https://drive.google.com/file/d/0B1...=sharing&resourcekey=0-JlLEG0Yi_nEVpc73579Mpw will tell you how a Graflex Focal Plane Shutter used in Graflex SLR's and Speed Graphics works and how to service them
however the controls on your Cycle Graphic are totally different and I will not hazard a guess on how to disassemble the controls.
The shutter in your camera is shot. The crinkled section is what happens to the curtain from poor storage, the strips hanging down on the right are the edges of an aperture that have torn off at the edge of an aperture. The curtain is rubberized silk with .007 inch thick copper stays folded over the edges of the aperture openings. They can be oped with a wood chisel, removed, cleaned and reused. The rubberized coating can be removed with Lacquer Thinner and the silk base reused if the silk is not deteriorated. Tears can be repaired by bonding new material of equal size to both sides of the curtain even if only one side is torn. Golden Heavy Body Artist Paint #1040 Carbon Black
https://www.goldenpaints.com/products/colors/heavy-body diluted no more than 1:1 with water painted on in thin layers or with an air brush can be used to recoat a complete curtain or patch pin holes in the curtain and bellows.
I suggest you carefully check the controls for the letters listed in the instructions as they are likely stamped into the metal and may be very difficult to see. Early Graflex SLR's and Speed Graphics controls were Silver plated brass and the use of metal polish will remove the silver plating as its very thin.
Folmer and Schwing used XXX Moroccan leather on their cameras until 1947 when the covering switched to Naugahyde. Using cotton balls or paper towels and 90% Isopropyl Alcohol wipe the leather down to remove the loose and embedded dirt from the leather then using cotton balls give the leather several light coats of Neatsfot oil.
https://tandyleather.com/products/dr-jacksons-pure-neatsfoot-oil?_pos=1&_sid=231ef3904&_ss=r
How do you know this camera is 1902 era? There are no recorded records from that time period just some sales receipts with the camera's serial number that have been reported.
Visit
https://www.graflex.org/ , sign up on the help board
https://www.graflex.org/helpboard/ and post a request for info in the Other Graflex Camera Help section and be patient as a responce may be slow. I'm a major contributor on that site and cannot help further than what I've posted here.