# 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:

- Lack of wiring in CAD
- Lack of grease in CAD
- 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.

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

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

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)

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

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

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

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

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

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

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

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

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