An umbrella is an external accessory that is commonly used by individuals to prevent exposure to weather factors such as sunlight, rain, and snow. Common umbrellas include compact travel umbrellas, straight umbrellas, three-fold umbrellas, etc.

    Many modern umbrellas have telescoping frames that contain an expansion spring and are connected to a second spring by the rider. Springs aid in the compression and automatic expansion of the umbrella, while structural arms connected to the telescoping frame by the rider help strengthen the canopy. They also help reduce the force the user has to input to close the umbrella.

    Umbrella manufacturers want to minimize the cost and time of the manufacturing process. What would they want to do for this?

    The simplicity of Design: Manufacturers need simple designs with simple geometries.

    The modularity of design: Manufacturers need a modular design that optimizes the manufacturing process.

    Materials: Low-cost and non-toxic materials minimize manufacturing costs.

    Manufacturing Process: A fast and low-cost process optimizes the price of manufacturing.

    Safety: Manufacturers require safe manufacturing procedures to minimize employee accidents on the job.

    Storage: Minimal weight and overall size make objects easier to store and transport.

    When a retractable umbrella opens, two things happen: (1) it extends vertically away from the handle; (2) it's eight arms extend outward to stretch the polyester cloth and protect the user from the elements. The opposite is true when the umbrella is closed. In the description below, specialized terms (in italics) are used. See Figure 5 and Figure 6 for a description of what these terms refer to.