T14 - Masses


Warning

The Masses as well as the Center of Mass positions taken in account in the robot models have been updated in order to remove the slight dissymmetry between left and right limbs.

Legend

This page details, for each solid (S) of a robot, the Mass, Center of Mass and Inertial matrix.

\text{Mass (kg)}

\text{CoM(S)} = \left[\begin{array}{c}
X_G \\ Y_G \\ Z_G
\end{array} \right]_{(o, R)} \text{(m)}

\left[I_o(S)\right]_R = \left[\begin{array}{ccc}
I_{xx} & I_{xy} & I_{xz} \\
I_{yx} & I_{yy} & I_{yz} \\
I_{zx} & I_{zy} & I_{zz}
\end{array}\right]_R (\text{kg}*\text{m}^2)

The Center of Mass position and the Inertial matrix are described relative to the local coordinate system of the current solid (S) (o, R).

All solids (S) and local coordinate system are described relative to the zero posture: with straight arms pointing forwards.

Whole robot

\text{Mass} = 2.8

Torso

(o, R) is located on: Torso.

/sites/default/files/repository/69_html_nao/_images/torso_t.png

\text{Mass} = 1.05767

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.00544 \\
                  0.00000 \\
                  -0.01049
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.00407798983 & 0.00001905036 & -0.00009699419 \\
                          0.00001905036 & 0.00383666587 & -0.00000729520 \\
                          -0.00009699419 & -0.00000729520 & 0.00191346075 \\
                        \end{array}
                        \right]_R

Arms

Right Shoulder

(o, R) is located on the joint: RShoulderPitch.

/sites/default/files/repository/69_html_nao/_images/hardware_rshouldermass_3.3.png

\text{Mass} = 0.09304

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.00165\\
                  0.02663\\
                  0.00014
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          8.4284300101e-05 & 2.0280199351e-06 & 2.3380000158e-08\\
                          2.0280199351e-06 & 1.4155610188e-05 & 1.9719999855e-08\\
                          2.3380000158e-08 & 1.9719999855e-08 & 8.6419488071e-05\\
                        \end{array}
                        \right]_R

Left Shoulder

(o, R) is located on the joint: LShoulderPitch.

\text{Mass} = 0.09304

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.00165\\
                  -0.02663\\
                  0.00014
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          8.4284300101e-05 & -2.0280199351e-06 & 2.3380000158e-08\\
                          -2.0280199351e-06 & 1.4155610188e-05 & -1.9719999855e-08\\
                          2.3380000158e-08 & -1.9719999855e-08 & 8.6419488071e-05\\
                        \end{array}
                        \right]_R

Right Biceps

(o, R) is located on the joint: RShoulderRoll.

/sites/default/files/repository/69_html_nao/_images/hardware_rbicepmass_3.3.png

\text{Mass} = 0.15777

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.02455\\
                  -0.00563\\
                  0.0033
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.00011012030882 & 7.6691307186e-05 & -2.6046069252e-05\\
                          7.6691307186e-05 & 0.00036757651833 & 1.2098280422e-05\\
                          -2.6046069252e-05 & 1.2098280422e-05 & 0.00035461771768\\
                        \end{array}
                        \right]_R

Left Biceps

(o, R) is located on the joint: LShoulderRoll.

\text{Mass} = 0.15777

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.02455\\
                  0.00563\\
                  0.0033
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          9.3899929198e-05 & -4.7144520067e-05 & -2.6994710424e-05\\
                          -4.7144520067e-05 & 0.00037151877768 & -2.4597700303e-06\\
                          -2.6994710424e-05 & -2.4597700303e-06 & 0.00034190082806\\
                        \end{array}
                        \right]_R

Right Elbow

(o, R) is located on the joint: RElbowYaw.

/sites/default/files/repository/69_html_nao/_images/hardware_relbowmass_3.3.png

\text{Mass} = 0.06483

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.02744\\
                  0\\
                  -0.00014
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          5.5971499933e-06 & 4.2099999042e-09 & 4.3189999133e-08\\
                          4.2099999042e-09 & 7.5433119491e-05 & -1.8400000412e-09\\
                          4.3189999133e-08 & -1.8400000412e-09 & 7.6443393482e-05\\
                        \end{array}
                        \right]_R

Left Elbow

(o, R) is located on the joint: LElbowYaw.

\text{Mass} = 0.06483

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.02744\\
                  0\\
                  -0.00014
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          5.5971499933e-06 & 4.2099999042e-09 & 4.3189999133e-08\\
                          4.2099999042e-09 & 7.5433119491e-05 & -1.8400000412e-09\\
                          4.3189999133e-08 & -1.8400000412e-09 & 7.6443393482e-05\\
                        \end{array}
                        \right]_R

Right ForeArm

(o, R) is located on the joint: RElbowRoll.

/sites/default/files/repository/69_html_nao/_images/hardware_rmotorizedforearmmass_3.3.png

\text{Mass} = 0.07761

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.02556\\
                  -0.00281\\
                  0.00076
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          2.5390700102e-05 & 2.3324300855e-06 & -6.0116997247e-07\\
                          2.3324300855e-06 & 8.9220360678e-05 & 2.6940000453e-08\\
                          -6.0116997247e-07 & 2.6940000453e-08 & 8.7248430646e-05\\
                        \end{array}
                        \right]_R

Left ForeArm

(o, R) is located on the joint: LElbowRoll.

\text{Mass} = 0.07761

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.02556\\
                  0.00281\\
                  0.00076
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          2.5332199584e-05 & -2.3427101041e-06 & 7.4589998178e-08\\
                          -2.3427101041e-06 & 8.91321979e-05 & -2.6549999532e-08\\
                          7.4589998178e-08 & -2.6549999532e-08 & 8.7287262431e-05\\
                        \end{array}
                        \right]_R

Right Hand

(o, R) is located on the joint: RWristYaw.

/sites/default/files/repository/69_html_nao/_images/hardware_rmotorizedhandmass_3.3.png

\text{Mass} = 0.18533

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.03434\\
                  0.00088\\
                  0.00308
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          7.0549329394e-05 & 5.715990028e-06 & -2.247437078e-05\\
                          5.715990028e-06 & 0.0003560623154 & 3.1777099139e-06\\
                          -2.247437078e-05 & 3.1777099139e-06 & 0.00035191932693\\
                        \end{array}
                        \right]_R

Left Hand

(o, R) is located on the joint: LWristYaw.

\text{Mass} = 0.18533

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.03434\\
                  -0.00088\\
                  0.00308
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          7.0549329394e-05 & 5.715990028e-06 & -2.247437078e-05\\
                          5.715990028e-06 & 0.0003560623154 & 3.1777099139e-06\\
                          -2.247437078e-05 & 3.1777099139e-06 & 0.00035191932693\\
                        \end{array}
                        \right]_R