Novel probabilistic rolling regular tetrahedron mechanism

doi:10.1007/s11465-020-0628-9

Front. Mech. Eng.

2021, Vol. 16

Issue (2) : 363-378 https://doi.org/10.1007/s11465-020-0628-9

RESEARCH ARTICLE

Novel probabilistic rolling regular tetrahedron mechanism

Yonghan GUAN, Yan’an YAO, Chao LIU(

), Ruiming LI

School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China; Key Laboratory of Vehicle Advanced Manufacturing, Measuring and Control Technology (Ministry of Education), Beijing Jiaotong University, Beijing 100044, China

Download: PDF(3557 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

With recent relevant publications on stochastic motion robots in Nature, Science, and other journals, research on such robots has gained increasing attention. However, theoretical and applied research on stochastic motion in the field of robotics and mechanisms face many challenges due to the uncertainty of stochastic motion. Currently, a large gap remains in the research of stochastic motion mechanism. In this study, a novel mechanism that can conduct probabilistic rolling is proposed to reach a designated position and achieve overlying movement over a particular area. The mechanism consists of a regular tetrahedron frame, a central node, and four connecting linear actuators. According to mobility and kinematic analyses, the mechanism can implement probabilistic rolling. Each rolling gait has three probable rolling directions, and the mechanism rolls in one of the three directions in probability. A kinematic simulation is conducted, and a control method is proposed on the basis of the moving path analysis. Furthermore, the mathematical principle of probabilistic rolling is revealed in terms of probability theory and statistics. Lastly, a prototype is fabricated. To achieve the rolling function, the design of the linear actuators is improved, and the extension ratio is increased from 0.58 to 1.13. Then, tests are conducted. In a 4 m² test site, the mechanism makes 11 moves to reach the target position and covers 29.25% of the site.

Keywords mobile mechanism probabilistic motion rolling mechanism stochastic motion

Corresponding Author(s): Chao LIU

Just Accepted Date: 15 January 2021 Online First Date: 10 March 2021 Issue Date: 15 June 2021

Cite this article:

Yonghan GUAN,Yan’an YAO,Chao LIU, et al. Novel probabilistic rolling regular tetrahedron mechanism[J]. Front. Mech. Eng., 2021, 16(2): 363-378.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-020-0628-9
https://academic.hep.com.cn/fme/EN/Y2021/V16/I2/363

Fig.1 General position of the regular tetrahedron probabilistic rolling mechanism: (a) 3D model, (b) specific structure of limb 2.

Fig.2 Schematic of the regular tetrahedron probabilistic rolling mechanism.

Fig.3 Two parts divided by the regular tetrahedron mechanism: (a) 3-UPU mechanism and (b) UPU chain.

Fig.4 Screw analysis of limb 1 of the 3-UPU mechanism.

Fig.5 Singularity position when limbs 1, 2, and 3 are coplanar: Node E (a) is in plane ABC, and (b) passes through plane ABC.

Fig.6 Simplified regular tetrahedron mechanism: (a) General view, (b) projected view on the xOz plane.

Fig.7 Diagram of the position changes of DADF in motion.

Fig.8 Label and position of the CM of each link.

Fig.9 Curve of x_CMin the process of increasing the length of limb 4.

Fig.10 Process of one rolling cycle to the right: (a) Initial state, (b) point E touches the ground, (c) regular tetrahedron mechanism rotates around point F, (d) link DF is about to land, and (e) regular tetrahedron mechanism returns to the initial state.

Fig.11 Simulation gaits of one rolling circle: (a) Initial state, (b) point A is off the ground, (c) proposed regular tetrahedron mechanism flips around line BC, (d) critical position, (e) proposed regular tetrahedron mechanism rolls along line BC, (f) point D lands, (g) point E moves back into the frame, and (h) regular tetrahedron mechanism returns to the initial state.

Fig.12 Probable rolling directions and positions.

Fig.13 Case of moving path and the region covered by the proposed regular tetrahedron mechanism.

Fig.14 General flowchart of the task of reaching a designated position.

Fig.15 Simulation result of a probabilistic motion.

Fig.16 Areas that can be reached by different moving steps.

Fig.17 Diagram of the proposed regular tetrahedron mechanism on a minesweeping.

Fig.18 Statistical result of 20 motion simulations.

Fig.19 Prototype of the proposed regular tetrahedron mechanism.

Fig.20 Control system for limb 4 of the prototype.

Fig.21 Measurements of single and double-sided linear actuators: (a) Original state of the single linear actuator, (b) maximum elongation state of the single linear actuator, (c) original state of the double-sided linear actuators, and (d) maximum elongation state of the double-sided linear actuators.

Tab.1 Measurement results of two kinds of actuators

Fig.22 Rolling test of the prototype: (a) Initial state, (b) point A is off the ground, (c) prototype flips around line BC, (d) point D lands, and (e) prototype returns to the initial state.

Fig.23 Moving test site: (a) Panorama of the test site, and (b) measurement of the length of the test site.

Fig.24 Moving test of the prototype: (a) First movement, (b) second movement, (c) third movement, (d) fourth movement, (e) fifth movement, (f) sixth movement, (g) seventh movement, (h) eighth movement, (i) ninth movement, (j) tenth movement, and (k) eleventh movement.

Tab.2 Summary of moving efficiency in different cases

1	S G Li, R Batra, D Brown, et al.Particle robotics based on statistical mechanics of loosely coupled components. Nature, 2019, 567(7748): 361–365 https://doi.org/10.1038/s41586-019-1022-9
2	W Savoie, S Cannon, J J Daymude, et al.. Phototactic supersmarticles. Artificial Life and Robotics, 2018, 23(4): 459–468 https://doi.org/10.1007/s10015-018-0473-7
3	G Kaloutsakis, G S Chirikjian. A stochastic self-replicating robot capable of hierarchical assembly. Robotica, 2011, 29(1): 137–152 https://doi.org/10.1017/S0263574710000780
4	A J Thubagere, W Li, R F Johnson, et al.A cargo-sorting DNA robot. Science, 2017, 357: eaan6558 https://doi.org/10.1126/science.aan6558
5	D Silver, A Huang, C J Maddison, et al.Mastering the game of Go with deep neural networks and tree search. Nature, 2016, 529(7587): 484–489 https://doi.org/10.1038/nature16961
6	V Mnih, K Kavukcuoglu, D Silver, et al.Human-level control through deep reinforcement learning. Nature, 2015, 518(7540): 529–533 https://doi.org/10.1038/nature14236
7	H Shirado, N A Christakis. Locally noisy autonomous agents improve global human coordination in network experiments. Nature, 2017, 545(7654): 370–374 https://doi.org/10.1038/nature22332
8	Y B Tian, Y Z Guo, C H Liu, et al.Single-DOF mobile linkage with possibility orientation movements. Journal of Mechanical Engineering, 2011, 47(3): 14–20 (in Chinese) https://doi.org/10.3901/JME.2011.03.014
9	Y H Guan, Y A Yao, C Liu. Single-DOF octahedron robot with probable rolling. Journal of Mechanical Engineering, 2020, 56(7): 44–51(in Chinese)
10	Y Z Li, Y A Yao, Y Y He. Design and analysis of a multi-mode mobile robot based on a parallel mechanism with branch variation. Mechanism and Machine Theory, 2018, 130: 276–300 https://doi.org/10.1016/j.mechmachtheory.2018.07.018
11	Z Wang, Y Z Li, Y A Yao. Motion and path planning of a novel multi-mode mobile parallel robot based on chessboard-shaped grid division. Industrial Robot, 2018, 45(3): 390–400 https://doi.org/10.1108/IR-01-2018-0001
12	Z Y Xun, Y A Yao, Y Z Li, et al.A novel rhombohedron rolling mechanism. Mechanism and Machine Theory, 2016, 105: 285–303 https://doi.org/10.1016/j.mechmachtheory.2016.07.005
13	R M Li, Y A. YaoEversible duoprism mechanism. Frontiers of Mechanical Engineering, 2016, 11(2): 159–169 https://doi.org/10.1007/s11465-016-0398-6
14	Z Huang, Q C Li. Construction and kinematic properties of 3-UPU parallel mechanisms. In: Proceedings of ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. New York: ASME, 2002, 1027–1033
15	X W Kong, C Gosselin. Type Synthesis of Parallel Mechanisms. Berlin: Springer, 2007, 42–49
16	J S Zhao, Z J Feng, K, et al Zhou. Analysis of the singularity of spatial parallel manipulator with terminal constraints. Mechanism and Machine Theory, 2005, 40(3): 275–284 https://doi.org/10.1016/j.mechmachtheory.2004.07.011
17	R Di Gregorio, V Parenti-Castelli. Mobility analysis of the 3-UPU parallel mechanism assembled for a pure translational motion. Journal of Mechanical Design, 2002, 124(2): 259–264 https://doi.org/10.1115/1.1471530
18	P Choudhury, A Ghosal. Singularity and controllability analysis of parallel manipulators and closed-loop mechanisms. Mechanism and Machine Theory, 2000, 35(10): 1455–1479 https://doi.org/10.1016/S0094-114X(00)00003-3
19	Z H Miao, Y A Yao, X W Kong. A rolling 3-UPU parallel mechanism. Frontiers of Mechanical Engineering, 2013, 8(4): 340–349 https://doi.org/10.1007/s11465-013-0282-6
20	L W Guan, J S Wang, L P Wang. Mobility analysis of the 3-UPU parallel mechanism based on screw theory. In: Proceedings of International Conference on Intelligent Mechatronics and Automation. New York: IEEE Press, 2004, 309–314
21	C Gosselin, J Angeles. Singularity analysis of closed-loop kinematic chains. IEEE Transactions on Robotics and Automation, 1990, 6(3): 281–290 https://doi.org/10.1109/70.56660
22	Y B Tian, D Zhang, Y A Yao, et al.A reconfigurable multi-mode mobile parallel robot. Mechanism and Machine Theory, 2017, 111: 39–65 https://doi.org/10.1016/j.mechmachtheory.2017.01.003
23	Z R Wang, Y B Tian, Y A Yao. A novel underactuated tetrahedral mobile robot. Journal of Mechanisms and Robotics, 2018, 10: 044506 https://doi.org/10.1115/1.4040438
24	Z R Wang, Y A Yao, D Zhang, et al.Redundantly actuated tetrahedron mobile robot structured by pure revolute joints. Journal of Mechanical Engineering, 2019, 55(3): 18–26 (in Chinese) https://doi.org/10.3901/JME.2019.03.018
25	Z Sheng, S Q Xie, C Y Pan. Probability Theory and Mathematical Statistics. 4th ed. Beijing: Higher Education Press, 2008, 28–33 (in Chinese)
26	G R Grimmett, D R Stirzaker. Probability and Random Processes. 3rd ed. Oxford: Oxford University Press, 2001, 87–91

[1]	Zhihuai MIAO, Yan’an YAO, Xianwen KONG. A rolling 3-UPU parallel mechanism[J]. Front Mech Eng, 2013, 8(4): 340-349.
[2]	Wan DING, Sung-Chan KIM, Yan-An YAO. A pneumatic cylinder driving polyhedron mobile mechanism[J]. Front Mech Eng, 2012, 7(1): 55-65.

Viewed

Full text

Abstract

Cited

Shared

Discussed