This bell-crank dynamometer measures the force exerted by a deflected belt on an idler pulley. A spring balance acts on the other arm of the bell crank. The animation shows how the belt force and spring force balance at the measuring station, illustrated as item 143 in Hiscox’s Mechanical Movements.
Bell-crank Dynamometer Interactive Calculator
Adjust the spring force, perpendicular lever arms, symmetric belt angle and belt speed. A separate return-side tension makes clear that transmitted power depends on a tension difference.
Equation Used
- Forces act perpendicular to their lever arms.
- Belt legs are symmetric about the upward resultant; x is measured from that resultant.
- Idler bearing drag and belt bending stiffness are neglected.
- Return tension is independently entered, not inferred from the spring reading.
- The animation illustrates steady belt motion, not a moving lever during a balanced reading.
Hiscox item 143 illustrates this belt-deflection dynamometer. Enter return-side tension separately to calculate net belt power from the tension difference.
How the Belt Dynamometer Works
The belt passes over a pulley carried by the short arm of a bell crank. A spring balance attached to the long arm opposes the belt’s resultant force. With the mechanism balanced and its stationary weight tared out, the two moments are equal.
Hiscox item 143 shows this arrangement on the power side of a belt drive. The two belt legs must make equal angles with their resultant force for the illustrated force relation to apply.
A Historical Belt-force Measurement
The arrangement provides a mechanical way to relate a spring reading to belt tension. It is useful for studying lever balance, belt deflection and the distinction between belt tension and transmitted power. No modern instrument accuracy or load rating is implied.
Moment Balance and Belt Tension
Let W be the tared spring force, B its perpendicular arm, and A the idler’s perpendicular arm. The idler force is R = WB/A. For equal belt tensions T and symmetric angles x measured from the resultant, R = 2T cos x.
Net belt power requires the difference between the driving-side and return-side tensions. In imperial units, power in horsepower is (T − Treturn) times belt speed in feet per minute, divided by 33,000. A single absolute tension reading alone does not establish net shaft power.
Worked Example
A tared spring force of 20 lbf acting at B = 10 in balances an idler at A = 5 in. The resultant is 40 lbf. With x = 60°, the measured belt tension is also 40 lbf. At 600 ft/min and a separately entered return-side tension of 20 lbf, ideal transmitted power is 0.364 hp.
Limits of This Model
Force balance assumes a freely turning idler, perpendicular lever forces and symmetric belt directions. Tare, calibration, belt stiffness, bearing drag and the measuring arrangement affect a real reading. The visual arm proportions are schematic; the displayed dimensions drive the arithmetic.
Questions
Is spring force equal to belt tension?
Usually not. The lever ratio and the two belt-leg directions both affect the conversion.
Why enter return tension?
A drive transmits power through the difference between its tight-side and slack-side tensions. Belt pretension alone does not transmit power.
Why is the lever stationary?
The calculator shows the balanced measuring position while belt material travels over the idler.
Primary Reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, item 143, Bell-crank Dynamometer.
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