For the water spray mechanism in Figure P1.51, classify the four-bar mechanism based on its possible motion, when the lengths of the links are $a = 12 \, \text{in.}$, $b = 3 \, \text{in.}$, $c = 12 \, \text{in.}$, and $d = 5 \, \text{in.}$.

a) Crank-rocker
b) Double-rocker
c) Rocker
d) Slider-crank

The four-bar mechanism described with link lengths of 12 in., 3 in., 12 in., and 5 in. can be classified as a crank-rocker type, according to Grashof's criterion.

Explanation:

The student's question pertains to the classification of a four-bar mechanism based on its link lengths and the resulting motion. The four-bar mechanism is a fundamental component in mechanical engineering and is used to convert motion types or to transfer movement from one part to another in a controlled manner. To classify the mechanism, one must apply Grashof's criterion, which states that the sum of the shortest and longest link lengths must be less than or equal to the sum of the remaining link lengths for at least one link to be capable of making a complete rotation (i.e., a crank).

In this case, the lengths are given as a = 12 in., b = 3 in., c = 12 in., and d = 5 in. According to Grashof's criterion, (shortest + longest) ≤ (sum of the two other links), or (3 + 12) ≤ (12 + 5). Since 15 ≤ 17, the linkage can have a rotating element, thus we have one link that can make a full rotation (a crank). Given that the shortest link is not the fixed link (ground), the configuration is a crank-rocker because one link (the crank) will rotate fully while the opposite link will rock.