Talk:Screw theory

Four parameters

With the statement "Four parameters are required to fully define a screw motion" are you implying that is it possible to describe a rigid body movement only with four parameters? That's really not the case! By the way, a screw is defined by six parameters: four to describe a line (ISA), one to specify the pitch and one to specify the amplitude of the movement (the angle). —Preceding unsigned comment added by Lplaus (talk • contribs) 12:32, 11 February 2009 (UTC)

"Well known"

I ran across a paper ("An Algebraic Solution to the Problem of Collision Detection for Rigid Polyhedral Objects") where it says "It is well known that there exists a screwing [describing the motion of the body]". This wikipedia page is the only thing I can find discussing screwing motion though, and it's not all that clear. I get lost after the section "Twists as general displacements" with the notation used. The only symbol I'm familiar with is R^n. My math background isn't lacking, so I'm guessing the section was paraphrased from another source that explained the notation earlier in the work?

Could someone either expand the Twists as general displacements section down, or link to something online that also discusses screwing motion? --Numsgil (talk) 21:25, 13 December 2007 (UTC)

The writer may be referring to A.T. Yang (1974) Calculus of Screws which is in the bibliography of this article. More details and possibilities are found in the article dual quaternion. The writer should have said "well-known in algebraic mechanical engineering" for more precision. One does not yet find this material integrated into common mathematical texts, except those found on WP.Rgdboer (talk) 20:39, 11 February 2009 (UTC)

Revisions to this article

I would like to make some revisions to this article to make it more clear why screw theory is a useful tool for the study of mechanical systems that move in three dimensional space.Prof McCarthy (talk) 21:06, 27 June 2011 (UTC)

I recommend this link:

• Joe Rooney William Kingdon Clifford, Department of Design and Innovation, the Open University, London.

Also see the Space Group section of Eduard Study, as Study's work in this area is still important. Unfortunately there is some confusion at dual quaternions, re associativity. Close attention to this subject that Yang popularized would be appreciated.Rgdboer (talk) 23:15, 29 June 2011 (UTC)

Thank you for these suggestions. I have found myself working on dual quaternions. There is some confusion in Baker's discussion of the associativity of dual quaternions. If one starts with the modern definition of Clifford algebras then the dual unit ε commutes with i, j, k which eliminates the problem Baker identifies. Prof McCarthy (talk) 16:21, 30 June 2011 (UTC)

The "Calculus of screws" section has been replaced with "Screws by reflection". The old paragraph had a reference but was poor. Rather than continue with geometric algebra in a contribution here, inversive geometry has been applied for context in tranformation science.Rgdboer (talk) 22:47, 1 July 2011 (UTC)

I hope it is proper, I have increased the quality and importance of this article a little.Prof McCarthy (talk) 03:23, 3 July 2011 (UTC)

Dual Number vs Dual Scalar

The article mentions dual scalar without any reference to dual numbers, which appear to be the same thing. Intellec7 (talk) 13:54, 8 April 2015 (UTC)

Problems with Basic Concept Definitions

The square root of a dual scalar needs to be defined (as in |S| = sqrt(S dot S). Also scalar multiplication with screws has not been explicitly defined but it's used in the definitions of the screw dot product and cross product. This is probably guessable, but should be explicitly listed. 20:53, 4 May 2016 (UTC) — Preceding unsigned comment added by Pulu (talk • contribs)

Reciprocal screws

The concept of orthogonality is used in robotics to investigate the mobility of robots. No energy exchange between twist and wrench screws and environment <=> mobility not restricted. If a wrench screw and a motion screw are orthogolal un this meaning, only the SUM of energy exchange is zero, but not single parts like torque and rotation. It seems that if any summand of energy is not zero, there is a restriction. Since recipocal screws are importent in robotics, this concept should be discussed in the article. Frank — Preceding unsigned comment added by 178.251.90.98 (talk) 09:42, 24 May 2016 (UTC)