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Diagonal spatial stiffness matrices
J. M. Selig,X. Ding +1 more
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In this paper, the conditions under which the stiffness matrix of a spatial system can be transformed into block-diagonal and diagonal form are studied, and the consequences of such transformations for the invariants of the system, principal screws, von Mises invariants and so forth, are also studied.Abstract:
In this work we study in detail the conditions under which the stiffness matrix of a spatial system can be transformed into block-diagonal and diagonal form. That is the existence of a coordinate frame in which the stiffness matrix takes on these simple forms. The consequences of a block-diagonal or diagonal stiffness matrix for the invariants of the system, principal screws, von Mises' invariants and so forth, are also studied.read more
Citations
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Compliance Analysis of a Three-Legged Rigidly-Connected Platform Device
Jian S. Dai,Xilun Ding +1 more
TL;DR: In this article, a compliant platform based on the von Mises compliance matrix is proposed for a bowl feeder, which is decomposed into a central compliance matrix and an adjoint transformation leading to the decomposition of the legs' parameter effect from the platform assembly influence.
Journal ArticleDOI
Algebra, Volume 1. By L. Rédei. Pp. vxiii. 819, £7. 1967. (Pergamon.)
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On the stiffness analysis of robotic manipulators and calculation of stiffness indices
TL;DR: In this article, the authors introduced new performance indices for robotic manipulators in order to evaluate the robot stiffness at the design embodiment stage, based on the calculation of the Cartesian stiffness matrix of a manipulator based on a matrix structural analysis methodology.
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Characteristic Equation-Based Dynamics Analysis of Vibratory Bowl Feeders With Three Spatial Compliant Legs
Xilun Ding,Jian S. Dai +1 more
TL;DR: A comprehensive study of the dynamics of this kind of compliant devices by applying von Mises' compliance study to each of the flat-spring legs and establishing a screw system of each leg is presented.
References
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Book
Geometrical Methods in Robotics
TL;DR: This book provides an introduction to the geometrical concepts that are important to applications in robotics and shows how these concepts may be used to formulate and solve complex problems encountered in the design and construction of robots.
Book
The screw calculus and its applications in mechanics
TL;DR: In this paper, the basic propositions of screw calculus on the basis of the elementary apparatus of modern vector algebra and some applications of its applications are discussed. But the authors focus on the algebra of screws.
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Normal forms of stiffness and compliance matrices
TL;DR: These results, obtained by using a Lie group approach, also extend the concept of the remote center of stiffness to generic generalized springs.
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The Theory of Screws 1
TL;DR: In this paper, the results of Ball's investigation in the theory of screws, as contained in his “Theory of Screws” and a series of publications in the Proceedings and Transactions of the Royal Irish Academy, are described.