4. A joint of a mechanism can be considered as a journal bearing. As shown in the following figure,
the radius of the bearing $r_B$ is greater than that of the journal $r_J$. Their difference is called a clearance,
and $r = r_B - r_J$.
Link i
Journal
Link j
Bearing
$r_J$
$r_B$
Y
r
X
As indicated in the following figure, the position (X, Y) of the center of the journal relative to the
center of the bearing is within a circle of radius r. This circle is called a clearance circle.
Y
r
(X,Y)
X
(a) The joint probability density function (PDF) of X and Y.
(b) The PDFs of X and Y.
(c) The means of X and Y.
(d) The variances of X and Y.
(e) The correlation coefficient between X and Y.