Structure and kinematic analysis of radially deployable planar linkages

Based on the structural geometrical connections of a radially foldable planar linkage, the locus of the hinged points in a scissor-like unit composed of angulated elements is derived, the structural constrained conditions of the scissor-like unit are discussed when the hinged points move radially. Then we present the kinematic equations of two inter-connected angulated elements and establish the kinematic model of deployment for foldable linkages using the method of coordinate transformation. Some new properties of this radially foldable linkages are revealed, including the condition for the maximum deployed extension and the angulated relationship between two inter-connected elements. And we have established the structure connections and kinematic model of multilayer deployable linkages by discussing the special case of all the hinged points in the deployable linkage moving radially. Finally, simulation examples verify the effectiveness of the kinematics analysis method.