A friction pulley with eccentric arms acts as a one-way clutch. Four pivoted arms connect to the shaft carrier inside the pulley rim. Friction tends to wedge the arms against the rim in one direction and turn them away from gripping in the other. Brown illustrates this arrangement in movement 267, with springs keeping the arms biased toward the rim.
Friction Pulley with Eccentric Arms Interactive Calculator
Watch the rim alternate between its driving and free-running directions. The five controls compare pulley geometry and two assumed outer-belt friction conditions. Their tension ratios describe the belt, not the gripping capacity of the internal arms.
Equation Used
The belt model assumes a flexible flat belt at impending slip, a uniform coefficient and negligible centrifugal tension. The normalized belt torque is (T_tight/T_slack − 1); multiply by slack-side tension and outer pulley radius to obtain torque. The entered pivot distance e is measured from the shaft center. An e at or beyond D/2 leaves no room for an internal arm; the drawing flags that geometry. The model does not calculate arm contact force, a locking condition, spring preload or clutch torque capacity.
A loose rim and a shaft-mounted carrier
The pulley rim can turn about the shaft. Inside it, a carrier fixed to the shaft supports four eccentric arms on pivots. Small springs bias the arms toward the inside of the rim. Their shape and pivot positions make the contact directional.
In the drawing’s counterclockwise direction, friction urges the arm tips into a gripping position. The rim then carries the arms, carrier and shaft around with it. In the clockwise direction, the arms can turn on their pivots to relax the grip. Brown describes the shaft remaining at rest while the rim turns in that direction.
The animation alternates these two directions. Blue marks track the rim; the central carrier and gold arms follow the shaft. During free running, the carrier holds its angle while the blue rim continues. A small exaggerated clearance makes the released position visible; the real spring-biased contact need not have a visible air gap. Speeds, cam profiles and spring shapes are illustrative.
The outer belt is a separate contact. Its highlighted arc follows the chosen wrap angle, and moving marks follow the rim’s direction. The internal arm pivots follow e relative to the entered outer radius, with an illustrative rim thickness. The drawing flags positions outside its inner rim instead of forcing the arms through it.
Transmitting one direction of rotation
This arrangement explains directional coupling: a rotating rim can drive its shaft one way and overrun it the other way. That is different from a clutch that slips at a specified overload torque in either direction.
A one-way drive can be useful wherever motion must be passed during one part of a reversing cycle. Actual overrunning clutches use various rollers, sprags, pawls or other contact arrangements. Their ratings and release behavior depend on the particular design; Brown’s illustration is not a selection chart for a modern machine.
Belt traction and arm geometry are separate
For a flexible flat belt at impending slip, the limiting tight-side to slack-side tension ratio is exp(μθ), with wrap θ in radians. This calculator applies that equation to the outer belt for two coefficients, A and B. Neither coefficient is a measured property of the historical pulley, and neither controls the internal cam grip.
If slack-side tension is T_slack and the outer pulley radius is R, belt torque is (T_tight − T_slack)R. Dividing by T_slack R gives the displayed normalized torque exp(μ_A θ) − 1. Absolute belt tension is not entered, so no torque in N·m is determined.
The geometry output is 100e/R = 200e/D percent. It describes pivot position only. Calculating whether an eccentric arm locks requires its contact profile, local force directions and friction at the inner rim. Spring and contact forces cannot be inferred from belt wrap or e/R alone.
Example: compare two outer-belt coefficients
With a 150 mm outer diameter and e = 8 mm, pivot distance is 10.67% of outer radius. At 160° wrap, θ is approximately 2.793 radians. Coefficient A = 0.40 gives a limiting belt tension ratio of 3.056:1 and normalized torque of 2.056. Coefficient B = 0.15 gives 1.520:1.
If the slack-side tension were 100 N, the A comparison would give about 305.6 N tight-side tension. At a 0.075 m radius, their difference corresponds to about 15.42 N·m of belt torque. That example concerns the belt contact only; it does not establish whether the internal clutch can carry that torque.
Increasing wrap or either coefficient increases that coefficient’s limiting tension ratio. Changing diameter or pivot distance changes the geometry ratio without changing the belt-tension ratios. The control extremes are comparison values, not recommended dimensions or operating conditions.
What the one-way action does not establish
Direction-sensitive gripping does not imply a calibrated overload release. Contact stress, local friction, arm stiffness, spring bias, clearance and wear all affect engagement. The animation prescribes driving and release states to explain the intended motion; it does not solve those forces.
The original engraving gives no universal shaft-speed limit, service interval, dimensional tolerances or spring rate. The calculation also omits belt bending stiffness, centrifugal effects and actual tension. It cannot size the arms, select a spring or certify protection for downstream equipment.
Frequently asked questions
Which direction drives the shaft?
In this view the counterclockwise rim motion drives the shaft. Clockwise rim motion releases the grip and the shaft holds still in the illustration. Reversing the arm orientation would reverse the gripping direction.
Do the arms press on the belt?
They act against the inside of the pulley rim. The belt contacts the outside and is a separate friction interface.
Why are there springs?
Brown describes springs holding the arms toward the rim. They bias the contact; their force and stiffness are not given by the belt-friction equation.
Does coefficient A control the one-way clutch?
No. A and B compare the outer belt’s limiting tension ratio. The animation’s internal gripping and free-running states are prescribed illustrations.
Why does changing diameter leave the tension ratio unchanged?
The ideal capstan tension ratio depends on coefficient and wrap angle. Radius is needed when converting a tension difference into torque.
What does the geometry message mean?
A pivot must fit inside the pulley rim. When it falls at or outside the illustrative inner rim, the drawing omits the arms and asks for a larger diameter or smaller pivot distance.
Is the gap during free running a dimension?
No. It is exaggerated to distinguish release from gripping. Real spring-biased arms can remain in light contact while the rim overruns them.
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