 
C, D, where C rotates about the point B, which is the centre of the block (3); and 
D rotates about the point A, which is the centre of the segments (4), each hole being 
capable of describing a complete circle; and the distances AB, BC, CD, and DA are 
(within limits) adjustable to any given values: the distance of the holes C, D is made 
equal to that of the two pegs next referred to. 
Connected herewith by means of cylindrical pegs working in the holes C, D 
respectively, we have a carrying-frame; viz. the fourth plane contains two sides (13) 
of this carrying-frame, and two moveable bars (14), attached to the remaining two 
sides (15) of the carrying-frame, and having on their lower surfaces the pegs which 
work in the holes C and D respectively—each bar being free to rotate about one 
extremity, and being clampable at the other extremity so as to allow the two pegs 
to be adjusted at a given distance from each other. And then in the fifth plane we 
have the remaining two sides (15) of the carrying-frame. 
Rigidly con nected with the carrying-frame we have the drawing-board ; or, to make 
the whole more complete, this should be adjustable to any given position in regard 
to the carrying-frame by giving it two sliding motions crosswise, and a rotating motion, 
in the manner of an eccentric chuck. 
To convert the apparatus into an oval chuck, we remove altogether the carrying- 
frame ; and in the third plane we fix to the sides (8) of the handle-frame two bars 
at right angles to these sides, by means of pegs on the lower surfaces of these bars 
fitting tightly into holes on the sides (8) (which holes and the ends of the bars are 
shown in the figure), in such wise that these bars include between them the piece 
(9), which is thereby kept in a direction at right angles to the sides (8), and thus 
slides between the two bars. There are thus in the handle-frame two lines at right 
angles to each other, which pass through the fixed points A and B respectively; so 
that, now connecting the drawing-board directly with the handle-frame, the apparatus 
has become an oval chuck, viz. the curve traced out on the drawing-board will be 
an ellipse. The drawing-board should be adjustable to any given position in regard to 
the handle-frame, in like manner as it was to any given position in regard to the 
carrying-frame ; it is easy to arrange as to this. 
It is hardly necessary to remark that the pencil should have two sliding motions 
crosswise, so as to allow it to be adjusted to any given position; and a small 
up-and-down motion, so that it may be loaded to press with the proper force upon 
the drawing-board. 
The variety of forms, even with a fixed adjustment of the chuck, only the position 
of the pencil being altered, is very considerable: among them we have bent ovals and 
pear-shapes, passing through cuspidal forms into bent figures-of-eight.
	        
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