= Inertial Tensors and Mass Properties for the BarrettHand BH8-280 =
The inertial properties calculated here represent the masses and inertias of each link of the BarrettHand BH8-280. All calculations were made using SolidWorks 2012 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 664 g while SolidWorks calculated the mass of the CAD model to be only 643 g. This discrepancy could come from a number of sources:
1. Lack of wiring in CAD
1. Lack of grease in CAD
1. 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 664 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.
[[Image(AllFrames_crop.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 ==
[[Image(HandFrameW_NoDialog_crop.jpg)]]
Output coordinate System: Frame W (opaque)
Mass = 0.60858 kilograms
Volume = 0.00024871 cubic meters
Surface area = 0.24908 square meters
Center of mass: (meters)
X = 5.0019e-005 Y = -0.0044561 Z = 0.037268
Principal axes of inertia and principal moments of inertia: (kilograms * square meters)
Taken at the center of mass.
|| Ix = (0.0025349, 0.91612, -0.4009) || Px = 0.00047536
|| Iy = (0.012636, -0.40089, -0.91604) || Py = 0.0006507
|| Iz = (-0.99992, -0.0027435, -0.012592) || Pz = 0.00069861
Moments of inertia: (kilograms * square meters)
Taken at the center of mass and aligned with the output coordinate system.
|| Lxx = 0.0006986 || Lxy = 2.7577e-007 || Lxz = -7.8138e-007
|| Lyx = 2.7577e-007 || Lyy = 0.00050354 || Lyz = -6.44e-005
|| Lzx = -7.8138e-007 || Lzy = -6.44e-005 || Lzz = 0.00062253
Moments of inertia: (kilograms * square meters)
Taken at the output coordinate system.
|| Ixx = 0.001556 || Ixy = 1.4013e-007 || Ixz = 3.5309e-007
|| Iyx = 1.4013e-007 || Iyy = 0.0013488 || Iyz = -0.00016547
|| Izx = 3.5309e-007 || Izy = -0.00016547 || Izz = 0.00063461
== Mass Properties for Frame W (hand base frame) without palm pad ==
[[Image(HandFrameW_NOPP_NoDialog_crop.jpg)]]
Output coordinate System: Frame W (opaque)
Mass = 0.59573 kilograms
Volume = 0.00023933 cubic meters
Surface area = 0.23262 square meters
Center of mass: (meters)
X = 5.1098e-005
Y = -0.0050433
Z = 0.036671
Principal axes of inertia and principal moments of inertia: (kilograms * square meters)
Taken at the center of mass.
|| Ix = (0.0027331, 0.90166, -0.43244) || Px = 0.00045391
|| Iy = (0.01699, -0.43242, -0.90151) || Py = 0.00063852
|| Iz = (-0.99985, -0.0048831, -0.016501) || Pz = 0.00067156
Moments of inertia: (kilograms * square meters)
Taken at the center of mass and aligned with the output coordinate system.
|| Lxx = 0.00067154 || Lxy = 2.9365e-007 || Lxz = -7.6321e-007
|| Lyx = 2.9365e-007 || Lyy = 0.00048844 || Lyz = -7.1984e-005
|| Lzx = -7.6321e-007 || Lzy = -7.1984e-005 || Lzz = 0.00060401
Moments of inertia: (kilograms * square meters)
Taken at the output coordinate system.
|| Ixx = 0.0014878 || Ixy = 1.4013e-007 || Ixz = 3.5309e-007
|| Iyx = 1.4013e-007 || Iyy = 0.0012896 || Iyz = -0.00018216
|| Izx = 3.5309e-007 || Izy = -0.00018216 || Izz = 0.00061916
== Mass Properties for Frame 1 (finger spread frame) ==
[[Image(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 ==
[[Image(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 ==
[[Image(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 ==
[[Image(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 ==
[[Image(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