|
University of Pennsylvania |
The Ohio State University |
Johns Hopkins University |
Georgia Tech |
|
|
|
|
|
|
The tutorial will focus on new mathematical tools and analytical techniques,
and their applications to understanding spatial kinematics and the design
of mechanisms. On-line copies of published papers and slides
that will be used at the presentation will be available to all registrants.
Date: Sunday, September 10, 2000
Time: 8:30AM
Place: TBD
Please check this site on or after Aug 22 for copies of reference material
and slides that will be used at the workshop.
(return
to top)
Tentative Outline
Screw theory
- history
- applications, motivation
- screws, infinitesimal twists, finite twists
- screw systems
Lie groups and algebras
- what are groups
- subgroups
- representations of SO(3), SE(2), SE(3) and why are they groups
- one parameter subgroups are finite twists
- infinitesimal twists form a lie algebra
Differential geometry
- what is a manifold
- tangent and co-tangent vectors
- twists and wrenches
- Lie algebras and twists revisited
- Exponential map
- Left actions of the Lie group SE(3)
- Subgroups of SE(3)
- Subalgebras of se(3)
New results in screw theory
- Inertia tensor for rigid bodies
- Stiffness mappings
- Eigenvalue problems on SE(3)
Applications
- Chasles, Euler's and Rodrigues theorems
- Analysis of kinematic chains
Brockett, R. W. and Loncaric, J. The geometry of compliance programming.
Theory and Applications of Nonlinear Control Systems. Ed. C.I. Byrnes and
A. Lindquist. Elsevier Science Publishers, 1986: pages 35-42.
Howard, W. S., Zefran, M., and Kumar, V., “On the 6x6 Stiffness Matrix for Three-Dimensional Motions,” Journal of Mechanism and Machine Theory, Vol. 33, No. 4, May 1998: 389-408. (Includes a tutorial on twists and wrenches and connnection to matrix Lie theory).
Karger, A. and Novak, J. Space Kinematics and Lie Groups. Gordon and Breach Science Publishers, 1985.
Lipkin, H. and Duffy, J. The
Elliptic Polarity of Screws, ASME Journal of Mechanisms, Transmissions,
and Automation in Design, vol.107, pp. 377-387, September 1985.
Lipkin, H. and Duffy, J. Hybrid Twist and Wrench Control for a Robotic Manipulator, ASME Journal of Mechanisms, Transmissions, and Automation in Design, vol. 110, pp. 138-144, June 1988.
Loncaric, J. Normal forms of stiffness and compliance matrices. IEEE Journal of Robotics and Automation. Vol. RA-3, No. 6, Dec. 1987: pages 567-572.
J. M. McCarthy, Introduction to Theoretical Kinematics, MIT Press, Cambridge, MA. 1991.
Park, F. C. and Brockett, R. W. Kinematic dexterity of robotic mechanisms. International Journal of Robotics Research. Vol. 13, No. 1, Feb. 1994: pages 1-15.
Samuel, A.E., McAree, P.R. and Hunt, K.H. Unifying screw geometry and matrix transformations. International Journal of Robotics Research. Vol. 10, No. 5, October 1991, pages 454-472.
1998 Tutorial on Screw System Theory by K. Waldron and V. Kumar.
Zefran, M., and Kumar, V., "A
Geometric Study of the Cartesian Stiffness Matrix," ASME Journal of
Mechanical Design, 2000 (in press).
Ball 2000 - Symposium
commemorating the works and life of Sir Robert Stawell Ball Upon
the 100th Anniversary of "A Treatise on the Theory of Screws"
1998
Tutorial on Screw System Theory by K. Waldron and V. Kumar.
Created: August 15, 2000
Maintained by:Vijay Kumar