2 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.
3 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 informationNecessary steps when looking for objects in certain viewsThere are more but these may be used in Leaving Certificate drawing.
4 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.
5 Points of contact (POC) Below you can see how the point of contact comes about.
6 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.
8 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.
9 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.
11 To draw a sphere in contact with a cone. Draw a sphere of radius15mm in contact withthe cone shown belowat point P and istangential to cone.
12 To draw a sphere in contact with a cone. First of all you draw planand elevation. The POC isup 20mm in elevation anddown 25mm in plan. Youproject down where the20mm line in elevationcuts the edge of the coneyou project this down tocentre line in and swing itdown until it cuts the 25mmline.
13 To draw a sphere in contact with a cone. This is then the POC in plan.Project this back up until itcuts the 20mm line and thisis it in elevation. Where the20mm cuts the extremegenerator project outperpendicular and mark off theradius of the sphere. We dothis as we can see the coneand sphere in contact as we lookin at 90˚ to both. Dropthis down to the centre line inplan.
14 To draw a sphere in contact with a cone. Project out the generatorthat the POC is on past thecone. Swing the initial centredown to meet this. This isthen the centre of the spherein plan.
15 To draw a sphere in contact with a cone. Bring the initial centrehorizontally to the leftand project the new centreup to meet this and this isthe correct centre. Thefinished sphere can then bedrawn in.
16 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.
17 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.
18 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.
19 Rolling of solids. Firstly draw your plan and and elevation of the givensolids.
20 Rolling of solids. We know the radius of the sphere is 15mm so we come up 15mm of the XY line anddraw a line parallel to the XY.
21 Rolling of solids. As the radius is 15mm we add on 15mm to the radius of the sphere andswing it until it cuts the15mm horizontal line.this is then dropped downonto the centre line in plan.
22 Rolling of solids. From the centre in plan we then swing this round in thedirection of the cylinder.we repeat these steps to thecylinder, but in elevation therewill be a vertical line out 15mmfrom the edge of the cylinder.
23 Rolling of solids. This once again is dropped down onto the centre line ofthe cylinder in plan. Thenswing this down until it cutsthe previous line. This is thefinished centre point for thesphere in plan.
24 Rolling of solids. To get this in elevation we simply just project it straight up until it cuts the15mm horizontal line wedrew earlier.
25 Rolling of solids.For practice in this area of the topic refer to your workbook.
26 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.
27 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.
28 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.
29 Auxiliaries in solids in contact. Draw all the informationthat you can from thequestion. As the sphere isradius 25mm, in elevationyou can draw a line parallelto the XY in construction.
30 Auxiliaries in solids in contact. We then start the auxiliaryby looking in at 90˚ to thesurface. As the surface inthis question is parallel tothe XY line all our projectionlines are simply horizontal,but you usually projectparallel to the surface.
31 Auxiliaries in solids in contact. We then set up a secondXY line and call it X1Y1.as this is an elevationbecause it is being projectedfrom a plan we can take allthe measurements from theexisting elevation and applythem over here to get thepyramid. Now we can see theedge of the surface.
32 Auxiliaries in solids in contact. As we did before in anelevation we apply theradius of the sphere to theedge of the pyramid andon to the X1Y1 line. Wherethese cross is the initialcentre of the sphere. This isthen projected back to plan.
33 Auxiliaries in solids in contact. Where this cuts the centreline is the centre of thesphere. This can then beprojected straight up toelevation and where it cutsthe 25mm line we earlierapplied is the centre of thesphere in elevation and thisis the drawing finished.
34 Auxiliaries in solids in contact. For practice in this area of the topic refer to your workbook.