Problem $2(30$ points$)$: The common configuration of a reciprocating engine is that of

the slider$-$crank mechanism shown. Assume that the crank OB has a constant clockwise

rotational speed of $.$ Our goal is to determine the angular velocity AB of the connecting

rod AB and the velocity vA of the piston A at the shown instant when the angle between

OA and OB equals $.$

Use three different methods to solve this problem:

$($i$)$ Absolute motion analysis;

$($ii$)$ Relative motion analysis by vector algebra;

$($iii$)$ Relative motion analysis by scalar algebra and geometry.

Update: $10/29/2024$ at $7$:$25$pm CT$.$ Huayi Li$,$ UK$-$Paducah, $20241$ of $2$