Some Link Motions — How to Draw a Straight Line 33 



are the same, therefore the distances of OP and O'C from DE are 

 the same, and OCPO' lie in the same straight line. That the product 

 OC.OP is constant is evident at once when we see that ODC is half 

 a "spear-head" and OAP half a "kite"; in like manner it may be 

 shown that O'P.O'C is constant, as also OC.CO' and OP.PO'. Em- 

 ploying then the Hart cell, with the extra link as we employed Peau- 

 cellier's, we get a five-link straight line motion. 



From the diagrams, it will readily be inferred that models of 

 these linkages may be constructed without much difficulty. Pins for 

 fixed pivots, strips of cardboard for links, string for the other pivots, 

 and a drawing board or other smooth surface for a fixed base, are 

 all we require. More durable links may be made of tin plate, or 

 thin strips of wood, with some suitable form of pivot. And thus 

 we can get our results visibly before us. 



There are other special forms for converting circular into recti- 

 linear motion — forms which involve "kites" and "spear-heads" ar- 

 ranged in a variety of ways. As special cases of one of these forms, 

 first shown by Mr. Kempe, we have the ordinary pantograph used 

 for enlarging or reducing any sort of plane figure, and the plagio- 

 graph (or skew pantograph) discovered by the celebrated mathe- 

 matician Sylvester, which not only enlarges the drawing but turns 

 it through an angle. 



Similar apparatus are used for drawing various curves, but a de- 

 scription of these is beyond the scope of this paper. For instance, 

 if in any of the forms of apparatus that I have described, instead 

 of making the extra link (the link which compels a pivot to move 

 in a circle) equal in length to the distance of its fixed end from the 

 fixed end of the cell, we make it longer or shorter, the point P will 

 describe, not a straight line, but a circle. This gives us an accurate 

 and elegant method of describing a circle of very large radius with- 

 out using its center. Again, there are linkages that enable not 

 only a single point but a whole piece to move in a straight line. 

 There are numerous instances in machinery where it is important 

 that this be done; for example, the slide rests in lathes, punches, 

 drills, draw-bridges, etc. The mathematician has discovered such 

 link-motions, and the mechanic has not been slow to make use of 

 these principles, often in a very elegant manner. 



For information on the subject of linkages, I would refer to 

 Kempe's "How to Draw a Straight Line", published by the MacMil- 

 lan Co. in London, 1877, but out of print; to articles by Hart and 



