RE: [Algorithms] How to derive transformation matrices

[Steve W. <Ste...@im...>]

> -----Original Message-----
> From: Klaus Hartmann [mailto:k_h...@os...]
> Steve,
> I'm not native to the English language, but I think it's 
> possible that you
> are confusing "shear" with "sheer"!?
> 

No...I mean shear.

> According to my English dictionary, "sheer" can be used as an adverb:
> B.1 Completely, absolutely, directly,
> B.2 Perpendicularly, very steeply, straight up or down
> 
> The English dictionary uses the term "shear" mostly for 
> 'parallel' things,
> like:
> 1. The bar, or either of the two parallel bars, forming the 
> bed of a lathe
> 2. "shear plane". [Geol.] a boundary surface between bodies 
> of rock or ice
> which have experienced relative motion parallel to the surface.
> 3. and a lot more samples, that include the term "parallel".
> 
> Niki
> 

Yes, a "shear plane" describes the plane where two surfaces move by each
other.  A force causing these surfaces to move is called a shear force and
is parallel to the shear plane, however it is perpendicular to the surface
of contact.  A dictionary sometimes doesn't provide what you might learn in
an engineering textbook.

Consider the following box and a force acting on it perpendicular to the
surface of contact:

                                         -------------------------
                   shear force --------> |                       |
                                         |                       |
                                         |                       |
                                         -------------------------

This is what happens if the box breaks apart with the top half moving and
the bottom half staying:

                                         -------------------------
                   shear force --------> |                       |
                                        -------------------------  this is
the shear plane
                                        |                       |
                                        -------------------------

That is what I learned in engineering about shear forces...I could be wrong,
but I think the physics is correct. I have a friend that went to the same
class and he argued for hours that the force was parallel, with the same
argument that you gave...that the text used the word parallel.  It's not
always the definition that counts, it's mostly the application of the
knowledge that makes the money.  If you want to handle shear planes, then
you need to use only the component of a force that is perpendicular to the
surface of contact to determine if shear occurs...afterwards if it does
occur then you will need to use the parallel component to determine the
resultant forces on the separated portion.

But, again I don't think the original poster (OP) has an object box breaking
apart and just wants to deform it, like turning a box into a trapezoid...in
other words a geometry solution and not a physics solution...so my bringing
up shear forces has gotten this thread off track.

R&R

R&R