Troubleshooting a Four Bar Equation for Personal Programming Project

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SUMMARY

This discussion focuses on troubleshooting a four bar linkage program involving dynamics and angular velocities. The user is working with specific parameters: an input link height of 80 pixels, angular velocity of π/12 rad/s, and a coupler length of 107.703296 pixels. The equations provided include angular velocity relationships and trigonometric identities necessary for solving the linkage problem. The user seeks assistance due to inconsistencies in the output of their equations, particularly with the Freudmann equation.

PREREQUISITES
  • Understanding of four bar linkage dynamics
  • Familiarity with angular velocity and trigonometric functions
  • Knowledge of rigid body motion and cross products
  • Experience with programming in a suitable language for simulations
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  • Research the implementation of four bar linkage simulations in Python using libraries like NumPy
  • Study the derivation and application of the Freudmann equation in mechanical systems
  • Explore advanced topics in kinematics, focusing on angular velocity transformations
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Mechanical engineers, robotics enthusiasts, and programmers working on dynamic simulations or kinematic analysis of four bar linkages will benefit from this discussion.

RandyPhantom
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Hello; I am trying to write a four bar program; it is not for school, but it is a personal project to refresh myself with programming and dynamics. I have a input with height 80 pixels, angular velocity of pi/12 rad/s and the initial angle is pi/2; the coupler is with length of 107.703296 pixels,an initial angle of .380506377 and the angular velocity was calculated to be 1.22597x10^-17 rad/s. the follower link's initial angle is pi/2 with a angular velocity of 0.1745329 rad/s and height of 120 pixels. I was assuming that linear equation would be (length*cos(initial angle + angular velocity*time),length*sin(initial angle+angularvelocity*time) but this only worked for the input link. so I know that the velocity of the second point on a rigid body is written as angular velocity of the first link cross product of the length and angle of the first point + the angular velocity of the second cross product of the length and angle of the second point.

Homework Equations



w1*r1*cos(phi1)+w2*r2*cos(phi2)+w3*r3*cos(phi3) = 0
-w1*r1*sin(phi1)-w2*r2*sin(phi2)-w3*r3*sin(phi3) = 0
w2 = -(w1*r1*cos(phi1)+w3*r3*cos(phi3))/(r2*cos(phi2))
w3 = -w1*r1*(-cos(phi1)*sin(phi2)+cos(phi2)*sin(phi1))/r3*(cos(phi2)*sin(phi3) - cos(phi3)*sin(phi2))

The Attempt at a Solution


I was using [x?,y?] = [r?*(cos(phi?+w?*t)),r?*sin(phi?+w?*t)), but this works only on the the input link
 
Last edited:
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I also went in another direction

r1*cos(theta1)+r2*cos(theta2) = r4*cos(theta0)+r3*cos(theta3)
r1*sin(theta1)+r2*sin(theta2) = r4*sin(theta0)+r3*sin(theta3)

solved for cos(theta2) and sin(theta2) and used (cos(theta2))^2+(sin(theta2))^2 = 1

came up with the equation:
r1^2-2*r1*sin(theta1)*r4*sin(theta0)-2*r1*r3*sin(theta1)*sin(theta3)+r4^2+2*r4*sin(theta0)*r3*sin(theta3)+c^2-2*r1*cos(theta1)*r4*cos(theta0)-2*r1*cos(theta1)*r3*cos(theta3)+2*r4*cos(theta0)*r3*cos(theta3)-r2 = 0
 
The Freudmann equation crashes also, so any suggestion would be appreciated.
 

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