Abstract: A collapsible umbrella with a three primary rib section type rib linkage system. A first feature of the rib linkage is that a stretcher rib, a control link, a center rib, and a control strut cooperate to define a rib linkage with a profile opening of generally quadrilateral configuration above the stretcher rib when the umbrella is held upright and the rib linkage is between full opened and full closed positions. A second feature is that the stretcher rib is comprised of an inner section, an outer section, and an offset section connecting the inner and outer sections. The offset section is sized and configured so that the inner section provides partial support for the umbrella's cover when the umbrella is opened.

Abstract: An umbrella includes a plurality of main links for securing an umbrella cloth and several shortened links each pivotally connected with a tail link which is operatively suspended horizontally to a stretcher link by a supporting link when opening an umbrella so that tail links with the secured umbrella cloth may be flattened horizontally to serve as a brim for shielding purpose without obstructing a user's sight. The tail links are folded to be linearly aligned with the shortened links to form a slim linkage of an umbrella for convenient handling or storage.

Abstract: A rib linkage system of the topless type. A stretcher rib connects the umbrella's runner with each cover rib, a support rib connects the umbrella's ferrule with each stretcher rib, and a control link connects each support rib with its associated cover rib. The connection of the support rib with the stretcher rib is by means of a split or bifurcated brace structure that enhances the stability of the linkage system when the umbrella is full opened. The control link, support rib, stretcher rib, and cover rib all cooperate to define a generally parallelogram configuration beneath the stretcher rib when the umbrella is in between its full opened and full closed positions, and to define a generally triangular configuration when the umbrella is full opened, again to enhance the stability of the linkage system when the umbrella is opened and also to permit the umbrella to collapse into a short and compact storage or full closed position.