Example $(5\mathrm{.}10)$:

Consider the crank$-$slider mechanism shown in Figure $(5\mathrm{.}19),$ The crank $O_2$A rotates with a regular angular velocity ${}_2=10\frac{r}{s}$ anticlockwise, i$.$e$.{}_2=0.$ Given the link lengths shown, find analytically the angular velocity ${}_3,$ the slider velocity $V_B,$ the angular accelerations ${}_3,$ and the slider acceleration $a_B.$ Then find the velocity and acceleration vectors for point C $,$ i$.$e$.V_C$ and $a_C.$

$\left[\begin{array}{cc}{r}_{4}j{e}^{j{}_4}& -r_{3}j{e}^{j{}_3}\\ -r_{4}j{e}^{-j{}_4}& r_{3}j{e}^{-j{}_4}\end{array}\right]\left[\begin{array}{c}{}_4\\ {}_3\end{array}\right]=\left[\begin{array}{c}A\\ \frac{?}{\text{b}\text{a}\text{r}}(A)\end{array}\right]$

for which $\frac{?}{\text{b}\text{a}\text{r}}(A)=$conj$(A).$ This equation can be solved directly using a proper software which can manage complex numbers such as MATLAB$.$

Figure $5\mathrm{.}19$ Position vectors assigned for crank$-$slider mechanism.$\{\{\{$i want solution by analytical method pva$\}\}\}$