Numerical Approach to the Kinematic Analysis of Deployable Structures Forming a Closed Loop

This article is concerned with spatial linkages forming a closed loop. In one extreme configuration (deployed), these linkages form a frame of polygonal shape, such as a square or a hexagon, and in the other extreme (folded), configuration form a tight bundle. Throughout their motion range, they have mobility one. These linkages have potential applications for next-generation deployable spacecraft structures. The article presents a systematic study of the kinematics of closed-loop structures with these special properties and a numerical scheme for simulating their deployment without making any assumptions about particular symmetry features. The proposed simulation technique is applied to three examples that show different behaviour during deployment.