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Basic knowledgeWhat does center of gravity and moment mean?

>Knowledge centerWhat does center of gravity
and moment mean?

Concept of "Center of Gravity" and Moment

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What is center of gravity?
A center of gravity is the center of the entire weight of an object.

What is moment or moment of force?
It is a measurement of the force required to rotate something along an axis.
>What does center of gravity and moment mean?

If flap or door has an consistent density like the figure on the right the center of gravity will be its center.
In this case X1=L1÷2.

  • This is why the formula in Sugatsune's catalogue is L1÷2.
  • This formula is for thin flap/door.

Moment formula

The picture above is the formula for calculating the maximum moment.
Moment depends on opening angle, and horizontal distance of rotational center to "center of gravity".

Point on selecting hinge/stay

FREE STOP

If multiple hinges/stays are used, total torque will be values multiplied by its quantity

Click here for FREE STOP tools



DAMPENING

If multiple hinges/stays are used, total torque will be values multiplied by its quantity

Click here for SOFT CLOSE tools

Calculation of "Center of gravity"

To calculate an L-shaped flap's center of gravity, first divide the shape into two simple shapes and calculate each's center of gravity. Then combine the two by adding them together.
*The same concept applies where a mirror is attached to a lid, whereeach may have separate centers of gravity. Let's see an example case where
an L-shaped flap is divided into 2 pieces.

TRY!

Let's calculation an example case where an L-shaped flap is divided into 2 pieces.

Center of gravity G1 of flap A

Height L1*

cm

Thickness t1*

cm

Please input negative values if the centre of gravity is lower than the rotational centre/axis.

Unit length is "cm", to make it easer to understand.

Weight m1

kg

X1 axial distance

X1=L1/2
-----

cm

Y1 axial distance

Y1=t1/2
-----

cm

Distance to center of gravity G1

La=√X1 2 + Y1 2
-----

cm

Angle formed by G1 and
X axis

θ1 = tan-1 Y1/X1
-----

°

Moment at A

X1 direction

MX1 = X1 × m1
-----

kgf・cm

Y1 direction

MY1 = Y1 × m1
-----

kgf・cm

Center of gravity G2 of flap B

Height L2*

cm

Thickness t2*

cm

Please input negative values if the centre of gravity is lower than the rotational centre/axis.

Unit length is "cm", to make it easer to understand.

Weight m2

kg

X2 axial distance

X2=L1-t2/2
-----

cm

Y2 axial distance

Y2=t2/2
-----

cm

Distance to center of gravity G2

La=√X2 2 + Y2 2
-----

cm

Angle formed by G2 and
X axis

θ2 = tan-1 Y2/X2
-----

°

Moment at B

X2 direction

MX2 = X2 × m2
-----

kgf・cm

Y2 direction

MY2 = Y2 × m2
-----

kgf・cm

Total center of gravity G

Total Weight

m = m1 + m2
-----

kg

Center of gravity on X axis

X = MX1+MX2 / m
-----

cm

-----

mm

Center of gravity on Y axis

Y = MY1+MY2 / m
-----

cm

-----

mm

Distance of rotational center to total center of gravity

L=√X 2 + Y 2
-----

cm

-----

mm

Angle formed by G and
X axis

θ = tan-1 Y/X
-----

°

3 places of decimals will be rounded.

If center of gravity is unknown

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If the center of gravity cannot be calculated as the flap/door is already installed, the required torque can instead be calculated by use of a spring scale. As per the chart below, you need to measure the value o the spring scales and distance of otational center (axis) to the scales' measuring point.
L1 × F1 =Flap/door moment
Max. value of L1 × F1 =Max. flap/ door moment

Example

If L1 is 100cm, and F1is 2.5kg, flap/door moment will be formulated as, 100cm x 2.5kg = 250kgf・cm In this case,
you need over 250kg・cm(=24.5 N・m) of torque for Free Stop.
It means "hinge/stay torque ≧ 250kg・cm(=24.5 N・m)".

Notes: It will be difficult to calculate center of gravity if something is attached to a flap/door. In this case, you first need to make a rough estimate of weight and center of gravity, and select hinge/stay tentatively. A correct torque can be found by using the method above after assembling. This means you can select appropriate hinges/stays.

>Distance of rotational center to measuring point L1 cm
Measured value by spring scales F1 kg
Door moment = L1×F1×9.80665÷100 ---- N・m

Calculation of other operating force

If direction is for lifting up

operating force=( torque* + door moment) ÷ distance to operating point

For downward-opening

operating force=( torque* - door moment) ÷ distance to operating point

There must be a shaft center generating torque in rotational center.