76 



KINEMATICS. 



[148. 



be equal, we can find the magnitude of v by drawing (Fig. 36} 

 from any point M parallels to u and v, laying off u to scale and 

 drawing through its extremity a perpendicular to the direction of 

 PQ ; this perpendicular will cut off the proper length on the 

 direction of v. 



Fig. 36. 



In applying this construction to our case it will be convenien 

 to turn the auxiliary diagram of velocities by an angle of 90 

 and place it so as to make M coincide with O ; u will then lie| 

 along OQ, and v at right angles to OP. Hence, if the scale ol 

 velocities be selected so as to have u represented in length by 

 OQ, v will be represented on the same scale by OR, that is, b4 

 the segment cut off by PQ produced on the perpendicular to- 

 OP drawn through O. 



148. The variation of the piston velocity in the course of 

 motion can best be exhibited graphically. Thus a polar curved 

 of piston velocity is obtained by laying off on OQ a length 

 OR' = OR, for a number of positions of OQ, and joining the 

 points R' by a continuous curve. 



Another convenient method consists in erecting perpendicu- 

 lars to OP at the various positions of P and laying off,' on these 

 perpendiculars, OR" = OR v. 



149. To derive an analytical expression for the piston velocit] 

 v, let $ be the angle OPQ which determines the position of thi 

 connecting rod. 



It follows from the construction of the velocity v given \\ 

 Art. 147 (see Fig. 36) that 



