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Help with a four bar equation

  1. Jul 15, 2010 #1
    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.

    2. Relevant 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))

    3. 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: Jul 15, 2010
  2. jcsd
  3. Jul 16, 2010 #2
    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
  4. Jul 21, 2010 #3
    The Freudmann equation crashes also, so any suggestion would be appreciated.
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