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### Counterbalancing Several Masses Located in a Single Plane Formulas and Calculator

Counterbalancing Several Masses Located in a Single Plane Formulas and Calculator

In all balancing problems, the product of the counterbalancing mass (or weight) and its radius are calculated; it is thus necessary to select either the mass or the radius and then calculate the other value from the product of the two quantities. Design considerations usually make this decision self-evident. The angular position of the counterbalancing mass must also be calculated. Preview Counterbalancing Several Masses Located in a Single Plane Calculator

Counterbalancing Several Masses Located in a Single Plane can be calculated by the following formulas:

Eq :

MB rB = [ ( ∑ M r cosθ )2 + ( ∑ M r sinθ )2 ]1/2

tanθB = - ( ∑ M r sinθ) / - ( ∑ M r cosθ ) = - y / - x

Image and Table 1
Relationship of Angle Function Signs to Quadrant in Which They Occur Angle θ Trigonmetric Function 0° to 90° 90° to 180° 180° to 270° 270° to 360° Signs of the Functions tan +y / +x +y / -x -y / -x -y / +x sine +y / +r +y / +r -y / +r -y / +r cosine +x / +r -x / +r -x / +r +x / +r

Where:

M1, M2, M3, ..., Mn = any unbalanced mass or weight, (kg, lb),
MB = counterbalancing mass or weight, (kg, lb),
r = radius to center of gravity of any unbalance mass or weitgh, (mm, in),
rB = radius to center of gravity of counterbalancing mass or weight, (mm, in),
θ = angular position of r of any unbalanced mass or weight, (degrees),
θB = angular position of rB of counterbalancing mass or weight, degrees

Reference:

Machinery's Handbook 30th edition

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