Select a six$-$bar mechanism, make sure that no one in class has selected this mechanism. Answer the following questions:

$1.$ Determine the degree of freedom of the mechanism.

$2.$ Draw the kinematic chain of the mechanism and identify its type.

$3.$ For a given input link angle $($position$),$ determine the velocity and angular velocity $($if applicable$)$ of the output link using the graphical method.

$4.$ For a given input link angle $($position$),$ determine the acceleration and angular acceleration $($if applicable$)$ of the output link using the graphical method.

$5.$ Obtain the position equations of this two$-$loop mechanism using complex number approach and demonstrate that they are solvable.

$6.$ Obtain the velocity equations of this two$-$loop mechanism using complex numbers and demonstrate that they are solvable.

$7.$ Obtain the acceleration equations of this two$-$loop mechanism using complex numbers and demonstrate that they are solvable.

$8.$ Using a convenient software such as MATLAB etc, solve the position, velocity and acceleration equations set by incrementing the input angle in steps of $5$ degrees to obtain the output link's position, velocity, and acceleration values.

$9.$ Obtain a position graph where the horizontal axis represents the input angle $(0-360$ degrees$)$ and the vertical axis represents the output link's position.

Ensure that the position values in the vertical axis at $0$ and $360$ degrees are identical.

$10.$ Obtain a velocity graph where the horizontal axis represents the input angle $(0-360$ degrees$)$ and the vertical axis represents the output link's velocity.

Ensure that the velocity values in vertical axis at $0$ and $360$ degrees are identical.

$11.$ Compare the velocity value obtained via the graphical method with the value from the graph obtained using the complex number model for the same input angle. Ensure they are equal.

$12.$ Obtain an acceleration graph where the horizontal axis represents the input angle $(0-360$ degrees$)$ and the vertical axis represents the output link's acceleration. Ensure that the acceretion values in the vertical axis at $0$ and $360$ degrees are identical.

$13.$ Compare the acceleration value obtained via the graphical method with the value from the graph derived using the complex number model for the same input angle. Ensure they are equal.