PROBLEM $2$: Design a $4-$bar linkage with the left link represented as vector $W$ and the right

link as vector $U$ to carry a body in the given figure through the three precision locations $P_1,P_2,$

and $P_3$ at the angles as shown. Use analytical synthesis method. All angles in the diagram below

are measured from horizontal line in counterclockwise direction. The dimensional unit in the

diagram is in inches.

Using Figure $5-4($the figure on the second page of $"07\_$Analytical$\_$synthesis$2.$pptx$"$ uploaded on

Canvas$)$ as reference, the suggested free choices for the $WZ$ dyad: ${}_2=40,{}_3=80$; The

suggested free choices for the US dyad: ${}_2=20,{}_3=50.$

$($a$)$ Determine the magnitudes and orientation of the position difference vectors $P_{21}$ and $P_{31}.$

$(1$ point$)$

$($b$)$ Determine the angle changes $()$ of the coupler between precision points. $(1$ point$)$

$($c$)$ Form the matrix to solve for the components of $W$ and $Z$ vectors. $(1$ points$)$

$($d$)$ Solve for Link $2$ on the left side dyad. $(1$ point$)$

$($e$)$ Repeat the same steps for the right side dyad to solve for Link $4.(2$ points$)$

$($f$)$ Sketch out the shape of the designed linkage with labels. $(1$ points$)$How to solve

PROBLEM $2$: Design a $4-$bar linkage with the left link represented as vector $W$ and the right

link as vector $U$ to carry a body in the given figure through the three precision locations $P_1,P_2,$

and $P_3$ at the angles as shown. Use analytical synthesis method. All angles in the diagram below

are measured from horizontal line in counterclockwise direction. The dimensional unit in the

diagram is in inches.

Using Figure $5-4($the figure on the second page of $"07\_$Analytical$\_$synthesis$2.$pptx$"$ uploaded on

Canvas$)$ as reference, the suggested free choices for the $WZ$ dyad: ${}_2=40,{}_3=80$; The

suggested free choices for the US dyad: ${}_2=20,{}_3=50.$

$($a$)$ Determine the magnitudes and orientation of the position difference vectors $P_{21}$ and $P_{31}.$

$(1$ point$)$

$($b$)$ Determine the angle changes $()$ of the coupler between precision points. $(1$ point$)$

$($c$)$ Form the matrix to solve for the components of $W$ and $Z$ vectors. $(1$ points$)$

$($d$)$ Solve for Link $2$ on the left side dyad. $(1$ point$)$

$($e$)$ Repeat the same steps for the right side dyad to solve for Link $4.(2$ points$)$

$($f$)$ Sketch out the shape of the designed linkage with labels. $(1$ points$)$