AXY:Rod forces model for Delta kinematics/Verification

Effective rod force

For better presentation of results, effective rod force is introduced as:

$Fr_{eff}={\frac {\left|{\overrightarrow {Fr}}_{i}\right|}{Rs_{i}}}$

In this way the load capacity reduction is included in the rod force.

Rod forces model

• Rod forces (effective) for motions in main directions (Z-level 800mm)
• Rod forces model for Delta kinematics - Verification X-direction (3D graph).png

  X-direction

• Rod forces model for Delta kinematics - Verification Y-direction (3D graph).png

  Y-direction

• Rod forces model for Delta kinematics - Verification Z-direction (3D graph).png

  Z-direction

The graphs above are created using the following aico.motionAnalyser script.

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);

Limitation of acceleration/deceleration

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.