Ex – 2 Draw the graphs of pinion and gear and determine its equations and tooth thickness

\[\text{A pair of spur gear consists of}\ (Z_p)\ =)\ 10\ teeth\ pinion\ meshing\ with\ (Z_g\ =)\ 60\ \hspace{10cm}\\ \text{teeth gear. Let the module be (m =) 2mm.}\ \hspace{10cm}\]

\[1.\ \text{To calculate the pitch circle diameters of the pinion and the gear using the fomulae}\ \hspace{10cm}\\ d_p\ =\ m\ Z_p\ and\ d_g=\ m\ Z_g.\hspace{10cm}\]

\[2.\ \text{Calculate the distance between the centers of the pinion and the gear using the fomulae}\ \hspace{10cm}\\ \frac{1}{2}\ (d_p\ +\ d_g).\ \hspace{10cm}\]

\[3.\ \text{To draw two externally touching circles to represent pinion and gear with appropriate}\ \hspace{10cm}\\ \text{centres and radii}\ \frac{1}{2}\ d_p\ and\ \frac{1}{2}\ d_g \hspace{10cm}\]

\[4.\ \text{To determine the equations of the pinion and gear.}\ \hspace{12cm}\]

\[5.\ \text{Calculate the distance between the centres of the circles from the graph and verify}\ \hspace{10cm}\\ \text{that it is equal to}\ \frac{1}{2}\ (d_p\ +\ d_g)\ \hspace{10cm}\]

\[6.\ \text{Calculate the tooth thickness using the formula t = 1.578m}\ \hspace{18cm}\]

\[7.\ \text{To calculate the gear ratio using the formula}\ i\ =\ \frac{Z_g}{Z_p}\ \hspace{18cm}\]

\[1.\ \text{Open Geogebra Classic 5 window}\ \hspace{19cm}\]

\[2.\ \text{To create a slider for}\ Z_p\ \text{with minimum = 1, maximum = 100}\ \hspace{15cm}\\ \text{and increment = 1}\ \hspace{12cm}\]

\[3.\ \text{Set}\ Z_p\ =\ 10\ \text{by using the input bar type Z_p = 10}\ \hspace{15cm}\\ \text{and press the Enter key}\ \hspace{12cm}\]

\[4.\ \text{Similarly, Create a slider for}\ Z_g\ =\ 60\ \hspace{18cm}\]

\[5.\ \text{Similarly, Create a slider for m with set m = 2}\ \hspace{18cm}\]

\[6.\ \text{To find the diameter of pinion by using the input bar to type d_p = m Z_p}\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[7.\ \text{To find the diameter of gear by using the input bar to type d_g = m Z_g} \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[8.\ \text{To find the radius of pinion by using the input bar to type R_p = d_p/2}.\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[9.\ \text{To find the radius of gearby using the input bar to type R_g = d_g/2}.\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[10.\ \text{To draw a circle for a gear by using the input bar to type C_g = Circle((0,0), R_g).}\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[11.\ \text{To plot the center of the gear by using the input bar to type c1 = Center (C_g)}.\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[12.\ \text{To draw the pinion circle by using the input bar to type C_p=Circle(R_p + R_g, 0), R_p)}.\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[13.\ \text{To plot the center of the pinion circle by using the input bar to type c2 = Center (C_p)}.\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[14.\ \text{To join the centers of the gear and pinion circles by using the input bar to type}.\ \hspace{12cm}\\ \text{c1c2 = Segment(c1, c2) and press the Enter key}\ \hspace{10cm}\]

\[15.\ \text{To find the gear ratio by using the input bar to type i = Z_g/Z_p}.\ \hspace{15cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[16.\ \text{To find the tooth thickness by using the input bar to type t = 1.578 m}.\ \hspace{12cm}\\ \text{and press the Enter key}\ \hspace{10cm}\]

\[17.\ \text{To create an input box for m link with m. By using the input box m,}\ \hspace{12cm}\\ \text{we can assign the different values of m}\ \hspace{10cm}\]