View source for AXY:Rod forces model for Delta kinematics/Verification

== Effective rod force ==

For better presentation of results, effective rod force is introduced as:
:<math>Fr_{eff} = \frac {\left |  \overrightarrow{Fr}_i  \right |} {Rs_i}</math>
In this way the load capacity reduction is included in the rod force.

== Rod forces model ==

<gallery widths=300px heights=200px caption="Rod forces (effective) for motions in main directions (Z-level 800mm)">
File:Control;Rod forces model for Delta kinematics - Verification X-direction (3D graph).png|X-direction
File:Control;Rod forces model for Delta kinematics - Verification Y-direction (3D graph).png|Y-direction
File:Control;Rod forces model for Delta kinematics - Verification Z-direction (3D graph).png|Z-direction
</gallery>

The graphs above are created using the following [[aico.motionAnalyser]] script.
<pre>
fAcc      = 100;          // Acceleration [m/s^2] 
cfAccDir  = [1; 0; 0];    // Moving direction
fZ        = 0.800;        // Z level [m]


DeltaDR1200 = delta_newDR1200_4S();

RecPDm  = record_new('PDm', [0; 0; 0]);
RecPDDm = record_new('PDDm', fAcc * (cfAccDir / norm(cfAccDir)));

[mfXmesh, mfYmesh] = meshgrid(-0.600:0.05:0.600, -0.600:0.05:0.600);
mfZmesh = zeros(mfXmesh);
  
for iI = 1 : size(mfXmesh, 1)
  for iJ = 1 : size(mfYmesh, 2)

  if (norm([mfXmesh(iI, iJ); mfYmesh(iI, iJ)]) > 0.600) then 
    mfZmesh(iI,iJ) = %nan;
    continue; 
  end
  
  RecPm   = record_new('Pm', [mfXmesh(iI, iJ); mfYmesh(iI, iJ); fZ]);
  
  [RecQRad, RecQDRad, RecQDDRad] = delta_inverseKinematics(DeltaDR1200, RecPm, RecPDm, RecPDDm);
  RecTcmd                        = delta_inverseDynamics(DeltaDR1200, RecQRad, RecQDRad, RecQDDRad, RecPm, RecPDm, RecPDDm);

  [RecRF, RecRed, RecRFeff]      = delta_rodForces(DeltaDR1200, RecQRad, RecQDRad, RecQDDRad, RecPm, RecPDDm, RecTcmd);
  
  mfZmesh(iI,iJ) = max(record_getData(RecRFeff));

  end // iJ
end // iI

figure_new('Z level: ' + string(fZ));
mesh(mfXmesh, mfYmesh, mfZmesh);
</pre>

== Limitation of acceleration/deceleration ==

[[File:Control;Rod forces model for Delta kinematics - Verification of acceleration limitation.png|1000 px]]

In this section the goal it to verify that the rod forces do not exceed the maximal allowed value.
To achieve this typical robot motions (adapted from real applications) are recorded and the rod forces are computed in [[aico.motionAnalyser]].

The graph shows that the rod forces during motion are within narrow tolerance.