Thread: 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

Originally Posted by Bosse

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.