Screw System Theory Tutorial

Screw System Theory and Kinematic Geometry of Mechanisms: A Tutorial 1998 ASME Design Engineering Technical Conferences Sunday, September 13, 1:30-5:30pm by Kenneth J. Waldron Deparment of Mechanical Engineering The Ohio State University and Vijay Kumar Department of Mechanical Engineering School of Engineering and Applied Science University of Pennsylvania

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Description

Notes

Slides

Announcements

Fee: $60 per attendee

Date: Sunday, September 13, 1998
Time: 1:30PM to 5:30PM
Place: Omni Hotel at CNN Center

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Description

The tutorial will provide an introduction to screw system theory and its use in understanding the kinematic geometry
of spatial mechanisms. The basic relationships of screw system combination and reciprocity will be presented, including screw
coordinates and other algebraic representations. The geometric characteristics of general screw systems of different orders will
be reviewed. The most important of the many special geometries will also be introduced. The tutorial will conclude with
examples of the use of screw system theory in solving problems in mechanism theory and practice.
Tentative Outline

Introduction (KJW, 10 mins)

Background (VK, 15 mins)

Geometric definition
screw system of joints
open chains, closed chains

What are Screw Systems? (VK, 20 mins)

Algebraic definition, screw coordinates, linear algebra
Examples
List of all screw systems
Important special screw systems

U-joint system
Spherical system
Planar system

Reciprocity (VK, 15 mins)

Definition
Motion of a joint versus wrench transmitted by a joint
Other examples
Reciprocal screw systems

Classification of Screw Systems (KJW, 25 mins)

Notation
Exhaustive list
Special screw systems

Coffee Break (15 mins)

Mechanisms (KJW, 20 mins)

Relationship of contact geometry to motion system
Over constrained mechanism examples

Robotics (VK, 30 mins)

Jacobian matrix and screws
Singularities
Parallel manipulators

Parallel mechanisms, grasping, walking (KJW, 30 mins)

Jacobian matrix and screws
Force generating systems
Singularities
Series parallel duality

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Mechanisms

Robotics

Parallel mechanisms, grasping, walking

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References

1. Waldron, K. J., Constraint Analysis of Mechanisms. J. Mechanisms Vol. 1, 1966: pages 101-114.

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2. Waldron, K. J., and Hunt, K.H. Series-Parallel Dualities in Actively Coordinated Mechanisms. Int. J. Robotics Research. Vol. 10. No. 5. Oct. 1991: pages 473-480.