Department of Technological Education Graphic Communication Nairn Academy

Department of Technological Education Graphic Communication Nairn Academy

Department of Technological Education Tangency – 90 o angle (1) Start the tangency with the two lines that are to be joined by the curve. In this case the two lines are drawn at right angles to each other. The two lines are to be joined by a 30 mm radius curve.

Department of Technological Education Tangency – 90 o angle (2) Draw two construction lines which are parallel with the outlines to be joined. 30 Because the curve to be drawn is 30 mm radius the two construction lines should be drawn 30 mm away from the outlines. 30 Where these two lines cross will be the centre for the tangency curve.

Department of Technological Education Tangency – 90 o angle (3) Mark where the two construction lines cross with a small dot as this will act as the centre of the curve to be drawn. Project two construction lines through this centre until they cross the outlines. These lines should be projected at 90 o to the outlines. Mark each of the points where the construction lines cross the outlines with a small dot. These are the two tangent points where the straight lines and the curve meet.

Department of Technological Education Tangency – 90 o angle (4) Draw a 30 mm radius arc using the centre found, and starting and ending at the tangent points. Note that it is usual to draw the curves first and then draw the straight lines after. Finish the drawing by adding the straight lines.

Department of Technological Education Tangency – <90 o angle (1) The second style of tangency will join together two lines that meet at less than a 90 o angle. Again the two lines will be joined with an arc which has a radius of 30 mm.

Department of Technological Education Tangency – <90 o angle (2) Two construction lines should be drawn 30 mm away from the outlines and they should also be parallel to the outlines. 30 30 Where these two lines cross gives the centre for the 30 mm radius tangency arc.

Department of Technological Education Tangency – <90 o angle (3) Mark the centre of the arc with a small dot. Project two construction lines from the centre at right angles to the outlines. Where these lines cross the outlines gives the tangent points for the 30 mm radius curve.

Department of Technological Education Tangency – <90 o angle (4) Using the centre found draw a 30 mm radius curve from the first tangent point to the second tangent point. Complete the drawing by adding the straight lines. R 30

Department of Technological Education Tangency – >90 o angle (1) The final method of drawing tangency arcs to two straight lines involves an angle of more than 90 o. Again, start with the two straight lines that are to be joined.

Department of Technological Education Tangency – >90 o angle (2) Draw two construction lines 30 mm away from the outlines. 30 Mark the point where the two construction lines cross with a small dot. This is the centre of the 30 mm tangency arc. 30 As with the previous two methods these construction lines should be parallel to the outlines.

Department of Technological Education Tangency – >90 o angle (3) Draw two construction lines through the centre point found. These lines should be at 90 o to the outlines. Mark each of the points where these two lines cross the outlines with a small dot to indicate where the tangent points are.

Department of Technological Education Tangency – >90 o angle (4) Draw a 30 mm radius arc using the centre found and starting and ending at the tangent points. Complete the drawing by adding the straight outlines. R 30

Department of Technological Education Tangency – Below two circles (1) The starting point for this type of tangency is finding the centres for the two circles that the tangency arc should touch. Two circles will be used which are 70 mm apart and positioned on a common horizontal centre line.

Department of Technological Education Tangency – Below two circles (2) The two circles are added to the drawing. The left circle has a radius of 30 mm, while the right circle has a radius of 20 mm.

Department of Technological Education Tangency – Below two circles (3) The circles are to be joined with an arc of 60 mm radius which touches underneath the circles. Draw a small arc 80 mm radius (60 mm radius for tangent arc plus 20 mm radius for circle) from the centre of the right circle. Indicate where the two arcs cross with a small dot. R 90 Draw a small arc 90 mm radius (60 mm radius for tangent arc plus 30 mm radius for circle) from the centre of the left circle. R 80 The centres for the two circles will be used to find the position of the tangent arcs centre.

Department of Technological Education Tangency – Below two circles (4) Draw a construction line from the centre of the two arcs that you have just found to the centres of each circle. Where this line crosses the circle is the tangent point and this position should be marked with a small dot.

Department of Technological Education Tangency – Below two circles (5) Using the centre just found, draw an arc from the first tangent point to the second tangent point. R 60

Department of Technological Education Tangency – Above two circles (1) This time the tangent arc will touch above the circles. Draw arcs of 80 mm radius from the left circle and 90 mm radius from the right circle, marking the crossing point with a small dot. R 80 As the centres of the circles will be closer to the tangencies centre than the tangent points it is now necessary to subtract the radius of the circle from the tangency dimension. R 9 0 A tangency arc of 110 mm will be used.

Department of Technological Education Tangency – Above two circles (2) The tangent points can now be marked. As with the previous version the centre of the tangent arc and the centres of the circles are joined with a straight line, but the line needs to be extended this time until it touches the top part of the circle. Mark the found tangent points with a small dot.

Department of Technological Education Tangency – Above two circles (3) Using the tangency centre just found and working from the first tangency point to the second, draw a 110 mm radius arc.

Department of Technological Education Tangency – Above two circles (4) Complete this drawing by adding the outlines to the remaining parts of the original circles.

Department of Technological Education Tangency – Inside and Outside circle (1) The next tangency problem will join two circles with a tangency arc which touches the inside of one circle and the outside of the second circle. In this case the dimensions of the tangency arc will be 100 mm radius.

Department of Technological Education Tangency – Inside and Outside circle (2) This tangency requires a combination of processes done in the previous examples. The second arc should be drawn at 120 mm radius (100 mm arc plus an extra 20 mm to reach the centre of the circle) from the centre of the right circle. Mark the centre of the tangency arc with a small dot and draw construction lines to find the position of the two tangent points. R 7 0 The first arc should be drawn at 70 mm radius (100 mm arc minus 30 mm to centre of circle) from the centre of the left circle. 20 1 R

Department of Technological Education Tangency – Inside and Outside circle (3) Draw the arc for the tangency first and when this is correctly in place finish the rest of the drawing. R 100

Power. Point Presentation produced by John Mc. Rae, Nairn Academy 2003