biomechanics
DESCRIPTION
Evaluation os Kinematics Human MovimentsTRANSCRIPT
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Biomechanics of Movement
Biomedical Engineering MCs
Instituto Superior Técnico
Presentation by Group 7:
Diana Santos, 72459
Joana Paulo, 72455
Marta Ornelas, 62840
Rui Pinto, 62842
Lisbon, November 2011
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Introduction
Movement description
Methodology Description
Results
Conclusion
References
Questions Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
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Biomechanics
Gait
Kinematics Analisys
Multybody System
Newton-Raphson
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
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What is Biomechanics?
The Biomechanics is the study of the behavior of
biological systems using and applying the concepts and
laws of mechanics.
Mechanical Analysis
Biological Systems
Biomechanics
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Antiquity Middle Ages
Renaissance Scientif
Revolution
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Enlightenment Century of the
Gait 20th Century
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Gait is the pattern of limb
movement of animals,
including humans, during
locomotion over a solid
substrate.
Its cycle is defined by the
period of time from the
initial point of contact of the
foot with the ground until
the next point of initial
contact. Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Figure 1. Example of Gait
+ Initial contact
Loading Response
Midstance
Terminal Stance
Preswing
Initial Swing
Midswing
Terminal Swing
Stance Phase
(60%)
Swing Phase
(40%)
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Figure 2. Phase Support - Contact the foot with the ground
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The classical analytical methods, for kinematic analysis,
are too difficult to use and its not a practical method for
systems of high complexity.
Alternatively, we use a multibody model
A set of two or more rigid or flexible bodies, connected by
joints or kinematic pairs, on which external forces can be
applied.
Its relative easy of computational implementation
They are used in various applications, including aerospace,
automotive systems (suspension) in the medical and robotics
(surgical robots).
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
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Vector of generalized coordinates (q)
𝑞 = {𝑞1, 𝑞2, … , 𝑞𝑛}
Vector Constraints (φ(q,t))
Φ 𝑞, 𝑡 =
Φ1
Φ2 𝑧…Φ𝑛ℎ
= 0
Degrees of Freedom 𝑛𝑔𝑙 = 𝑛𝑐 − 𝑛ℎ
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
𝜙𝑃𝐼 𝑟𝑖 , 𝑟𝑗 , 𝑟𝑘 , 𝑟𝑙= 𝑟𝑖𝑗
𝑇𝑟𝑘𝑙 − 𝐿𝑖𝑗𝐿𝑘𝑙 cos(𝜃 𝑡 )
𝜙𝑞𝑃𝐼 = −𝑟𝑘𝑙
𝑇 𝑟𝑘𝑙𝑇 −𝑟𝑖𝑗
𝑇 𝑟𝑖𝑗𝑇
𝜙𝑃𝐸 𝑟𝑖 , 𝑟𝑗 , 𝑟𝑘 , 𝑟𝑙= 𝑟 𝑖𝑗
𝑇𝑟𝑘𝑙 − 𝐿𝑖𝑗𝐿𝑘𝑙 𝑠𝑖𝑛(𝜃 𝑡 )
𝜙𝑞𝑃𝐸 = −𝑟 𝑘𝑙
𝑇 𝑟𝑘𝑙𝑇 −𝑟𝑖𝑗
𝑇 𝑟𝑖𝑗𝑇
𝜙𝑞𝑃𝐼 𝑟𝑖 , 𝑟𝑗 = 𝑟𝑖𝑗
𝑇𝑟𝑖𝑗 − 𝐿𝑖𝑗2
𝜙𝑞𝐽𝑅 = −𝐼 𝐼
𝜙𝐽𝑅 𝑞 = 𝑟𝑖𝑗 = 0
Global Vector Constraints
Inner Product
Rigid Body
External Product
Explicit Revolution Joints
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
𝜙𝐺𝐿 𝑞, 𝑡
= 𝜙𝑃𝐼 𝑟𝑖 , 𝑟𝑗, 𝑟𝑘 , 𝑟𝑙 = 𝑟𝑖𝑗
𝑇𝑟𝑘𝑙 − 𝐿𝑖𝑗𝐿𝑘𝑙 𝑐𝑜𝑠∗(𝜃 𝑡 )
𝜙𝑃 𝑟𝑖 , 𝑟𝑗 , 𝑟𝑘 , 𝑟𝑙 = 𝑟𝑖𝑗𝑇𝑟𝑘𝑙 − 𝐿𝑖𝑗𝐿𝑘𝑙𝑠𝑖𝑛
∗(𝜃 𝑡 )
Guiding Constraints
Rotation (Angular)
Translational (linear)
Trajectory
Φ𝐺𝐿 𝑞, 𝑡 = Φ𝑃𝐼 𝑞, 𝑡 = 𝑟𝑖𝑗𝑇𝑟𝑖𝑗 − 𝐿𝑖𝑗
2∗(𝑡) = 0
Φ𝐺𝑇 𝑞, 𝑡 = Φ𝑃𝐼 𝑞, 𝑡 = 𝑟𝑖 − 𝑟𝑖∗ = 0
Φ𝐺𝑇𝑞 𝑞 = [𝐼]
𝜙𝐺𝐴 𝑞, 𝑡
= 𝜙𝑃𝐼 𝑟𝑖 , 𝑟𝑗 , 𝑟𝑘 , 𝑟𝑙 = 𝑟𝑖𝑗
𝑇𝑟𝑘𝑙 − 𝐿𝑖𝑗𝐿𝑘𝑙 𝑐𝑜𝑠∗(𝜃 𝑡 )
𝜙𝑃𝐼 𝑟𝑖 , 𝑟𝑗 , 𝑟𝑘 , 𝑟𝑙 = 𝑟𝑖𝑗𝑇𝑟𝑘𝑙 − 𝐿𝑖𝑗𝐿𝑘𝑙𝑠𝑖𝑛
∗(𝜃 𝑡 )
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Figure 3. Outline of the Laboratory
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Figure 4. Real Model
1
2
3
4
5
6
7=8=9
10=11 12=13
14=15 16=17
18 19
21 20
Figure 4. Computational
Representation of the Model Used
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Natural coordinates 42
Rigid Bodies 12
Segments 16
Revolute Joints 12
Rigid Body Constraints 16
Explicit Joins Contraints 12
Guiding Constraints 14
Number of Constraints 42
Table 1. Characteristics of the multibody system
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Table 2. Anthropometric Parameters of the Model
Body Part Average Length (cm) Measured Length (cm)
Head - Neck 32.7 31,0
Shoulder - Left Elbow 28.6 30,3
Shoulder – Right Elbow 31.5 29,6
Elbow - Left Hand 26.4 26,7
Elbow - Right Hand 26.2 26,8
Body 48.9 51
Hip – Right Knee 43.7 42,9
Hip – Left Knee 45.5 41,5
Knee - Right Ankle 42,4 42,4
Knee - Left Ankle 39,3 42,5
Ankle - Right Heel 6,6 7,9
Ankle - Left Heel 6,5 7,9
Ankle - Right Metatarsus 11,2 12,3
Ankle - Left Metatarsus 10,2 13,0
Heel - Right Metatarsus 15,3 18,5
Heel - Left Metatarsus 13,9 18,2
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Angles
In the Lab
Data
Position Low Pass
filtered
with a
frequency
of 3 Hz.
Interpolation
Using Splines
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
Mapping
Table
Constraints
Angular Trajectory
Guiding
Constraints
Updated at
every time
point
We need to solve the system: φ(q,t) = 0
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
After solving the system with the Newton-Raphson method, for
each instant of time, we get:
Positions Velocities Accelerations
For each point of the multibody model.
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Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+ Biomechanics of
Movement
1st Semester, 4th
Year
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+ Biomechanics of
Movement
1st Semester, 4th
Year
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+ Biomechanics of
Movement
1st Semester, 4th
Year
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Lisbon, November 2011
+ Biomechanics of
Movement
1st Semester, 4th
Year
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Lisbon, November 2011
+ Biomechanics of
Movement
1st Semester, 4th
Year
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Lisbon, November 2011
+
Lisbon, November 2011
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+
The proposed multibody model was correctly
implemented in Matlab;
The velocity and acceleration results are consistent with
gait;
Body segment angles were in agreement with the
references – normal gait.
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
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M. Silva, Apontamentos sobre Contributos Históricos para a
Biomecânica do Movimento, DEM, IST, 2004.
M. Silva, Apontamentos sobre Cinemática, DEM, IST, 2010.
Thies, Sibylle B. et al, Influence of an irregular surface and low
light on the step variability of patients with peripheral neurpahty
during level gait, University of Michigan, USA, 19 August 2004.
Pinto, Susana, A Marcha Humana em Análise, Seminário na
Faculdade de Medicina de Lisboa.
Perry J. Gait Analysis: Normal and Pathological Function. 1992.
Winter David; The Biomechanics and Motor Control of Human
Gait: Normal, Elderly and Pathological, University of Waterloo
press, Second Edition.
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011
+
Group 7
Diana Santos
Joana Paulo
Marta Ornelas
Rui Pinto
Biomechanics of
Movement
1st Semester, 4th
Year
Lisbon, November 2011