This page now separates the defining Proell linkage topology from a declared rotating-mass worksheet. The calculator does not solve sleeve equilibrium, operating speed, sensitivity, stability, effort, power, control response or safe design.
Proell Rotating-Mass Explorer
Enter declared spindle speed, ball mass and ball radius. The connected animation preserves two balls on extensions of the lower links and a shared sliding sleeve while the worksheet reports only ideal radial kinematics and force.
Equation Used
- Spindle speed N, ball mass m and ball-center radius r are declared inputs.
- Each ball is treated as a point mass in uniform circular motion for the radial ledger.
- The pair sum assumes two equal balls at the same declared radius.
- The animation uses exact equal-link closure for a prescribed qualitative cycle, independent of calculator inputs.
- Ball-extension geometry, pivots, sleeve mass, gravity, friction, arm forces, equilibrium, sensitivity, stability, effort, power, control linkage, dynamics, ratings, wear and safety are excluded.
Replaces the invalid extension-as-radius model with declared rotating-mass identities and a connected Proell topology.
Proell balls sit on extensions of the lower links
IRIMEE's Theory of Machines distinguishes the Proell governor from the Porter arrangement by placing the balls on extensions of the lower arms. Its gravity-controlled linkage connects those arms to a sliding central sleeve.
The animation preserves that topology with equal-link geometric closure, but its cycle is prescribed and does not calculate operating equilibrium.
Use this page only to audit declared rotating-mass arithmetic
The worksheet converts declared rpm to angular speed, computes omega²r, multiplies by declared ball mass and sums two equal radial-force magnitudes.
It cannot size, set, tune or evaluate a governor or predict sleeve position or engine response.
Keep radius distinct from link extension
Here r is the declared ball-center radius from the spindle axis. A Proell equilibrium solution additionally requires the actual linkage geometry, weights, gravity and friction.
A transparent rotating-mass example
For N=230 rpm, m=2.5 kg and r=180 mm, omega is 24.086 rad/s, radial acceleration is 104.420 m/s², ideal radial force per ball is 261.1 N, and the sum of two equal magnitudes is 522.1 N.
No sleeve-load or governing-speed conclusion follows.
Radial force is not governor equilibrium
Actual analysis needs every arm and extension dimension, pivot location, ball and sleeve weights, gravity, sleeve friction and a specified configuration. Sensitivity, stability, effort and power require multiple equilibrium states and a control linkage model.
The former use of arm extension as radius, unsupported extension moment and central-load ratio are removed.
Proell-governor ledger questions
Is ball radius the lower-arm extension length?
No; radius is measured from spindle axis to ball center.
Does F_pair act directly on the sleeve?
No; link forces and moment arms are required.
Does the animation determine speed?
No.
Can this predict sensitivity or stability?
No.
Proell-governor references
- IRIMEE, Theory of Machines — Governors: gravity-controlled classification and balls on extensions of the lower arms.
- CDLSIET Dynamics of Machinery laboratory manual: extension arms carry flyweights and the sleeve carries a central mass in a documented apparatus.
- NITK Virtual Labs, Proell Governor: gravity-controlled centrifugal-governor context.
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