144 KINEMATICS. [265. 



265. Parallelogram: 4 i =3 2 = a, 43 = i 2 = b (Fig. 61). The 

 link i 2 has evidently a motion of translation, its instantaneous 

 centre lying at the intersection of the parallel lines 41, 32. 



The space centrode is the line at infinity ; the body centrode 

 may be regarded as a circle of infinite radius described about 

 the midpoint of 3 4 as centre. 



Fig. 61. 



To find the equation of the path of any point P rigidly con- 

 nected with i 2, let x, y be the rectangular co-ordinates, with 

 respect to 4 as origin and 4 3 as axis of x> and x^ y^ its co-ordi- 

 nates for parallel axes through i ; then, putting ^ 3 4 i = 6, we 

 have 



hence, eliminating 0, 



which represents a circle of radius a whose centre has the fixed 

 co-ordinates x^ y v 



For the velocity of P we have dx/dt= aw sin0, dyjdt 

 = aa)cos0; hence v = aa>, as is otherwise apparent. 



266. If in the parallelogram 1234 the point 4 alone be fixed, 

 we have a linkage called the pantograph. 



It can serve to trace a curve similar to a given curve. 

 Indeed, any line through 4 (Fig. 62) cuts the opposite links 



