This paper studies the representations of a subset of the allowable motions for an N-dimensional ellipsoid inside another slightly larger ellipsoid without collision based on the idea of the Kinematics of Containment. As an extension to the previous work on the closed-form lower bounds, this paper proposes another two lower bounds based on the first-order algebraic condition of containment and the closed-form Minkowski difference between two ellipsoids respectively. Querying processes for a specific configuration of the moving ellipsoid and the calculations of the volume of the proposed lower bounds in configuration space (C-space) are introduced. Examples for the proposed lower bounds in 2D and 3D Euclidean space are implemented and the corresponding motion volumes in C-space are compared with different shapes of the ellipsoids. Finally a case study of the application on automated assembly is introduced.
Skip Nav Destination
Lower Bounds of the Allowable Motions of One
ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 26–29, 2018
Quebec City, Quebec, Canada
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5181-4
PROCEEDINGS PAPER
Lower Bounds of the Allowable Motions of One N -Dimensional Ellipsoid Contained in Another
Sipu Ruan,
Sipu Ruan
Johns Hopkins University, Baltimore, MD
Search for other works by this author on:
Gregory S. Chirikjian,
Gregory S. Chirikjian
Johns Hopkins University, Baltimore, MD
Search for other works by this author on:
Jianzhong Ding
Jianzhong Ding
Beihang University, Beijing, China
Search for other works by this author on:
Sipu Ruan
Johns Hopkins University, Baltimore, MD
Gregory S. Chirikjian
Johns Hopkins University, Baltimore, MD
Jianzhong Ding
Beihang University, Beijing, China
Paper No:
DETC2018-85851, V05BT07A081; 10 pages
Published Online:
November 2, 2018
Citation
Ruan, S, Chirikjian, GS, & Ding, J. "Lower Bounds of the Allowable Motions of One N-Dimensional Ellipsoid Contained in Another." Proceedings of the ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5B: 42nd Mechanisms and Robotics Conference. Quebec City, Quebec, Canada. August 26–29, 2018. V05BT07A081. ASME. https://doi.org/10.1115/DETC2018-85851
Download citation file:
15
Views
0
Citations
Related Proceedings Papers
Related Articles
On Shaping With Motion
J. Mech. Des (December,2000)
Quadratic Constraints on Rigid-Body Displacements
J. Mechanisms Robotics (November,2010)
Force Equilibrium Approach for Linearization of Constrained Mechanical System Dynamics
J. Mech. Des (March,2003)
Related Chapters
Containments for Transportation and Storage of Spent Nuclear Fuel and High-Level Radioactive Material and Waste
Online Companion Guide to the ASME Boiler and Pressure Vessel Codes
Containments for Transportation and Storage of Spent Nuclear Fuel and High-Level Radioactive Material and Waste 1
Companion Guide to the ASME Boiler and Pressure Vessel Codes, Volume 1, Fifth Edition
Tooth Forms
Design and Application of the Worm Gear