2;i.] PLANE MOTION. 



270. To determine the linear velocity v of A' along DA' 

 when the angular velocity co of the link OB is given, we notice 

 that the instantaneous centre C of the link BA' lies at the 

 intersection of OB with the line drawn through A' parallel to 

 OO'. Let a) r be the angular velocity of BA' about C. Then 

 v = a)' - CA' ; also since the point B describes a circle about O, 

 a)l>=a)' CB \ hence 



CA' , 



If BA' intersect OO' in E, we have from similar triangles 

 CA':CB=OE\OB; hence 



v=w OE. 



The variable length OE depends on the angles EOB Q and 

 = (f> t which. are connected by the relation (Art. 269) 



The figure gives OE=&cos 6 + b sin 6 cot $ ; hence, finally, 

 v=wb sin #(cot # + cot </>). 



271. In the steam engine and other machines mechanisms 

 are required for transforming the alternating rectilinear motion 

 of the piston into the reciprocating circular motion of a crank, 

 eccentric, or beam ; a mechanism of this kind is called, rather 

 inappropriately; a parallel motion. The problem of effecting this 

 transformation has been solved in various ways. Peaucellier's 

 inversor (1864) was the first accttrate solution. Generally, an 

 approximate solution is sufficient for practical purposes. The 

 most common of such approximations is Watt's parallel motion. 

 This mechanism is a combination of a linked parallelogram 

 with a four bar linkwork with crossed links. 



