Screw theory | Wikipedia audio article
Channel: wikipedia tts
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Screw_theory


00:01:54 1 Basic concepts
00:02:39 1.1 Screw
00:03:08 1.2 Wrench
00:03:42 1.3 Twist
00:04:35 2 Algebra of screws
00:11:13 3 Wrench
00:13:48 4 Twist
00:17:52 4.1 Revolute joints
00:18:27 4.2 Prismatic joints
00:18:55 5 Coordinate transformation of screws
00:22:59 6 Twists as elements of a Lie algebra
00:23:37 7 Screws by reflection
00:27:36 8 Homography
00:28:28 9 Work of forces acting on a rigid body
00:29:07 9.1 Reciprocal screws
00:29:25 9.2 Twists in robotics
00:30:14 10 See also
00:33:04 11 References
00:34:12 12 External links
00:42:48 Reciprocal screws
00:43:36 Twists in robotics
00:45:12 See also



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SUMMARY
=======
Screw theory is the algebra and calculus of pairs of vectors, such as forces and moments and angular and linear velocity, that arise in the kinematics and dynamics of rigid bodies.  The mathematical framework was developed by Sir Robert Stawell Ball in 1876 for application in kinematics and statics of mechanisms (rigid body mechanics).Screw theory provides a mathematical formulation for the geometry of lines which is central to rigid body dynamics, where lines form the screw axes of spatial movement and the lines of action of forces.  The pair of vectors that form the Plücker coordinates of a line define a unit screw, and general screws are obtained by multiplication by a pair of real numbers and addition of vectors.An important result of screw theory is that geometric calculations for points using vectors have parallel geometric calculations for lines obtained by replacing vectors with screws.  This is termed the transfer principle.Screw theory has become an important tool in robot mechanics, mechanical design, computational geometry and multibody dynamics. 
This is in part because of the relationship between screws and dual quaternions which have been used to interpolate rigid-body motions. Based on screw theory, an efficient approach has also been developed for the type synthesis of parallel mechanisms (parallel manipulators or parallel robots).Fundamental theorems include Poinsot's theorem (Louis Poinsot, 1806) and Chasles' theorem (Michel Chasles, 1832). Felix Klein saw screw theory as an application of elliptic geometry and his Erlangen Program. He also worked out elliptic geometry, and a fresh view of Euclidean geometry, with the Cayley-Klein metric. The use of a symmetric matrix for a von Staudt conic and metric, applied to screws, has been described by Harvey Lipkin. Other prominent contributors include Julius Plücker, W. K. Clifford, F. M. Dimentberg, Kenneth H. Hunt, J. R. Phillips.