Center of gravity, geometrical center

In Robot, the positions of the center of gravity and the geometrical center of a structure are determined in the following manner:

Geometrical center

i = x,y,z

Center of gravity

• For a 3D structure:

  The dead load acts in the Z direction.

  Xc[0] = Sum(My(0,0,0))/Sum(Pz)

  The dead load acts in Z direction.

  Xc[1] = -Sum(Mx(0,0,0))/Sum(Pz)

  The dead load acts in X direction.

  Xc[2] = -Sum(My(0,0,0))/Sum(Px)

• For plates and grillages:

  The dead load acts in Z direction.

  Xc[0] = Sum(My(0,0,0))/Sum(Pz)

  The dead load acts in Z direction.

  Xc[1] = - Sum(Mx(0,0,0))/Sum(Pz)

  Xc[2] = 0

• For 2D frames and trusses as well as plane stress / deformation structures:

  The dead load acts in Z direction.

  Xc[0] = Sum(My(0,0,0))/Sum(Pz)

  Xc[1] = 0

  The dead load acts in X direction.

  Xc[2] = -Sum(My(0,0,0))/Sum(Px)

• For axisymmetric structures:

  The dead load acts in Y direction.

  Xc[0] = 0

  Xc[1] = 0

  The dead load acts in X direction.

  Xc[2] = -Sum(My(0,0,0))/Sum(Px)