Chapter 6.3, Problem 57PE

A piston in an engine is attached to a connector rod of length $L$ at the wrist pin at point $P$ . As the piston travels back and forth, the connector cap at point $Q$ travels counterclockwise along a circular path of radius $r$ . If $L>2r$ , and a represents $\angle PCQ$ .

a. Use the law of cosines to show that the distance $x$ from the wrist pin to the crank circle is given by $x=r\cos \alpha +\sqrt{r^2{\cos }^{2}a-r^2+L^2}-r$ .

b. Find the distance between the wrist pin and crank circle for a truck engine with connector rod of length $5.9\text{ in}\text{.}$ and crank radius of $1.7\text{ in}\text{.}$ when $a=105°.$ Round to the nearest tenth of an inch,

c. Find the maximum and minimum distances that the wrist pin is to the crank circle, using the values from part (b).