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.

Effective insights into the geometric stability of symmetric skeletal structures under symmetric variations

“…Further, most skeletal structures are symmetric (Guest et al, 2010;Wei and Dai, 2010), as they can be transformed into configurations that are physically indistinguishable from the original configuration. Recently, group theory has been utilized as a systematic mathematical tool for studying the stability of symmetric structures Nikbakht, 2008, 2010;Kettle, 2008;Zingoni, 2009), as well as for designing novel deployable structures based on an existing deployable structure (Sareh and Guest, 2015a,b).…”

Geometric Constraint of an Evolved Deployable Ball Mechanism

“…This forms an overconstrained mechanism of mobility one with radially reciprocating motion in such a way that vertexes V 0 , V 4 , V 5 and V 6 move towards central point O C and vertexes V 1 , V 2 , V 3 and V 7 move away from point O C and vice versa. The mobility of this mechanism has been proved by using the screw-loop equation method (37) and the above presents a new method of constructing overconstrained deployable mechanisms. Using this method, a family of overconstrained mechanisms that perform transferring of rotation motion to radially reciprocating motion can be obtained (38) .…”

“…1 (37) . The mechanism is similar to the paper-fold form presented by Wohlhart in 1995 (5) through making up of four modular Heureka linkages (8) and through integrating CRRC chains (7) .…”

“…The Hoberman switch-pitch structure has several loops each of which can be regarded as an eight-bar radial linkage with the entire vertices moving radially towards the centre of the ball while the ball folds and expands radially. Though mobility of the Hoberman switch-pitch structure was investigated by Wei et al (37) , much of the geometric constraint that leads to construction of the structure and its evolved mechanism and linkages has not been investigated and the their kinematics is still required to be investigated. This paper reveals the geometric constraint of the structure particularly its evolved 20-bar ball mechanism without bevel gears in vertexes and uses the constraint to study the construction of the ball mechanism with both simulation and prototyping.…”

A novel 2-DOF planar translational mechanism composed by scissor-like elements

“…Kaveh et al (1999) studied the kinematically optimal design of pantograph foldable structures. Dai and Rees (1999), Wei et al (2010), Ding (2011), and Lu et al (2017) analyzed the mobility of the foldable structures by screw theory from the viewpoint of kinematics. All the achievements with SLEs were mainly focused on deployable mechanisms.…”