Biomechanics of Movement: The Science of Sports, Robotics, and Rehabilitation

Preface
1 First Steps
Part I Locomotion
2 Walking
3 Running
Part II Production of Movement
4 Muscle Biology and Force
5 Muscle Architecture and Dynamics
6 Musculoskeletal Geometry
Part III Analysis of Movement
7 Quantifying Movement
8 Inverse Dynamics
9 Muscle Force Optimization
Part IV Muscle-Driven Locomotion
10 Muscle-Driven Simulation
11 Muscle-Driven Walking
12 Muscle-Driven Running
13 Moving Forward
Symbols
References
Image Credits
Index
List of tables
Chapter 2
Table 2.1 Changes observed when walking in various conditions
Chapter 5
Table 5.1 Five muscle-specific parameters used by the Hill-type
model
Table 5.2 Values of muscle-specific parameters for major lowerextremity
muscles…
Table 5.3 Four dimensionless curves used by the Hill-type model
Chapter 6
Table 6.1 Calculation of muscle forces during standing in two
scenarios
Table 6.2 Calculation of moment arm from tendon-excursion data
Chapter 12
Table 12.1 Variation of running parameters with speed: toe-off
timing, stride le…
List of figures
Chapter 1
Figure 1.1 Page from Leonardo da Vinci's notebook showing his
concept of muscle…
Figure 1.2 Static analysis of human muscles and joints by Giovanni
Borelli, oft…
Figure 1.3 Sequence of photographs from Eadweard Muybridge, a
pioneer in motion…
Figure 1.4 The red-headed agama uses its tail to control its body
orientation d…
Figure 1.5 Highly functional prosthetic hands are now within reach.
Image court…
Figure 1.6 Image from the movie Avatar and the performance artist
Jenn Stafford…
Figure 1.7 Biomechanical studies help create sports equipment that
maximizes at…
Figure 1.8 Mark Muhn competing at the Cybathlon. Image courtesy
of Paul and Gab…
Figure 1.9 Example of a muscle-driven biomechanical model used to
tune muscle e…
Figure 1.10 Trajectories of markers affixed to the skin, captured
during a fron…
Figure 1.11 Smartphone data from over 68 million days of activity by
717,527 in…
Figure 1.12 Elements of a typical forward dynamic simulation.
Movement arises f…
Figure 1.13 Elements of a typical inverse dynamic analysis. The
analysis begins…
Figure 1.14 Organization of this book.
Figure 1.15 Anatomical planes and directions in a human.
Figure 1.16 Motions of the shoulder, elbow, pelvis, and hip in the f…
Figure 1.17 Motions of the knee and ankle in the sagittal plane.
Figure 1.18 Major bones, anatomical landmarks, and muscles in the
human lower l…
Figure 1.19 Body segments and major muscles in the human lower
limb (posterior …
Chapter 2
Figure 2.1 Astronauts rarely “walk” on the surface of the moon,
preferring a ho…
Figure 2.2 The walking gait cycle and its constituent events (e.g., foot
contac…
Figure 2.3 Measurements of gait in the horizontal (ground) plane.
Figure 2.4 Representative ground reaction forces during walking at
1.55 m/s. Ve…
Figure 2.5 Ground reaction forces measured by two force plates
durin…
Figure 2.6 Representative ground reaction force applied to the foot
during walk…
Figure 2.7 Vertical motion of the center of mass over one walking
gait cycle.
Figure 2.8 Representative gravitational potential and forward kinetic
energies …
Figure 2.9 The ballistic walking model described by Mochon and
McMahon (1980) i…
Figure 2.10 Even during a race, elephants always keep at least one
foot on the …
Figure 2.11 Cost of transport varies with walking speed. The energy
required to…
Figure 2.12 Experiment during which oxygen consumption and
carbon dioxide produ…
Figure 2.13 Replica of a walking machine described by Tad McGeer
(1990). This m…
Figure 2.14 The dynamic walking model described by Kuo and
Donelan (2010). This…
Figure 2.15 The first two-legged passive dynamic walker. Photo
courtesy of Stev…
Figure 2.16 Normal and anti-normal arm swing emerge
spontaneously in a passive …
Figure 2.17 Example model used in gait analysis. The model includes
rigid bodie…
Figure 2.18 Representative pelvis orientations over the gait cycle
when walking…
Figure 2.19 Joint motions over the gait cycle when walking at several
speeds. A…
Figure 2.20 Representative ground reaction forces over the gait cycle
when walk…
Figure 2.21 Crouch gait is characterized by excessive knee flexion
during stanc…
Figure 2.22 Stiff-knee gait is characterized by diminished and
delayed knee fle…
Chapter 3
Figure 3.1 The running gait cycle and its constituent events (e.g., foot
contac…
Figure 3.2 Representative ground reaction forces during running
when landing on…
Figure 3.3 Representative ground reaction forces during running
when landing on…
Figure 3.4 Representative gravitational potential and forward kinetic
energies …
Figure 3.5 The stance phase of running (left) and a mass–spring
model thereof (…
Figure 3.6 Modes of locomotion in kangaroos. During slow
locomotion, kangaroos …
Figure 3.7 Energetics of kangaroo locomotion. Mass-normalized rate
of oxygen co…
Figure 3.8 The motion of Raibert's planar robot resembles that of a
hopping kan…
Figure 3.9 Examples of modern running robots. Photos of the Spot
robot (left) a…
Figure 3.10 Conceptual model used by McMahon and Greene for
predicting running …
Figure 3.11 Schematic used to derive equations of motion for the
conceptual mod…
Figure 3.12 Foot contact time vs. track stiffness. Both axes are
logarithmic sc…
Figure 3.13 Step length (normalized by step length on a hard surface)
vs. track…
Figure 3.14 Force–deformation curves of two running shoes. As force
is applied …
Figure 3.15 Leg length defined as the distance between the center of
pressure a…
Figure 3.16 Vertical ground reaction force normalized by body
weight (left) and…
Figure 3.17 Vertical component of ground reaction forces as speed
increases. Le…
Figure 3.18 Cost of transport at various speeds. When moving at a
particular sp…
Figure 3.19 An inverted pendulum model of walking on stiff legs
(left) and a ma…
Figure 3.20 Representative joint motions over the gait cycle when
running at se…
Figure 3.21 Representative ground reaction forces over the gait cycle
when runn…
Chapter 4
Figure 4.1 The push-me–pull-you device described by Abbott et al.
(1952).
Figure 4.2 Multiscale structure of muscle. Skeletal muscle is
structured hierar…
Figure 4.3 The cross-bridge cycle describes the process by which
actin and myos…
Figure 4.4 Schematics of myosin (top), interaction of thick and thin
filaments …
Figure 4.5 A schematic of a myofibril (top) shows its highly
organized microsco…
Figure 4.6 The active force generated by a sarcomere is a function of
its lengt…
Figure 4.7 Titin attaches the thick filaments to the Z-discs at either
end of t…
Figure 4.8 The active force–length curve can be determined by
subtracting measu…
Figure 4.9 Muscle fiber force and power as functions of the fiber's
velocity. F…
Figure 4.10 Molecular changes during muscle activation. When a
muscle is relaxe…
Figure 4.11 The structure of a muscle fiber enables rapid propagation
of action…
Figure 4.12 Muscle force resulting from different stimulation
frequencies. Fibe…
Figure 4.13 Motor unit recruitment. A motor unit comprises a motor
neuron and t…
Figure 4.14 Processing of electromyographic (EMG) signals. Raw
EMG signals incr…
Figure 4.15 Inputs and outputs of a muscle–tendon model. In
computational model…
Figure 4.16 A computational model of activation dynamics relates
excitation (u(…
Figure 4.17 Muscle force-generating capacity varies with fiber length
and veloc…
Figure 4.18 The nervous system modulates muscle force through rate
encoding and…
Chapter 5
Figure 5.1 Muscle architecture and function vary throughout the
body. The flexo…
Figure 5.2 Muscles with longer optimal fiber lengths have broader
active force–…
Figure 5.3 Examples of muscles with different architectures: parallelfibered,
…
Figure 5.4 Simplified geometric representation of muscle fibers and
tendon. Mus…
Figure 5.5 The muscles shown on the left have the same volume but
different PCS…
Figure 5.6 Some muscles in chicken and fishes comprise primarily
fatigue-resist…
Figure 5.7 Tendon stress–strain relationship.
Figure 5.8 Tendon compliance affects muscle force generation. In
both cases sho…
Figure 5.9 Effects of tendon compliance on the active force–length
curve. Incre…
Figure 5.10 Imaging provides data needed to calibrate models of
muscle–tendon d…
Figure 5.11 Schematic of a typical Hill-type muscle–tendon model
(A) and the co…
Figure 5.12 Muscle fiber length (ℓM(t)) is integrated forward in time
to comput…
Figure 5.13 A model of the gluteus maximus from Blemker and Delp
(2005). Finite…
Chapter 6
Figure 6.1 Free-body diagrams (left) and model (right) used to
estimate plantar…
Figure 6.2 Definition of moment arm r associated with the generation
of a momen…
Figure 6.3 Estimating muscle moment arm from a magnetic
resonance image. MRI co…
Figure 6.4 Demonstration of how a muscle's moment arm (r) depends
on the angle …
Figure 6.5 Tendon-excursion data and the corresponding momentarm
data, calcula…
Figure 6.6 Tendon excursions and moment arms for major muscles
crossing the elb…
Figure 6.7 Two muscles with the same optimal fiber length but
different moment …
Figure 6.8 A muscle with a larger moment arm (blue) will shorten at
a higher ve…
Figure 6.9 The hamstrings cross posterior to the hip and knee. The
muscle shown…
Figure 6.10 Models of musculoskeletal geometry (center) can be used
to calculat…
Figure 6.11 Skeletal muscles generate movement by pulling on the
bones to which…
Figure 6.12 Measurement of the maximum isometric moment
generated by the elbow …
Figure 6.13 The peak moment generated by a muscle occurs at a joint
angle that …
Figure 6.14 Application of muscle force and moment arm concepts to
decision-mak…
Figure 6.15 Representation of the psoas wrapping over the pelvic
brim (left) an…
Figure 6.16 Representations of fiber geometries of the psoas (left)
and gluteus…
Figure 6.17 Process for estimating the force (FM) and moment arms
() of a muscl…
Chapter 7
Figure 7.1 Yea or neigh? In 1872, Leland Stanford hired Eadweard
Muybridge to d…
Figure 7.2 Fluoroscopic images showing bone motions in a healthy
shoulder (top …
Figure 7.3 Inertial measurement units, the orange sensors on the
runner's pelvi…
Figure 7.4 Inertial measurement units can measure the angular
velocity of the s…
Figure 7.5 Kinematic measurements for monitoring athlete health. A
mouthguard i…
Figure 7.6 Optical motion capture (mocap) is a popular technique for
quantifyin…
Figure 7.7 The location of each marker is determined in each
camera's local 2D …
Figure 7.8 Typical process for computing joint angles from mocap
data. The traj…
Figure 7.9 A reference frame fixed to a body is defined by a point on
that body…
Figure 7.10 Joint angles can be calculated by comparing the
orientations of ref…
Figure 7.11 Body-fixed reference frames determined from markers
mounted on anat…
Figure 7.12 Yaw, pitch, and roll describe the three angles of rotation
in the p…
Figure 7.13 The relative position and orientation of any two reference
frames c…
Figure 7.14 An inverse kinematics algorithm may produce more
accurate estimates…
Figure 7.15 A kinematic model of the shoulder. Adapted from Seth et
al. (2016).
Figure 7.16 Root-mean-squared error (RMSE) of scapular kinematics
in the presen…
Figure 7.17 Soccer players landing in a risky pose where the knee is
in a valgu…
Chapter 8
Figure 8.1 X-ray of a knee showing signs of osteoarthritis. Notice
that the bon…
Figure 8.2 A force plate measures the forces and moments applied
between the gr…
Figure 8.3 Pressure distributed over the foot during walking. Adapted
from Pata…
Figure 8.4 Experimental setup (left) and approximate sagittal-plane
model (righ…
Figure 8.5 Free-body diagram for the foot segment of the model
shown in Figure …
Figure 8.6 Free-body diagram for the shank segment of the model
shown in Figure…
Figure 8.7 Free-body diagram for the thigh segment of the model
shown in Figure…
Figure 8.8 Free-body diagram for the head, arms, and torso (HAT) of
the model s…
Figure 8.9 Representative joint moments over the gait cycle when
walking at sev…
Figure 8.10 Representative joint moments over the gait cycle when
running at se…
Figure 8.11 The ground reaction force generates an external knee
adduction mome…
Chapter 9
Figure 9.1 The “Fosbury flop” high-jump technique. Photo of
Ma’ayan Furman-Shah…
Figure 9.2 A musculoskeletal model of the shank and foot with the
key plantarfl…
Figure 9.3 The force exerted by each muscle in Figure 9.2 to generate
ankle pla…
Figure 9.4 Graphical representation of an objective function in two
variables, …
Figure 9.5 The force exerted by each muscle in Figure 9.2 to generate
all possi…
Figure 9.6 Electromyographic (EMG) signals from the gastrocnemius
lateralis (le…
Figure 9.7 Global optimization methods like the covariance matrix
adaptation ev…
Figure 9.8 Net joint moments generated in the sagittal plane by one
subject whi…
Figure 9.9 A simple musculoskeletal model of the leg can be used to
study muscl…
Figure 9.10 Muscle forces for one subject (male, 67.1 kg) walking at
freely sel…
Figure 9.11 Sagittal-plane joint moments generated during walking at
1.67 m/s b…
Figure 9.12 Muscle forces for one subject (male, 69.4 kg) running at
5 m/s, com…
Figure 9.13 Sagittal-plane joint moments generated during running at
5 m/s by t…
Figure 9.14 Planar model used to estimate ankle joint loads during
running at 5…
Figure 9.15 A dynamic optimization proceeds by selecting a
candidate solution, …
Figure 9.16 A planar model with five segments and seven degrees of
freedom for …
Figure 9.17 Joint torques during the ground contact phase when
unassisted (left…
Chapter 10
Figure 10.1 Actions of the soleus muscle during single-limb stance,
ignoring (l…
Figure 10.2 A biarticular muscle can induce a joint acceleration that
opposes t…
Figure 10.3 The process for creating and analyzing muscle-driven
simulations in…
Figure 10.4 Elements of a muscle-driven simulation. Excitations
from a neural c…
Figure 10.5 Planar musculoskeletal models of the upper and lower
extremity used…
Figure 10.6 Detailed neck and upper-extremity musculoskeletal
models used to ge…
Figure 10.7 A curve representing the excitation of a muscle can be
parameterize…
Figure 10.8 A rigid-tendon approximation can greatly reduce the time
required t…
Figure 10.9 In many studies, the complex biological contact surfaces
in the kne…
Figure 10.10 Horizontal (top) and vertical (bottom) ground reaction
forces duri…
Figure 10.11 Simulated activations and EMG recordings of four
muscles when runn…
Figure 10.12 Tibiofemoral contact force estimated in simulation
(blue) and meas…
Figure 10.13 Average metabolic power consumed during typical
walking and when w…
Figure 10.14 OpenSim can be used to generate forward dynamic and
inverse dynami…
Chapter 11
Figure 11.1 Visualization of a muscle-driven simulation of walking.
The colors …
Figure 11.2 Actions of the gluteus medius, vasti, soleus, gluteus
maximus, and …
Figure 11.3 Contribution to ground reaction force from stance-limb
muscles (red…
Figure 11.4 The knee flexes rapidly during double support, resulting
in a high …
Figure 11.5 The rectus femoris is active in early swing and
accelerates the lim…
Figure 11.6 Methods used to compare increase in peak knee flexion
when rectus f…
Figure 11.7 Peak knee flexion of lower-limb model (left) during
simulation of p…
Figure 11.8 Average normalized EMG patterns for eleven muscles
measured at four…
Figure 11.9 The tibialis anterior is active at heel strike and generates
force …
Figure 11.10 Visualizations from muscle-driven simulations of a
representative …
Figure 11.11 Contributions to the acceleration of the body's center …
Figure 11.12 Musculoskeletal models used to create muscle-driven
simulations of…
Figure 11.13 During crouch gait, the vasti and plantarflexors are
active throug…
Figure 11.14 Fore–aft accelerations of the center of mass produced by
the gastr…
Figure 11.15 Average knee flexion angle (top), compressive knee
force (center),…
Figure 11.16 Dynamic optimizations that minimize cost of transport
predict calc…
Figure 11.17 Illustration from a nineteenth-century patent describing
the inven…
Figure 11.18 One of the first exoskeletons to help patients with stroke
and spi…
Figure 11.19 Muscle-driven simulations predicted the performance of
seven ideal…
Figure 11.20 Muscle-level analysis of ankle plantarflexion device for
assisting…
Chapter 12
Figure 12.1 Generic musculoskeletal model used to generate muscledriven
simula…
Figure 12.2 Actions of the gluteus medius, quadriceps, soleus,
gluteus maximus,…
Figure 12.3 Average EMG from 11 muscles during running. Adapted
from Arnold et …
Figure 12.4 Visualizations from muscle-driven simulations of a
representative s…
Figure 12.5 Increases in running speed are achieved primarily by
increasing str…
Figure 12.6 Mean and one standard deviation (n = 5) of the force–
velocity multi…
Figure 12.7 The opposing angular momenta of the arms and legs
about a vertical …
Figure 12.8 Swing-assist mechanism and effect on EMG during
treadmill running. …
Figure 12.9 Foot-strike patterns in running.
Figure 12.10 Muscle activation and fiber dynamics of plantarflexor
m…
Figure 12.11 Tendon elastic energy (top) and power (bottom) for
plantarflexor m…
Figure 12.12 Reductions in the energy expended by lower-extremity
muscles when …
Figure 12.13 Activations of nine representative lower-extremity
muscles in simu…
Figure 12.14 The hip extension device of Lee et al. was more
effective at reduc…
Figure 12.15 Time-lapse photographs of a runner using a spring
connecting the l…
Figure 12.16 Mechanism of energetic savings when running with a
spring connecti…
Chapter 13
Figure 13.1 Wearable motion sensor and neurostimulator for reducing
hand tremor…
Figure 13.2 Activity inequality predicts obesity. Individuals in the
five count…
Figure 13.3 Use of data science methods in human movement
biomechanics studies …
Figure 13.4 Method to estimate gastrocnemius length. An OpenSim
model recreated…
Figure 13.5 Long-term outcomes following gastrocnemius
lengthening surgery. Cas…
Figure 13.6 OpenSim model of an ostrich, the fastest biped on the
planet. Model…
Figure 13.7 Frames from a simulation of landing on an incline to
study ankle in…
Figure 13.8 Locations of visitors to the OpenSim documentation in a
recent one-…