507] 
151 
507. 
ON THE MECHANICAL DESCRIPTION OF CERTAIN QUARTIC 
CURVES BY A MODIFIED OVAL CHUCK. 
[From the Proceedings of the London Mathematical Society, vol. iv. (1871—1873), 
pp. 186—190. Read December 12, 1872.] 
The geometrical principle of the oval chuck is the well-known one that if a 
plane move in such manner that two lines Ox, Oy, fixed in the plane and moveable 
with it, pass through two fixed points A, B, respectively, then any fixed point P traces 
out on the plane an ellipse. The point A is on the (geometrical) axis of the mandril; 
there is connected with the head a guide-ring moving horizontally; the point B is 
the centre of the guide-ring, this being a ring connected with the head, moveable 
horizontally at right angles to the axis in such wise that the distance AB of the 
two centres is adj ustable to any given value; the fixed point P is the tool, which 
practically is held on the level of the axis, that is, at a point in the line AB. The 
guide-ring remains fixed during the motion of the lathe. 
It occurred to me that a chuck applicable to ornamental turning might be con 
structed by giving to the guide-ring a reciprocating motion synchronous with the 
rotation of the mandril; viz. for this purpose it is only necessary to affix to the axis 
of the mandril an eccentric, working in a frame attached to the guide-ring so as to 
move the centre B of the guide-ring backwards and forwards along the line AB: 
the curve is thus that described by the fixed point P upon a plane moving in such 
manner that the lines Ox, Oy pass always through the points A, B respectively; the 
former of these being a fixed point, the latter of them a point moving according to 
determinate law backwards and forwards along a fixed line through A. 
The plan is carried out in a drawing apparatus which I have had constructed 
in wood, the axis being here vertical instead of horizontal, and the details of course 
different from what they would be for a lathe.