Solving Statics HW Problem: Piston Velocity & Acceleration

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SUMMARY

This discussion focuses on solving a statics homework problem related to a simple reciprocating engine, specifically determining the piston velocity and acceleration at point D as functions of the crankshaft angle, θ. The dimensions provided are LAB=1.875”, LBD=6.0”, and the crankshaft speed is ωAB=8000rpm. The solution involves using the Relative Motion Method for mechanism analysis or the Instantaneous Centers of Rotation. A recommended resource for further reading is a book detailing the relative motion method in mechanisms.

PREREQUISITES
  • Understanding of kinematics in mechanical systems
  • Familiarity with the Relative Motion Method for mechanism analysis
  • Knowledge of Instantaneous Centers of Rotation
  • Basic proficiency in plotting functions and interpreting graphs
NEXT STEPS
  • Study the Relative Motion Method for mechanism analysis
  • Learn about Instantaneous Centers of Rotation in mechanical systems
  • Practice plotting velocity and acceleration functions in relation to angular displacement
  • Review kinematic equations relevant to reciprocating engines
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Students in mechanical engineering, particularly those tackling kinematics and dynamics of mechanisms, as well as educators seeking to provide additional resources for teaching these concepts.

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Homework Statement



Using the diagram shown below for a simple reciprocating engine, determine (a) the piston velocity (velocity at point D) and (b) the piston acceleration (acceleration at point D) as functions of the crankshaft angle, θ. The dimensions are as follows: LAB=1.875”, LBD=6.0”, and ωAB=8000rpm. (c) Plot your results: VD vs. θ and AD vs. θ.



Homework Equations





The Attempt at a Solution



I don't know where to start
 

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Hmmm, you want help on an extra credit problem that you "don't know where to start" so you can hand it in for extra credit. What's wrong with this picture? Under those circumstances I will give you only one small hint, which is probably more than I should do:

Call AD "x" and write x in terms of the known sides and angle. And use letters instead of numbers until the end.
 

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