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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, vB, using bar AB, and then solve for the velocity of point C, vC, using vB and bar BC.
  • Apply the relative velocity equation for a rigid body for both bar AB and bar BC,

    vB = vA + vB/A
     
   
 
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