Masses - V3.2

See also

NAO - Technical overview

V5 | V4 | V3.3 | V3.2

H25 | H21 | T14 | T2


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} =       4.83592

Torso

(o, R) is located on: Torso.

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

\text{Mass} = 1.02628

CoM(S) = \left[
         \begin{array}{c}
             -0.00480 \\
             +0.00000 \\
             +0.04227
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00487953284 & +0.00001428591 & +0.00019545651 \\
               +0.00001428591 & +0.00470360698 & -0.00002224589 \\
               +0.00019545651 & -0.00002224589 & +0.00156713520
             \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.png

\text{Mass} = 0.06984

CoM(S) = \left[
         \begin{array}{c}
             -0.00178 \\
             +0.02507 \\
             +0.00019
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00007101854 & +0.00000202458 & +0.00000001713 \\
               +0.00000202458 & +0.00001404920 & +0.00000004410 \\
               +0.00000001713 & +0.00000004410 & +0.00007314467
             \end{array}
             \right]_R

Left Shoulder

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

\text{Mass} = 0.06984

CoM(S) = \left[
         \begin{array}{c}
             -0.00178 \\
             -0.02507 \\
             +0.00019
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00007101854 & -0.00000202458 & +0.00000001713 \\
               -0.00000202458 & +0.00001404920 & -0.00000004410 \\
               +0.00000001713 & -0.00000004410 & +0.00007314467
             \end{array}
             \right]_R

Right Bicep

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

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

\text{Mass} = 0.12166

CoM(S) = \left[
         \begin{array}{c}
             +0.02067 \\
             -0.00388 \\
             +0.00362
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00005931793 & +0.00000193929 & -0.00001564503 \\
               +0.00000193929 & +0.00020221058 & +0.00000368731 \\
               -0.00001564503 & +0.00000368731 & +0.00018421556
             \end{array}
             \right]_R

Left Bicep

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

\text{Mass} = 0.12166

CoM(S) = \left[
         \begin{array}{c}
             +0.02067 \\
             +0.00388 \\
             +0.00362
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00005931793 & -0.00000193929 & -0.00001564503 \\
               -0.00000193929 & +0.00020221058 & -0.00000368731 \\
               -0.00001564503 & -0.00000368731 & +0.00018421556
             \end{array}
             \right]_R

Right Elbow

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

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

\text{Mass} = 0.05959

CoM(S) = \left[
         \begin{array}{c}
             -0.02573 \\
             +0.00001 \\
             -0.00020
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00000549462 & +0.00000002242 & +0.00000006771 \\
               +0.00000002242 & +0.00006224789 & -0.00000000559 \\
               +0.00000006771 & -0.00000000559 & +0.00006323010
             \end{array}
             \right]_R

Left Elbow

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

\text{Mass} = 0.05959

CoM(S) = \left[
         \begin{array}{c}
             -0.02573 \\
             -0.00001 \\
             -0.00020
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00000549462 & -0.00000002242 & +0.00000006771 \\
               -0.00000002242 & +0.00006224789 & +0.00000000559 \\
               +0.00000006771 & +0.00000000559 & +0.00006323010
             \end{array}
             \right]_R

Right Motorized ForeArm

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

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

\text{Mass} = 0.03770

CoM(S) = \left[
         \begin{array}{c}
             +0.01940 \\
             -0.00304 \\
             +0.00250
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00001271101 & +0.00000131460 & -0.00000143626 \\
               +0.00000131460 & +0.00003056901 & +0.00000020686 \\
               -0.00000143626 & +0.00000020686 & +0.00002976287
             \end{array}
             \right]_R

Left Motorized ForeArm

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

\text{Mass} = 0.03770

CoM(S) = \left[
         \begin{array}{c}
             +0.01940 \\
             +0.00304 \\
             +0.00250
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00001271101 & -0.00000131460 & -0.00000143626 \\
               -0.00000131460 & +0.00003056901 & -0.00000020686 \\
               -0.00000143626 & -0.00000020686 & +0.00002976287
             \end{array}
             \right]_R

Hands - motorized

Right Motorized Hand

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

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

\text{Mass} = 0.14314

CoM(S) = \left[
         \begin{array}{c}
            +0.03241 \\
            -0.00268 \\
            -0.00272
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00005692620 & +0.00000822213 & +0.00001136287 \\
               +0.00000822213 & +0.00027230907 & -0.00000181780 \\
               +0.00001136287 & -0.00000181780 & +0.00026611399
             \end{array}
             \right]_R

Left Motorized Hand

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

\text{Mass} = 0.14314

CoM(S) = \left[
         \begin{array}{c}
            +0.03241 \\
            +0.00268 \\
            -0.00272
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00005692620 & -0.00000822213 & +0.00001136287 \\
               -0.00000822213 & +0.00027230907 & +0.00000181780 \\
               +0.00001136287 & +0.00000181780 & +0.00026611399
             \end{array}
             \right]_R

Legs

Right Pelvis

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

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

\text{Mass} = 0.07244

CoM(S) = \left[
         \begin{array}{c}
           -0.00717 \\
           +0.01187\\
           +0.02705
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00009064495 & +0.00000488819 & +0.00001221925 \\
               +0.00000488819 & +0.00010665780 & -0.00002783820 \\
               +0.00001221925 & -0.00002783820 & +0.00006742859
             \end{array}
             \right]_R

Left Pelvis

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

\text{Mass} = 0.07244

CoM(S) = \left[
         \begin{array}{c}
           -0.00717 \\
           -0.01187\\
           +0.02705
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00009064495 & -0.00000488819 & +0.00001221925 \\
               -0.00000488819 & +0.00010665780 & +0.00002783820 \\
               +0.00001221925 & +0.00002783820 & +0.00006742859
             \end{array}
             \right]_R

Right Hip

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

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

\text{Mass} = 0.13530

CoM(S) = \left[
         \begin{array}{c}
           -0.01649 \\
           -0.00029 \\
           -0.00475
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00002791309 & -0.00000004982 & -0.00000530968 \\
               -0.00000004982 & +0.00010146905 & -0.00000000049 \\
               -0.00000530968 & -0.00000000049 & +0.00009209358
             \end{array}
             \right]_R

Left Hip

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

\text{Mass} = 0.13530

CoM(S) = \left[
         \begin{array}{c}
           -0.01649 \\
           +0.00029 \\
           -0.00475
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00002791309 & +0.00000004982 & -0.00000530968 \\
               +0.00000004982 & +0.00010146905 & +0.00000000049 \\
               -0.00000530968 & +0.00000000049 & +0.00009209358
             \end{array}
             \right]_R

Right Thigh

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

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

\text{Mass} = 0.39798

CoM(S) = \left[
         \begin{array}{c}
           +0.00131 \\
           -0.00201 \\
           -0.05386
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00166558985 & -0.00000043251 & +0.00008250512 \\
               -0.00000043251 & +0.00162499686 & -0.00003174281 \\
               +0.00008250512 & -0.00003174281 & +0.00030492852
             \end{array}
             \right]_{(o, R)}

Left Thigh

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

\text{Mass} = 0.39798

CoM(S) = \left[
         \begin{array}{c}
           +0.00131 \\
           +0.00201 \\
           -0.05386
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00166558985 & +0.00000043251 & +0.00008250512 \\
               +0.00000043251 & +0.00162499686 & +0.00003174281 \\
               +0.00008250512 & +0.00003174281 & +0.00030492852
             \end{array}
             \right]_{(o, R)}

Right Tibia

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

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

\text{Mass} = 0.29706

CoM(S) = \left[
         \begin{array}{c}
           +0.00471 \\
           -0.00210 \\
           -0.04891
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00118033782 & -0.00000030542 & +0.00004017104 \\
               -0.00000030542 & +0.00112927811 & -0.00003573639 \\
               +0.00004017104 & -0.00003573639 & +0.00019349009
             \end{array}
             \right]_{(o, R)}

Left Tibia

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

\text{Mass} = 0.29706

CoM(S) = \left[
         \begin{array}{c}
           +0.00471 \\
           +0.00210 \\
           -0.04891
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00118033782 & +0.00000030542 & +0.00004017104 \\
               +0.00000030542 & +0.00112927811 & +0.00003573639 \\
               +0.00004017104 & +0.00003573639 & +0.00019349009
             \end{array}
             \right]_{(o, R)}

Right Ankle

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

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

\text{Mass} = 0.13892

CoM(S) = \left[
         \begin{array}{c}
           +0.00142 \\
           -0.00028 \\
           +0.00638
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00003882578 & +0.00000004942 & +0.00000221321 \\
               +0.00000004942 & +0.00007211579 & -0.00000000674 \\
               +0.00000221321 & -0.00000000674 & +0.00005351987
             \end{array}
             \right]_{(o, R)}

Left Ankle

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

\text{Mass} = 0.13892

CoM(S) = \left[
         \begin{array}{c}
           +0.00142 \\
           +0.00028 \\
           +0.00638
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00003882578 & -0.00000004942 & +0.00000221321 \\
               -0.00000004942 & +0.00007211579 & +0.00000000674 \\
               +0.00000221321 & +0.00000000674 & +0.00005351987
             \end{array}
             \right]_{(o, R)}

Right Foot

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

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

\text{Mass} = 0.16304

CoM(S) = \left[
         \begin{array}{c}
           +0.02489 \\
           -0.00330 \\
           -0.03208
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00026759800 & +0.00000592718 & +0.00013729918 \\
               +0.00000592718 & +0.00064314836 & -0.00001869769 \\
               +0.00013729918 & -0.00001869769 & +0.00052649738
             \end{array}
             \right]_{(o, R)}

Left Foot

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

\text{Mass} = 0.16304

CoM(S) = \left[
         \begin{array}{c}
           +0.02489 \\
           +0.00330 \\
           -0.03208
         \end{array}
         \right]_{(o, R)}

[I_O(S)]_R = \left[
             \begin{array}{ccc}
               +0.00026759800 & -0.00000592718 & +0.00013729918 \\
               -0.00000592718 & +0.00064314836 & +0.00001869769 \\
               +0.00013729918 & +0.00001869769 & +0.00052649738
             \end{array}
             \right]_{(o, R)}