Mobility and Geometric Analysis of the Hoberman Switch-Pitch Ball and Its Variant

Abstract

This paper investigates the mobility and kinematics of the Hoberman switch-pitch ball, and particularly, its variant that does not resort to bevel gears. The ball variant is a general case of the Hoberman switch-pitch ball and constitutes the ball. This paper starts from examining the geometry of the ball variant and its composition, and decomposes it into loops containing eight-bar radially foldable linkages. To investigate the eight-bar radially foldable linkage, constraint matrices are developed using the screw-loop equation. This paper extends the study to the ball variant and investigates the singularity and various configurations based on the geometry and kinematics of the ball variant. This leads to the investigation of the Hoberman switch-pitch ball as a special case of the ball variant with bevel gears to simultaneously drive three joints in every vertex of the ball mechanism. The analysis is then followed by a numerical demonstration of the kinematic characteristics of the Hoberman switch-pitch ball.