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Research Papers

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

[+] Author and Article Information
Guowu Wei

Division of Engineering, King’s College London, University of London, Strand, London WC2R 2LS, UKguowu.wei@kcl.ac.uk

Xilun Ding

School of Mechanical Engineering, Beihang University, Beijing 100083 P.R. Chinaxlding@buaa.edu.cn

Jian S. Dai

Chair of Mechanisms and Robotics, Division of Engineering, King’s College London, University of London, Strand, London WC2R 2LS, UKjian.dai@kcl.ac.uk

J. Mechanisms Robotics 2(3), 031010 (Jul 23, 2010) (9 pages) doi:10.1115/1.4001730 History: Received January 01, 2009; Revised March 02, 2010; Published July 23, 2010; Online July 23, 2010

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.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

The Hoberman switch-pitch ball and its structure

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Figure 2

Skeleton of the Hoberman switch-pitch ball

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Figure 3

Configurations of the Hoberman switch-pitch ball

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Figure 4

Schematic representation of the ball variant

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Figure 5

Schematic diagram of the ball variant

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Figure 6

The eight-bar radial linkage

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Figure 7

Constraint graph of the eight-bar radial linkage

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Figure 8

Topological representation of the ball variant with two eight-bar linkages

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Figure 9

Decomposition of the ball variant for mobility analysis

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Figure 10

Three-loop linkage in cubic configuration

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Figure 11

Constraint graph of the three-looped linkage

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Figure 12

Singularity configurations when θ=α

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Figure 13

Two possible configurations

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Figure 14

Trajectories of the center points of the deltoid vertexes

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Figure 15

Velocities of center points of the deltoid vertexes

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