HELP WITH HAND CALCULATIONS. Rigid$-$Body Kinematics Project

Instructions

Bar $AB$ rotates about the fixed point A with constant angular velocity ${}_0.$ The system starts with bar

$AB$ horizontal.

Use the relative velocity equation to find the velocity of $C$ in terms of the angles $$ and $$ and

their derivatives.

Determine the lengths of bars $AB$ and $BC$ so that as bar $AB$ rotates, the collar $C$ moves back

and forth between the positions $D$ and $E.$ A design constraint is that bar $BC$ must be longer

than bar $AB($as shown in sketch$).$

You are given the design constraint that the magnitude of the acceleration of collar $C$ must

not exceed $200\frac{m}{s^2}.$ What is the maximum allowable value of ${}_0?$

Create the following plots for a complete revolution of bar $AB$ using the values for lengths

and angular velocity determined above:

$$ and $$ versus time as $2$ sub$-$plots.

Position, velocity, and acceleration of $C$ versus time as $3$ sub$-$plots.

Velocity and acceleration of $C$ versus its position as $2$ sub$-$plots.

Use your plotted results to describe the motion of the system $-$ where does it start, which

way does it move initially, where do the min and max occur, etc.

Solve the problem with a MATLAB LiveScript using the Symbolic Toolbox. Use hand calculations as

needed to support your solution. Include your analytical work $($hand calculations$)$ in the Live Script.