From: Mark Cutkosky <cutkosky@stanford.edu>
Date: August 7, 2006 13:19:19 PDT
To: Matthew Spenko <mspenko@stanford.edu>
Cc: cutkosky@stanford.edu
Subject: Fwd: geckofoot question

Begin forwarded message:
From: Sangbae Kim <sangbae.kim@gmail.com>
Date: August 18, 2005 22:59:38 PDT
To: Mark Cutkosky <cutkosky@stanford.edu>
Subject: Re: geckofoot question
Reply-To: sangbae@stanford.edu

Oooops, yes..you are right.  I thought the cable bridge is parabolic...
Thanks for correction!
 
On 8/18/05, Mark Cutkosky <cutkosky@stanford.edu> wrote:
Sangbae -- I have a question about your parabolic cable trajectory
assumption. Are you sure it should not 
be a catenary? (Brachistochrone?)

Let x be a horizontal coordinate from the tip of the toe toward the
root. It seems that the normal force, Fn, per unit length should be
like:

deltaFn = -F sinA + F sin(A+dA) where "A" is the angle at each x and F 
is the cable tension.

sin(A+dA) =  sinA * cosdA + cosA*sindA = sinA + cosA*dA,   if dA is
small.

so deltaFn = F*cosA*dA    where dA = (dA/dx)*dx

so dFn/dx = FcosA*(dA/dx)*dx   = constant (we desire). 

Now, if slope, A = cx  (so height goes as x^2) and c is a constant,
then dFn/dx is not a constant.


cheers,

Mark

On Aug 18, 2005, at 8:32 PM, Sangbae Kim wrote:

> Hi Mark,
> 
> Here is the ppt file.. it is a little bit big..But you can shrink
> them down..
>
> 
> On 8/18/05, Mark Cutkosky <cutkosky@stanford.edu> wrote: I have put a 
> slightly modified version onto Chewie (v2)
>> (in RiSE/telecon/telecon05-08-19)
>>
>> Still to do:
>> * Sangbae's "cartoon" ?need it soon if we are going to include
>> something.
>> * various bits of cleaning up & editing - + maybe a figure from Alan?
>> * create links to the movies that Matt did.
>>
>>  I guess i will finish up after dinner this evening and send out to 
>> RiSE
>> PIs before I turn in tonite.
>>
>> Mark
>>
>
>
>
> --
> Sangbae Kim
> Ph.D Candidate
> Biomimetic & Dexterous Manipulation Lab 
> Mechnical engineering
> Stanford University
> 650-996-9288<diffentiation.ppt>