Inertial Tensors and Mass Properties for the BarrettHand BH8-282

The inertial properties calculated here represent the masses and inertias of each link of the BarrettHand BH8-280. All calculations were made using SolidWorks 2013 SP 3.0 and CAD models that include all mechanical components of the hand (including fasteners) and all electrical components except wiring. To verify that the SolidWorks model was correct, assemblies and parts of an actual hand were massed for comparison.

The mass of an actual finger was measured at 179 g, which matches the mass of the CAD model. The hand base (including pucks and finger motors) measured 388 g while SolidWorks calculated the mass of the CAD model to be only 367 g. This discrepancy could come from a number of sources:

  1. Lack of wiring in CAD
  2. Lack of grease in CAD
  3. Inadequately modeled PCB and components

Further investigation narrowed the source of error to electrical subassemblies with dozens of strands of wire, all of which were omitted in the CAD model. To replicate the mass of these wires, slugs of the missing mass were created to fill the cavities in which wires could run. The base CAD model used in the calculations below measures 367 g.

In the following images, all parts are left transparent to display all parts of the mass calculations. Yellow denotes frame parts, red denotes electrical pieces, and blue is for motors and drivetrain components.

The following inertial frames are established on the hand. In each of the following diagrams, coordinate systems are oriented with the Z-axis coincident to the axis of rotation of each joint. These inertial frames follow the same convention as on the BarrettHand BH8-262. http://web.barrett.com/supportFiles/wikiFiles/AllFrames_crop_282.JPG

Since no one is likely to wish to attempt computed-torque control on the Hand axes (since the frictions in the Hand are very high), the backdriven, reflected drive inertias of the drives were not computed. Since backdriven drive inertias have no effect on gravity terms, the frame inertias should give you good results for controlling the WAM arm and wrist torques as functions of hand-finger positions.

You may also view mass properties of the entire hand in various configurations here: http://web.barrett.com/support/BarrettHand_Documentation/BarrettHand280MassProp-2010Dec10.pdf

Mass Properties for Frame W (hand base frame) with palm pad

http://web.barrett.com/supportFiles/wikiFiles/HandFrameW_NoDialog_crop_282.JPG

Output coordinate System: Frame W (opaque)

Mass = 0.36699 kilograms

Volume = 0.00011798 cubic meters

Surface area = 0.18541 square meters

Center of mass: (meters)

X = -2.506e-005 Y = 0.034479 Z = -.0072785

Principal axes of inertia and principal moments of inertia: ( kilograms * square meters ) Taken at the center of mass.

Ix = (0.0018855, -0.15008, 0.98867) Px = 0.00021984
Iy = (-0.21340, -0.96595, -0.14623) Py = 0.00040405
Iz = (0.97696, -0.21070, -0.033849) Pz = 0.00040831

Moments of inertia: ( kilograms * square meters ) Taken at the center of mass and aligned with the output coordinate system.

Lxx = 0.00040811 Lxy = 0.00000082 Lxz = 0.00000048
Lyx = 0.00000082 Lyy = 0.00040009 Lyz = -0.00002736
Lzx = 0.00000048 Lzy = -0.00002736 Lzz = 0.00022400

Moments of inertia: ( kilograms * square meters ) Taken at the output coordinate system.

Ixx = 0.00086379 Ixy = 0.00000051 Ixz = 0.00000055
Iyx = 0.00000051 Iyy = 0.00041950 Iyz = -0.00011939
Izx = 0.00000055 Izy = -0.00011939 Izz = 0.00066026

Mass Properties for Frame W (hand base frame) without palm pad

http://web.barrett.com/supportFiles/wikiFiles/HandFrameW_NOPP_NoDialog_crop_282.JPG

Output coordinate System: Frame W (opaque)

Mass = 0.34867 kilograms

Volume = 0.00010856 cubic meters

Surface area = 0.16889 square meters

Center of mass: ( meters )

X = -2.63759e-005 Y = 0.033662 Z = -0.0087593

Principal axes of inertia and principal moments of inertia: ( kilograms * square meters ) Taken at the center of mass.

Ix = (0.0017695, -0.19274, 0.98124) Px = 0.00020570
Iy = (0.81607, 0.56738, 0.10998) Py = 0.00037703
Iz = (-0.57794, 0.80057, 0.15830) Pz = 0.00037892

Moments of inertia: ( kilograms * square meters ) Taken at the center of mass and aligned with the output coordinate system.

Lxx = 0.00037765 Lxy = 8.17141e-007 Lxz = 4.70601e-007
Lyx = 8.17141e-007 Lyy = 0.00037187 Lyz = -3.26426e-005
Lzx = 4.70601e-007 Lzy = -3.26426e-005 Lzz = 0.00021211

Moments of inertia: ( kilograms * square meters ) Taken at the output coordinate system.

Ixx = 0.00079952 Ixy = 5.07559e-007 Ixz = 5.51157e-007
Iyx = 5.07559e-007 Iyy = 0.00039862 Iyz = -0.00013545
Izx = 5.51157e-007 Izy = -0.00013545 Izz = 0.00060722

Mass Properties for Frame 1 (finger spread frame)

http://web.barrett.com/supportFiles/wikiFiles/HandFrame1_NoDialog_crop.JPG

Output coordinate System: F1 (opaque)

Mass = 0.14109 kilograms

Volume = 3.919e-005 cubic meters

Surface area = 0.058268 square meters

Center of mass (meters):

X = 0.030616 Y = -7.3219e-005 Z = -0.011201

Principal axes of inertia and principal moments of inertia (kilograms * square meters), taken at the center of mass:

Ix = (-0.99149, -0.0047957, -0.13013) Px = 1.9838e-005
Iy = (0.13011, 0.0033343, -0.99149) Py = 6.904e-005
Iz = (0.0051888, -0.99998, -0.0026819) Pz = 7.4106e-005

Moments of inertia (kilograms * square meters), taken at the center of mass and aligned with the output coordinate system:

Lxx = 2.0672e-005 Lxy = 2.6024e-007 Lxz = 6.3481e-006
Lyx = 2.6024e-007 Lyy = 7.4105e-005 Lyz = 1.7118e-008
Lzx = 6.3481e-006 Lzy = 1.7118e-008 Lzz = 6.8207e-005

Moments of inertia (kilograms * square meters), taken at the output coordinate system:

Ixx = 3.8374e-005 Ixy = -5.604e-008 Ixz = -4.2034e-005
Iyx = -5.604e-008 Iyy = 0.00022405 Iyz = 1.3283e-007
Izx = -4.2034e-005 Izy = 1.3283e-007 Izz = 0.00020045

Mass Properties for Frame 2 (finger inner link frame) without fingertip torque sensor

http://web.barrett.com/supportFiles/wikiFiles/HandFrame2_NOSG_NoDialog_crop.JPG

Output coordinate System: F2_Origin

Mass = 0.05832 kilograms

Volume = 1.629e-005 cubic meters

Surface area = 0.026068 square meters

Center of mass (meters):

X = 0.022042 Y = 0.00082603 Z = 0.0005526

Principal axes of inertia and principal moments of inertia (kilograms * square meters), taken at the center of mass:

Ix = (-0.99971, -0.016746, 0.017324) Px = 4.7372e-006
Iy = (0.016611, -0.99983, -0.007873) Py = 4.1939e-005
Iz = (0.017453, -0.0075829, 0.99982) Pz = 4.3077e-005

Moments of inertia (kilograms * square meters), taken at the center of mass and aligned with the output coordinate system:

Lxx = 4.7592e-006 Lxy = 6.2295e-007 Lxz = -6.6417e-007
Lyx = 6.2295e-007 Lyy = 4.1929e-005 Lyz = -2.1644e-009
Lzx = -6.6417e-007 Lzy = -2.1644e-009 Lzz = 4.3066e-005

Moments of inertia (kilograms * square meters), taken at the output coordinate system:

Ixx = 4.8168e-006 Ixy = 1.6848e-006 Ixz = 4.6191e-008
Iyx = 1.6848e-006 Iyy = 7.0281e-005 Iyz = 2.4457e-008
Izx = 4.6191e-008 Izy = 2.4457e-008 Izz = 7.144e-005

Mass Properties for Frame 2 (finger inner link frame) with fingertip torque sensor

http://web.barrett.com/supportFiles/wikiFiles/HandFrame2_NoDialog_crop.JPG

Output coordinate System: F2_Origin

Mass = 0.062139 kilograms

Volume = 1.7634e-005 cubic meters

Surface area = 0.028654 square meters

Center of mass (meters):

X = 0.023133 Y = 0.00078642 Z = 0.00052792

Principal axes of inertia and principal moments of inertia (kilograms * square meters), taken at the center of mass:

Ix = (-0.99972, -0.015048, 0.018278) Px = 4.7942e-006
Iy = (0.014917, -0.99986, -0.0073066) Py = 4.3325e-005
Iz = (0.018386, -0.0070319, 0.99981) Pz = 4.4454e-005

Moments of inertia (kilograms * square meters), taken at the center of mass and aligned with the output coordinate system:

Lxx = 4.8162e-006 Lxy = 5.7981e-007 Lxz = -7.2483e-007
Lyx = 5.7981e-007 Lyy = 4.3317e-005 Lyz = -2.6653e-009
Lzx = -7.2483e-007 Lzy = -2.6653e-009 Lzz = 4.4441e-005

Moments of inertia (kilograms * square meters), taken at the output coordinate system:

Ixx = 4.872e-006 Ixy = 1.7103e-006 Ixz = 3.4041e-008
Iyx = 1.7103e-006 Iyy = 7.6588e-005 Iyz = 2.3133e-008
Izx = 3.4041e-008 Izy = 2.3133e-008 Izz = 7.7733e-005

Mass Properties for Frame 3 (fingertip frame) without fingertip pressure pad

http://web.barrett.com/supportFiles/wikiFiles/HandFrame3_NOPP_NoDialog_crop.JPG

Output coordinate System: F3 (opaque)

Mass = 0.041377 kilograms

Volume = 1.5627e-005 cubic meters

Surface area = 0.019684 square meters

Center of mass (meters):

X = 0.022825 Y = 0.0010491 Z = 0.00042038

Principal axes of inertia and principal moments of inertia (kilograms * square meters), taken at the center of mass:

Ix = (-0.99921, -0.032055, 0.023536) Px = 3.0842e-006
Iy = (0.023767, -0.0068431, 0.99969) Py = 1.568e-005
Iz = (-0.031884, 0.99946, 0.0075995) Pz = 1.6826e-005

Moments of inertia (kilograms * square meters), taken at the center of mass and aligned with the output coordinate system:

Lxx = 3.1053e-006 Lxy = 4.3996e-007 Lxz = -2.9595e-007
Lyx = 4.3996e-007 Lyy = 1.6812e-005 Lyz = -1.8205e-008
Lzx = -2.9595e-007 Lzy = -1.8205e-008 Lzz = 1.5673e-005

Moments of inertia (kilograms * square meters), taken at the output coordinate system:

Ixx = 3.1582e-006 Ixy = 1.4308e-006 Ixz = 1.0106e-007
Iyx = 1.4308e-006 Iyy = 3.8376e-005 Iyz = 0
Izx = 1.0106e-007 Izy = 0 Izz = 3.7275e-005

Mass Properties for Frame 3 (fingertip frame) with fingertip pressure pad

http://web.barrett.com/supportFiles/wikiFiles/HandFrame3_NoDialog_crop.JPG

Output coordinate System: F3 (opaque)

Mass = 0.04166 kilograms

Volume = 1.5911e-005 cubic meters

Surface area = 0.02168 square meters

Center of mass (meters):

X = 0.02295 Y = 0.0010739 Z = 0.00041752

Principal axes of inertia and principal moments of inertia (kilograms * square meters), taken at the center of mass:

Ix = (-0.99919, -0.032581, 0.023483) Px = 3.0982e-006
Iy = (0.023724, -0.0070039, 0.99969) Py = 1.5816e-005
Iz = (-0.032406, 0.99944, 0.0077712) Pz = 1.6962e-005

Moments of inertia (kilograms * square meters), taken at the center of mass and aligned with the output coordinate system:

Lxx = 3.1199e-006 Lxy = 4.5115e-007 Lxz = -2.9813e-007
Lyx = 4.5115e-007 Lyy = 1.6948e-005 Lyz = -1.8635e-008
Lzx = -2.9813e-007 Lzy = -1.8635e-008 Lzz = 1.5809e-005

Moments of inertia (kilograms * square meters), taken at the output coordinate system:

Ixx = 3.1752e-006 Ixy = 1.4779e-006 Ixz = 1.0106e-007
Iyx = 1.4779e-006 Iyy = 3.8897e-005 Iyz = 0
Izx = 1.0106e-007 Izy = 0 Izz = 3.78e-005
Last modified 4 years ago Last modified on Aug 16, 2013, 2:47:38 PM