Chapter 5, Problem 21A

A double-threaded square-thread screw is shown in Figure 5-7. The pitch of a screw is the distance from the top of one thread to the same point on the top of the next thread. The lead is the distance the screw advances for each complete turn or revolution of the screw. In a double-threaded screw, the lead is twice the pitch. Given the number of turns and the amount of screw advance, determine the lead and pitch.

To determine

(a)

Evaluate the lead and pitch of the square thread A.

Answer to Problem 21A

The lead and pitch of the square thread A are $\frac{21}{80}\text{in}$ and $\frac{21}{160}\text{in}$ respectively.

Explanation of Solution

Given:

Square advance is $2\frac{5}{8}$ and number of turns is $10$.

Concept used:

For lead divide the square advance by number of turns. For pitch divide the lead by number of start.

Calculation:

Lead of the square thread is calculated as follows:

Divide the square advance $2\frac{5}{8}$ by number of turns $10$ as follows:

  $\begin{array}{l}l=2\frac{5}{8}÷10\\ l=\frac{21}{8}\times \frac{1}{10}\\ l=\frac{21}{80}\text{in}\end{array}$

Pitch of the square thread is calculated as follows:

  $\begin{array}{l}p=\frac{l}{2}\\ p=\frac{21}{80\times 2}\\ p=\frac{21}{160}\text{in}\end{array}$

Thus, the lead and pitch of the square thread A are $\frac{21}{80}\text{in}$ and $\frac{21}{160}\text{in}$ respectively.

Conclusion:

The lead and pitch of the square thread A are $\frac{21}{80}\text{in}$ and $\frac{21}{160}\text{in}$ respectively.

To determine

(b)

Evaluate the lead and pitch of the square thread B.

Answer to Problem 21A

The lead and pitch of the square thread 'B' are $\frac{5}{16}\text{in}$ and $\frac{5}{32}\text{in}$ respectively.

Explanation of Solution

Given:

Square advance is $6\frac{61}{64}$ and number of turns is $22\frac{1}{4}$.

Concept used:

For lead divide the square advance by number of turns. For pitch divide the lead by number of start.

Calculation:

Lead of the square thread is calculated as follows:

Divide the square advance $6\frac{61}{64}$ by number of turns $22\frac{1}{4}$ as follows:

  $\begin{array}{l}l=6\frac{61}{64}÷22\frac{1}{4}\\ l=\frac{445}{64}\times \frac{4}{89}\\ l=\frac{5}{16}\text{in}\end{array}$

Pitch of the square thread is calculated as follows:

  $\begin{array}{l}p=\frac{l}{2}\\ p=\frac{5}{16\times 2}\\ p=\frac{5}{32}\text{in}\end{array}$

Thus, the lead and pitch of the square thread 'B' are $\frac{5}{16}\text{in}$ and $\frac{5}{32}\text{in}$ respectively.

Conclusion:

The lead and pitch of the square thread 'B' are $\frac{5}{16}\text{in}$ and $\frac{5}{32}\text{in}$ respectively.

To determine

(c)

Evaluate the lead and pitch of the square thread C.

Answer to Problem 21A

The lead and pitch of the square thread 'C' are $\frac{5}{8}\text{in}$ and $\frac{5}{16}\text{in}$ respectively.

Explanation of Solution

Given:

Square advance is $10\frac{5}{16}$ and number of turns is $16\frac{1}{2}$.

Concept used:

For lead divide the square advance by number of turns. For pitch divide the lead by number of start.

Calculation:

Lead of the square thread is calculated as follows:

Divide the square advance $10\frac{5}{16}$ by number of turns $16\frac{1}{2}$ as follows:

  $\begin{array}{l}l=10\frac{5}{16}÷16\frac{1}{2}\\ l=\frac{165}{16}\times \frac{2}{33}\\ l=\frac{5}{8}\text{in}\end{array}$

Pitch of the square thread is calculated as follows:

  $\begin{array}{l}p=\frac{l}{2}\\ p=\frac{5}{8\times 2}\\ p=\frac{5}{16}\text{in}\end{array}$

Thus, the lead and pitch of the square thread 'C' are $\frac{5}{8}\text{in}$ and $\frac{5}{16}\text{in}$ respectively.

Conclusion:

The lead and pitch of the square thread 'C' are $\frac{5}{8}\text{in}$ and $\frac{5}{16}\text{in}$ respectively.

To determine

(d)

Evaluate the lead and pitch of the square thread D.

Answer to Problem 21A

The lead and pitch of the square thread 'D' are $\frac{19}{64}\text{in}$ and $\frac{19}{128}\text{in}$ respectively.

Explanation of Solution

Given:

Square advance is $3\frac{9}{16}$ and number of turns is $12$.

Concept used:

For lead divide the square advance by number of turns. For pitch divide the lead by number of start.

Calculation:

Lead of the square thread is calculated as follows:

Divide the square advance $3\frac{9}{16}$ by number of turns $12$ as follows:

  $\begin{array}{l}l=3\frac{9}{16}÷12\\ l=\frac{57}{16}\times \frac{1}{12}\\ l=\frac{19}{64}\text{in}\end{array}$

Pitch of the square thread is calculated as follows:

  $\begin{array}{l}p=\frac{l}{2}\\ p=\frac{19}{64\times 2}\\ p=\frac{19}{128}\text{in}\end{array}$

Thus, the lead and pitch of the square thread 'D' are $\frac{19}{64}\text{in}$ and $\frac{19}{128}\text{in}$ respectively.

Conclusion:

The lead and pitch of the square thread 'D' are $\frac{19}{64}\text{in}$ and $\frac{19}{128}\text{in}$ respectively.