hi all,
x=L1cos q1+L2 cos(q1+ q2);
y=L1sin q1+L2 sin(q1+q2);
x,y and L1 L2 values are know..
how to find q1 and q2...
In other words, From the given diagram...
x,y, L1,L2 are known...
how to find q1& q2...
hi all,
x=L1cos q1+L2 cos(q1+ q2);
y=L1sin q1+L2 sin(q1+q2);
x,y and L1 L2 values are know..
how to find q1 and q2...
In other words, From the given diagram...
x,y, L1,L2 are known...
how to find q1& q2...
Hello, nani!
I have part of the solution.
Those subscripts are messy; I'll modify the problem.
Solve for $\displaystyle p$ and $\displaystyle q.$
. . $\displaystyle \begin{array}{ccc}x &=& L\cos(p) + M\cos(p+q) \\
y &=& L\sin(p) + M\sin(p+q) \end{array}$
$\displaystyle x,y,L,M$ are constants.
Square the equations: . $\displaystyle \begin{array}{ccc}
x^2 &=& L^2\cos^2(p) + 2LM\cos(p)\cos(p+q) + M^2\cos^2(p+q) \\
y^2 &=& L^2\sin^2(p) + 2LM\sin(p)\sin(p+q) + M^2\sin^2(p+q)
\end{array}$
$\displaystyle \text{Add: }\;x^2+y^2 \;=\;L^2\underbrace{\bigg[\sin^2(p) + \cos^2(p)\bigg]}_{\text{This is 1}}$ $\displaystyle + \;2LM\underbrace{\bigg[\cos(p)\cos(p+q) + \sin(p)\sin(p+q)\bigg]}_{\text{This is }\cos(q)}$ $\displaystyle + \;M^2\underbrace{\bigg[\sin^2(p+q) + \cos^2(p+q)\bigg]}_{\text{This is 1}}$
We have: .$\displaystyle x^2+y^2 \;=\;L^2 + 2LM\cos(q) + M^2 \qquad\Rightarrow\qquad \cos(q) \;=\;\frac{(x^2+y^2) - (L^2+M^2)}{2LM} $
Therefore: . $\displaystyle q \;=\;\cos^{-1}\left[\frac{(x^2+y^2) - (L^2+M^2)}{2LM}\right] $