(Solved): The planar mechanism shown above has two links with lengths L1=0.55m and L2=0.25m. In the ...

The planar mechanism shown above has two links with lengths ${\mathrm{L}}_1=0.55\mathrm{m}$ and ${\mathrm{L}}_2=0.25\mathrm{m}$. In the position shown, the link angles are ${?}_1=35^{?}$ and ${?}_2=60^{?}$. 1. Determine the $x$ and $y$ coordinates of endpoint $P$. (Hint: it is worthwhile to write general expressions for $x$ and $y$ as a function of $L_1,L_2,{?}_1$, and ${?}_2$. This will help with the other problems). 2. The links both rotate clockwise at the same angular velocity of $5\mathrm{rad}/\mathrm{s}$. What are the $x$ and $y$ velocities of point $P$ ? (Hint: chain rule) 3. Point $P$ is constrained to move along a vertical line at $x=0.55\mathrm{m}$. The second joint is made passive so ${?}_2$ is no longer controlled. For ${?}_1=35^{?}$, determine the link angle ${?}_2$ and the $x$ and $y$ coordinates of endpoint $P$. 4. Link 1 rotates counterclockwise at an angular velocity of $5\mathrm{rad}/\mathrm{s}$. For the same conditions as problem 3 , determine the angular velocity of link 2 , and the $x$ and $y$ velocities of endpoint $P$.