Analytical Vector methods for a four bar linkage

In summary, the problem involves a four bar linkage with given dimensions and an initial angular velocity for one of the links. The equations used to solve for the unknown angles are shown, but there is uncertainty on how to proceed. A visual representation of the linkage is also requested.
  • #1
painkiller72
2
0

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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  • #2
A picture of the linkage would be nice.
 

FAQ: Analytical Vector methods for a four bar linkage

What are analytical vector methods for a four bar linkage?

Analytical vector methods for a four bar linkage involve using vector equations and mathematical calculations to analyze the motion and forces of a four bar linkage system. This method is often used in mechanical engineering to design and optimize four bar linkages for various applications.

How do analytical vector methods differ from graphical methods for analyzing four bar linkages?

Graphical methods for analyzing four bar linkages involve drawing and manipulating scaled diagrams to determine the motion and forces of the system. Analytical vector methods, on the other hand, use mathematical equations and vector calculations to analyze the system. This allows for a more precise and detailed analysis of the linkage system.

What are the advantages of using analytical vector methods for a four bar linkage?

One advantage of using analytical vector methods is that they provide a more accurate and quantitative analysis of the linkage system. This can be especially useful for optimizing the design of the linkage for specific applications. Additionally, analytical methods can be used to analyze more complex four bar linkage systems that may be difficult to analyze graphically.

Are there any limitations to using analytical vector methods for four bar linkages?

One limitation of analytical vector methods is that they require a strong understanding of vector mathematics and equations. This can make them more challenging for some individuals to use compared to graphical methods. Additionally, analytical methods may not account for certain real-world factors such as friction and wear, which can affect the performance of the linkage system.

How can analytical vector methods be applied to real-world four bar linkage systems?

Analytical vector methods can be used to analyze and optimize real-world four bar linkage systems in various industries, such as robotics, automotive engineering, and machinery design. By accurately determining the forces and motion of the linkage system, engineers can design more efficient and reliable systems for a wide range of applications.

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