Problem #$3.(25$ points$).$ Design a Grashof Fourbar quick$-$return mechanism $($QRM$)$ shown in Figure #$2$ with the following requirements:

a$.$ A time ratio of $1\mathrm{.}36.$

b$.$ An output rocker angle of $({}_4{)}_{\text{m}\text{a}\text{x}}=45.$

c$.$ Time per cycle for the mechanism $($or complete revolution of the crank$)$ of $t=1\mathrm{.}2$ seconds.

d$.$ The mechanism must fit and operate within a design space of $811$ inches.

Figure #$2.$ Finished Linkage with its Toggle $($or Limits$)$ Positions of the Rocker.

$(5$ points$).$ Calculate the required outward$-$stroke and the return$-$stroke for the given time ratio and the time per cycle.

$(5$ points$).$ For your design, determine the minimum transmission angle, $,$ as shown in Figure #$2.$

$(5$ points$).$ Calculate the Grashof condition for the Fourbar mechanism for your design