Creating a 2D coiled spring along a circular path

Question

Looking to create a perfect coiled spring similar to this image, but with less numbers of coils (below image having 8):

How would I go about creating an image like this with 4, 6 or 10 coils, shaped in a circular shape? Thank you in advance.

Answer 1

1. Draw with the pen a 2 node curve. That's a half-loop. Hold shift to get exactly horizontal node handles.

2. Make a reflected copy. Drag the half-loops to meet exactly in the bottom node. The result is a surely symmetric full loop. Have smart guides and snap to points on. Select an item and drag a node with the direct selection tool. The rest of the shape follows.

3. Make copies. Here I have total 5 loop. Drag them to the Brushes collection an define them to be an art brush.

4. draw a circle

5. apply the brush

Pattern brush works also and it needs only one loop (=image 2) if you let the pattern to be stretched to fill the circle perimeter (=stretch to fit) in the brush definition dialog. The number of the loops depend on the length of the circle perimeter.