(Solved): 4. (18 pts) In the design of timing mechanism, the motion of the pin P in the fixed circular slot o ...

4. (18 pts) In the design of timing mechanism, the motion of the pin $P$ in the fixed circular slot of the disk $B$ is controlled by the guide $A$, which is being elevated by its lead screw. Guide $A$ starts from rest with pin $P$ at the lowest point in the circular slot, and accelerates upward at a constant rate until it reaches speed of $v$ at the halfway point of its vertical displacement. The guide then decelerates at a constant and comes to stop with pin $P$ at the uppermost point in the circular slot. Answer the following questions, assuming that pin $P$ is at the lower half of the semicircle throughout this problem. a. (3pts) Identify a mechanism similar to the given structure that's used in real-world applications, or suggest a potential application for it. (This problem is designed to hone your engineering intuition for physical phenomena. To do this, try to answer the question without solving the equations of motion. Instead, rely on your gut feeling and understanding of the physical principles involved. An incorrect prediction will not affect your grade.) b. (9pts) Define Cartesian, N-T, Polar coordinates and formulate the velocity vector respectively (If needed, assume the pin has traveled $?$ around the slot from the starting position). (3pts each) c. (3pts) Determine the $n$ - and $t$-components of the velocity of pin $P$ once the pin has traveled $?$ around the slot from the starting position. d. (3pts) Determine the $n$ - and $t$-components of the acceleration of pin $P$ once the pin has traveled $?$ around the slot from the starting position.