On Sunday 06 May 2012 17:47:28 Joachim Franek wrote:
> 
> On Sunday 06 May 2012 17:40:25 Yishin Li wrote:
> > On Sun, May 6, 2012 at 10:38 PM, dave <dengv...@charter.net> wrote:
> > 
> > > On Sun, 6 May 2012 19:53:58 +0800
> > > Yishin Li <y...@araisrobo.com> wrote:
> > >
> > > > On Tue, May 1, 2012 at 3:34 AM, dave <dengv...@charter.net> wrote:
> > > >
> > > > > On Mon, 30 Apr 2012 13:41:12 -0400
> > > > > EBo <e...@sandien.com> wrote:
> > > > >
> > > > > Sorry all of your text went away when I hit reply.
> > > > > I just posted this in a reply to Andy.
> > > > >
> > > > > caris.mech.ubc.ca/Publications/sonja.pdf
> > > > >
> > > > > But alway remember: Good, Fast, Cheap ... pick any two. ;-)
> > > > >
> > > > >
> > > > I tried Sonja's approach for final deceleration and approaching
> > > > target. However, I can not get the same accel/vel curves while
> > > > approaching target.
> > > >
> > > > Has anyone tried Sonja's method?
> > > >
> > > > -Yishin
> > >
> > > Hi,
> > > Any idea what is limiting the accel, etc? Of course, the real question
> > > is how smooth is it and then can you speed it up? Thanks for trying it.
> > >
> > >
> > Instead of follow the whole Sonja's algorithm sets, I just tried to limit
> > the final accel with sin template.
> > (3.2' (modified 3.2)): a(t) = 0.5 * acc * sin(PI * t /dtmax - PI/2) - 0.5 *
> > acc
> > (3.4) dtmax = 0.5 * PI * acc / jmax
> > I think I made mistakes for integrating 3.2' for vel(t) and pos(t).
> > 
> > I would like to learn how to use octave to integrate 3.2'.
> > I'm newbie to octave. Any guide would be appreciate.
> > 
> > -Yishin
> 
> Octave is primary for numerical math.
> Try maxima, a CAS (computer algebra system).
> http://maxima.sourceforge.net/
> 
> Joachim
> 

jjf@Z61m:~$ maxima

Maxima 5.22.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.

(%i1) (amax / 2) * sin((%pi * t / dtmax) -(%pi / 2) ) + amax /2 ;
                                            %pi t
                                   amax cos(-----)
                            amax            dtmax
(%o1)                       ---- - ---------------
                             2            2
(%i2) integrate(%o1,t)
;
                                                %pi t
                                 amax dtmax sin(-----)
                        amax t                  dtmax
(%o2)                   ------ - ---------------------
                          2              2 %pi
(%i3) integrate(%o2,t);
                                 2     %pi t
                       amax dtmax  cos(-----)         2
                                       dtmax    amax t
(%o3)                  ---------------------- + -------
                                    2              4
                               2 %pi
(%i4) 

(%i4) fortran(%o2);
      amax*t/2.0E+0-amax*dtmax*sin(%pi*t/dtmax)/%pi/2.0E+0
(%o4)                                done
(%i5) fortran(%o3);
      amax*dtmax**2*cos(%pi*t/dtmax)/%pi**2/2.0E+0+amax*t**2/4.0E+0
(%o5)                                done


Joachim

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