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Orientation change of a two-dimensional articulated figure of zero angular momentum
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Image of Fig. 1.
Fig. 1.

The three solid objects that make up our model are joined together by the vectors. is embedded in the body of the object and points to the joint that is shared with the object.

Image of Fig. 2.
Fig. 2.

(Left) The articulated figure with each element’s angle defined with respect to the positive direction. (Right) The same figure with the center element defined with respect to the positive direction, but with the other two elements defined with respect to the center element.

Image of Fig. 3.
Fig. 3.

The contour in space determines how the angles and behave over time. Because the path is closed, the angles will return to their original values once the path is complete. The absolute angle will be changed by as found from Eq. (11).

Image of Fig. 4.
Fig. 4.

Nine frames of the animated articulated figure shown in Fig. 2. The values of and are shown in each frame. To clarify how the figure’s orientation is changing, an arrow shows the orientation of the piece.

Image of Fig. 5.
Fig. 5.

An example of the general model described in Sec. II. The two degrees of freedom are in the motion of the shoulder and hip joints. The three “pieces” of the body are more complex than the three equivalent rods used to construct the simple model in Sec. III.

Image of Fig. 6.
Fig. 6.

Nine frames of the human model performing a 1.2 s long dive. The center of mass of the model is made to move in a parabolic trajectory, as would be the case in a real dive. The angular momentum of the body is zero, but the body experiences a net backward rotation.


Generic image for table
Table I.

Values used for the human body model in Fig. 5, taken from Ref. 7. To simplify the model, the data for the feet and calves are combined into one body part.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Orientation change of a two-dimensional articulated figure of zero angular momentum