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How to Draw an Arc of a Given Radius (Connecting Two Lines or an Angle)

Published in Technical Drawing 4 mins read

Drawing an arc of a given radius, especially one that connects two lines or fits within a specific angle, is a fundamental skill in design, drafting, and geometry. This technique ensures precision and tangency, making it applicable to a wide range of fields from architecture to mechanical engineering.

Understanding the Basics of Arc Drawing

Before diving into the steps, it's essential to grasp the core components:

  • Arc: A continuous portion of the circumference of a circle.
  • Radius: The distance from the center of a circle (or arc) to any point on its circumference. When drawing an arc of a "given radius," you are starting with a predefined length for this distance.
  • Center Point: The central point from which all points on the arc are equidistant (at the length of the radius).
  • Tangency: The state of two geometric objects (like an arc and a line) touching at a single point without intersecting. For an arc connecting two lines, it will be tangent to both.

Essential Steps to Draw an Arc with a Specified Radius

The process of drawing an arc of a given radius, particularly when connecting two lines or an angle, relies on accurately determining the arc's center point and then using that point with the specified radius to draw the curve. According to the reference, "this technique is applicable to any angle."

Here's a breakdown of the typical steps:

  1. Step 1: Set Up Your Environment and Determine Radius Size

    • Action: The first step is open your computer so determine how the size of the radius. This means preparing your drawing tools, whether it's a digital drafting program (CAD software) or traditional instruments like a compass and ruler.
    • Insight: In CAD software, you will typically input the desired radius value directly into a command or tool setting. If drawing manually, you'll set your compass opening to the specified radius measurement using a ruler.
  2. Step 2: Identify the Reference Lines or Angle

    • Action: Pinpoint the two lines or the specific angle where the arc needs to be drawn and made tangent. These lines will serve as the boundaries for your arc.
    • Insight: The video reference emphasizes that "this technique is applicable to any angle," meaning the method works whether your lines meet at a sharp corner, a right angle, or an obtuse angle.
  3. Step 3: Locate the Arc's Center Point

    • Action: This is the most crucial geometric step. To find the center of an arc that's tangent to two lines, you'll need to perform an offset operation:
      • Manual: From each of the two reference lines, draw a parallel line inward, at a distance equal to your given radius. The point where these two new parallel lines intersect will be the exact center of your arc.
      • CAD Software: Many CAD programs have a "Fillet" or "Arc" command that automatically calculates this center point once you select the two lines and input the radius.
    • Example: If your given radius is 10 units, you would draw lines parallel to your existing lines, 10 units inward.
  4. Step 4: Draw the Arc

    • Action: Once the center point is accurately located and your radius is set:
      • Manual: Place the compass needle on the located center point. With the pencil lead set to the determined radius, draw the arc so that it smoothly touches both original reference lines tangentially.
      • CAD Software: Use the appropriate arc drawing tool (e.g., "Arc by Center, Start, End" or "Fillet"). Click on the calculated center point, then define the start and end points on the original lines where the arc will be tangent.
    • Outcome: As the reference states, "There we go. So there you see it." This indicates the successful completion of the arc, visibly connecting the two lines with the specified radius.

Practical Insights & Benefits

Method Key Tool/Feature Radius Determination Typical Application
Manual Drawing Compass, Ruler, Pencil Set compass opening on ruler Traditional drafting, basic geometry
CAD Software Fillet Tool, Arc Tool Input numerical value Precision engineering, architectural plans
  • Precision: Using a given radius ensures consistent and accurate curves in your designs.
  • Design Consistency: Applying the same radius creates uniformity across multiple features in a drawing.
  • Versatility: This technique is foundational for creating rounded corners, smooth transitions, and complex curves in various design contexts.