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Math Help - Solve Rotation-Type Matrix Problem

  1. #1
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    Solve Rotation-Type Matrix Problem

    Hi,

    Im working as a mechanical designer. In the current project I need to calculate the angle of one arm as a function of another arms angle. The two arms are connected with a third arm. All the geometry is known but I cant solve the equation describing the angles.

    The problem boils down to the following:

    1) A*sin(X)+B*cos(Y)=C
    2) A*cos(X)-B*sin(Y)=D

    A & B are known constants.
    C & D are known variables (functions of the driving angle in my mechanical design).

    I need to know how X & Y varies according to C and/or D

    Best regards
    Bosse
    Sweden
    Last edited by Ackbeet; August 19th 2011 at 05:21 AM. Reason: Solve Rotation-Type Matrix Problem
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  2. #2
    A Plied Mathematician
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    Re: Solve Rotation-Type Matrix Problem

    Quote Originally Posted by Bosse View Post
    Hi,

    Im working as a mechanical designer. In the current project I need to calculate the angle of one arm as a function of another arms angle. The two arms are connected with a third arm. All the geometry is known but I cant solve the equation describing the angles.

    The problem boils down to the following:

    1) A*sin(X)+B*cos(Y)=C
    2) A*cos(X)-B*sin(Y)=D

    A & B are known constants.
    C & D are known variables (functions of the driving angle in my mechanical design).

    I need to know how X & Y varies according to C and/or D

    Best regards
    Bosse
    Sweden
    I suggest you hand the problem over to Mathematica or some other computer algebra system. Mathematica gave me 4 solutions, all of them quite complicated. If you were solving for A and B with respect to C and D, your problem would be much simpler. I think you could simply invert the coefficient matrix (which, while not strictly a rotation matrix, is extremely close to one) in that case.
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