how can i construt a deltoid in engineering drawing?

Question

how can i construct a deltoid using ruler and pair of compasses ? That is, the step by step procedure of constructing it.

Answer 1

1.Draw a circle
2.Draw (a ghost) equilateral triangle within that circle. The vertices of that triangle are the vertices of the deltoid
3.Using a compass find a point that is equally spaced between any two vertices and the middle of the deltoids arc. (It will take a little trial and error)

For more information please see reference supplied below

Answer 2

Since the deltoid is a type of cycloid, it has a continuously changing radius of curvature and so it cannot be drawn precisely with a compass. You certainly can draw a excellent approximation though.

Begin by drawing a circle inside which the deltoid will be inscribed. Call the radius of this circle R. Consturct 3 rays from the center of the circle at 120 degree angles. Mark off a point on each ray that is 2.583 R from the center (I used the analytic value of 31/12 * R). Call this distance S. Set your compass at 2.256 R (analytically, that is sqrt(S^2 - S + 1)). Strike off an arc from each of the points on the rays, drawing only the portion that falls within the circle. While not exact, this construction is accurate to within a 1%.

I did a little more work on getting a good fit and found that