$2.(10$ points$)$ You are given a slider$-$crank mechanism, where:

$-$ Crank: The rotating arm connected to a motor, with a length of $48\mathrm{.}2$ mm ;

$-$ Coupler: The link between the crank and the slider, with a length of $151\mathrm{.}8$ mm ;

$-$ Stroke length of the slider: This is the total distance the slider moves back and forth, which is $146\mathrm{.}1$ mm ;

$-$ Motor offset: The motor that drives the crank is $100$ mm away from the track that the slider moves along;

$-$ The crank is rotating at a constant speed;

$-$ The frictional coefficient between the track and slider: $0\mathrm{.}4$ without lubrication or $0\mathrm{.}15$ with grease lubrication.

Your task is to verify whether grease lubrication is necessary for this mechanism when it operates cyclically. $($Hint: You need to review HW $2$ and Lecture $22,$ and notice that the Phi angle in the solution of HW $2$ is different from the angle we used in Lecture $22.)$