Critical configurations of planar robot arms

Details Critical configurations of planar robot arms Critical configurations of planar robot arms

2012-01-26

arxiv.org/abs/1201.5447v1

Mathematics

Differential Geometry

Scientific paper

It is known that a closed polygon P is a critical point of the oriented area function if and only if P is a cyclic polygon, that is, $P$ can be inscribed in a circle. Moreover, there is a short formula for the Morse index. Going further in this direction, we extend these results to the case of open polygonal chains, or robot arms. We introduce the notion of the oriented area for an open polygonal chain, prove that critical points are exactly the cyclic configurations with antipodal endpoints and derive a formula for the Morse index of a critical configuration.

Affiliated with

Also associated with

No associations

Rating

Critical configurations of planar robot arms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Critical configurations of planar robot arms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Critical configurations of planar robot arms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-445122