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Generalized Rotational Mechanics
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The motion of general mechanical systems can be related to the rotational motion of rigid bodies. One approach to doing this is to equate the generalized coordinates of a system with the Rodrigues parameters of an equivalent rotational motion. Here are some movies that demonstrate this for two different systems: a planar body and a three-link robotic manipulator. In each, the motion of the system is shown along with the equivalent rotational motion of a rigid body (the "beachball").
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PlanarMotion.avi - This movie shows the three cardinal motions of a planar body.
PlanarMotion2.avi - This is a case of more general motion.
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NomMotionFF.avi - Rotation in each joint of a three-link robot is demonstrated.
RegMotion.avi - The motion of the robot is now controlled using a spacecraft-attitude control law. |
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(Note: These movies were created using the Indeo codec. To play in Windows Media Player they need to be saved to your hard drive.)
The last movie demonstrates a main application of this approach to system dynamics. It allows the work done in spacecraft-attitude control to be leveraged to any 3-DOF system. The concept can also be extended to systems with more than three degrees of freedom by considering rotations in higher dimensions, but it gets tough to visualize!
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