148 



KINEMATICS. 



[269. 



269. Peaucellier's cell is another inversor (Fig. 67). It con- 

 sists of the linked rhombus A B A' B ! whose side we denote by 

 a, and the two equal links OB, OB' of length b. If O be fixed, 

 A and A' evidently describe inverse curves for O as pole. 



Fig. 67. 



The practical application of inversors is based on the property 

 that they enable us to transform circular motion into rectilinear 

 motion (see Art. 271). 



The inverse of a circle r=2c cos# passing through the pole 

 is a straight line ; for we have for the radius vector / of the 

 inverse curve r 1 = K 2 /r= K?/2 c cos 6 ; hence /cos = K 2 /2 c which 

 is the equation of a straight line at right angles to the polar 

 axis, at the distance /c 2 / 2 c from the pole. 



If therefore the point A of an inversor be made to describe 

 an arc of a circle passing through O, the point A' will describe 

 a segment of a straight line. The vertex A (Fig. 67) can beji 

 compelled to describe a circle by inserting the additional link; 

 O'A turning about the fixed point O'. If O' be selected so as 

 to make O'O = O f A, say = , the circle described by A will pass 

 through O\ and the motion of A' will be confined to the 

 straight line A'D perpendicular to OO f , at the distanc^ 

 OD = (t> 2 -a 2 )/2cfrom O. 



The linkage has thus become a linkwork, OO' being the fixed 

 link. 



