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BIODYNAMICS OF HUMAN MOVEMENT

In my Biomechanics III course during the second semester of my junior year, the main focus of the class was the analysis of human movement. This discipline is used in clinical and research settings to understand how various pathologies impact movement and how interventions can be implemented to aid those affected by movement disorders. We covered the fundamentals of biomechanics of human movement using mechanical modeling techniques, with a major focus on kinematic analyses in three dimensions using matrix techniques. 

Euler Angles Lab

OBJECTIVE:

Find the bilateral 3D Euler knee angles during the three movements recorded at the Human Movement and Balance Laboratory (gait, squat, and jump).

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Static Trial:

Find the transformation matrix reflecting the relationship between the measured and anatomical coordinate systems for the thigh and shank during the static trial:

  • Find the relationship between the global coordinate system and the average thigh measured coordinate system (TS-G-Th.Meas )

  • Similarly, for the shank, find TS-G-Sh.Meas

  • Find the relationship between the global coordinate system and the average thigh anatomical coordinate system (TS-G-Th.Ana)

  • Similarly, for the shank, find TS-G-Sh.Ana

  • Calculate the transformation matrix relating the measured and anatomical coordinate systems of the thigh (TS-Th.Meas-Th.An = TD-Th.Meas-Th.An )

  • Similarly for the shank, calculate TS-Sh.Meas-Sh.An (= TD Sh.Meas-Sh.An )

Dynamic Trial:

Find the transformation matrix reflecting the relationship between the anatomical coordinate system of the shank and thigh (TD-Th.An-Sh.An ) at each frame of the dynamic trials, following the two steps below:

  • Find the relationship between the global coordinate system and the measured coordinate system of the thigh (TD-G-Th.Meas ) and shank (TD-G-Sh.Meas )

  • Compute the transformation matrix reflecting the relationship between the global coordinate system and the anatomical coordinate system of the thigh (TD-G-Th.An) and the shank (TD-G-Sh.Ana ) using the following relationships: TD-G-Th.Ana = TD-G-Th.Meas *TD-Th.Meas-Th.Ana and TD-G-Sh.Ana = TD-G-Sh.Meas *TD-Sh.Meas-Sh.Ana

  •  Find the transformation matrix reflecting the relationship between the anatomical coordinate system of the shank and that of the thigh (TD-Th.An-Sh.An ) using results from steps 1-2.

Euler Angles:

  • Calculate the joint angles using a Euler decomposition of the rotation matrix R D-Th.An-Sh.An.

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Joint Rotation Convention based on a Joint Coordinate System

OBJECTIVE:

Find the 3D knee joint angles using the joint rotation convention method based on a joint coordinate system.

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Static Trial:

Compute a transformation between global and anatomical coordinate system for the
shank and thigh: TS-G-Th.Ana and TS-G-Sh.Ana

  • For the shank, i.e. TS-G-Sh.Ana , use the following:

    • Origin = midpoint of the malleoli

    • z = vector from midpoint of the malleoli to the midpoint of the epicondyle; Normalize z = e 3 = k

    • y = w x z, with w = vector from medial to lateral epicondyle; y pointing anteriorly; Normalize y = e 3r = j

    • x = y x z; x pointing laterally to the right; Normalize x = e 3g = i

  • ​For the thigh, i.e. TS-G-Th.Ana , use the following:

    • ​Origin = midpoint of the epicondyle

    • Z = vector from midpoint of epicondyles to the greater trochanter; Z pointing up; Normalize Z = e 1g = K

    • Y = w x K, with w = vector from medial to lateral epicondyle; Y pointing anteriorly; Normalize Y = e1r = J

    • X = Y x Z; X pointing laterally to the right; Normalize Z = e 1 = I

  • Compute transformation between measured and anatomical coordinate system for the thigh and shank (constant for static and dynamic trials): TS-Th.Meas-Th.An (= TD-Th.Meas-Th.An ) and TS-Sh.Meas-Sh.An (= TD-Sh.Meas-Sh.An)

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Dynamic Trial:

  • Find the transformations between global and measured coordinate systems for the shank and thigh for each frame: TD-G-Sh.Meas and TD-G-Th.Meas

  • As in Lab 2, compute develop a transformation between global and anatomical coordinate system for the shank and thigh for each frame: TD-G-Sh.An and T D-G-Th.An

  • Find (e1 , e1r ) and (e3 , e3r ) by decomposing the TD-G-Th.An and TD-G-Sh.An into its vectors, respectively.

  • Find e2 by computing e3 x e1 = k x I

  • Use the equations from the Grood and Suntay paper to find 𝛼, 𝛽 and 𝛾. Note that e 1r = J; e3r = j; e1 = I; and e3 = k

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equations.png

OpenSim Lab

OBJECTIVE:

In this assignment you will use stepping data from a young healthy adult (male, age = 23 years, m = 79.80 kg, h = 1760 mm) and an older healthy adult (male, age = 73 years, m = 92.50 kg, h = 1743 mm), and use OpenSim to derive joint angles for four stepping conditions (long quick, short quick, long self-selected, & short self-selected) and compare the kinematic behavior of the two subjects. Data was collected at the Human Movement and Balance Laboratory as part of a pilot study investigating the lower extremity muscle contributions to rapid voluntary stepping in the elderly.

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Static Trial:

  • Scale the generic model

  • Report (in centimeters), in a table, the total squared error, RMS error, and maximum marker error

  • Report (in degrees), in a table, the static pose joint angles derived from the last step of the automated scale analysis for both subjects

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Dynamic Trial:

  • Use the dynamic motion capture data (long quick, short quick, long self-selected, and short self-selected) and the subject-specific models, to run OpenSim’s Inverse Kinematics Tool to derive joint angles for all four stepping conditions

  • Report (in centimeters), in a table, the total squared error, RMS error, and maximum marker error shown in the last frame of each dynamic motion

  • Compare stance (right) leg hip flexion/extension, knee, and ankle angles between the two subjects.

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