1. Shawlands Academy Department Of Technical Education
Graphic Communication

2. Tangency – 90o 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 30mm radius curve.

3. Tangency – 90o angle (2) 3
Draw two construction lines which are parallel with the outlines to be joined.
Where these two lines cross will be the centre for the tangency curve.
Because the curve to be drawn is 30mm radius the two construction lines should be drawn 30mm away from the outlines. 3

4. Tangency – 90o 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 90o 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.

5. Tangency – 90o angle (4)
Draw a 30mm 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.

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

7. Tangency – <90o angle (2)
Two construction lines should be drawn 30mm away from the outlines and they should also be parallel to the outlines.
Where these two lines cross gives the centre for the 30mm radius tangency arc. 3 3

8. Tangency – <90o 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 30mm radius curve.

9. Tangency – <90o angle (4)
Using the centre found draw a 30mm radius curve from the first tangent point to the second tangent point.
Complete the drawing by adding the straight lines. R 3

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

11. Tangency – >90o angle (2)
Draw two construction lines 30mm away from the outlines.
As with the previous two methods these construction lines should be parallel to the outlines.
Mark the point where the two construction lines cross with a small dot. This is the centre of the 30mm tangency arc. 3 3

12. Tangency – >90o angle (3)
Draw two construction lines through the centre point found.
These lines should be at 90o 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.

13. Tangency – >90o angle (4)
Draw a 30mm radius arc using the centre found and starting and ending at the tangent points.
Complete the drawing by adding the straight outlines. R 3

14. 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 70mm apart and positioned on a common horizontal centre line.

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

16. Tangency – Below two circles (3)
The circles are to be joined with an arc of 60mm radius which touches underneath the circles.
The centres for the two circles will be used to find the position of the tangent arcs centre.
Draw a small arc 90mm radius (60mm radius for tangent arc plus 30mm radius for circle) from the centre of the left circle.
Draw a small arc 80mm radius (60mm radius for tangent arc plus 20mm radius for circle) from the centre of the right circle.
Indicate where the two arcs cross with a small dot. R 9 R 8

17. 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.

18. Tangency – Below two circles (5)
Using the centre just found, draw an arc from the first tangent point to the second tangent point. R 6

19. Tangency – Above two circles (1)
This time the tangent arc will touch above the circles.
A tangency arc of 110mm will be used.
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.
Draw arcs of 80mm radius from the left circle and 90mm radius from the right circle, marking the crossing point with a small dot. R 8 R 9

20. 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.

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

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

23. 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 100mm radius.

24. Tangency – Inside and Outside circle (2)
This tangency requires a combination of processes done in the previous examples.
The first arc should be drawn at 70mm radius (100mm arc minus 30mm to centre of circle) from the centre of the left circle.
The second arc should be drawn at 120mm radius (100mm arc plus an extra 20mm 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 R 1 2

25. 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 1

26. PowerPoint Presentation produced by John McRae, Nairn Academy 2003
Department Of Technical Education
PowerPoint Presentation produced by John McRae, Nairn Academy 2003