
DYNAMICS  CASE STUDY



Introduction

Problem Diagram 

A car engine manufacturer needs to know the maximum linear velocity of the piston head in a new prototype engine. The technicians know the rotational speed of the crankshaft but are unable to determine the linear velocity of the actual piston head.
What is known:
 The crankshaft rotates at 3,000 rpm.
 The crank rod length is 1 inch.
 The connecting rod length is 3 inches.
 The piston head is constrained to move in the vertical direction.





Question



What is the maximum velocity of the piston head over a complete rotation?




Linear Motion Conversion to
Rotation Motion


Approach


 The problem can be solved by splitting it into two parts. First, solve for the velocity of point B, v_{B}, using bar AB, and then solve for the velocity of point C, v_{C}, using v_{B} and bar BC.
 Apply the relative velocity equation for a rigid body for both bar AB and bar BC,
v_{B} = v_{A} + v_{B/A}




