A partial bevel gear can engage two opposed gears in turn. When the side gears are connected to the same shaft, contact on opposite sides drives that shaft in opposite directions. One input revolution gives an outward stroke, a tooth-free interval, a return stroke and another interval.
Continuous to Alternating Crank Gear Interactive Calculator
Explore a partial bevel driver that reaches two opposed output gears half a turn apart. Adjust the toothed arc, pitch-diameter ratio and input speed to compare angular stroke and the tooth-free intervals.
Equation Used
- One toothed driver arc, no larger than 180°, passes two opposed bevel mesh locations.
- Two equal side gears are fixed to one output shaft, with their tooth phasing set for alternating engagement.
- Pitch geometry gives constant signed speed while engaged. Tooth profiles and engagement edges are schematic.
- The output is assumed stationary in tooth-free intervals without an external driving torque; these intervals are not inherently locked.
- Instantaneous changes of ideal velocity are not dynamically realizable under finite inertia; contact impacts and acceleration are not calculated.
One toothed arc engages at two opposed contact locations. The two side gears are connected to a common output shaft in this model. During tooth-free intervals the unloaded output is assumed stationary; no locking surface is synthesized.
One partial driver and two opposed contacts
The illustrated arrangement follows the bevel-sector principle in Brown’s movement 74. A toothed arc on the vertical driver passes output gear A and then gear B, half a turn later. The side gears share a horizontal output shaft in this model. Their common-axis connection makes both engagement locations drive the same output shaft.
The driver has one toothed arc, not two identical opposed arcs. The two working intervals come from that arc reaching two different mesh positions. An axial view highlights when each contact is covered by the teeth.
Between contacts there is no positive drive. The animation assumes the unloaded output remains stationary. No locking arc is drawn or calculated, and the blank portion of the gear does not establish a holding capability.
A model of reversing motion
This arrangement illustrates how continuous rotation can produce alternating shaft motion without reversing the input. It is useful for comparing ideal angular stroke and timing.
The calculator does not identify the internal drive of any specific mixer, textile machine or animatronic system. Applying the principle to a loaded machine requires tooth-entry design, shaft support and a method of controlling the output during disengagement.
Stroke and timing
Let α be the driver’s toothed arc in degrees and G=N_driver/N_output the pitch-diameter ratio. While engaged, output angular speed has magnitude G times input speed. Each stroke therefore spans αG degrees.
The contact positions are 180° apart, so each tooth-free gap is 180°−α. One input turn contains both strokes, giving one cycle per revolution and two direction changes per cycle. At n rpm, a gap lasts (180−α)/(6n) seconds.
The count entered for the driver is the number of teeth on an equivalent full circumference. Arbitrary arc settings do not constitute a manufactured tooth-sector design: entry and exit teeth, assembly phase, clearances and contact ratio must be resolved separately.
Compare the default setting
At 30 rpm, a 150° toothed arc and 24:48 tooth-count ratio give 75° output travel in each direction. Each tooth-free gap is 30° of input rotation, lasting about 0.167 s. A complete out-and-back cycle takes 2 s.
Increasing the arc to 180° gives 90° travel per direction and eliminates both gaps. This creates an abrupt ideal reversal; the animation does not predict the impact forces of a real loaded mechanism.
Timing is not a load rating
In the ideal graph, output velocity jumps when a sector enters or leaves mesh. Real inertia requires finite acceleration and creates contact loads. The model does not calculate tooth stress, fatigue life, noise or an allowable operating speed.
A disengaged shaft can be moved by its load. A suitable holding device or separately designed locking surfaces may be necessary. The displayed dwell duration is a timing interval, not proof that the output will hold position under torque.
Questions about alternating engagement
Why is there only one toothed arc?
It reaches two opposed contacts half a driver turn apart. Those contacts drive the common output shaft in opposite directions.
Do the two output gears turn independently?
No. They are fixed to one shaft in this illustrated reversing arrangement.
Does the blank arc lock the shaft?
No. The model assumes an unloaded output remains still during disengagement. It does not design a lock.
Are the displayed teeth ready to manufacture?
No. Pitch radii follow the entered ratio, but tooth shape, entry clearance and assembly phase require detailed design.
Can output travel exceed 360°?
Yes. A sufficiently large ratio can produce several turns before reversal. The graph tracks the full angular stroke even though a pointer repeats its visible orientation.
References
Henry T. Brown, Five Hundred and Seven Mechanical Movements, movement 74, shows the partial bevel driver and opposed gears. The model connects the two side gears to a common output shaft to produce reversing motion.
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