GeoGebra-for-Engineering-drawi/C2/Orthographic-Projection-of-a-Regular-Hexagon/English

From Script | Spoken-Tutorial
Jump to: navigation, search

Title of script: Engineering Drawing with Geogebra

Authors: Komal B, Jitendra Shah

Keywords: Video Tutorial, Engineering Drawing, Geogebra


Visual Cue Narration
Slide 1 Welcome to this Spoken Tutorial on Engineering Drawing with Geogebra: Orthographic Projection of a Regular Hexagon.
Slide 2 In this tutorial we will learn

how to draw the orthographic projection of a regular hexagon.

To demonstrate

the effect of changes in dimensions on the projections of a plane using Geogebra.

We will do this through animation.

Slide 3 You will need to have a working knowledge of Geogebra.


Please go through the tutorials on the Spoken Tutorial website on Geogebra if required.

You also need to have a good knowledge of engineering drawing.

Slide 4 Here we are using Geogebra 3.2.40.0 on Ubuntu 10.10.
Now, let's first open Geogebra.
Click on Applications >> Science >> point to Geogebra Click on the Applications menu.

Select Science and then click on Geogebra.



Point to the Graphics

window.

You will be working mostly on the graphics

window.

Point to the icons on the toolbar.

Point to the Input box.

You can use the icons on the toolbar to draw the constructions.

You can also do this by writing commands in the input box.

I have opened a Geogebra file that shows the basic principles of Orthographic Projection.
Point to the Front view


Point to the Top view


Point to the Horizontal Plane and the Vertical Plane.


In Engineering Drawing we draw an object in 3D space using views that appear on the planes of projection.


The Front view, Top view and Profile views are used to visualize the geometrical object.

The Vertical, Horizontal and Profile planes (VP,HP,PP) are the principal planes of projection.

In an Orthographic projection, the object is viewed along parallel lines.

The lines are perpendicular to the plane of the drawing.

The lines drawn from a given view to obtain the other views are called generators.

Point to the Line Segment tool Let us now draw the Orthographic Projection of a regular hexagon.

Click on File>>New to open a new Geogebra window.

Select the Segment between 2 points icon.

Click twice on the graphics window to get a line segment.

Right click on one point and select rename and enter X in the window that opens.

Similarly, label the other point Y.

We have drawn the XY line.


You will notice that when we create a line segment the points, lines etc of this construction appear on the algebraic window. Point coordinates, distances, areas, equations , etc, are also shown here. You can use the algebraic window to select a particular object and make necessary changes. preview the same in the graphics window. You will learn more about this later in the tutorial.


Select the Insert Text icon.

Enter VP in the window that opens.

Similarly, write HP below the XY line.

The plane above the XY line is the VP and the plane below the XY line is the HP.

The intersection of the HP and VP is the XY line.



Point to the arrow in the Polygon tool. Here we will draw the Top view and Front view of a plane surface, a Regular Hexagon.

Let us construct the hexagon now.

Click the arrow in the polygon icon

Select the Regular Polygon icon.

Click the Regular Polygon icon. You will have to specify two points and enter the number of vertices.
Point to the Graphics window. Click twice on the Graphics window and enter the number of vertices in the window that opens.
Type 6 in the Regular Polygon>> Points window. Since we are drawing a Regular Hexagon, I will enter 6.
Point to the hexagon on the drawing pad. A regular hexagon appears on the drawing pad.
To draw the Top view, we have to draw the generators of the Hexagon.
Select the perpendicular line icon. To do this we will select the perpendicular line icon.
Now let's draw perpendicular lines through the vertices of the hexagon.
Select a point on the hexagon. Select a point.
Select a line. Then select the XY line. You will obtain the perpendicular through the point.

Draw the other generators similarly.

Point to the generator Next we have to mark the required points on the generators to get the Top view.
Point to the Top view The Top view of the Hexagon is a line.

Here, we view the hexagonal plane on the HP .

Point to the New point tool. Use the New Point tool and the Line Segment tool to draw the Top View.
Select the New Point icon Select the New Point icon.

Use the grid to mark a point 2 units from the XY line.

Click on the generator to create a point.

Similarly, create a point on the other generator.

Now, select the Segment between 2 points icon.

Select the 2 points.

A line segment appears on the screen.

This is the Top view. This is the front view we have drawn earlier.

Point to the vertices. As you can see, some of the vertices are coincident.
Point to the construction line When we show the generators, the construction lines should not be visible.

What we see in the final drawing are the lines from the vertices of the hexagon on the Front view to the points on the line which is the Top view.

Point to the Segment between two points tool. To draw this, use the Segment between 2 points tool.

Select the topmost vertex of the hexagon, then select the point on the Top view.

Similarly, draw the other generators.

Now hide the construction lines. To do this right click on the object and deselect the Show Object option.

We have drawn the generators.



Point to the hexagon. We will now look at the formatting so that we can arrive at the final drawing.


Here we have hidden the grid and the axes as this is required only for the purpose of construction.


Here we have shown the projection lines as this is required to arrive at the final drawing.

You can view the Object Properties of the geometrical object you create.
Select the Object >> Right-click Select the object and right-click to get the Object menu.
Select Object Properties. Select Object Properties.
A new window opens.
Select the color. You can choose any color on the color menu of the Object Properties menu.

Use this to show the Top view and the Front view.


Preview the object in the Graphics window.

Here we have selected Black and Grey.As you can see, the sides of the hexagon are Black and the inside of the Hexagon is grey.

Choose a color on the Object Properties>>Color menu

Point to the generator

You can choose any color on the Color menu of the Object Properties.

Use this to show the Top View and Front view.

Point to the object in the Graphics window. Preview the object in the Graphics window.
Point to the line. The lines that are not visible in the given view and axial lines are drawn as dotted lines.


Select the line h, under Objects>>Line and preview the selection in the Graphics window.



Select a dotted line on the Object properties>>Style >>Line Style menu option. You can select a dotted line on the Style menu here.
Uncheck the Object Properties>>Basic>>

Show Object option.

You can choose to hide the object by unchecking the Show Object option.

Go to Basic, select the line under Objects>>Line Uncheck the Show Object option.

Use this to hide lines and points used in the construction.

Now let us view the generators. To do this click the line segment , say k,under Objects>>Segment
Move the Style>>Line thickness slider. You can change the line thickness using

the slider.

Generators are thin lines.

Use this option to make thin lines when you draw generators.

Point to the Object Properties menu. You can use the Object Properties menu to hide points used in the construction.

Click the circular icon beside the name of the point under Objects>>Point. Similarly , hide the other points in the drawing.

As you can see,when we click the icon the point disappears on the graphics window.

Now, let us label the drawing.
Point to the Insert text icon. Use the Insert Text tool to do this.

We will first label the vertices of the hexagon in the front view.

Select the Insert Text icon.

Click in the graphics window to place the cursor, where you want the text to appear.

Enter the name of the point in the window that opens.

Label all the points similarly.

Now let us label the points projected in the Top view.

Place the cursor inside the Graphic s window. Now we will add a text annotation to show the Top view and the Front view.

We will use the Insert text tool to do this.

Select the Insert Text icon.

Let us put the text Top view here.

Click inside the Graphics window.

A new window opens.

Enter the text in the Edit Box and click on OK.



Point to the segment between 2 points tool. Now let us add the Dimensioning.


Use the Segment between 2 points tool to do this.

Click twice on the Graphics window to get the Line segment.

Hide the points created in the construction.

Similarly, draw the other Dimension lines.

Change the Point style on the Object Properties menu to show the arrowheads.

Now use the Insert Text tool to show the length of the side of the hexagon.

We have drawn the dimension lines.



Point to the Command List. You can view the commands on the Command List here.
Point to the commands on the Command List. You can draw a Polygon or a perpendicular using

commands too.

Now let us add an annotation to our drawing.
Point to the Input box.

Type Text[“Orthographic Projection”] .

For this we will use the Text command.

Orthographic Projection of a Regular Hexagon.

Select the Move icon.

Now select the Title text and drag it to the required position.

Point to the geometrical object. In any Engineering Drawing problem, you will have to visualize a geometrical Object and its transformations.


Here we are showing the grid and the axes which will be useful in viewing the transformation.

Select the Move icon. Select a point on the hexagon and drag with the mouse. You can use the Move icon or sliders to change the dimensions of the geometrical figure.
Point to the Slider icon.
Point to the Applets menu>>File>>Export>>Dynamic Worksheet as webpage(html) You might also want to look at Applets.

You can create a dynamic webpage with input parameters and view the Geogebra animation in the form of an applet.

You can read more about this on the Spoken tutorial website (www.spoken-tutorial.org)



Point to the Geogebra animation. In Engineering Drawing, we view a geometrical object in 3D space, with views in 2D space.
Point to the Top view. Generally, the Top view and Front view of the geometrical object is used.
Point to the other views. But the Right Side view, Left Side view, Bottom view and Rear view can also be used in this regard.
Right click on the slider. Click on Animation On. In an orthographic projection, a geometrical object is viewed perpendicularly.
Point to the Top view and Front view. Hence, the object is in true shape in the Top view or Front view.

The Front view is in true shape here.

Click on Animation On to stop it. Let us see, how to view the transformation using Geogebra

You can view the variation in length of sides,in number of vertices.

Here we are showing the vertices of the hexagon, as we will use the points to increase the side length using the Move tool.


Select the Move icon. Now select one of the free points and drag the mouse to increase the side length.

Click on the Move tool. .
Select a point on the polygon and drag with the mouse. We see the variation in the size of the polygon.
Select the Slider on the Graphics window. Right click and click on Animation On. We will now demonstrate the change in the number of sides using animation.


I have opened a ggb file, which is the geogebra file format, that shows an animation created with Geogebra.


You can learn more about making animations with sliders on the Spoken Tutorial website.


We will use the Slider to vary the number of sides.

Right click on the slider and click on Animation On

Point to the polygon You will observe the change in the shape of the polygon.
Point to the slider. The number of vertices changes from 3 to 10 which is set on the slider.

You can view the change in the Top view and the Front view with change in the number of sides.

Click on Animation On to stop the animation. Right click on the slider and click on Animation On to stop the animation.
This is how the geometrical object is visualized with Computer Aided Drawing using Geogebra.
This brings us to the end of this Spoken Tutorial.
Slide 6 To summarize-

We have seen how Geogebra can be used

  1. To draw the Orthographic Projection of a Regular Hexagon.
  2. To demonstrate by animation, the effect of changes in dimensions on the projections of a plane using Geogebra.
  3. We have learnt
        1. How to make geometrical constructions

using Geogebra.

2. How to change the parameters to view

the corresponding changes in the

geometrical figures.

3. How to draw the different views using

Geogebra.



Slide 7 Assignment

1. Draw the orthographic projection of a regular pentagon.

Show the transformation

  1. With variation in position with respect to the HP and VP
  2. With movement of vertices.
  3. When base is on HP
  4. When one of the corners is on HP
  5. At a given distance in front of VP


Slide 8

About SlideAbout the Spoken Tutorial Project


Watch the video titled, ‘What is a spoken tutorial’ on the Spoken Tutorial website.


You can download the tutorial if required.

Slide 9

About SlideSpoken Tutorial WorkshopsThe Spoken Tutorial Project Team

  • Conducts workshops using spoken tutorials
  • Gives certificates for those who pass an online test
  • For more details, please write to contact@spoken-tutorial.org


The Spoken Tutorial Project Team
  • Conducts workshops using spoken tutorials
  • Gives certificates for those who pass an online test


Slide 10 Acknowledgment SlideAcknowledgments
  • Spoken Tutorial Project is a part of the Talk to a Teacher project
  • It is supported by the National Mission on Education through ICT, MHRD, Government of India
  • More information on this Mission is available at
  • http://spoken-tutorial.org/NMEICT-Intro


* Spoken Tutorial Project is a part of the Talk to a Teacher project
  • It is supported by the National Mission on Education through ICT, MHRD, Government of India
  • More information on this Mission is available at


Slide 11

About the contributor SlideAbout the contributor

  • This tutorial has been contributed by Komal from Mysore
  • It is shared under the Creative Commons license
  • Thanks for joining


* This is Komal from SJCE, Mysore
  • Hope you enjoyed this Spoken Tutorial.
  • Thank you have a good day.


Contributors and Content Editors

Chandrika

Retrieved from "https://script.spoken-tutorial.org/index.php?title=GeoGebra-for-Engineering-drawi/C2/Orthographic-Projection-of-a-Regular-Hexagon/English&oldid=40"