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Hexapod Math help

Discussion in 'New users start here - FAQ' started by CrazyD, Sep 16, 2010.

  1. CrazyD

    CrazyD New Member

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    I'm trying to evaluate a Hexapod using Matlab, but its been a few years since I did matrix maths or Matlab so I'm a bit stuck.

    I have built a rough and ready 3D module and im trying to build a Matlab program to the same parameters.
    [​IMG]

    I have read both the following posts.

    control-of-6-dof-stewart-platform-t967-10.html
    new-6dof-stewart-platform-for-school-project-t1622-20.html

    Im am OK with calculating the leg lengths form know base and platform points

    Code:
    PF1 = [210,0,0;0,-200,0;0,0,-350] ;% position matrix for Fixed point Leg 1
PM1 = [80,0,0;0,-300,0;0,0,-50]; % Position matrix for moving point Leg 1

% calculating leg length 1%
L1CALC = (PM1-PF1)^2;
L1SQU = L1CALC(1,1)+L1CALC(2,2)+L1CALC(3,3);
L1 = sqrt(L1SQU); %ans = 341.9064
    ;

    although its not neat and i could reduce the number of calculations steps it works ok.

    so onto my problem.

    when the platform moves the PM(i) points will move in relation to the datum of the platform. with a simple X,Y,Z move it would be a simple translation.

    Code:
    T=[50,0,0;0,200,0;0,0,-300]; % example translation of datum
PMT1 = PM1+T;
    but what happens if I have to rotate, Pitch, Roll, Yaw. I have the use Euler angles to calculate the resultant position in space.
    say for example i have a point x=500 y=1000 z=0 from the movable platform datum and I want to Pitch,roll and yaw by 3,4,5 degree respectfully.

    I'm struggling with applying the maths.

    the suggestion is as follows, and although I can evaluate this i do not get the correct result.

    PMT= (PF + T) * [R]

    so lets give it a go, but with no translation.

    Code:
    PM1=[500,0,0;0,1000,0;0,0,0]; %defines the initial PM1 position in relation to platform datum
T = [0,0,0;0,0,0;0,0,0]; % at this point there is no translation

pla = 3 * pi / 180; % alpha angle
plb = 4 * pi / 180; % Beta angle
plg = 5 * pi / 180; % gamma angle 

%now to construct the Euler Matrix

R = 
[cos(pla)*cos(plg), (cos(plg)*sin(pla))+(cos(pla)*cos(plb)*sin(plg)), sin(plb)*sin(plg);
(-cos(plb)*cos(plg)*sin(pla))-(cos(pla)*sin(plg)),(cos(pla)*cos(plb)*cos(plg))-(sin(pla)*sin(plg)),cos(plg)*sin(plb);
sin(plg)*sin(plb),-cos(pla)*sin(plb),cos(plb)];

%%and to evaluate it.

MPT1 = (MP1 + T) * R;

%% the result is as follow

PMT1 = [498.1,60.8,3;
-121.7,988.8,86.9;
0,0,0] 

%this isn't correct.
    can anybody help me?
    CrazyD, Sep 16, 2010
    #1