Thanks.   It'll probably take me a while to understand that lot though...

--

Mark Hanford
http://www.mrhanford.com/povray


"Mark Wagner" <mar### [at] gtenet> wrote in message
news:3c6cbfa7@news.povray.org...
> Mark Hanford wrote in message <3c6c36ae@news.povray.org>...
> >Dear gathered pro's...
>
> >I am trying to move the tip of Joint2 (blue) to the target.  The circle
is
> >an exagerated tollerance boudary, anywhere within this circle will be
> >alright (bailout).
>
> >Where I'm getting totally lost is when I'm trying to move two joints at
> >once, and I can't work out if I'm assuming something incorrectly about
the
> >tangent vector R or
> >what.    AAAaaaarrrgghhh....
>
> What I did for my entry in the IRTC "Robots" round was to approximate the
> section between Joint1 and the fingertip as a single segment of the
finger,
> using a formula to estimate the amount of bending of Joint2.  After
figuring
> out where Joint1 was, I used Joint1 as the base of a single-joint finger
to
> find out where exactly Joint2 would be.
>
>
>
> Just in case you're interested, here's the macro I used to create a single
> finger on my robot's left hand.  LeftWristUp is the "up" vector for the
back
> of the robot's left hand.
>
> //Helper macro for Finger -- returns the joint position given two fixed
> points and the lengths of the
> // segments between them, with a value to multiply LeftWristUp by
> #macro FindJoint(Start, End, R1, R2, Sign)
>  #local _d = vlength(Start-End); //Distance between spheres
>  #local _r = sqrt(-(_d+R2+R1)*(_d-R2+R1)*(_d+R2-R1)*(_d-R2-R1))/(2*_d);
> //Radius of circle of intersection
>  #local _q = ((_d*_d)+(R2*R2)-(R1*R1))/(2*_d);
>  #local _v = vnormalize(End-Start) * _q; //The position along the line
> between End and Start where the two spheres intersect.  This is also the
> direction from End to Start
>  #local _p = vcross(_v, (LeftWristUp-LeftWristPivot) * Sign); // Find the
> vector perpendicular to the line between Start and End and LeftWristUp
>  vnormalize(vcross(_p,_v)) * _r - _v + End //Find the vector perpendicular
> to the previous vector and the line.
>  // This is the absolute 3D space joint position
> #end
>
> // Creates a finger given a base point, a point for the tip, finger
> thickness, and finger length
> #macro Finger(Start, End, Length, Thick)
>  #warning "Start and End:\n"
>  #warning concat( Vstr(Start/in,2,2),"\n")
>  #warning concat( Vstr(End/in,2,2),"\n")
>  #local _Length = vlength(Start-End);
>  //Lengths of sections of finger
>  #local _Top = Length/2;
>  #local _Middle = Length/3;
>  #local _Tip = Length/6;
>  #warning concat(str(Length/in,4,4),", ",str(_Length/in,4,4),"\n")
>  //Approximate _Joint2 position from distance between Start and End
>  #local _J2Theta = acos(_Length/Length)/2;  //Angle formed by joint
>  #local _J2Length = _Tip*cos(_J2Theta)+_Middle*cos(_J2Theta); //Combined
> length of finger tip
> // #warning concat(str(_J2Theta,2,2),"\n")
>
>  #local _handAxis = LeftWristFinger - LeftWristPivot;
>     //Handle special case of Start-End being parallel to LeftWristUp
>     #if(vdot(vnormalize(LeftWristUp-LeftWristPivot),vnormalize(Start-End))
=
> 1)
>      #local __temp = LeftWristUp;
>      #declare LeftWristUp = LeftWristFinger;
>      #local _Joint1 = FindJoint(Start, End, _Top, _J2Length, 1);
>   #if((vdot((Start-_Joint1),_handAxis)/vlength(Start-_Joint1)) > 0 ) //If
> finger has "snapped through" and is pointing the wrong way, fix it
>    #local _Joint1 = FindJoint(Start, End, _Top, _J2Length, -1);
> //   #warning "Special Case\n"
>   #end
>      #declare LeftWristUp = __temp;
>  #else
>   //Compute _Joint1 position by finding intersection point of 2 spheres
for
> which
>   // length in either the positive or negative LeftWristUp direction is a
> maximum
>   #local _Joint1 = FindJoint(Start, End, _Top, _J2Length, 1);
>   #if((vdot((Start-_Joint1),_handAxis)/vlength(Start-_Joint1)) > 0 ) //If
> finger has "snapped through" and is pointing the wrong way, fix it
>    #local _Joint1 = FindJoint(Start, End, _Top, _J2Length, -1);
> //   #warning "Inv1\n"
>   #end
>  //  #local _Joint1 = FindJoint(Start, End, _Top, _J2Length, -1);
>  // #end
>  #end
> // #warning concat( str(vdot(_Joint1, z),3,3),"\n")
> // #warning concat( vstr(_Joint1/in,2,2),"\n")
>
> // #warning concat( vstr(_handAxis/in,2,2),"\n")
>
> // #warning concat( "Vector
> ",str(abs(vdot((End-_Joint1),_handAxis)/vlength(End-_Joint1)),3,3),"\n")
>
>  #if((vdot((End-_Joint1),_handAxis)/vlength(End-_Joint1)) < 0 ) //If
> fingertip position is closer to hand along axis of hand than joint1 is,
>   #local _Joint2 = FindJoint(_Joint1,End,_Middle,_Tip,-1); //invert
> LeftWristUp for computing Joint2 position
> //  #warning "Inverted\n"
>  #else
>   #local _Joint2 = FindJoint(_Joint1,End,_Middle,_Tip,1); //otherwise,
> calculate it normally
>  #end
>
>  //Build finger
>  union{
>   //Finger
>   cylinder{Start, _Joint1, Thick texture{ArmTexture}}
>   cylinder{_Joint1, _Joint2, Thick texture{ArmTexture}}
>   cylinder{_Joint2, End, Thick texture{ArmTexture}}
>   sphere{End, Thick texture{ArmTexture}}
>   //Joints
>   sphere{Start, Thick*1.1 texture{JointTexture}}
>   sphere{_Joint1, Thick*1.1 texture{JointTexture}}
>   sphere{_Joint2, Thick*1.1 texture{JointTexture}}
>  }
> #end
>
>
>

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