The differential mobility of a rigid body may be expressed in terms of the Plucker coordinates of a line, a generalization of the concept of slope and intercept to 3-D. The combination of a rate of rotation with a rate of translation is thus expressed as a 6-element twist vector while the combination of a force and a moment constraint has a 6-element wrench vector. While gross body displacements have an associative-but-not-commutative operator, differential displacements operating on these 6-vectors are fully associative and commutative, allowing use of linear algebra operations and algorithms well-known to signal processing to determine the ways a machine mechanism may move.
While this method has seen wide application, differential mobility may lead to paradoxical predictions of full-cycle mobility of some mechanisms for certain postures. Lie groups have been applied to extending differential mobility to full-cycle mobility, but the number of mechanisms that are Lie group generators is limited. Recent work on the Lie bracket, a 6-vector version of the vector cross product, determines full-cycle mobility for a less restrictive set of mechanisms.
Time and Place: Wed., Jan. 30, at 3:30 pm in 4610.
SYSTEMS SEMINAR WEB PAGE: http://homepages.cae.wisc.edu/~gubner/seminar/schedule.html