JABATAN KEJURUTERAAN AEROANGKASA

WORK SHEET 3

GEOMETRIC CONSTRUCTION – DRAW ARCS, CIRCLES AND TANGENT

EAS 3721

ENGINEERING DRAWING

LECTURER: Prof. Madya Ir. Mohd. Saleh bin Yahaya / En Faisal

Instruction:

1.0 All work sheet has to drawn in A3 paper size and to be submmited after laboratory timei.

2.0 All laboratory work is considered as course work.

3.0 Make sure your course work is complete with title block.

4.0 All dimension shall be in millimeter (mm) unless stated or otherwise.

EAS 3721 – Engineering Drawing

Work Sheet 4 – Basic Geometric Construction – Arcs, Circles and Tangent.

Background Theory:

4.1.1 Arcs – Through Three Points

We can draw an arc through three points by connecting the points with two lines and drawing perpendicular bisectors through each line to locate the center of the circle as shown in Figure 4.1.

4.1.2 Parallel Lines Using Two Equal Radius Arcs

We may draw one line parallel to another by using method shown in Figure 4.2.

Figure 4.1 - Arc through Three Points

Figure 4.2 - Parallel Lines Using Two Equal Radius Arcs

4.1.3 Tangents – Points of Tangency

A point of Tangency is the theoretical point at which a line joins an arc or two arcs join without crossing. Figure 4.3 shows how to find the point of tangency with triangles by constructing a perpendicular line to the tangent line from the arc’s center. Figure 4.4 shows the conventional methods of marking points of tangency.

Figure 4.3 – Location a Tangent Point

Figure 4.4 – Marking a Tangent Points

4.1.4 Line Tangents to an Arc

We can draw a line from point A to point of tangent to an Arc as shown in Figure 4.5. Connect point A to the arc’s center and bisect line AC (step 1); swing an arc from point M through point C locating tangent point T (step 2); draw tangent to T (step 3); and mark the tangent point (step 4). The point of tangency may be found using triangle, as show in Figure 4.6.

Figure 4.5 – Line Tangent to an Arc from a point

Figure 4.6 – A Tangent to an Arc from a point

4.1.5 Arc Tangent to a Line from a Point

To construct an arc that is tangent to line DE at T and that passes through point P as shown in Figure 4.7, draw the perpendicular bisector of line TP. Draw a perpendicular to line DE at point T to locate the center at point C and swing an arc with radius OT. A similar problem in Figure 4.8, requires drawing an arc of given radius that is tangent to line AB and that passes through point P. An arc with its outer at C is tangent to the line.

Figure 4.7 – An Arc through two points

Figure 4.8 – An Arc tangent to line through a point

4.1.6 Arc Tangent to Two Lines

To construct an arc of given radius tangent to two non-parallel lines that form acute angle is as shown in Figure 4.9. The same steps apply to constructing an arc tangent to two lines that form obtuse angle as shown in Figure 4.10. In both cases, the points of tangency are located with the line drawn from the centers perpendicular and past the original lines. Figure 4.11 shows a technique for finding an arc tangent to perpendicular lines only.

Figure 4.9 – An Arc Tangent to lines making an acute angle

Figure 4.10 – An Arc Tangent to lines making an obtuse angle

Figure 4.11 – An Arc Tangent to perpendicular lines

4.1.7 Arc Tangent to an Arc and a Line

Figure 4.12 shows the steps for constructing an arc tangent to an arc and a line. Figure 4.13 shows variation of this technique for an arc drawn tangent to a given arc and line with the arc reversed.

Figure 4.12 – An Arc Tangent to an Arc and a Line

Figure 4.13 – An Arc Tangent to an Arc and a Line

4.1.8 Arc Tangent to Two Arcs

Figure 4.14 shows how to draw an arc tangent to two arcs concave from the top. Drawing a convex arc tangent to the given arcs requires that its radius be greater than the radius of either of the given arcs, as shown in Figure 4.15. One variation of this problem, shown in Figure 4.16, is to draw an arc of given radius tangent to top of one arc and the bottom of the other. Another, as shown in Figure 4.17, is to draw an arc tangent to a circle and a larger arc.

Figure 4.15 - Convex Arc Tangent to Two Arcs

Figure 4.14 - Concave Arc Tangent to Two Arcs

V

Figure 4.17 - Arc Tangent to Two Arcs

Figure 4.16 - An Arc Tangent to Two Circles

4.2 Course Work 4

You are required to construct the 3D model and the drawing for the given shapes on A3 paper size. Choose scale that will best fit to the paper size Mark all points of tangency and show different line type (center line, outline etc.)

4.2.1 Lever Crank (Assume the crank thickness is 15mm.)

4.2.2 Hook Construction (Assume the hook thickness and apply fillet radii of 12

mm.)

4.2.3 Gear Arm Construction (Assume the flange thickness is 20mm, and web

thickness is 10mm.)