H21 - 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: standing with straight legs and arms pointing forwards.

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

Whole robot

\text{Mass} = 5.029339

Torso

(o, R) is located on: Torso.

/sites/default/files/repository/69_html_nao/_images/hardware_thoraxmass_3.3.png

\text{Mass} = 1.0496

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.00413\\
                  0\\
                  0.04342
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.0050623407587 & 1.4311580344e-05 & 0.00015519082081\\
                          1.4311580344e-05 & 0.0048801358789 & -2.7079340725e-05\\
                          0.00015519082081 & -2.7079340725e-05 & 0.001610300038\\
                        \end{array}
                        \right]_R

Arms

Shoulders

Left

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

\text{Mass} = 0.07504

\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

Biceps

Right

(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

(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

Elbows

Right

(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

(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

Motorized ForeArms

Right

(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

(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

Hands - not motorized

Right Not Motorized Hand

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

/sites/default/files/repository/69_html_nao/_images/hardware_rnonmotorizedhandmass_3.3.png

\text{Mass} = 0.18405

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.06530 \\
                  -0.00114 \\
                  0.00051
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          +0.00007810423 & -0.00001233383 & +0.00000744169 \\
                          -0.00001233383 & +0.00112084378 & -0.00000054551 \\
                          +0.00000744169 & -0.00000054551 & +0.00112214306 \\
                        \end{array}
                        \right]_R

Left Not Motorized Hand

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

\text{Mass} = 0.18405

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.06530 \\
                  0.00114 \\
                  0.00051
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          +0.00007810423 & -0.00001233383 & +0.00000744169 \\
                          -0.00001233383 & +0.00112084378 & -0.00000054551 \\
                          +0.00000744169 & -0.00000054551 & +0.00112214306 \\
                        \end{array}
                        \right]_R

Legs

Pelvis

Right

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

/sites/default/files/repository/69_html_nao/_images/hardware_rpelvismass_3.3.png

\text{Mass} = 0.06981

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.00781\\
                  0.01114\\
                  0.02661
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          8.9971952548e-05 & 5.0021899369e-06 & 1.2735249584e-05\\
                          5.0021899369e-06 & 0.00010552610911 & -2.7700800274e-05\\
                          1.2735249584e-05 & -2.7700800274e-05 & 6.6887238063e-05\\
                        \end{array}
                        \right]_R

Left

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

\text{Mass} = 0.06981

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.00781\\
                  -0.01114\\
                  0.02661
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          8.1502330431e-05 & -4.9944901548e-06 & 1.2748169866e-05\\
                          -4.9944901548e-06 & 0.00010132555326 & 2.3454740585e-05\\
                          1.2748169866e-05 & 2.3454740585e-05 & 6.2623628764e-05\\
                        \end{array}
                        \right]_R

Hips

Right

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

/sites/default/files/repository/69_html_nao/_images/hardware_rhipmass_3.3.png

\text{Mass} = 0.13053

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.01549\\
                  -0.00029\\
                  -0.00515
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          2.7586540455e-05 & -1.91900007e-08 & -4.108219855e-06\\
                          -1.91900007e-08 & 9.8269956652e-05 & 2.5099999856e-09\\
                          -4.108219855e-06 & 2.5099999856e-09 & 8.8103319285e-05\\
                        \end{array}
                        \right]_R

Left

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

\text{Mass} = 0.13053

\text{CoM(S)} = \left[
                \begin{array}{c}
                  -0.01549\\
                  0.00029\\
                  -0.00515
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          2.7583539122e-05 & -2.2329999183e-08 & -4.0816398723e-06\\
                          -2.2329999183e-08 & 9.8270553281e-05 & -4.1899999026e-09\\
                          -4.0816398723e-06 & -4.1899999026e-09 & 8.8099732238e-05\\
                        \end{array}
                        \right]_R

Thighs

Right

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

/sites/default/files/repository/69_html_nao/_images/hardware_rthighmass_3.3.png

\text{Mass} = 0.38968

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.00138\\
                  -0.00221\\
                  -0.05373
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.0016374820843 & -8.3954000729e-07 & 8.5883009888e-05\\
                          -8.3954000729e-07 & 0.0015922139864 & -3.9176258724e-05\\
                          8.5883009888e-05 & -3.9176258724e-05 & 0.00030397824594\\
                        \end{array}
                        \right]_R

Left

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

\text{Mass} = 0.38968

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.00138\\
                  0.00221\\
                  -0.05373
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.001636719564 & 9.2451000455e-07 & 8.5306681285e-05\\
                          9.2451000455e-07 & 0.001591072767 & 3.8361598854e-05\\
                          8.5306681285e-05 & 3.8361598854e-05 & 0.00030374340713\\
                        \end{array}
                        \right]_R

Tibia

Right

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

/sites/default/files/repository/69_html_nao/_images/hardware_rtibiamass_3.3.png

\text{Mass} = 0.29142

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.00453\\
                  -0.00225\\
                  -0.04936
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.0011828296119 & -8.96500012e-07 & 2.7996900826e-05\\
                          -8.96500012e-07 & 0.0011282785563 & -3.8476038753e-05\\
                          2.7996900826e-05 & -3.8476038753e-05 & 0.00019145276747\\
                        \end{array}
                        \right]_R

Left

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

\text{Mass} = 0.29142

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.00453\\
                  0.00225\\
                  -0.04936
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.0011820796644 & 6.3362000446e-07 & 3.6496971006e-05\\
                          6.3362000446e-07 & 0.0011286522495 & 3.949522943e-05\\
                          3.6496971006e-05 & 3.949522943e-05 & 0.00019322744629\\
                        \end{array}
                        \right]_R

Ankle

Right

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

/sites/default/files/repository/69_html_nao/_images/hardware_ranklemass_3.3.png

\text{Mass} = 0.13416

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.00045\\
                  -0.00029\\
                  0.00685
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          3.8508129364e-05 & 6.4339999994e-08 & 3.8746597966e-06\\
                          6.4339999994e-08 & 7.4310817581e-05 & -4.5799999349e-09\\
                          3.8746597966e-06 & -4.5799999349e-09 & 5.491311822e-05\\
                        \end{array}
                        \right]_R

Left

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

\text{Mass} = 0.13416

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.00045\\
                  0.00029\\
                  0.00685
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          3.8509781007e-05 & -2.6340000403e-08 & 3.8619400584e-06\\
                          -2.6340000403e-08 & 7.4265262811e-05 & 1.8339999741e-08\\
                          3.8619400584e-06 & 1.8339999741e-08 & 5.4865398852e-05\\
                        \end{array}
                        \right]_R

Feet

Right

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

/sites/default/files/repository/69_html_nao/_images/hardware_rfootmass_3.3.png

\text{Mass} = 0.16184

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.02542\\
                  -0.0033\\
                  -0.03239
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.00026930202148 & 5.8750501921e-06 & 0.00013913327712\\
                          5.8750501921e-06 & 0.00064347387524 & -1.8849170374e-05\\
                          0.00013913327712 & -1.8849170374e-05 & 0.00052503478946\\
                        \end{array}
                        \right]_R

Left

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

\text{Mass} = 0.16184

\text{CoM(S)} = \left[
                \begin{array}{c}
                  0.02542\\
                  0.0033\\
                  -0.03239
                \end{array}
                \right]_{(o, R)}

\left[I_o(S)\right]_R = \left[
                        \begin{array}{ccc}
                          0.00026944180718 & -5.6957201195e-06 & 0.00013937948097\\
                          -5.6957201195e-06 & 0.00064434250817 & 1.8740920495e-05\\
                          0.00013937948097 & 1.8740920495e-05 & 0.00052575673908\\
                        \end{array}
                        \right]_R