Geneva drive – indexing kinematics

How to use the Geneva drive calculator

Enter the number of slots in the wheel, the number of pins on the crank and either the centre distance C or the crank radius a. Add the roller diameter and the crank speed, or switch Speed from to a step time, a dwell time or steps per minute and the crank speed follows. Move the crank angle slider, or press Play motion, to see the wheel, the roller and the locking disc at any point of the cycle. The orange result shows the peak wheel acceleration with the step and dwell times; the charts below give wheel angle, speed, acceleration and jerk over one crank revolution.

Geneva drive calculator drawing of a six-slot Geneva wheel with the roller in a slot and the locking disc on the crank, drawn to scale — Roller in the slot at θ = −40°: the wheel accelerates, the locking disc has released it.

Geneva mechanism design: what the calculator gives

An external Geneva mechanism turns a crank at constant speed into intermittent rotation of the wheel. The geometry follows from the slot count: crank radius a = C·sin(180°/z), the roller enters the slot at R = C·cos(180°/z) and the crank turns 180° − 360°/z per step. The calculator returns the wheel step, the crank index angle, step and dwell time, steps per minute, the pin travel in the slot, slot width and depth, the wheel diameter and the proportions of the locking arc and locking disc. Checks warn when the pins do not fit, the web between slot ends is too thin, the locking disc has no room or no dwell is left.

Geneva wheel held by the convex locking disc of the crank during the dwell period, roller outside the slot — Dwell: the locking disc bears on the concave arc and holds the wheel.

Geneva drive kinematics

Wheel angle, angular velocity and angular acceleration come from the closed-form relations for radial slots with tangential roller entry. Peak wheel speed is ω1·λ/(1 − λ) at mid-step, λ = sin(180°/z). The acceleration does not start at zero: at roller entry and exit it jumps to tan(180°/z)·ω1², the soft impact that limits the speed of every Geneva indexing drive. The jerk chart shows how fast the acceleration changes inside the step.

Result panel with peak wheel acceleration next to charts of Geneva wheel angle, angular velocity, angular acceleration and jerk over one crank revolution — Wheel speed, angle, acceleration and jerk over one crank revolution.

Method and limits

Rigid parts, a constant crank speed, a roller on a rolling bearing in a slot 0.1 mm wider than the roller, with the roller centre on the slot axis. Validated against a worked example and an own CAD reference wheel. Torques, roller force, contact pressure and the effect of slot clearance are not included in the free version. A Pro version with the dynamics of the step, wheel inertia from its outline and slot clearance impacts is in preparation.