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Theory
Categories
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TheoryThis part of the help manual will try to give a small introduction to the theory of the kinematics and kinetics of the lower extremety. Mathematical modelThe joint angle definition is based on Grood and Suntay (1983) which uses traditional anatomical joint angles (flexion/extention, abduction/adduction and internal/external rotation).
When calculating net joint moments, a ridgid free body diagram is used.
Using Newtonian rules the following mathematical model can be obtained:
AnthropometricsWhen estimating body segment parameters (mass, center of mass, moments of initia) it is important to normalize between subjects. The following measurement are needed:
More accurate description of the measurements must be supplied! Body markersDetermining segment orientation in 3D space requires at least 3 markers. The marker setup used in the 3Dkin is a 15 marker configuration for a analysis of both legs:
It is important for the 3Dkin that the marker configuration is exactly as shown, despite that only one leg is calculated. If only one leg is analysed the markers not used can in the digitizing process be configured as missing.
Forceplate markersLocating the forceplate in respect to the subject a marker must be mounted in one of the four corners of the forceplate. If 2 plates are used, it is possible to use the setup from the APAS analog file to locate forceplate #2 with respect to forceplate #1. If this option is not to be used, a second marker must be placed on the second forceplate. The forceplate markers must be configured as following:
Marker size considerationMany things influence the choice of reflective marker size like room light, background color, subject color, floor color and so on. If more than two views are used the option of auto digitizing in the 3DKin.exe program must be considered. The success of auto digitizing is crucial to the choice of reflective marker size. The best way of choosing the optimal reflective marker size is to experiment with various types and sizes and also to modify the room color, light, and maybe using thin dark pants for the subject. Joint center calculationThe joint center is calculated using a
local coordinate system created from the body markers. Using three parameters
(Uv,Uu,Uw)
representing the relative position for each joint the center is calculated. Joint center parametersThe joint center parameters are often gathered using stereo X-rays or MRI techniques and adjusting for variability within subjects using anthropometric parameters but only a few studies have been made for this purpose. In the 3Dkin program it is possible to use four different methods for determining the various joint centers:
Calculating or digitizing joint centers a separate file must be provided the 3Dkin program. The Marker configuration must be as following:
Linear aspects of segment motionThe linear aspects of segment motion is
concentrated around the linear acceleration of the segment CM. The calculation is based on
finite difference theory:
Angular aspects of segment motionThe relative orientation of a segment is defined by a position (X,Y,Z) and three angles (Euler angles). The position is obtained from marker trajectory. Using a reference system embedded into the segment three euler angles are calculated. The Euler angles are used for calculating angular velocity, acceleration and momentum.
Dynamics of jointsAfter all parameters are found (linear acceleration, angular acceleration, ground reaction forces and so on) the resultant net joint forces and moments can be calculated. As stated previously the model used is the free body diagram (FBD) where Newtons's second law of motion is applied to each segment. The law has both linear and angular aspects. SummaryThe final stage in the analysis of dynamic human motion is complete. The next step would be to calculate the tension of invidual muscles around the joints but the number of unknowns excedes the number of equations thus making it almost impossible.
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