Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes

doi:10.1007/s11465-019-0567-5

Frontiers of Mechanical Engineering

2020, Vol. 15

Issue (1): 89-99 https://doi.org/10.1007/s11465-019-0567-5

本期目录

Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes

Xuemin SUN¹, Yan-An YAO¹(

), Ruiming LI²(

)

¹. School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China
². Robotics Institute, Beihang University, Beijing 100191, China

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Abstract：

This study proposes a method of constructing type II generalized angulated elements (GAEs II) Hoberman sphere mechanisms on the basis of deployment axes that intersect at one point. First, the constraint conditions for inserting n GAEs II into n deployment axes to form a loop are given. The angle constraint conditions of the deployment axes are obtained through a series of linear equations. Second, the connection conditions of two GAEs II loops that share a common deployable center are discussed. Third, a flowchart of constructing the generalized Hoberman sphere mechanism on the basis of deployment axes is provided. Finally, four generalized Hoberman sphere mechanisms based on a fully enclosed regular hexahedron, arithmetic sequence axes, orthonormal arithmetic sequence axes, and spiral-like axes are constructed in accordance with the given arrangement of deployment axes that satisfy the constraint conditions to verify the feasibility of the proposed method.

Key words： deployable mechanism type II generalized angulated elements Hoberman sphere mechanism deployment axes constraint conditions

收稿日期: 2019-05-12 出版日期: 2020-02-21

Corresponding Author(s): Yan-An YAO,Ruiming LI

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2020, 15(1): 89-99.
Xuemin SUN, Yan-An YAO, Ruiming LI. Novel method of constructing generalized Hoberman sphere mechanisms based on deployment axes. Front. Mech. Eng., 2020, 15(1): 89-99.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-019-0567-5
https://academic.hep.com.cn/fme/CN/Y2020/V15/I1/89

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

i	$θ i$ /(° )	$θ ′ i$ /(° )	$θ ″ i$ /(° )	l₂_i_–1/mm	l₂_i/mm
1	15.5	7.25	8.25	37.86	43.05
2	17.5	8.25	9.25	43.05	48.22
3	19.5	9.25	10.25	48.22	53.38
4	21.5	10.25	11.25	53.38	58.53
5	23.5	11.25	12.25	58.53	63.65
6	25.5	12.25	13.25	63.65	68.76
7	27.5	13.25	14.25	68.76	73.85
8	29.5	14.25	15.25	73.85	78.91

Tab.1

Fig.12

j	$ζ j$ /(° )	$ζ ′ j$ /(° )	$ζ ″ j$ /(° )	L₂_j_–1/mm	L₂_j/mm
1	22.65	9.25	13.40	48.22	69.53
2	22.50	11.25	11.25	58.53	58.53
3	20.32	11.25	9.07	58.53	47.30
4	36.37	13.25	23.12	68.76	117.81

Tab.2

Fig.13

i	$θ i$ /(° )	$θ ′ i$ /(° )	$θ ″ i$ /(° )	l₂_i_–1/mm	l₂_i/mm
1	45.00	22.50	22.50	45.00	45.00
2	46.65	22.50	24.15	45.00	48.12
3	55.24	24.15	31.09	48.12	60.72
4	61.68	31.09	30.59	60.72	59.85
5	61.68	30.59	31.09	59.85	60.72
6	55.24	31.09	24.15	60.72	48.12
7	46.65	24.15	22.50	48.12	45.00
8	45.00	22.50	22.50	45.00	45.00

Tab.3

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