BIZOMAT MAKEOS · Mechanics
Geneva Drive Design (Acceleration, Pin Force and Drive Torque)
How hard does this Geneva wheel accelerate the load, what force does the drive roller see, and what torque must the driver supply?
Dynamic check of an external Geneva indexing drive: crank radius, index and dwell times and peak wheel speed (as the Geneva mechanism tool), the wheel’s angular velocity and acceleration through the indexing stroke found point by point, the torque to accelerate the wheel and load inertia plus friction, the force on the roller in the slot, and the driver torque by power balance, checked against your roller and drive ratings.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of slots | Number of slots in the Geneva wheel (indexes per turn). | |
| Centre distance | mm | Distance between the driver and wheel centres. |
| Driver speed | rpm | Speed of the driving crank (one index per turn). |
| Roller diameter | mm | Diameter of the drive roller. |
| Wheel and load inertia | kg·m² | Inertia of the wheel, table and load about the wheel axis. |
| Friction torque on the wheel | N·m | Friction torque resisting the wheel. |
| Allowable roller force | N | Allowable load on the roller and its pin (your value from the bearing or pin rating). |
| Driver torque rating | N·m | Torque rating of the gearbox or motor driving the crank. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Number of slots
- What it is
- The number of radial slots in the Geneva wheel, which is how many indexes the wheel makes per revolution. It sets the crank radius, the index angle and the motion.
- Units and format
- Enter a plain number with no unit. The form accepts 3 to 24. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More slots give a smaller crank radius and a shorter share of each turn spent indexing.
- Get it right
- Count the slots on the wheel, not the driver pins; this tool assumes one roller on the driver.
What this means: Centre distance
- What it is
- The distance between the axis of the driving crank and the axis of the Geneva wheel.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger centre distance lowers the roller force for the same wheel torque.
- Get it right
- Measure axis to axis; the crank radius is worked out from it and the slot count.
What this means: Driver speed
- What it is
- The rotational speed of the driving crank. Each crank revolution makes one index of the wheel followed by a dwell.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 2000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Angular acceleration rises with the square of speed, so faster drives load the roller and driver much harder.
- Get it right
- This is the crank speed, not the wheel speed or the motor speed before a gearbox.
What this means: Roller diameter
- What it is
- The diameter of the roller on the driving crank that enters the wheel slots. It sets the slot width the wheel needs.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The current calculation does not use this value; size the roller and its pin against the roller force result.
What this means: Wheel and load inertia
- What it is
- The mass moment of inertia about the wheel axis of everything the wheel turns: the wheel itself, the index table and the load on it.
- Units and format
- Enter a number in kg·m²: kilogram square metres (mass moment of inertia). The form accepts 0 kg·m² to 100000 kg·m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.05 kg·m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The inertia torque on the wheel rises in direct proportion to it.
- Get it right
- Include the table and fixtures, which usually dominate; take values from CAD or calculate them, and refer any geared load to the wheel axis.
What this means: Friction torque on the wheel
- What it is
- The constant friction torque resisting the wheel as it indexes, from bearings, seals and any sliding load, measured at the wheel axis.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0 N·m to 1000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- It adds directly to the wheel torque, roller force and driver torque.
- Get it right
- Measure it with a torque wrench on the wheel shaft if you can; it is added to the inertia torque throughout the index.
What this means: Allowable roller force
- What it is
- The largest force the roller, its bearing and its pin can carry, compared with the peak force between roller and slot during indexing.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N to 10000000 N. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Take it from the roller or cam follower catalogue rating and the pin’s own strength, using the lower.
What this means: Driver torque rating
- What it is
- The torque the gearbox or motor driving the crank can supply at the crank shaft, compared with the peak driver torque.
- Units and format
- Enter a number in N·m: newton-metres. The form accepts 0.000001 N·m to 10000000 N·m. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 N·m as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the rating at the crank shaft, after any gearbox, and allow for its service factor.
Method and formulas
- λ = sin(π ÷ n); crank radius a = λC; index angle of the driver 180° − 360° ÷ n (as the Geneva mechanism tool).
- With crank angle θ from the line of centres: ω_w ÷ ω = λ(cos θ − λ) ÷ (1 − 2λ cos θ + λ²); α_w ÷ ω² = λ(λ² − 1) sin θ ÷ (1 − 2λ cos θ + λ²)².
- Wheel torque = J |α_w| + T_f; roller force = wheel torque ÷ (C √(1 − 2λ cos θ + λ²)); driver torque = wheel torque × ω_w ÷ ω, each taken at its peak through the stroke.
- Example: a 4-slot wheel at 60 rpm peaks at 213.46 rad/s²; the roller sees 352.16 N and the driver needs 21.746 N·m.
Limitations
- Rigid parts and no clearance; impact at roller entry is not included.
- Friction treated as constant.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size the drive for a Geneva index table
- Check the roller and slot loads
- Compare slot numbers for smoother indexing
Who it is for
- Machine designers
- Automation engineers
- Design engineers
What you get
- Geometry, timing and peak wheel speed
- Peak angular acceleration and wheel torque
- Roller force and driver torque
Interpreting the result
- More slots lower the acceleration for the same index time but leave a shorter dwell.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 171. Topic reference; no source tables or recommended settings are reproduced.
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Open the Geneva Drive Design (Acceleration, Pin Force and Drive Torque) calculator