Object Autopsy
I have decided to dissect an umbrella. Although it is an everyday object, and most of its workings are easily visible, I have never really taken a good look at how one works. Also, I really wanted to autopsy a mechanical object and not an electrical one.
I started by cutting the threads that connect the cloth part of the umbrella to the metal structure. It is connected with thread in four places: at the tips of each point, and at three points along the metal ribs.
This leaves the cloth only connected to the handle at the top of the umbrella by a hard plastic top.
At the top of the post, under a little frill of umbrella cloth, you can see how the metal ribs are connected to the main post. Only a thin wire wraps around them all, holding them in a notched circle of metal. When I removed the wire, the ribs sprung out of the notches, 
leaving the notched cylinder empty.
The ribs were connected to the post in two other places: 
first by way of a short wire that slides into a hole on the first segment of each rib and is held on the post at the other end by a circle of wire; 
and second at another end of the rib structure, also held on the post by a circle of wire.
Once I untwisted the three wires holding the ribs to the post, I had a seven-fingered metal claw, and once the wires were threaded out of the holes in the ribs, I had seven separate fingers.
Each finger is made up of five lengths of metal. Two of them are cylindrical in shape - basically thick wires -, two are flat metal that have been shaped into half-cylinders to give them greater stability against bending, and one is flat metal that has been shaped into a full cylinder - basically a hollow wire.
The post, bereft of ribs, holds only the cloth covering and the springs and notched cylinders that keep the ribs in place.
To get the springs off, I had to separate the two sections of the post (this was a collapsible umbrella). They do not slide apart easily because they have been pinched together where they meet.
The metal fin, when depressed, allows you to slide the tubes closer into each other, but it was impossible to pull them apart.
However, with brute force, I was able to separate the tubes from each other, mostly intact. The fin is an interesting shape, 
and I’m not really sure the purpose of the shape. The end of the inner post broke off inside the outer post, so perhaps the answer to the mystery lies inside.
Remember back to the plastic top holding the cloth on the post? 
I destroyed the plasic taking it off, and what remained was the the post, 
a cloth ruffle, and 
the main piece of cloth.
Here are all the pieces of the umbrella:
Conclusions
1. It is understandable why umbrellas flip open so often; the ribs, despite being formed to resist the forces of wind, are still quite flimsy.
2. The structure and method of construction is for the most part quite simple and understandable. Although I don’t have access to pieces of exactly the same shape, I could reconstruct a working umbrella based on the same structure out of metal wires or thin wooden strips. The cloth is a simple repeating shape that is sewed one to the other until it forms a circle. The ribs are pieces of metal with pin connections holding them together. The cloth is sewn onto the ribs. The post would be the most complex part, especially if I wanted it to snap open with the push of a button.