Topic introduction

  As shown in the photo, the mechanism is the framework of the folding umbrella. An umbrella framework usually has several branches surrounding the central bar which is held by users’ hands. And a waterproof cloth covers the whole framework. 

  Since all branches have the same dimension and motion, I focus on only one branch with the central bar. Here, I mainly discuss on the opening motion of the umbrella framework from folding state to the fully stretched state.