A spherical Geneva drive converts continuous rotation into intermittent rotation on an intersecting shaft. Its pin enters a slot in a cup-shaped wheel, moves the wheel through one station, then leaves while a locking surface holds the wheel. This animation shows the right-angle form, with equal half-turn periods for indexing and dwell.
Spherical Geneva Drive Interactive Calculator
Choose slot count, spherical radius and input speed. The pin follows the curved slot during each index; a semicircular driver surface fits a recess during dwell. The shaft angle stays at 90 degrees in this model.
Equation Used
These relations describe the illustrated intersecting-axis geometry. R is the radius from the common shaft intersection to the pin centre. Cone angle is measured from the input-shaft axis. A single pin produces one step per input turn. Each index and dwell occupies half a turn, independently of slot count. The display runs at one tenth of the entered speed. At zero speed the mechanism stops and the two time results are undefined. Contact surfaces are idealized; thickness, clearances, bearing loads and wear are not calculated.
A pin indexes the cup, then a surface holds it
The input and output axes meet at the centre of the spherical geometry. The input driver carries a pin around a circle. During one half-turn, the pin travels along a slot on the output cup and turns it through one station. It exits at the rim with zero output angular velocity.
The blue semicircular locking surface turns with the input. During dwell, its curved edge fits the corresponding recess between the cup slots. During indexing, the relieved portion gives the cup room to move. This is a surface-contact illustration, not a specified pin fit or manufactured wall section.
The cup and its output shaft move together. The input shaft continues rotating throughout the dwell. The changing slot positions make the difference between continuous input and intermittent output visible.
The illustrated spherical construction
Take the output axis as x and input axis as z, with their intersection at the origin. Let α=π/n radians, r=R sin α and a=R cos α. The pin position is P=(r cos θ, r sin θ, a), so its distance from the origin is always R.
A slot follows a meridian of that sphere about the output axis. While the pin is on the cup side, −π/2≤θ≤π/2, its meridian angle is ψ=atan2(a,r sin θ). This changes from π/2+α to π/2−α: a total step of 2α=2π/n. The sign depends on the viewing direction.
The derivative dψ/dθ=−ar cos θ/(a²+r² sin²θ) is zero at both ends of engagement. The wheel then dwells for the remaining π radians of input motion. At constant input speed N rpm, indexing and dwell each last 30/N seconds. Slot count changes the step and motion curve, but not the half-cycle dwell fraction.
Four slots at 30 rpm
With four slots, the wheel steps 90 degrees per input turn and the pin-cone half-angle is 45 degrees. For R=70 mm, the pin-circle radius and axial offset are both approximately 49.5 mm.
At 30 rpm, a complete input turn takes 2 seconds. Indexing takes 1 second and dwell takes 1 second. The slowed animation shows that complete turn over 20 seconds. Six slots change the step to 60 degrees and the cone half-angle to 30 degrees; at the same input speed, the two time intervals remain 1 second each.
Indexing between intersecting shafts
The spherical arrangement is useful to study when an intermittent output is required on an axis that intersects the input axis. John H. Bickford illustrates a four-slot spherical Geneva in Mechanisms for Intermittent Motion, figure 9-3, and distinguishes its half-turn dwell from external and internal planar Genevas.
Station count, shaft arrangement, permitted motion, load and required dwell determine whether a particular indexing mechanism is suitable.
Geometry does not set a universal operating rating
More slots reduce the angle of each index. The input still spends half its turn moving the output and half its turn in dwell. A higher input speed shortens both intervals and changes acceleration, but there is no universal speed limit or service life in these geometric equations.
Real mechanisms need sufficient slot clearance, appropriate locking surfaces, aligned bearings and suitable materials. Those details depend on scale, load, lubrication and manufacturing method. The model uses ideal spherical surfaces and a small visible slot opening to explain engagement; it does not calculate contact stress, backlash or thermal expansion.
Frequently asked questions
What fraction of each turn is dwell?
In this right-angle spherical construction, index and dwell each occupy half an input revolution. Slot count sets the output step but does not change that fraction.
Is the pin-cone angle always 45 degrees?
No. In the illustrated construction it is 180 degrees divided by slot count. It is 45 degrees for four slots and 30 degrees for six.
Can I change the shaft angle?
This model uses intersecting axes at 90 degrees. Other axis arrangements require their own geometry; they are not obtained by simply changing this model’s shaft angle.
What prevents output movement during dwell?
The driver’s semicircular locking surface fits a recess in the cup. The real fit and load capacity require a detailed contact design.
Does doubling input speed change the index step?
No. It halves the indexing and dwell times while the step remains 360 degrees divided by slot count.
What does zero input speed show?
The mechanism stays still. Index and dwell times are undefined because the input does not complete either interval.
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