2.2 Friction angle

110 Pages·2013·12.31 MB·English

Design and Analysis of Jammable Granular Systems
by
Nadia G.C heng
B.S. Aerospace Engineering, University of California, San Diego, 2007
S.M. Mechanical Engineering, Massachusetts Institute of Technology, 2009
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy ARCHIVES
AASSArNUSE1h
at the
Massachusetts Institute of Technology
June 2013
@ 2013 Massachusetts Institute of Technology. All rights reserved.
Signature of A uth or........................................................,...... . . . . ..... ....... ........
Department of Mechanical Ji 'ineering
a 10, 2013
Ce rtifie d b y .......................................................................................................................................
Karl Iagnemma
Principal Research Scientist of Mechanical Engineering
Thesis Supervisor
Ce rtifie d b y .................................................................................... - ................. ............................
Anette Hosoi
Associate Professor of Mechanical Engineering
Thesis Supervisor
A ccep te d b y ................................................................................... K 7..'........................................
David E. Hardt
Professor of Mechanical Engineering
Graduate Officer
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Design and Analysis of Jammable Granular Systems
by
Nadia G.C heng
Submitted to the Department of Mechanical Engineering
on May 10, 2013 in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy in
Mechanical Engineering
ABSTRACT
Jamming-the mechanism by which granular media can transition between liquid-like and
solid-like states-has recently been demonstrated as a variable strength and stiffness
mechanism in a range of applications. As a low-cost and simple means for achieving
tunable mechanical properties, jamming has been used in systems ranging from
architectural to medical ones. This thesis explores the utility of jamming for robotic
manipulation applications, both at a fundamental level of understanding how granular
properties affect the performance of jammed systems, and at a more applied level of
designing functional robotic components.
Specifically, the purpose of this thesis was to enable engineers to design jammable
robotic systems in a principled manner. Three parallel yet related studies were conducted
to work towards this goal. First, an experimental analysis was conducted to determine
whether the bulk shear strength of granular systems can be correlated with grain
properties-such as ones concerning shape, size distribution, and surface texture-
extracted from 2D silhouettes of grains. Second, a novel medium composed of a mixture of
hard and soft spheres was proposed to achieve variable strength and stiffness properties as
a function of confining pressure; experimental analysis was conducted on this system with
not only varying confining pressures but also varying mixing ratios of hard and soft
spheres. Finally, the design and analysis of a novel jammable robotic manipulator-with
the goal of maximizing both the strength and articulation of the system-is presented.
Thesis Supervisors: Karl lagnemmal and Anette (Peko) Hosoi2
Title: 'Principal Research Scientist and 2Associate Professor of Mechanical
Engineering
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ACKNOWLEDGEMENTS
First and foremost, I thank my thesis advisors Dr. Karl Iagnemma and Prof. Anette (Peko)
Hosoi. Their constant support, encouragement, and enthusiasm have enabled me to
steadily learn and mature as a researcher and engineer. It has been an absolute honor to
be mentored by them. I also extend my gratitude to the other members of my thesis
committee, Prof. Sangbae Kim and Dr. John (Jack) Germaine; their wisdom and thoughtful
advice have not only contributed to the quality of my work but also to my growth as a
researcher.
Much of the knowledge and lifelong friendships I developed have been through the
collaborative research project I was part of (funded by the DARPA Chemical Robots and M3
programs) throughout my entire time at MIT. Thank you to, in addition to my advisors,
Prof. Gareth McKinley, Prof. Martin Culpepper, Dr. Arvind Gopinath, Dr. Bian Qian, the folks
at Boston Dynamics, (now Prof.) Randy Ewoldt, Sarah Bates, Maria Telleria, Jeff Morin,
Ahmed Helal, and Nick Wiltsie. I could not have asked for a more supportive and fun group
of people to work towards challenging deadlines with.
I am also very grateful to all the UROPs I have worked with: Katy Gero, Hao Chen,
Stephan Hawthorne, Alexis Hakimi, Sara Falcone, Shaymus Hudson, and Jorge Perez. I
greatly appreciate all their patience and trust in me, and I hope that they have benefited as
much as I have from our time working together. I am also extremely thankful to those who
have selflessly taken the time to help me in my work: Steven Keating, Mark Belanger, Amy
Adams, Stephen Rudolph, Dr. Germaine, Robin Deits, and Max Lobovsky.
I also thank all the students and postdocs who have been part of the Robotic
Mobility Group, Team Peko, as well as the Laboratory for Manufacturing and Productivity
and the Hatsopoulos Microfluids Laboratory. I have been so lucky to learn from and be
surrounded by such talented and kind individuals every day.
I have also been very fortunate to have the opportunity to work on exciting and
challenging side projects that have made my time at MIT all the more fruitful. Many thanks
to my brilliant and wonderful collaborators: Lisa Burton, Lining Yao, Sayamindu Dasgupta,
Jason Spingarn-Koff, Ostap Rudakevych, Natan Linder, Sean Follmer, Daniel Leithinger, and
Alex Olwal.
I am forever grateful to my talented and inspiring teachers and mentors from
various stages and aspects of my life: Diana Ng Cheng, Dr. Victor Cheng, Prof. Claire Tomlin,
Dr. P. K. Menon, Dr. Banavar Sridhar, Dr. Shon Grabbe, Prof. Keiko Nomura, Dr. Evelyne
Kolb, Mrs. Paula Spaulding, Zoe Austin, Carlos Carvajal, Christine Leslie, and Robin Offley-
Thompson. Their patience and faith in me have given me courage to keep challenging
myself with the knowledge that even if I come up short, I am bettering myself.
Thank you to my college colleagues and dear friends-Greg Nichols, Jean-Paul
LaMarche, and Michael Everett-who helped me overcome the initial hurdles during my
engineering studies.
Many, many thanks to Ahmed Helal, Maria Telleria, and Lisa Burton for not only
being wonderful colleagues but also some of my dearest friends. I know that I have been
very fortunate to be around such selfless individuals who inspire those around them to be
better people.
Thank you to Max, my partner and best friend.
And last but not least, I thank my family, especially my sister, Lara, and my parents,
whose sheer love and belief in me have propelled me further than I ever would have
thought possible at every step of my life.
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Dedicated to my parents, whose love and teachings in the value of hard work
have given me the most blessed life.
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CONTENTS
Ab stract ..................................................................................................................................................................... 3
Ac know ledgem ents ............................................................................................................................................... 5
Contents....................................................................................................................................................................8
Figures....................................................................................................................................................................11
Tables ...................................................................................................................................................................... 16
1 Introduction .......................................................................................................................... 17
1.1 Mo tivation and overview ........................................................................................................ 17
1.1.1 Research goals............................................................................................................................. 18
1.2 Soft robotics: background........................................................................................................ 20
1.2.1 Tunable strength and stiffness mechanisms ............................................................. 21
1.3 Jam m ing of granular m edia: background ........................................................................ 22
1.3.1 Physics............................................................................................................................................ 23
1.3.2 Soil m echanics ............................................................................................................................. 23
1.3.3 Jam m ing applications ............................................................................................................... 24
2 Relating granular properties to bulk performance ...................................................... 26
2.1 Background and m otivation .................................................................................................. 26
2.1.1 Characterizing "microscopic" grain properties: background ............................... 28
2.2 Friction angle.................................................................................................................................... 29
2.3 Experim ental m ethods and procedure.............................................................................. 30
2.3.1 Grain selection............................................................................................................................. 30
2.3.2 Im aging analysis ......................................................................................................................... 30
2.3.3 Di rect shear tests........................................................................................................................ 34
2.3.4 Triaxial tests................................................................................................................................. 37
2.3.5 Di rect shear vs. triaxial tests............................................................................................. 39
2.4 R esults and discussion .................................................................................................................. 40
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2.4.1 Circularity and polydispersivity vs. friction angle .................................................... 40
2.4.2 Density vs. friction angle ..................................................................................................... 42
2.4.3 Surface properties...................................................................................................................... 44
2.5 Conclusions ....................................................................................................................................... 45
2.6 Recom mended next steps........................................................................................................ 46
3 Exploration of stress-dependent properties in granular systems ............................... 47
3.1 Background and motivation .................................................................................................. 47
3.1.1 Rubber-sand mixtures in soil mechanics studies ..................................................... 49
3.2 Experimental methods and procedure................................................................................... 50
3.2.1 Determining -3f or the case of no applied vacuum pressure ............. 52
3.3 Results and Discussion ................................................................................................................. 53
3.3.1 Bulk compression modulus and yield stress ............................................................. 53
3.3.2 Bulk compression modulus, effective friction angle, and percolation............... 57
3.3.3 Effective friction angle and angle of repose................................................................ 59
3.3.4 Predictive models for the bulk compression modulus ............................................ 61
3.4 Conclusions ....................................................................................................................................... 67
3.4.1 Recom mended next steps.................................................................................................. 67
4 Design and analysis of a jammable robotic manipulator .............................................. 69
4 .1 Ov erv iew ............................................................................................................................................ 6 9
4.2 Hyper-redundant robotics: background............................................................................ 70
4.3 Strength-to-weight performance.......................................................................................... 71
4.3.1 Experimental methods and procedure ........................................................................ 71
4.3.2 Experimental results and discussion............................................................................... 73
4.4 Design of jammable manipulator prototypes ................................................................ 75
4.4.1 Overview ........................................................................................................................................ 75
4.4.2 Prototype 1................................................................................................................................... 76
4.4.3 Prototype 2................................................................................................................................... 77
4.4.3.1 Design of jammable segments ................................................................................ 77
4.4.3.2 System components .......................................................................................................... 79
4.5 Prototype performance and analysis ................................................................................. 79
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4.5.1 Speed............................................................................................................................................... 79
4.5.2 Strength..........................................................................................................................................80
4.5.3 Dexterity and articulation w ith sim ple control.......................................................... 82
4.6 Predicting the bending strength of a jam m able beam .................................................. 84
4.6.1 Com paring theory w ith experim ental results............................................................. 85
4.7 Conclusions ....................................................................................................................................... 87
4.8 Recom m ended next steps........................................................................................................ 87
4.8.1 M anipulator design.................................................................................................................... 87
4.8.2 Feedback and control ............................................................................................................... 88
4.8.3 Potential applications............................................................................................................... 88
5 Conclusions ........................................................................................................................... 90
A Derivation for predicting the maximum bending moment of a jammable beam ....... 93
A.1 Mo deling a "jam m able" beam as a com posite beam .................................................... 93
A.1.1 Empirically determining parameters for compressive and tensile jammable
elem ents....................................................................................................................................................... 98
References...........................................................................................................................................................102
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