Improved flexible joint arrangements employ at least one flexure member that interfaces with wrapping surfaces defined on the bases to which the ends of the flexure member are connected. The flexure members are configured to define a traveling instantaneous axis of rotation that moves along a path defined by the interface of the flexure and the wrapping surfaces as the bases move relative to each other. The flexure members and the bases can be constructed of a monolithic material. The wrapping surfaces of the bases can be asymmetric in cross-sectional shape. The radius of curvature of the traveling instantaneous axis of rotation can be configured to change only in discrete quantum steps without reversals. In other embodiments, the flexible joint arrangement can be configured as one or more three bar linkages in which the middle bar is rigid and the outer bars are flexure members in accordance with the various embodiments.