Mechanical design of the legs of Dolomedes aquaticus

102 Pages·2010·5.76 MB·English

Mechanical design of the legs of
Dolomedes aquaticus
Novel approaches to quantify the hydraulic contribution to joint movement
and to create a segmented 3D spider model
Stefan Reußenzehn
A thesis submitted for the degree of
Master of Science in Zoology
at the University of Otago, Dunedin
New Zealand
June 2010
Abstract
Abstract
Recent findings of integrative studies of locomotion have revealed that the principles
of exploiting natural interactions of the moving body and its mechanical coupling with
its environment are essential for efficient locomotion. Thus agility depends as much on
mechanical design as on neural control. This work investigates specific aspects of me-
chanicaldesignofspiders relevant toagilelocomotion. Likeotherarthropods,spidersare
capable of agile movement, but the anatomical mechanisms underlying this behavior are
somewhat unique: instead of leg articulation being solely driven by muscle movement,
spiders employ a hydraulic system to extend certain joints exclusively by hemolymph
pressure. Thus the mechanical design of their legs is different from that of insects exam-
ined in previous studies. This makes spiders particularly interesting for further research
in this area. The methods developed in this study provide a quantitative description
of the angle-volume characteristics for femur-patella and tibia-metatarsus joints in the
nursery web spider Dolomedes aquaticus, a semi aquatic arachnid from New Zealand. I
designed anapparatusbasedontheprinciple ofjointvolume shift caused bypassive joint
movement to measure the displacement of hemolymph as a leg is flexed. Computational
image analysis of video recordings fromexperimental trials was achieved using a custom-
made algorithm. I fitted exponential, polynomial, power-law and hyperbolic models to
the angle-volume data and used Akaike Information Criterion (AIC) to evaluate how
well eachmodeldescribed thehydraulic characteristic ofeachjoint. BasedonAIC values
the polynomial modelhad thebest fit. Angle-volume characteristics for tibia-metatarsus
joints revealed a continuous increase in volume-shift with more posterior position of the
individual leg. For femur-patella joints the angle-volume characteristic of the most pos-
terior leg was also the most pronounced. In contrast to the tibia-metatarsus joint the
angle-volume characteristic of the anterior third leg showed the least volume-shift while
the anterior second leg was almost equal to that of the most posterior leg. Results
for standardized angle-volume characteristics suggest that joint volume in D. aquaticus
scales according to geometric similarity. However, no consistent pattern for the stan-
dardization factor could be identified. In addition to the angle-volume characteristics a
3D model of D. aquaticus was reconstructed. I used modern micro-CT technology to
generate a surface rendering dataset of a specimen. This technique provided sufficient
accuracy to reproduce the topography of the external geometry. The surface model was
segmented using position of joint axes as a reference. Segments were reconstructed man-
ually using simple mesh geometries which were superimposed on the CT surface model.
ii
Abstract
The resulting 3D model closely resembled the segmented exoskeleton and provides a
platform for the construction of a fully functional biomechanical model of this species
which will allow numerical simulations of inverse and forward-dynamics. Mechanical leg
design is expected to be a key determinant of gait and locomotor efficiency. This study
represents a further step towards an integrative analysis of mechanical leg design and its
effect on locomotor dynamics. The findings contribute to an integrative understanding
of the unique locomotor strategy employed by spiders. Furthermore, information and
data are provided for computational modelling and technical applications in the field of
robotics.
Key words
arthropod, arachnid, Dolomedes aquaticus, legged locomotion, mechanical design,
hydraulic leg joint, 3D model, robotics
iii
Acknowledgements
Acknowledgements
I wish to thank Mike Paulin for supervision and for giving me the chance to conduct
this very interesting research project. Thank you for supporting me particularly with
the reconstruction of the 3D model and for showing me things that can be done with a
computer that I didn’t think were possible before.
Yuri Springer has become a great friend during his stay at the Zoology Department and
has been so involved in my endeavors to make this thesis a sound scientific piece of work.
Thank you Yuri for your great feedback, encouragement, and for our ice cream breaks
in the park!
I am grateful to all the staff and students of the Zoology Department. In particular,
Anne Ryan for her skills and patience making the glass capillaries. This work would not
have been possible without this hand made piece of the measurement apparatus. To Ken
Miller, who hasbeen extremely helpfulwith finding the necessary camera equipment and
for taking pictures of the specimens. Barry Baxter and Murray McKenzie for building
all the parts I needed in a matter of days. Keith Payne for wiring and testing the
stepper motor. To the following people who provided very useful bits and pieces for my
experiment: Alison Mercer, Jan Littelton, Karen Judge, Mark Lokman, Nicky McHugh,
Shelley Cameron, Tania King, and Vivienne McNaughton. To Amy Armstrong for the
continuous "spider food" supply and Shinichi Nakagawa for statistical advice and hints
on programming in R. Thanks to my small "lab group": Kiri Pullar who shared the lab
space with me and helped me a great deal to get the tracking algorithm going. Travis
Monk for his great sense of humor. Last but not least, representative for all the friendly
faces in the Department, I wish to thank Marc Schallenberg and Sue Heath for their
friendly nature - a smile makes working a lot more pleasant:-)
Iwould also like toexpress my thanks toAndrew McNaughton (Department of Anatomy
and Structural Biology) for showing me how to run the micro-CT scanner and intro-
ducing me to the reconstruction software Amira. Furthermore, Phil Christensen (Fastec
Imaging, San Diego, CA, USA) for tweaking the high speed camera software which made
recordings in "slow motion" possible. Jun Ng and Michael Macknight (ADInstruments,
Dunedin, NZ) for introducing me to the PowerLab data acquisition system. Cor Vink
(AgResearch, Christchurch, NZ) for providing measurements on leg joints of Tegenaria
atrica.
iv
Acknowledgements
I owe further thanks to Konstanze Gebauer, Matthew Hamilton, Tina Bayer and Roni
Alder for proof reading and comments on the manuscript.
This research has been graciously supported by the Marsden Fund and by the German
National Academic Foundation.
A special thanks to my partner Simone, for her loving support and endless patience and
last but not least, my son Jaspar and his sibling soon to arrive, for helping me to focus
on the really important things in life.
I owe all spiders!
v
Contents
Contents
Abstract ii
Acknowledgements iv
List of Figures ix
List of Tables x
List of Abbreviations xi
1 General introduction 1
1.1 Legged locomotion and passive dynamics . . . . . . . . . . . . . . . . . . 1
1.2 Spider anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Nurseryweb spider Dolomedes aquaticus . . . . . . . . . . . . . . . . . . 3
1.4 Computational modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 Biologically inspired robotics - learning from animals . . . . . . . . . . . 5
1.6 Objectives of this study and thesis outline . . . . . . . . . . . . . . . . . 6
2 Acquisition of angle-volume characteristics 8
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Locomotion and mobility of leg segments . . . . . . . . . . . . . . 8
2.1.2 Hydraulic system for leg extension . . . . . . . . . . . . . . . . . 9
2.2 Material and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Animal collection and care in the lab . . . . . . . . . . . . . . . . 12
2.2.2 Design and setup of measurement apparatus . . . . . . . . . . . . 12
2.2.2.1 Removal and image taking of spider legs . . . . . . . . . 12
2.2.2.2 Leg attachment to stepper motor assembly . . . . . . . . 13
2.2.2.3 Positioning of dye in glass capillary . . . . . . . . . . . . 14
2.2.3 Apparatus settings . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3.1 Effect of time on angle-volume characteristics . . . . . . 15
2.2.3.2 Effect ofhydrostatic pressure onangle-volume character-
istics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3.3 Direction of joint movement . . . . . . . . . . . . . . . . 15
2.2.3.4 Stepper motor setup . . . . . . . . . . . . . . . . . . . . 16
2.2.3.5 Lighting and camera/video settings . . . . . . . . . . . . 16
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Contents
2.2.4 Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.5 Image analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.5.1 Calibrating glass capillary . . . . . . . . . . . . . . . . . 17
2.2.5.2 Tracking displacement of dyed fluid . . . . . . . . . . . . 18
2.2.5.3 Acquiring joint angle and width . . . . . . . . . . . . . . 21
2.2.5.4 Calculating volume change and effective step width . . . 22
2.2.6 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.6.1 Testing the effect of time on angle-volume characteristics 22
2.2.6.2 Fitting models to data . . . . . . . . . . . . . . . . . . . 23
2.2.6.3 Evaluating model fit . . . . . . . . . . . . . . . . . . . . 24
2.2.6.4 Testing the effect of power exponent value on the stan-
dardization factor . . . . . . . . . . . . . . . . . . . . . . 24
2.2.6.5 Quantifying effect of joint width on the standardization
factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.2.6.6 Standardizing angle-volume characteristics to mean joint
width . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1 Preliminary findings . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1.1 Effect of time on angle-volume characteristics . . . . . . 28
2.3.1.2 Effect ofhydrostatic pressure onangle-volume character-
istics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.2 Model performance . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.3 Effect of power exponent on standardization factor . . . . . . . . 31
2.3.4 Effect of joint width on standardization factor . . . . . . . . . . . 32
2.3.5 Angle-volume characteristic of leg joints . . . . . . . . . . . . . . 33
2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Effect of time on angle-volume characteristics . . . . . . . . . . . 37
2.4.2 Effect of hydrostatic pressure on angle-volume characteristics . . . 37
2.4.3 Model performance . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.4.4 Effect of power exponent on standardization factor . . . . . . . . 40
2.4.5 Effect of joint width on standardization factor . . . . . . . . . . . 40
2.4.6 Angle-volume characteristic of leg joints . . . . . . . . . . . . . . 41
2.4.6.1 Volume-shift in different leg joints . . . . . . . . . . . . 41
2.4.6.2 Scaling of angle-volume characteristics . . . . . . . . . . 45
vii
Contents
3 Reconstruction of 3D spider model 47
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.1 Forward and inverse solutions in movement biomechanics . . . . . 47
3.1.2 3D imaging using micro-CT . . . . . . . . . . . . . . . . . . . . . 48
3.2 Material and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2.1 Exoskeleton geometry acquisition . . . . . . . . . . . . . . . . . . 51
3.2.1.1 Preparation of specimen . . . . . . . . . . . . . . . . . . 51
3.2.1.2 Micro-CT scan and numerical reconstruction . . . . . . . 51
3.2.1.3 Construction of Isosurface . . . . . . . . . . . . . . . . . 51
3.2.1.4 Exoskeleton segmentation . . . . . . . . . . . . . . . . . 52
3.2.1.5 Body segment reconstruction . . . . . . . . . . . . . . . 52
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.1 Threshold adjustment . . . . . . . . . . . . . . . . . . . . . . . . 54
3.3.2 Segmented 3D model . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4 Discussion 59
4.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.2 Suggestions for further research . . . . . . . . . . . . . . . . . . . . . . . 59
References 62
Appendix 74
viii
List of Figures
List of Figures
1.2.1 External anatomy of a spider . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Dolomedes aquaticus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 Ranges of movement for leg joints in D. aquaticus . . . . . . . . . . . . 9
2.1.2 Hydraulic extension mechanism in hinge joints . . . . . . . . . . . . . . 10
2.2.1 Autotomy of spider leg . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Design and setup of measurement apparatus . . . . . . . . . . . . . . . 14
2.2.3 Calibration characteristic . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.4 Procedure of acquiring angle-volume characteristics . . . . . . . . . . . 20
2.2.5 Procedure of measuring joint angles . . . . . . . . . . . . . . . . . . . . 21
2.2.6 Fitted polynomial model . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.7 Procedure of aquiring the standardizing factor . . . . . . . . . . . . . . 26
2.3.1 Effect of time on angle-volume characteristics . . . . . . . . . . . . . . . 28
2.3.2 Effect of increasing internal pressure on angle-volume characteristics . . 29
2.3.3 Boxplot for AIC percentiles . . . . . . . . . . . . . . . . . . . . . . . . 30
2.3.4 Effect of joint width on standardizing factor . . . . . . . . . . . . . . . 33
2.3.5 Standardized angle-volume characteristics for femur-patella joints . . . 34
2.3.6 Standardized angle-volume characteristics for tibia-metatarsus joints . . 36
2.4.1 Comparison of angle-volume characteristics . . . . . . . . . . . . . . . . 42
3.1.1 Principle of computer tomography . . . . . . . . . . . . . . . . . . . . . 49
3.2.1 Segmentation of surface model . . . . . . . . . . . . . . . . . . . . . . . 52
3.2.2 Reconstruction of 3D segment . . . . . . . . . . . . . . . . . . . . . . . 53
3.3.1 Comparison of isosurfaces at different threshold settings . . . . . . . . . 54
3.3.2 Visual comparison of wire frame mesh geometries with spider leg . . . . 55
3.3.3 3D model of D. aquaticus . . . . . . . . . . . . . . . . . . . . . . . . . . 56
A.1.1 Main display of tracking GUI . . . . . . . . . . . . . . . . . . . . . . . 74
A.1.2 Effect of custom convolution filter and threshold setting . . . . . . . . . 75
A.2.1 Effect of decreasing internal pressure on angle-volume characteristics . . 85
A.2.2 Angle-volume characteristics for femur-patella joints . . . . . . . . . . . 86
A.2.3 Angle-volume characteristics for tibia-metatarsus joints . . . . . . . . . 87
ix
List of Tables
List of Tables
2.3.1 Visualization of selected models according to lowest AIC-value . . . . . 31
2.3.2 Standard deviations of standardized angle-volume characteristics . . . . 32
3.3.1 Number of vertices and faces for master segments . . . . . . . . . . . . 55
A.2.1 Joint width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
x