Technical Drawing - Interpenetration - Square into Square Offset

Here we are going to look at the construction of the lines of Interpenetration between two square based prisms one of which is offset.  Below you can see the problem which you can create yourself with your own dimensions.

You can see from the drawing that the horizontal square based prism (HSBP) is offset towards the back of the vertical square based prism (VSBP).  Continue below to see how to do this problem.

In order to setup the question you need an End View as well as the Elevation and Plan.  You will also need this End View later in order to find some of the points of Interpenetration.  Do not forget to label the edges of the two solids.

For clarity we have removed the construction lines necessary to setup the question.  You should not rub these out when you are doing problems.

From the Plan it is easy to see where the edges 1, 2, 3 and 4 of the HSBP intersect with the surfaces of the VSBP.  Project these points into the Elevation to locate four of the points of Interpenetration.  At this stage you should be begining to see the value of labeling.

From the Plan we can see that the edge a of the VSBP intersects the HSBP, but we cannot see where this intersection occurs.  We need the End View for this.  In the End View we can see that the edge a of the VSBP intersects the edge 1,2 of the HSBP at point 5, and the edge 2,3 of the HSBP at point 6.  Project these points across to the Elevation.

Now you are ready to draw in the lines of Interpenetration in the Elevation.  The simplest way to do this is to follow the order of the points in the End View.  Draw these lines lightly first.  1 to 5 to 2 to 6 to 3 to 4 to 1.  Now you need to determine which of these lines are hidden and which are visible from your point of view.  If this is not clear the lines 5 to 1, 1 to 4, 4 to 3 and 3 to 6 are all behind the VSBP and so are hidden.

Finally line out your drawing remembering that the part of the edge a on the VSBP between points 5 and 6 no longer exists and so should not be lined in.