Assessing Position Order in Rigid Body Guidance: An Intuitive Approach to Fixed Pivot Selection
Document Type
Article
Publication Date
12-2008
Publication Source
Journal of Mechanical Design
Abstract
Several established methods determine if an RR dyad will pass through a set of finitely separated positions in order. The new method presented herein utilizes only the displacement poles in the fixed frame to assess whether a selected fixed pivot location will yield an ordered dyad solution. A line passing through the selected fixed pivot is rotated one-half revolution about the fixed pivot, in a manner similar to a propeller with infinitely long blades, to sweep the entire plane. Order is established by tracking the sequence of displacement poles intersected. With four or five positions, fixed pivot locations corresponding to dyads having any specified order are readily found.
Five-position problems can be directly evaluated to determine if any ordered solutions exist. Additionally, degenerate four-position cases for which the set of fixed pivots corresponding to ordered dyads that collapse to a single point on the center point curve can be identified.
Inclusive pages
014502-1 to 014502-5
ISBN/ISSN
1050-0472
Copyright
Copyright © 2008, American Society of Mechanical Engineers
Publisher
American Society of Mechanical Engineers
Volume
131
Issue
1
Peer Reviewed
yes
Sponsoring Agency
National Science Foundation
eCommons Citation
Myszka, David H.; Murray, Andrew P.; and Schmiedeler, James P., "Assessing Position Order in Rigid Body Guidance: An Intuitive Approach to Fixed Pivot Selection" (2008). Mechanical and Aerospace Engineering Faculty Publications. 183.
https://ecommons.udayton.edu/mee_fac_pub/183
COinS
Comments
Permission documentation is on file.
Material is based on work supported by the National Science Foundation under Grant No. 0422731.