Contemporary 3-D modelling programs can create the complex form of an involute tooth gear with simple transformations. However, 2-D computer aided design (CAD) programs require traditional methods of construction using orthographic projection. Although the process takes more time than modelling programs, the involute curves and gear teeth can be easily and accurately represented using lines, circles and splines to create the gear's plan and elevation.
- Skill level:
- Moderately Easy
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Things you need
- CAD program
- Involute tooth gear
Draw the overall limits of the gear and teeth as a circle in plan. Mark the centre point of the circle. Draw the interior extents of the gear teeth and the gear's axle as circles using the previously drawn centre point. All three circles share the same centre point but have different radii.
Examine the top and the bottom of the gear. Note the bottom's tooth edge locations relative to the top of the gear. Draw the profile of the bottom of the gear over the limits of the gear and teeth in Step 1. Overlay the profile of the gear's top using a different colour to differentiate it with the bottom profile. Double-check the orientation of the two profiles relative to the rotation of the gear teeth on the involute gear.
Draw a horizontal line through the centre point of the circles and gear profiles. Draw below the plan two vertical lines from the intersections of the horizontal line through the overall limits. Note the overall height of the cylindrical gear. Draw two horizontal lines, over the vertical lines, separated in distance by the dimension of the overall height. This creates a rectangle that is the profile of the involute gear. Lightly draw a horizontal line through the centre of the constructed rectangle, and draw two more light horizontal lines to divide the rectangle into four equal pieces. The five lines drawn at the top, bottom, middle and quarter points of the rectangle will correspond with the plan projection of the gear's curving teeth.
Go to the plan view with overlaid top and bottom profiles. Draw a light line from the centre point through each of the tooth edges for both the top and bottom profiles. Use different colours for clarity. Note the rotation of the profiles from top to bottom. For each tooth, mark the rotation with an arc from the tooth edge bottom to tooth edge top. This will denote the angle of the tooth rotation about the centre point. Bisect the angle of tooth rotation with a line through the centre point. Bisect the two new angles, again. Now, there are four equal angles whose sum equals the overall angle of tooth rotation about the centre point. Repeat this for each tooth on separate drawing layers for clarity. The five lines that constitute the legs of the four angles will correspond with the five lines drawn on the constructed elevation.
Because the involute curve spirals at a constant angle over a cylinder's face, the involute curve's distance from the gear end is directly related to the angle of rotation. So, points can be plotted on the elevation related to the location and rotation of the gear profiles in plan.
For each tooth, draw a line down from the interior and exterior of each tooth edge, in plan, to the corresponding height on the elevation. Therefore, the bottom profile will be plotted on the lowest line of the elevation, and the top profile will be plotted on the highest line of the elevation. The lines of the bisected angle of rotation should be plotted on the middle line of the elevation, and the seconds bisections should be plotted on the quarter-point lines. Draw a spline through the five plotted points of each interior and exterior tooth edge. Remember, the elevation shows an exterior orthographic view of one side of the involute gear; erase overlapping splines that are hidden from the elevation's view.
Tips and warnings
- 3-D projections can be constructed from the plan and elevation drawings (see Resources section).
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