Chapter 46, Problem 65A

To determine

(a)

To solve problem for unknown using the appropriate formula.

Answer to Problem 65A

  $D=\text{260mm}\text{.}$

Explanation of Solution

Given information:

  $\text{Module}(m)=10\text{mm,No of teeth }(T)=26.$

Calculation:

Its known that from the given problem

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

Following formula can be used to solve the problem

  $\text{Pitch Diameter}(D)=mT$

Now substitute the values and simplify

  $\begin{array}{l}\Rightarrow D=10\times 26\\ \Rightarrow D=\text{260}\text{mm}\end{array}$

To determine

(b)

To solve problem for unknown using the appropriate formula.

Answer to Problem 65A

  ${\text{P}}_{\text{c}}=31.416mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=10\text{mm;No of teeth }(T)=26$

Calculation:

Its known that from the given problem

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

  $\begin{array}{l}{\text{Circular Pitch(P}}_{\text{c}}\text{)=}\pi \times \text{m}\\ \Rightarrow P_c=\pi \times 10\\ \Rightarrow P_c=3.1416\times 10mm\\ \Rightarrow {\text{P}}_{\text{c}}=31.416mm\end{array}$

To determine

(c)

To solve problem for unknown using the appropriate formula.

Answer to Problem 65A

  ${\text{D}}_{\text{o}}=280mm$

Explanation of Solution

Given information:

  $\text{Module(m)}=10mm\text{,No of teeth }(T)=26$

Calculation:

Its known that from the given problem

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

  $\text{Outside diameter }(D_o)=\text{Pitch Diameter}(D)+\text{2}\times \text{module}(m)$

Substitute the values and simplify

  $\begin{array}{l}\Rightarrow {\text{D}}_{\text{o}}=260+2(\text{10})=280mm\\ \Rightarrow {\text{D}}_{\text{o}}=280mm\end{array}$

To determine

(d)

To solve problem for unknown using the appropriate formula.

Answer to Problem 65A

  $a=10mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=10\text{mm,No of teeth }(T)=26$

Calculation:

Its known that from the given problem

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

  $\begin{array}{l}\text{Addendum }(a)=1\text{module}\\ \Rightarrow \text{Addendum }(a)\text{=1}\times \text{10mm}\\ \Rightarrow a=10mm\end{array}$

To determine

(e)

To solve problem for unknown using the appropriate formula.

Answer to Problem 65A

  $w=20mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

Calculation:

Its known that from the given problem

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

  $\text{working depth}(w)=2m$

Substitute the given values and simplify

  $\begin{array}{l}\Rightarrow \text{w}=2\times 10mm\\ \Rightarrow w=20mm\end{array}$

To determine

(f)

To solve problem for unknown using the appropriate formula.

Answer to Problem 65A

  $t=15.705mm$

Explanation of Solution

Given information:

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

Calculation:

Its known that from the given problem

  $\text{Module}(m)=10mm\text{,No of teeth }(T)=26$

  $\text{Tooth thickness }(t)=\frac{P_c}{2}$

Substitute the values and simplify

  $\begin{array}{l}\Rightarrow t=\frac{31.416}{2}mm\\ \Rightarrow t=15.705mm\end{array}$