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Estimation Method of Center of Rotation of Functional Shoulder Joint

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Research Objective - Compatibility for Analytic Model -

In the analytical model, for example, a digital manikin has a structure that generally shows body segmentation by rigid body links bound at the joints. When human posture is applied to these analytical models, even with a digital manikin that has the same body shape and posture as a human, a margin of error will arise at the fingertips when the arms are extended forward horizontally. The reason this occurs is because a digital manikin's shoulder joint is modeled as a ball joint. An actual human shoulder is more of a free joint so that when an arm is extended, the clavicle and scapula move along with it, resulting in translational movement for the center of the shoulder joint. Consequently, the additional movement may have a bad influence on product designs or CG since neither the area the upper limb can access nor the movable range can be accurately modeled.

As a solution to this problem, the conformance of the shoulder joint structure of the analytic model, as compared to the human body, must be considered in more detail. However, in fact, it is difficult to obtain detailed body data, and a great amount of anatomical knowledge will be required.

For these reasons, we propose to obtain the center of a human shoulder joint by applying the geometric constraint conditions of the analytical model to motion measurements. According to this new method, the center of a shoulder joint will be the point that is constrained inside the brachial joint. In this case, the position of the measured shoulder joint will not become a fixed point from the perspective of the trunk, and it allows for translational movements. More specifically, the geometric errors between this model and the analytical model will be essentially absorbed by the difference between the center of a shoulder joint that should be anchored on the trunk and the position along the translational vector of the center of a shoulder joint that originates at the brachial joint. This deviance represents the motion displacement by an actual human clavicle and scapula.

Estimation Method for Finding the Centers of Shoulder Joints

In this method using more than 3 reference point groups marked on a brachial joint, the vector of the center of a shoulder joint on the brachial coordination system is obtained by implementing pre-defined "Estimated Motions of Shoulder Joint Centers". Consequently, by making a rotational matrix of the brachial coordinate system from the reference point groups, it will be possible to define the center of a shoulder joint within the measurement space for the movements that actually need to be measured. The following shows how to obtain the vector of the center of this shoulder joint.

Provided that the torso does not move, the center of a shoulder joint exists as a fixed point in an absolute coordinate system as the time interval approaches zero. Therefore, the distance between the reference points marked on a bicep and the center of a shoulder joint should become respectively fixed within any given microtime. By sorting these, the position of shoulder joint can be plotted like the diagram to the left.

At the same time, suppose that the vector of the center of a shoulder joint from the perspective of a brachial joint coordinate system is always fixed on the brachial joint. This is to keep the length of link constant at any moment. At this time, the position of the shoulder joint can be obtained by making the modeled basic posture the same as the anatomical basic posture, and displaying the differences as displacements on a rotational matrix.

These virtual centers of a shoulder joints can all be calculated as time-series data. Consequently, for all times for which the differences of the center of a shoulder joint based on these 2 methods will be minimal, we can obtain the vector of the center of the shoulder joint from the perspective of brachial joint coordinate system by optimization.
This method requires "Estimated Motions of Shoulder Joints," and the quality of the estimations depends on the type of motion. Therefore, the types of movements do need to be reviewed.

Determination of Estimated Motion Patterns for the Centers of Shoulder Joints

In order to determine estimated motion patterns of the center of a shoulder joint, we made a virtual brachial model, and by flexing and extending, and rotating internally and externally, we studied the relationships between the range of motion and the estimated motions of shoulder joint centers.

Reference points were attached outside of the virtual brachial model. Then, displacements based on motions were given. The reason that the reference points were put outside was that if they were put inside the model, it would be possible for them to have contact with the torso in actual movements. Also, the references points could be occluded by the model's own body.
In addition, random noise of }5mm was given to reference point displacement, and errors at the time of measurement were modeled. Movements consisting of extension, flexion, internal and external rotations were conducted independently of each other.

By putting them together, the following 3 points were found:

  1. Errors are larger for movements with small amplitude.
  2. Errors in front and back positioning can be offset by flexing and extending.
  3. Errors in the horizontal positioning can be offset by internal and external rotations.

These suggest that combination movements consisting of flexing and extending, and internal and external rotational movements are necessary for estimated motions of shoulder joints. Simple movements are inadequate for estimations.

Therefore, the movements pictured at the right have been suggested. This is the sinusoidal wave combination of movements with amplitudes of flexion 60, extension 10, external rotation 90, and internal rotation 30. The center vector of a shoulder joint that is anchored at the brachial joint coordinate system may now be obtained by conducting estimated motions of shoulder joints like this.
Also, in a case where errors of }5mm were added to reference point displacement, the true value of shoulder joint center can be estimated with a margin of error of approximately }3mm. Consequently, some degree of robustness was found for measurement errors.

Validation of This Method

A validation experiment was conducted using a skeletal model and a living body in order to examine whether this technique was applicable to the actual skeletal system. Details are explained below.

In actual measurements of estimated motions of shoulder joints, the body is never fixed completely. Therefore, this technique was verified using a skeletal model that had relatively relaxed geometric constraints. Also, for the location of the caput humeri, said to represent the center of the shoulder joint anatomically, the area was measured in advance using a 3-D digitizer.
As a result, it was found that the location of a shoulder joint center that was estimated by this technique existed within the range of the caput humeri. Therefore, it is considered to be possible to obtain a shoulder joint center even with relaxed geometric constraints.

In addition, in an actual motion measurement, problems with skin deformation arise. Therefore, we studied how the estimation technique is influenced by actually measuring skin deformation on a living body. In addition, when measuring a living body, we measured the location of reference points and the caput humeri in advance. By doing this, the location of the caput humeri in motion can be found.
As a result, the shoulder joint center obtained by this technique was found to exist inside the measurement of the caput humeri. Therefore, robustness was also found to be high in the case of skin deformation.

For each result, the location of the shoulder joint center was estimated inside the fit of the humerus in the socket of the scapula, and so the estimated position is considered to be relatively correct.
This technique is considered to be easy enough to be applied to other joints as it does not depend on anatomical knowledge and will not limit the useful positioning of reference points.