Design and Analysis of a Spherical Continuously Variable Transmission
In this article we propose the design of a novel continuously variable transmission, the spherical continuously variable transmission (S-CVT). The S-CVT consists of a sphere, input and output discs, a...
In this article we propose the design of a novel continuously variable transmission, the spherical continuously variable transmission (S-CVT). The S-CVT consists of a sphere, input and output discs, a...
A Polynomial Equation for a Coupler Curve of the Double Butterfly Linkage
This paper presents a closed-form polynomial equation for the path of a point fixed in the coupler links of the single degree-of-freedom eight-bar linkage commonly referred to as the double butterfly ...
This paper presents a closed-form polynomial equation for the path of a point fixed in the coupler links of the single degree-of-freedom eight-bar linkage commonly referred to as the double butterfly ...
A Geometrical Approach to the Study of the Cartesian Stiffness Matrix
J. Mech. Des. -- March 2002 -- Volume 124, Issue 1, 30 (9 pages)
doi:10.1115/1.1423638
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Author(s):
Milo
efran
Dept. of Electrical and Computer Engineering, University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL 60607
Vijay Kumar
GRASP Laboratory, Dept. of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, 3401 Walnut St., Philadelphia, PA 19104-6228
Milo
Dept. of Electrical and Computer Engineering, University of Illinois at Chicago, 851 S. Morgan St., Chicago, IL 60607
Vijay Kumar
GRASP Laboratory, Dept. of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, 3401 Walnut St., Philadelphia, PA 19104-6228
The stiffness of a rigid body subject to conservative forces and moments is described by a tensor, whose components are best described by a 6×6 Cartesian stiffness matrix. We derive an expression that is independent of the parameterization of the motion of the rigid body using methods of differential geometry. The components of the tensor with respect to a basis of twists are given by evaluating the tensor on a pair of basis twists. We show that this tensor depends on the choice of an affine connection on the Lie group, SE(3). In addition, we show that the definition of the Cartesian stiffness matrix used in the literature [1,2] implicitly assumes an asymmetric connection and this results in an asymmetric stiffness matrix in a general loaded configuration. We prove that by choosing a symmetric connection we always obtain a symmetric Cartesian stiffness matrix. Finally, we derive stiffness matrices for different connections and illustrate the calculations using numerical examples.
©2002 ASME
| History: | Received Oct. 1998 | |
| doi: | http://dx.doi.org/10.1115/1.1423638 | |
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