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README.md
In massProps: Calculate Mass Properties and Uncertainties of Tree Structures
massProps
The massProps package extends rollupTree with functions to
recursively calculate mass properties (and optionally, their
uncertainties) for arbitrary composition trees. Formulas implemented are
described in a technical paper published by the Society of Allied Weight
Engineers (Zimmerman and Nakai 2005).
Installation
install.packages("massProps")
You can install the development version of massProps from
GitHub with:
# install.packages("pak")
pak::pak("jsjuni/massProps")
Example
Suppose we have the following mass properties table:
library(massProps)
test_table
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 2 A.2 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 3 A.3 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
POIconv indicates the products of inertia sign convention. In the
negative convention, for example, $I_{XY} \equiv -\int{xy \rho \, dV}$.
In the positive convention, $I_{XY} \equiv \int{xy \rho \, dV}$.
Ipoint indicates whether this object is to be considered a point mass.
The same algebraic result can be achieved by setting all moments and
products of inertia to zero, but rollup_mass_props() by default
ensures that all leaf items in the tree have mass properties that
correspond to physically-realizable objects. A zero inertia tensor will
fail this check. Rather than relax the check (which is essential for
trustworthy results), a TRUE value for Ipoint indicates that the
inertia tensor should be excluded from computations.
We construct a graph with edges representing child-parent relations:
library(igraph)
E(test_tree)
#> + 11/11 edges from 7d8200c (vertex names):
#> [1] A.2->A.1 A.3->A.1 C.1->A.1 P.1->A.2 P.2->A.2 P.3->A.2 P.4->A.2 P.5->A.3
#> [9] P.6->A.3 P.7->A.3 P.8->A.3
We can roll up mass properties to non-leaf elements as follows:
rollup_mass_props(test_tree, test_table)
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 21 0 0 0 144 -4.8 -24.8 144 -23.2 139 - FALSE
#> 2 A.2 A.1 8 1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 3 A.3 A.1 8 -1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
Note that, although the table shows the parent of each element for
clarity of exposition, the child-parent relations are coneveyed only
by the tree passed as the first argument.
The input data may include mass properties uncertainties as well:
test_unc_table
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 2 A.2 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 3 A.3 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> sigma_mass sigma_Cx sigma_Cy sigma_Cz sigma_Ixx sigma_Iyy sigma_Izz
#> 1 NA NA NA NA NA NA NA
#> 2 NA NA NA NA NA NA NA
#> 3 NA NA NA NA NA NA NA
#> 4 0.5 0.0 0.0 0.0 8.0 8.0 7.5
#> 5 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 6 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 7 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 8 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 9 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 10 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 11 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 12 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> sigma_Ixy sigma_Ixz sigma_Iyz
#> 1 NA NA NA
#> 2 NA NA NA
#> 3 NA NA NA
#> 4 0.40 2.40 2.40
#> 5 0.01 0.01 0.01
#> 6 0.01 0.01 0.01
#> 7 0.01 0.01 0.01
#> 8 0.01 0.01 0.01
#> 9 0.01 0.01 0.01
#> 10 0.01 0.01 0.01
#> 11 0.01 0.01 0.01
#> 12 0.01 0.01 0.01
Mass properties and their uncertainties can be rolled up as follows:
rollup_mass_props_and_unc(test_tree, test_unc_table)
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 21 0 0 0 144 -4.8 -24.8 144 -23.2 139 - FALSE
#> 2 A.2 A.1 8 1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 3 A.3 A.1 8 -1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> sigma_mass sigma_Cx sigma_Cy sigma_Cz sigma_Ixx sigma_Iyy sigma_Izz
#> 1 0.7549834 0.03809524 0.03809524 0.03809524 8.313844 8.275264 7.792946
#> 2 0.4000000 0.05000000 0.07071068 0.07071068 1.600000 1.200000 1.200000
#> 3 0.4000000 0.05000000 0.07071068 0.07071068 1.600000 1.200000 1.200000
#> 4 0.5000000 0.00000000 0.00000000 0.00000000 8.000000 8.000000 7.500000
#> 5 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 6 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 7 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 8 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 9 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 10 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 11 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 12 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> sigma_Ixy sigma_Ixz sigma_Iyz
#> 1 1.0586784 2.5924506 2.5924506
#> 2 0.4004997 0.4004997 0.6931089
#> 3 0.4004997 0.4004997 0.6931089
#> 4 0.4000000 2.4000000 2.4000000
#> 5 0.0100000 0.0100000 0.0100000
#> 6 0.0100000 0.0100000 0.0100000
#> 7 0.0100000 0.0100000 0.0100000
#> 8 0.0100000 0.0100000 0.0100000
#> 9 0.0100000 0.0100000 0.0100000
#> 10 0.0100000 0.0100000 0.0100000
#> 11 0.0100000 0.0100000 0.0100000
#> 12 0.0100000 0.0100000 0.0100000
References
Zimmerman, Robert L., and John H. Nakai. 2005. “Are You Sure?
Uncertainty in Mass Properties Engineering.” In *64th Annual
International Conference on Mass Properties Engineering*, 123–60.
Society of Allied Weight Engineers.
Try the massProps package in your browser
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massProps documentation built on April 4, 2025, 1:45 a.m.
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massProps
The massProps package extends rollupTree with functions to
recursively calculate mass properties (and optionally, their
uncertainties) for arbitrary composition trees. Formulas implemented are
described in a technical paper published by the Society of Allied Weight
Engineers (Zimmerman and Nakai 2005).
Installation
install.packages("massProps")
You can install the development version of massProps from GitHub with:
# install.packages("pak")
pak::pak("jsjuni/massProps")
Example
Suppose we have the following mass properties table:
library(massProps)
test_table
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 2 A.2 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 3 A.3 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
POIconv indicates the products of inertia sign convention. In the
negative convention, for example, $I_{XY} \equiv -\int{xy \rho \, dV}$.
In the positive convention, $I_{XY} \equiv \int{xy \rho \, dV}$.
Ipoint indicates whether this object is to be considered a point mass.
The same algebraic result can be achieved by setting all moments and
products of inertia to zero, but rollup_mass_props() by default
ensures that all leaf items in the tree have mass properties that
correspond to physically-realizable objects. A zero inertia tensor will
fail this check. Rather than relax the check (which is essential for
trustworthy results), a TRUE value for Ipoint indicates that the
inertia tensor should be excluded from computations.
We construct a graph with edges representing child-parent relations:
library(igraph)
E(test_tree)
#> + 11/11 edges from 7d8200c (vertex names):
#> [1] A.2->A.1 A.3->A.1 C.1->A.1 P.1->A.2 P.2->A.2 P.3->A.2 P.4->A.2 P.5->A.3
#> [9] P.6->A.3 P.7->A.3 P.8->A.3
We can roll up mass properties to non-leaf elements as follows:
rollup_mass_props(test_tree, test_table)
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 21 0 0 0 144 -4.8 -24.8 144 -23.2 139 - FALSE
#> 2 A.2 A.1 8 1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 3 A.3 A.1 8 -1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
Note that, although the table shows the parent of each element for clarity of exposition, the child-parent relations are coneveyed only by the tree passed as the first argument.
The input data may include mass properties uncertainties as well:
test_unc_table
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 2 A.2 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 3 A.3 A.1 NA NA NA NA NA NA NA NA NA NA - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> sigma_mass sigma_Cx sigma_Cy sigma_Cz sigma_Ixx sigma_Iyy sigma_Izz
#> 1 NA NA NA NA NA NA NA
#> 2 NA NA NA NA NA NA NA
#> 3 NA NA NA NA NA NA NA
#> 4 0.5 0.0 0.0 0.0 8.0 8.0 7.5
#> 5 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 6 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 7 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 8 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 9 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 10 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 11 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> 12 0.2 0.1 0.1 0.1 0.4 0.4 0.4
#> sigma_Ixy sigma_Ixz sigma_Iyz
#> 1 NA NA NA
#> 2 NA NA NA
#> 3 NA NA NA
#> 4 0.40 2.40 2.40
#> 5 0.01 0.01 0.01
#> 6 0.01 0.01 0.01
#> 7 0.01 0.01 0.01
#> 8 0.01 0.01 0.01
#> 9 0.01 0.01 0.01
#> 10 0.01 0.01 0.01
#> 11 0.01 0.01 0.01
#> 12 0.01 0.01 0.01
Mass properties and their uncertainties can be rolled up as follows:
rollup_mass_props_and_unc(test_tree, test_unc_table)
#> id parent mass Cx Cy Cz Ixx Ixy Ixz Iyy Iyz Izz POIconv Ipoint
#> 1 A.1 21 0 0 0 144 -4.8 -24.8 144 -23.2 139 - FALSE
#> 2 A.2 A.1 8 1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 3 A.3 A.1 8 -1 0 0 32 -0.4 -0.4 24 0.4 24 - FALSE
#> 4 C.1 A.1 5 0 0 0 80 -4.0 -24.0 80 -24.0 75 - FALSE
#> 5 P.1 A.2 2 1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 6 P.2 A.2 2 1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 7 P.3 A.2 2 1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 8 P.4 A.2 2 1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 9 P.5 A.3 2 -1 1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 10 P.6 A.3 2 -1 1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 11 P.7 A.3 2 -1 -1 1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> 12 P.8 A.3 2 -1 -1 -1 4 -0.1 -0.1 4 0.1 4 - FALSE
#> sigma_mass sigma_Cx sigma_Cy sigma_Cz sigma_Ixx sigma_Iyy sigma_Izz
#> 1 0.7549834 0.03809524 0.03809524 0.03809524 8.313844 8.275264 7.792946
#> 2 0.4000000 0.05000000 0.07071068 0.07071068 1.600000 1.200000 1.200000
#> 3 0.4000000 0.05000000 0.07071068 0.07071068 1.600000 1.200000 1.200000
#> 4 0.5000000 0.00000000 0.00000000 0.00000000 8.000000 8.000000 7.500000
#> 5 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 6 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 7 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 8 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 9 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 10 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 11 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> 12 0.2000000 0.10000000 0.10000000 0.10000000 0.400000 0.400000 0.400000
#> sigma_Ixy sigma_Ixz sigma_Iyz
#> 1 1.0586784 2.5924506 2.5924506
#> 2 0.4004997 0.4004997 0.6931089
#> 3 0.4004997 0.4004997 0.6931089
#> 4 0.4000000 2.4000000 2.4000000
#> 5 0.0100000 0.0100000 0.0100000
#> 6 0.0100000 0.0100000 0.0100000
#> 7 0.0100000 0.0100000 0.0100000
#> 8 0.0100000 0.0100000 0.0100000
#> 9 0.0100000 0.0100000 0.0100000
#> 10 0.0100000 0.0100000 0.0100000
#> 11 0.0100000 0.0100000 0.0100000
#> 12 0.0100000 0.0100000 0.0100000
References
Zimmerman, Robert L., and John H. Nakai. 2005. “Are You Sure?
Uncertainty in Mass Properties Engineering.” In *64th Annual
International Conference on Mass Properties Engineering*, 123–60.
Society of Allied Weight Engineers.
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