Tangency in Engineering Drawing

The use and construction of tangents is very essential in designing and drawing engineering objects, parts, or structures. Tangencies or tangent conditions can be constructed by using engineering drawing tools/equipment such as T-square, triangles, and compass. Also, CAD which is a digital engineering drawing tool/equipment, can be used to construct tangents, easily and automatically.

What is a tangent in engineering drawing?

A tangent is a line that passes through, touches, or intersects only one point located on the surface of an arc or on the circumference/surface of a circle. The point where a tangent line intersects a circle is called the “point of tangency”.

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A point of tangency or tangent condition occurs when a straight line intersects a curve at only one point. In other words, a line is tangent if it touches only one point on a surface.

What is tangency in engineering drawing?

Tangency is a condition whereby lines intersect at only one point without crossing each other. For example, a circle and a line are in a state of tangency (i.e., they are tangent to each other) if the circle intersects or touches only one point on the line. It’s also possible for two curves to be tangent to each other in the same way—by touching each other at only one point.

Figure 1: Different tangent conditions or tangency in engineering drawing

Figure 2: Tangent and non-tangent conditions, respectively, in engineering drawing

How to use the combination of a triangle and compass to draw an arc tangent to a line at a given point

Take the following steps to draw an arc tangent to a line using the combination of a triangle and compass (see Figure 3):

(i) Draw line AB and establish or locate tangent point T, then use a triangle to draw a line perpendicular to AB such that it is touching point T.

(ii) Mark the desired radius on the perpendicular line to establish the center of the arc, place the compass’s point at the center of the arc, use the lead/pencil to target the radius of the arc, and draw the arc to be tangent to line AB and touch point T.

Figure 3: Using or applying the combination of a triangle and compass to draw an arc tangent to a line at a given point

How to use a T-square and triangle or two triangles to draw lines tangent to two circles

Take the following steps to draw lines tangent to two circles:

(i) Set the T-square and two triangles or one triangle (Figure 4) and create tangent lines by placing one side of one of the two triangles between the two circles and projecting a line that is tangent to the circles; adjust the other triangle so its vertex passes through the center of one of the two circles, and use a pencil to mark the points of tangency (which are the points where the line is tangent to the two circles, respectively) on the circumference of the two circles, and draw the tangent line. Repeat this step to draw the second tangent line.

(ii) Draw lines from the centers of the circles perpendicular to the tangent lines, and label the tangent points (T₁, T₂, T₃, and T₄) at the points where the lines from the centers of the circles intersect with the tangent lines.

Figure 4: Using a T-square and triangle or two triangles to draw lines tangent to two circles

How use CAD to draw a tangent

Most CAD systems can automatically locate tangent points. The TAN command is used in drawing tangents in AutoCAD; it enables users to draw a line that is tangent to an arc or circle. After selecting the arc or circle for tangency, the “TAN” command should be used via the command line. The TAN or TANGENT command can be used to draw a line that is tangent to two curves. In AutoCAD, the point of tangency is determined by using the INTERSECTION option to snap the tangent point.