Solids in contact.

Introduction. Solids in contact is in relation to cones, spheres and other cylindrical objects in contact. Sometimes you can get objects with flat surfaces also in contact. E.G. cubes, prisms, rectangles. In a question you are usually asked to locate a sphere in contact with a point of contact that you are given or maybe given the point of contact in plan or elevation and obtain it in the other view.

Background. Solids in contact generally work with cylindrical objects. E.G. cones, spheres, hemispheres, cylinders, etc. Three things you need to understand are: Points of Contact (POC) Location of objects when given certain pieces of information Necessary steps when looking for objects in certain views There are more but these may be used in Leaving Certificate drawing.

Points of contact. (poc) These are points where two objects meet and are represented by POC on your drawings. When you have two spheres/sphere and a cone/sphere and a cylinder you get a point of contact. This is not the case if you have a cylinder or a cone in contact with a cube or a flat surface left against the side of the cone or cylinder.

Points of contact (POC) Below you can see how the point of contact comes about.

Point of contact (cone) On a cone there are a series of lines running up to the top of the cone. These are called GENERATORS. The outer two generators are known as the extreme generators. These can be obtained by dividing the cone up in plan with your 60/30 set-square, projected to XY line and then joined to the vertex.

Example of a cone with generators

Establish POC. This aspect is in relation to establishing a POC between two objects. These can be got between spheres, cones, cylinders, hemispheres. The general rule is that where two objects touch then a POC is established.

Establish poc. When you require to get the POC you join the two centre points first. Then drop the POC from elevation until it meets the centre line of the object in plan. Then swing this point up until it meets the line you used to join the two centre points. This is then the POC and you bring this point back up to the elevation and bring the initial POC across until it meets this line and this is it in elevation.

Establish poc.

To draw a sphere in contact with a cone. Draw a sphere of radius 15mm in contact with the cone shown below at point P and is tangential to cone.

To draw a sphere in contact with a cone. First of all you draw plan and elevation. The POC is up 20mm in elevation and down 25mm in plan. You project down where the 20mm line in elevation cuts the edge of the cone you project this down to centre line in and swing it down until it cuts the 25mm line.

To draw a sphere in contact with a cone. This is then the POC in plan. Project this back up until it cuts the 20mm line and this is it in elevation. Where the 20mm cuts the extreme generator project out perpendicular and mark off the radius of the sphere. We do this as we can see the cone and sphere in contact as we look in at 90˚ to both. Drop this down to the centre line in plan.

To draw a sphere in contact with a cone. Project out the generator that the POC is on past the cone. Swing the initial centre down to meet this. This is then the centre of the sphere in plan.

To draw a sphere in contact with a cone. Bring the initial centre horizontally to the left and project the new centre up to meet this and this is the correct centre. The finished sphere can then be drawn in.

To draw a sphere in contact with a cone. In a question you may be asked to draw a sphere in contact with a point P and is on the horizontal plane. This simply means it is on the ground or the XY line.

Rolling of solids. This relates to rolling solids around each other in order to get their finished position. This is usually done with circular objects. You add the radius to the object and swing it round about itself in plan. As mentioned before you get it in elevation as you look in at it and then drop it down to its corresponding centre line and swing it round until it meets the other line you obtained by doing the similar steps.

Rolling of solids. This is an example of rolling a sphere into place. Draw the projections of a sphere radius 15mm which will be in contact with the sphere and the cylinder shown below.

Rolling of solids. Firstly draw your plan and and elevation of the given solids.

Rolling of solids. We know the radius of the sphere is 15mm so we come up 15mm of the XY line and draw a line parallel to the XY.

Rolling of solids. As the radius is 15mm we add on 15mm to the radius of the sphere and swing it until it cuts the 15mm horizontal line. this is then dropped down onto the centre line in plan.

Rolling of solids. From the centre in plan we then swing this round in the direction of the cylinder. we repeat these steps to the cylinder, but in elevation there will be a vertical line out 15mm from the edge of the cylinder.

Rolling of solids. This once again is dropped down onto the centre line of the cylinder in plan. Then swing this down until it cuts the previous line. This is the finished centre point for the sphere in plan.

Rolling of solids. To get this in elevation we simply just project it straight up until it cuts the 15mm horizontal line we drew earlier.

Rolling of solids. For practice in this area of the topic refer to your workbook.

Auxiliaries in solids in contact. Sometimes, depending on the question we may need to acquire an auxiliary in order to see the necessary information within a question. By completing an auxiliary we see the component in a different orientation the position of the components will not change. By doing an auxiliary it allows us to look in at a surface at 90˚ and get and edge view of it. We can work like it was an elevation and start applying heights.

Auxiliaries in solids in contact. An auxiliary which is projected from the plan is an auxiliary elevation. An auxiliary which is projected from the elevation is an auxiliary plan.

Auxiliaries in solids in contact. A simple auxiliary question: Draw the given plan and elevation in order to get the sphere in its true position.

Auxiliaries in solids in contact. Draw all the information that you can from the question. As the sphere is radius 25mm, in elevation you can draw a line parallel to the XY in construction.

Auxiliaries in solids in contact. We then start the auxiliary by looking in at 90˚ to the surface. As the surface in this question is parallel to the XY line all our projection lines are simply horizontal, but you usually project parallel to the surface.

Auxiliaries in solids in contact. We then set up a second XY line and call it X1Y1. as this is an elevation because it is being projected from a plan we can take all the measurements from the existing elevation and apply them over here to get the pyramid. Now we can see the edge of the surface.

Auxiliaries in solids in contact. As we did before in an elevation we apply the radius of the sphere to the edge of the pyramid and on to the X1Y1 line. Where these cross is the initial centre of the sphere. This is then projected back to plan.

Auxiliaries in solids in contact. Where this cuts the centre line is the centre of the sphere. This can then be projected straight up to elevation and where it cuts the 25mm line we earlier applied is the centre of the sphere in elevation and this is the drawing finished.

Auxiliaries in solids in contact. For practice in this area of the topic refer to your workbook.