NDLI: The stiffness matrix in elastically articulated rigid-body systems

Content Provider	Springer Nature Link
Author	Kövecses, J. Angeles, J.
Copyright Year	2007
Abstract	Discussed in this paper is the Cartesian stiffness matrix, which recently has received special attention within the robotics research community. Stiffness is a fundamental concept in mechanics; its representation in mechanical systems whose potential energy is describable by a finite set of generalized coordinates takes the form of a square matrix that is known to be, moreover, symmetric and positive-definite or, at least, semi-definite. We attempt to elucidate in this paper the notion of “asymmetric stiffness matrices”. In doing so, we show that to qualify for a stiffness matrix, the matrix should be symmetric and either positive semi-definite or positive-definite. We derive the conditions under which a matrix mapping small-amplitude displacement screws into elastic wrenches fails to be symmetric. From the discussion, it should be apparent that the asymmetric matrix thus derived cannot be, properly speaking, a stiffness matrix. The concept is illustrated with an example.
Starting Page	169
Ending Page	184
Page Count	16
File Format	PDF
ISSN	13845640
Journal	Multibody System Dynamics
Volume Number	18
Issue Number	2
e-ISSN	1573272X
Language	English
Publisher	Springer Netherlands
Publisher Date	2007-07-26
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Stiffness matrix Structure Multi-body Elastic joint Wrench and twist Automotive and Aerospace Engineering, Traffic Mechanical Engineering Electronic and Computer Engineering Optimization Vibration, Dynamical Systems, Control
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Mechanical Engineering Aerospace Engineering Modeling and Simulation Computer Science Applications

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