Technical Drawing - Interpenetration - Square into Square

In this the first section where we are looking at the Interpenetration of actual solids we will examine the simple exercise of finding the lines of Interpenetration between two square based prisms.  Below you can see the setup drawing for this problem.

You can draw this yourself if you wish but you will have to come up with your own dimensions.  To the left in grey there is a section view of the smaller square based prism which is penetrating the larger square based prism.  We need this to help us rotate the Plan view into the Elevation view and maintain the correct dimensions.  (You could just use measurements in the Elevation but it is good practice to do it as above as you will need this skill later where measurements will not work so easily.)

You can see the labelling that we have used here in this drawing and why we have used the section of the smaller square based prism to provide our Elevation drawing.  Remember to draw the lines lightly at this stage.  As you can see there is no need to label every corner of the prisms, just so long as we can recognise the edges.

It is obvious where the edges 1 and 3 of the small prism intersect with edge a of the larger prism and these are points we can use to start with.  In the Plan you can see where edge 2 of the small prism intersects with the surface ab of the large prism.  Project this point into the Elevation to find the point of intersection there.  You will also notice that edge 4 of the small prism intersects the surface ad of the large prism along the same construction line.  You can now draw in the lines of Interpenetration in the Elevation.  Draw the lines folowing the section view, edge 1 joins to edge 2, joins to edge 3, joins to edge 4, and back to edge 1 again.  You can only see the lines of Interpenetration joining edges 1, 2 and 3.

Line out your drawing and it should look like the drawing above.