How can I deform 2D pattern onto curved surface
Since I was working without the benefit of your drawing, things will look somewhat different but the concept is the same. The size of the peanuts must be scaled relative to the distance each peanut is from the center of the main circle.
Using a 7.5 degrees angle, a pattern was created from half peanuts (the red pattern shown) and then mirrored (the blue pattern) and everything made into a 15 degree block. The array command was used and 24 blocks over 360 degrees completed the full pattern.
The picture below along with the referenced post should provide enough information for you to do what want - perhaps it will requiring some trial and error. You will not get the results you want by tracing over unless the diameters and spacing of the circles somehow matches your requirements. I'm not going to post the drawing - if this is an assignment you need to put in the effort. If this is work related, you should learn the procedure so you know what to do next time.
Intersection points, centerpoints and tangent locations are key to the layout.
I understand, I agree it will be more valuable if I learn from it.
That being said, I attempted your method, but I am confused on why your red circles go above the outer radius? At least in the context of your previous picture of the full peanut structure, you were able to get 3 unit cells alternating in a line.
The picture I provided below is me trying to recreate your unit cells. However, my circles are not really "hugging" each other which I want so that the curves between the peanuts are joined. I know you have minor lines offsetting your blue and black circles. How did you determine the arc angles for that? I am afraid if I try to alter the angle I will get overlapping circles or if I try to scale the circles down I will lose the arc angle and will not be able to do polar array evenly.
Thanky you for your advice!
The red circle confusion is easy to resolve - create a new outside arc.
As I alluded to earlier - trial and error may be required.
If the orange arc in your drawing are the inner and outer arcs to be filled, you might have to change the circle diameters to get it to work.
You asked how did I determine the arc angles? Everything was ARBITRARY - inner arc, outer arc, and all of the circle diameters.
How did you determine your circle diameters? what determines the arcs you use? Is 15 degrees a requirement?
Are you limited to the number of peanut rows? Why did you place three black circles side to side at those two locations?
These are multiple variables which need to be considered. The right side of the picture was included to illustrate why you can't just scale from a drawing. The inner and outer arc diameters determine the size of the circles making up the peanuts and the number of peanut rows needed.
Suggestion: Get rid of the middle black circles and resize the circle diameters.
This is an interesting topic.
I have created a design based on my idea, wherein the peanut shapes are progressively scaled down from the outer perimeter towards the center in accordance with a specific rule. Consequently, I have established tangential circles with lines drawn from the center of the large circle, symmetrically arranged across the vertical axis. This configuration automatically scales down the peanut shapes towards the center of the large circle. The sole adjustment required is to modify the radius 'a' of the uppermost peanut shape, and all subsequent peanut shapes will automatically resize proportionally.
Your design is really clean! I started to just use the tangents of the circle to see if I could fit it. I like how even your cells are as well. My horizontal cells are skinnier than the vertical ones. How did you determine the scaling tangent lines?
The two yellow lines and the vertical axis serve as primary reference lines. The two yellow lines form a 15-degree angle and are symmetrical about the vertical axis, intersecting the center of the vertical peanut shapes.
Subsequently, horizontal peanut shapes are created, and all circles are made tangential to each other using geometric constraints (see tangency symbols). The circles of the peanut shapes are then constrained to be tangential to the red and green lines.
Crucially, the tangent lines must be symmetrical about the vertical axis, and the circles must remain tangential to each other.
It is not necessary to increase the items in the array from 24 to 27. If the angle between two vertical peanut shapes is 15 degrees, then the quantity should remain at 24.
I should have responded with a little more specificity......I assumed the OP wanted the peanuts to consist of circles tangent to each other (see below).
Eliminating this assumed requirement would allow the 15 degree (or any other angle) work but the "peanut" shape would become distorted.
Retaining tangent circles (and keeping the same number of peanuts) would require a change in either the angle or the distance between the major inner and outer arcs.
