Short Answer:

In engineering sketches, tangents and normal lines are drawn to show directions at specific points on curves or circles. A tangent is a straight line that just touches the curve at one point without crossing it, while a normal line is drawn perpendicular to the tangent at the same point.

To construct them, first find the point on the curve, then draw a straight line that just touches the curve (tangent), and from that point draw another line at a 90° angle to it (normal). These constructions help in understanding motion, force direction, and geometry in mechanical parts.

Detailed Explanation:

Construction of tangents and normal lines in engineering sketches

In mechanical and engineering drawings, tangents and normal lines are used frequently to represent directions of motion, forces, contact, and geometry. Especially when dealing with curves, circles, cams, gears, and trajectories, it’s important to know how to correctly construct these lines using basic tools like a compass, ruler, and protractor.

Tangent line construction

A tangent is a line that touches a curve at exactly one point without crossing it. It shows the instantaneous direction of the curve at that point. Tangents are used in many situations such as:

• Drawing velocity directions in cams and gears
• Creating smooth transitions between curves and straight lines
• Showing path of motion in mechanisms

Steps to draw a tangent to a circle:

1. Draw the circle with a known radius and mark the center (O).
2. Mark the point on the circle where you need the tangent (P).
3. Draw a line from the center (O) to point P. This line is the radius.
4. At point P, use a set square or protractor to draw a line at 90° to the radius.
5. This line is the tangent to the circle at point P.

Steps to draw a tangent to a curve:

1. Identify the point on the curve where you want the tangent.
2. Draw a smooth part of the curve around that point.
3. Using a French curve or compass, draw a line that just touches the curve at that point without crossing it.
4. Adjust with trial if needed until the line is smooth and only touches the curve at one point.

Normal line construction

A normal line is a line drawn perpendicular to the tangent at the point of contact. It represents the direction of force or pressure, especially in physics and mechanics.

Steps to draw a normal to a circle:

1. Once the tangent at point P is drawn, use a protractor or 90° angle tool.
2. At point P, draw a line at 90° to the tangent.
3. This is your normal line, and it will pass through the center of the circle in case of circular curves.

For non-circular curves:

1. After constructing the tangent line at the required point, use a set square or compass to construct a perpendicular from that point.
2. This perpendicular line is the normal to the curve at that location.

Importance in mechanical drawings

• Cams: Tangents and normals are used to analyze motion paths of cam followers.
• Gears: Tooth contact is analyzed using tangents and normals.
• Forces: Normal and tangential force directions are studied in stress and friction problems.
• Curves: In sketching and machine part design, tangents help join curves smoothly.

Understanding and drawing tangents and normals correctly helps in accurate mechanical design, motion analysis, and stress calculations.

Conclusion:

Tangents and normal lines are essential in engineering sketches to show directions, motion paths, and contact forces. A tangent touches a curve at one point and shows direction, while a normal is perpendicular to it and often points toward the center or force line. These lines are constructed using simple tools and play a big role in designing cams, gears, curves, and mechanical parts. Clear knowledge of these constructions improves drawing quality and helps in real-world mechanical design.