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# How to Calculate the Center of Gravity

Introduction

There are n load cells: LC1, …, LCn.

The illustrations below describe systems with 2, 3 or 4 load cells.

However, the formulas used are general for n >= 2.

All the n load cells are calibrated the same.

There is some reference point that serves as the origin of the X,  Y axes.

Notations

The ‘i’ index in all the expressions below goes from 1 to n(e.g., for n=3: i = 1, 2, 3).

(Xi,Yi)= The position of LCi.

Wi = The weight reading of LCi.

Wt = total weight = sum of all Wi.

(Xcg,Ycg)= The position of the CoG (Center of Gravity).

MXi = The X-Momentof LCi = Wi*Xi.

MYi = The Y-Moment of LCi = Wi*Yi.

MXt = The totalX-Moment= sumof all MXi= Wt*Xcg

MYt = The totalY-Moment= sumof all MYi = Wt*Ycg

Xcg = MXt / Wt

Ycg = MYt / Wt

Application

Given(input)

1. Weight units (e.g., kg).

2. Length units (e.g., cm).

3. Position reports format:

# of digits after the decimal point for the CoG X/Y position(e.g., 2).

4. Weightreport’s format:

# of digits after the decimal point for the CoG weight(e.g., 0).

5. n(e.g., 3).

6. Weight(Wi) and position(Xi, Yi) of all load cells.

Note: You may specify the weight & position in free format. That is, you are not subject to the format defined in paragraphs 3 & 4:The effect of these formats is only on the application’s output.

Notes

* You may set the “input” of the application to any of the following 6 examples: Select the corresponding serial # (01 à06) in application’s “Example” field.

* Changing the position (X and/or Y) of a load cell might throw its location out of graph limits. Therefore, it is recommended to click “Graph Settings” after changing the load cells position, and verify that graph limits are OK. However, in case a load cell exceeds the limits, the application gives a proper message.

* The application keeps the input of the last report or graph –next time you run, this input will be used automatically.