An eccentric slot in a pivoted lever can move a gear carrier along a guide, changing the distance between two gear centres. Explore that motion in the animation, then use the calculator to compare ideal hand force for an assumed perpendicular lever and follower moment arm. The force calculation is separate from the illustrated slot geometry.
Gear-disengaging Cam Lever Interactive Calculator
Compare ideal hand force using lever length, an assumed follower moment arm and follower load. The static calculation is independent of the animated slot.
Equation Used
The calculation balances perpendicular moments. The Cam Radius value is used as an assumed follower moment arm; it is not derived from the slot-contact force direction.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Ideal perpendicular moment balance; friction is neglected.
- Use millimetres for both moment arms; torque is displayed in N·m.
- Follower load is the assumed resisting force for this static comparison.
How the lever moves the gear carrier
The lever turns around a fixed pivot. Its circular slot is offset from that pivot, so turning the lever moves the slot centre. A carrier pin follows the slot while a vertical guide restricts the carrier to straight motion. The moving gear therefore approaches or withdraws from the fixed gear.
The drawing uses illustrative dimensions and pitch circles. Pitch-circle separation is not tooth-tip clearance, and the drawn rotation is prescribed rather than calculated from contact between the gears. It does not establish when actual teeth would fully disengage.
Parts to follow
- The blue lever supplies the input rotation.
- The offset circular slot guides the carrier pin.
- The vertical guide constrains the moving gear centre.
- The lower gear remains on a fixed centre.
A complete mechanism also needs suitable bearings, tooth clearances and position retention. This illustration does not determine whether a drive can be shifted under load or while rotating.
What this arrangement demonstrates
A lever and slot provide a compact way to move a gear carrier between positions. The useful design questions are how far the gear centre moves, whether the teeth clear, and what force the operator must apply through the throw.
Those questions require different calculations. The animation shows a possible carrier path. The calculator below the drawing covers only a selected ideal moment balance. A lead-screw half-nut, a sliding dog clutch and a friction clutch connect or disconnect drive differently and should not be treated as interchangeable examples of this gear-carrier arrangement.
Ideal hand-force calculation
For perpendicular forces about one pivot, equal opposing moments give Fhand × L = Ffollower × r. Here r is the assumed follower moment arm; a cam radius is equal to that arm only for the corresponding force direction.
MA = L/r
Fhand = Ffollower/MA
Thand = Fhand × L/1000
Enter L and r in millimetres and follower load in newtons. Hand torque is then in newton-metres. The calculation neglects friction and does not derive a changing moment arm from the animated slot, so the numerical results remain constant as the animation plays.
Example: a 200 mm lever
Use L = 200 mm, r = 25 mm and follower load = 80 N. The ideal force ratio is 200/25 = 8. Hand force is 80/8 = 10 N, and hand torque is 10 × 200/1000 = 2 N·m.
Increasing L to 300 mm gives a ratio of 12 and reduces hand force to 6.67 N. The required torque remains 2 N·m because the assumed follower load and its moment arm are unchanged. Increasing r to 50 mm with L = 200 mm instead gives a ratio of 4, hand force of 20 N and torque of 4 N·m.
These are hypothetical static comparisons, not measurements of a particular machine or predictions of force throughout a cam throw.
Force, travel and engagement
| Change or question | What the calculator tells you | What needs the actual mechanism |
|---|---|---|
| Longer hand lever | Less hand force for the same required torque | Available space and handle travel |
| Larger assumed follower moment arm | More hand force and torque at the same follower load | Slot profile and force direction through the motion |
| Gear disengagement | No tooth-clearance result | Gear geometry, carrier travel and clearances |
| Position retention | No detent or holding-force result | A suitable retaining arrangement and its loads |
Frequently asked questions
Why do the force outputs stay constant while the lever moves?
The calculator uses the entered lever length, assumed moment arm and follower load. It does not calculate their changing relationship from the animated slot.
Does a larger force ratio mean the teeth are clear?
No. Force ratio is L/r. Tooth clearance requires the gear dimensions and sufficient carrier movement; it is not calculated here.
Why does hand torque stay the same when I increase lever length?
At fixed follower load and moment arm, required torque is Ffollower × r. A longer lever supplies that torque with less hand force.
Is the Cam Radius input the true moment arm at every position?
No. In the force calculation it is used as an assumed perpendicular moment arm. The real moment arm depends on the line of action of the slot-contact force and changes with geometry.
Can this tool decide whether it is safe to disengage a running drive?
No. It does not calculate tooth loading, contact dynamics or release under power. Follow the machine’s specified operating procedure.
Reference
OpenStax, University Physics: Torque explains force, perpendicular moment arm and torque.
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