An Exceptional Spherical Five-bar Used as a Deployable Control Surface

Abstract A spherical five-bar linkage generally has two degrees-of-freedom. However, some configurations arise where the mechanism is able to move with an additional degree-of-freedom, even with both input angles fixed. These configurations are termed exceptional. They appear in a configuration surface as embedded straight lines in the direction of its outputs. Without prior knowledge, these lines can be discovered by structured slicing of the configuration surface using the tools of polynomial homotopy continuation. This search procedure is conducted for spherical five-bars of equal-link-length. Cases for adjacent and nonadjacent input angles are analyzed. An equal-link-length spherical five-bar with 90 deg links is used for the design of a deployable control surface for an aircraft. Taking advantage of the exceptional sets in the mechanism, one motor is able to lock, deploy, and articulate the control surface.