CHAPTER XVIII 
PISTON OR SLIDER AND CONNECTING - ROD 
VELOCITY AND ACCELERATION DIAGRAMS 
260. Piston or Slider Velocity Diagrams.—In the direct-acting 
engine the reciprocating motion of the piston is converted into the rotary 
motion of the crank shaft by means of the crank and connecting-rod. In 
what follows it is really the motion of the cross-head which is studied, 
but the piston and cross-head have exactly the same motion. Referring 
to Fig. 467, A is the axis of the cross-head pin, AB the axis of the con- 
necting-rod, B the axis of the crank pin, BC the crank, and C the axis of 
the crank shaft. The line of stroke of the piston when produced is 
assumed to pass through C. Let O, be the instantaneous centre for the 
* Fig. 467. 
connecting-rod when in the position shown. Let V be the linear velocity 
of the crank pin, and v the velocity of the cross-head, then — 3 
OB" 
Through C draw CD’ perpendicular to AC. Make CB’=V to ‘any 
convenient velocity scale, and draw B’D’ parallel to AB to meet CD’ at D’, 
then, since the triangles O,AB and CD’B’ are similar, red -OE-y" 
therefore CD’=v. Since V, the velocity of the crank pin, is usually 
uniform, it is generally convenient to select the velocity scale such that 
CB=V, then if AB be produced to meet CD’ at D, CD=v. Drawing 
DE parallel to the line of stréké to meet’ AE perpendicular to the line of 
stroke at E determines a point on the piston velocity-space curve. If Cd 
(on the crank) be made equal to CD, then d is a point on the polar 
velocity curve for the piston. A point on another form of the polar 
velocity curve is obtained by making Be (on the crank produced) =CD, 
300 
