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Assembly centre of gravity & inertia calculator

Engineering calculators (Beta)

Combine part masses, centre positions and centroidal inertias.

Inputs

Choose units and enter numbers. Full-width digits and fractions such as 1/8 or 1 3/8 are accepted. Changing a unit converts the entered value.

Results

Reference calculation only. Results do not certify suitability for an actual design or its safety.

Diagram

Inputs: select a blue symbol to edit Results: red-orange values and lines

Formula and applicability

c = Σ(mi ci)/Σmi; Jx(O) = Σ[Jxi + mi((yi−oy)²+(zi−oz)²)]

Displayed values are rounded. Diagrams illustrate the calculation conditions. Initial material and fluid properties are examples; replace them with values for the actual material, temperature and conditions.

Reference
Using this information as a reference

Equations assume particular loads, supports and deformation ranges. Check inputs, units and the applicability of each equation. Diagrams explain conditions; they are not manufacturing drawings or proof of safety.

Material values are typical values or reference ranges, not certified product properties or ready-to-use design allowables. They vary with standards, product form, dimensions, temper and temperature. Check the specifications and inspection certificates for the actual product.

Displayed safety factors and checks apply only to the supplied inputs and calculation model. They do not automatically establish the safety of a complete design, including code compliance, service life, fatigue or joints. For actual design, manufacture and use, separately verify applicable regulations and standards, product specifications, and the necessary tests and engineering review.

この計算で求められること

部品ごとの質量・重心位置・重心軸慣性を合成します。

入力・結果・適用条件を確認する

選択した形状・計算方法により、使う項目は変わります。実際の計算は上の図と入力欄で行えます。

主な入力

  • 駆動へ渡す軸 (—)
  • 指定軸が通る点 x (mm / cm / m)
  • 指定軸が通る点 y (mm / cm / m)
  • 指定軸が通る点 z (mm / cm / m)

得られる結果

  • 合計質量 (kg)
  • 重心 x (mm)
  • 重心 y (mm)
  • 重心 z (mm)
  • 指定点を通るx軸の慣性 (kg·m²)
  • 指定点を通るy軸の慣性 (kg·m²)
  • 指定点を通るz軸の慣性 (kg·m²)
  • 選択した駆動軸の慣性 (kg·m²)

計算式の概要

c = Σ(mi ci)/Σmi; Jx(O) = Σ[Jxi + mi((yi−oy)²+(zi−oz)²)]

1〜30部品。各部品のJx/Jy/Jzは、その部品の重心を通り全体のx/y/zに平行な軸の値です。0なら質点近似です。姿勢を変えるテンソル回転は行いません。

現在選択中の方法には、操作欄の「計算式・適用条件」を使ってください。参考計算であり、設計全体の安全性を保証するものではありません。

関連する計算

What this calculator does

Combine part masses, centre positions and centroidal inertias.

Inputs, outputs and applicability

The selected model determines which of these inputs and outputs apply. Use the working diagram and input panel above to calculate.

Inputs

  • Axis for drive transfer (—)
  • Axis point x (mm / cm / m)
  • Axis point y (mm / cm / m)
  • Axis point z (mm / cm / m)

Calculated results

  • Total mass (kg)
  • Centre x (mm)
  • Centre y (mm)
  • Centre z (mm)
  • Inertia about x through axis point (kg·m²)
  • Inertia about y through axis point (kg·m²)
  • Inertia about z through axis point (kg·m²)
  • Selected drive-axis inertia (kg·m²)

Formula overview

c = Σ(mi ci)/Σmi; Jx(O) = Σ[Jxi + mi((yi−oy)²+(zi−oz)²)]

1–30 parts. Each intrinsic Jx/Jy/Jz is about its own centre, parallel to the assembly axes. Zero uses a point-mass approximation. No orientation tensor rotation is performed.

The displayed formula and conditions in the working panel apply to the currently selected model. Reference calculation only; it does not certify a complete design.

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目的から順に確認する設計ガイド

図で条件を整理してから計算し、最後に実際の部品仕様を確認します。

Purpose-based design guides

Understand conditions with diagrams, calculate, then verify actual specifications.