Analytical Vector methods for a four bar linkage

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SUMMARY

The discussion focuses on solving a four bar linkage problem with given parameters: r0=30mm, r1=10mm, r2=35mm, r3=20mm, and an initial angle theta1=45 degrees. The objective is to calculate the angles theta2 and theta3, as well as the linear and angular velocities Vc, W2, and W3, assuming W1=30 rad/s counterclockwise. The equations governing the system are derived from the geometric relationships of the linkage, specifically utilizing cosine and sine laws for the angles involved.

PREREQUISITES
  • Understanding of four bar linkage mechanisms
  • Proficiency in trigonometric equations
  • Familiarity with angular velocity concepts
  • Basic knowledge of vector analysis in mechanical systems
NEXT STEPS
  • Study the derivation of the four bar linkage equations
  • Learn about the graphical method for analyzing linkages
  • Explore the use of simulation software for mechanical linkages
  • Investigate the impact of varying angular velocities on linkage performance
USEFUL FOR

Mechanical engineering students, practitioners in kinematics, and anyone involved in the design and analysis of mechanical linkages will benefit from this discussion.

painkiller72
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Homework Statement


In a four bar linkage r0=30mm, r1=10mm, r2=35mm, r3=20mm and theta1=45 degrees. Calculate theta2, theta3, Vc, W2, and W3 assuming that W1=30 rad/s ccw.


Homework Equations


R1*costheta1 + R2*costheta2 - R3*costheta3 - R0*costheta0 = 0 (3-x)
R1*sintheta1 + R2*sintheta2 - R3*sintheta3 - R0*sintheta0 = 0



The Attempt at a Solution


I wasn't sure about this equation from the start since I think it relies on knowing two angles and I only know one.
I first plugged in for
10*cos45+35*costheta2-20*costheta3-30*costheta0
10*sin45+35*sintheta2-20*sintheta3-30*sintheta0
equals
5.252+35*costheta2-20*costheta3-30*costheta0
8.509+35*sintheta2-20*sintheta3-30*sintheta0

and I'm already wondering what I should do from here.
 
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A picture of the linkage would be nice.
 

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