Solving Freudensteins Equation for Four-Bar Linkage in Matlab

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In summary, the conversation discusses the difficulty of solving trigonometric equations in MATLAB, specifically the "freudensteins equation" in the context of creating a four-bar linkage. The speaker has all the necessary information, such as link lengths and input angle, but is struggling to find a solution using equations and variables. They ask for help and suggest using the "solve" function in the symbolic toolbox, but have been struggling for several hours.
  • #1
nradam
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I was making a code for creating four-bar linkage in matlab. So somewhere in between i had to solve the 'freudensteins equation'. I have all the link lengths and two angles of links known, and i have two equations and two variables (the other two angle of links) to find. So here are the equations :

a*sin(alpha)=b*sin(theta)+c*sin(beta)
d+a*cos(alpha)=b*cos(theta)+c*cos(beta)

I know the link lengths a,b,c,d and the input angle theta. I need to find alpha and beta by solving the two equations.

But always some sort of crazy error comes up like :

Warning: Explicit solution could not be found.
> In solve at 81
In Untitled22 at 9

ans =

[ empty sym ]


OR

Invalid mathematical expression

OR

More variable than equations


Please tell me how to solve this. It would be good if you can tell me the code for solving it because i am brainstorming for past 2 hours on this and i am blanked out :(

Thanks in advance
 
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  • #2
Someone please tell me how to solve these kinda trigonometric equations in matlab! Its urgent and i am stuck for 8-9 hrs now :(
 

What is Freudenstein's equation and why is it important in four-bar linkage analysis?

Freudenstein's equation is a mathematical model used to determine the position and orientation of a four-bar linkage system. It is important because it allows for the analysis and optimization of various mechanical systems and can be used in the design process of machines and mechanisms.

How do I solve Freudenstein's equation for a four-bar linkage in Matlab?

To solve Freudenstein's equation for a four-bar linkage in Matlab, you will need to define the geometry of the four-bar linkage using its link lengths and joint angles. Then, use the built-in functions in Matlab, such as the "fsolve" function, to solve the system of equations. You can also create a script or function to automate the process for different input values.

What are the main challenges in solving Freudenstein's equation for a four-bar linkage?

One of the main challenges in solving Freudenstein's equation for a four-bar linkage is dealing with the singularity problem, where the system of equations becomes indeterminate. This can happen when the input and output links are in a straight line. Another challenge is dealing with numerical errors and convergence issues when using iterative methods to solve the equations.

Can I use other software or programming languages to solve Freudenstein's equation for a four-bar linkage?

Yes, you can use other software or programming languages to solve Freudenstein's equation for a four-bar linkage. Some examples include Python, Mathematica, and Maple. The process may vary slightly depending on the software or language used, but the underlying principles and equations remain the same.

What are some practical applications of solving Freudenstein's equation for a four-bar linkage?

Solving Freudenstein's equation for a four-bar linkage has many practical applications, including in robotics, automotive systems, and machinery. It can be used to optimize the design of linkages for desired motion paths, improve the efficiency of mechanical systems, and analyze the performance of existing mechanisms. It is also a valuable tool in the field of kinematics and can aid in the understanding of complex mechanical systems.

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