A planar rigid body velocity measure based on the instantaneous velocity of all particles that constitute a rigid body is developed. This measure compares the motion of each particle to an “ideal”, but usually unobtainable, motion. This ideal motion is one that would carry each particle from its current position to its desired position on a straight-line path. Although the ideal motion is not a valid rigid body motion, this does not preclude its use as a reference standard in evaluating valid rigid body motions. The optimal instantaneous planar motions for general rigid bodies in translation and rotation are characterized. Results for an example planar positioning problem are presented.
A Computationally Efficient Planar Rigid Body Velocity Measure
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Criales, LE, & Schimmels, JM. "A Computationally Efficient Planar Rigid Body Velocity Measure." Proceedings of the ASME 2009 International Mechanical Engineering Congress and Exposition. Volume 10: Mechanical Systems and Control, Parts A and B. Lake Buena Vista, Florida, USA. November 13–19, 2009. pp. 147-152. ASME. https://doi.org/10.1115/IMECE2009-11602
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