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From: gooch@portia.Stanford.EDU (Carl Gooch)
Newsgroups: comp.robotics,sci.math,sci.physics,sci.engr
Subject: Re: dynamics equation for robot
Message-ID: <1991Feb15.054131.20039@portia.Stanford.EDU>
Date: 15 Feb 91 05:41:31 GMT
References: <puchm.666615329@cutmcvax.cs.curtin.edu.au>
Organization: AIR, Stanford University
Lines: 59

In article <puchm.666615329@cutmcvax.cs.curtin.edu.au>
puchm@cutmcvax.cs.curtin.edu.au (RichardPuchmayer) writes:

>
>    Dear netters,
>
>        The following question refers to :
>
>        Bayliss C. McInnis and Cheng-Kang Frank Liu (1986) "Kinematics
>        and Dynamics in Robotics: A Tutorial Based Upon Classical
>        Concepts of Vectorial Mechanics",IEEE Journal of Robotics
>        and Automation. Vol:RA-2, No:4, December 1986.
>
>        If you don't have this article please ignore this posting.
>
>        The authors differentiate equation (2) on page 181 to get
>        equation (3).
>
>        (2):
>            Vp = Vi + P(o)i/i + Wi X Pi
>
>            to get
>
>        (3):
>            Ap = Ai + P(oo)i/i + 2Wi X P(o)i + W(dot)i X Pi +
>                 Wi X ( Wi X Pi) ^
>                                 |
>                                 |
>            I only get one of these. ie. a one instead of a two.

Well, I haven't seen the article, but I can tell you where that term
comes from.  When you take the time derivative of a vector which is in
a rotating frame, what you get is:

	dA/dt = (dA/dt)rel + omega x A

That is, the time rate of change of A is equal to the time rate of
change of A with respect to the rotating coordinate system plus a term
which accounts for the fact that the vector is rotating (that's the
omega x A).  With that in mind, the first term on the RHS of (2) leads
to the first term on the RHS of (3).  The second term in (2) gives the
second term and one of the Wi x P(o)i terms.  The other Wi x P(o)i
comes from the third term in (2), which also gives the fourth term in
(3) by direct differentiation and the final term as omega x A.

Any standard dynamics text (Greenwood, Meirovitch, etc) will have a
much more detailed discussion of this.


>            Apologies for the way that I have done sub/super
>            scripts.

Ditto.

-- 
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Carl Gooch                       |        Why am I inside at a keyboard when 
gooch@leland.stanford.edu        |        I could be outside riding bike?
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