Hiscox 1169 describes a double tri-toothed pendulum escapement with a fly. The long teeth lock alternately on opposite sides of the pallet frame, while a small triangular arbor acts on the curved pallets. The illustration distinguishes that central triangular part from the long locking teeth.
Double Tri-Toothed Escapement · Step Motion and Timing
Three teeth per set, two locking planes and a triangular centre. Compare pendulum period, tip radius and selected transfer duration.
Equation Used
- Both locking sets share one arbor.
- Each set has three teeth at 120° intervals.
- Alternate locking positions are 60° apart in this reconstruction.
- Full pendulum period contains two beats.
- Selected transfer follows 3u²−2u³.
- Contact profiles and clearances are illustrative.
No invented pallet-angle tolerances or clock accuracy claims. Tip speed is geometric motion at the entered radius, not an impact prediction.
Long locking teeth and a small triangular centre
Two three-tooth sets occupy separate axial planes on a common arbor. Their alternate teeth meet the stops on opposite sides of the pallet frame. The two sets turn together; one set cannot remain stationary while the other turns.
The source identifies the small triangular arbor as the part acting against the curved pallets. The reconstruction shows this centre in gold and the two locking planes in blue and red. The fly is shown separately so that it does not obscure the pallet contacts.
The selected timing places the two locking sets 60° apart and advances one 60° step per pendulum swing. Arm travel, triangular contact profiles and clearances are explanatory. The illustration is not a dimensioned construction drawing or a force analysis.
Compare release timing and tip motion
The calculator uses full pendulum period, locking-tip radius and a chosen transfer duration. It retains three teeth per set because that is the mechanism being shown. There are 120° between successive teeth of one set and 60° between the alternate locking positions.
The radius sets the physical arc distance travelled by a long-arm tip in each release. The diagram fits the available screen space automatically, so it displays the entered dimension without resizing the whole mechanism.
The transfer-time control describes how much of a beat the arbor spends moving. Its speed outputs are consequences of the chosen timing, not a prediction of what a particular fly or drive torque will produce.
One 60° step per swing
For full pendulum period T, the beat interval is B=T/2. A 60° step on each beat gives mean common-arbor speed n=20/T rpm. For selected transfer share q percent, the step time is tₛ=Bq/100.
At locking-tip radius R, arc distance per release is s=Rπ/3. Mean tip speed during the transfer is s/tₛ, and mean angular speed during the transfer is 60/tₛ degrees/s. These differ from averages over the full beat, which includes the stopped interval.
The animation selects a smooth step ψ=60°(3u²−2u³), where u runs from 0 to 1 during the transfer. Its peak angular speed is 90/tₛ degrees/s, reached at u=0.5. This is a chosen motion profile, not a solved fly-braking law.
No locking-face, drop-angle or impulse-face tolerance is inferred from these timing relations.
A 2 s pendulum period and 80 mm tip radius
The beat interval is 1 s and mean arbor speed 10 rpm. At a 10% transfer share, each 60° movement takes 0.1 s.
The tip moves 80π/3≈83.776 mm along its circular arc. During the movement its mean speed is about 837.758 mm/s. Mean angular speed is 600°/s; the selected smooth-step peak is 900°/s.
Doubling radius doubles tip distance and linear speed without changing angular speed. Doubling period halves mean arbor speed and the transfer speeds when the selected share remains fixed.
What the engraving does not specify
The source identifies the locking teeth, curved pallets, triangular centre and fly. It does not give universal pallet angles, manufacturing tolerances, clock accuracy or contact loads.
The timing model does not calculate pendulum energy, drive torque, tooth impact or wear. A fly may moderate the rapid transfer, but its actual motion depends on geometry, air resistance and inertia that are not specified here.
Tri-toothed escapement questions
Can one of the two sets stay still while the other moves?
No. Both are carried by the same arbor.
Why is tooth count fixed?
The page depicts two three-tooth sets. Changing that number would describe a different arrangement.
What makes the small centre different from the long teeth?
The long teeth provide alternating locking, while the source describes the triangular centre acting on the curved pallets.
Are the peak speeds measured clock performance?
No. They are calculated from the selected smooth-step timing.
Primary mechanism reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, device 1169, printed page 288: double tri-tooth pendulum escapement, alternating long-tooth locks, curved pallets, small triangular arbor and fly. The timing and dimensional example are explanatory selections.
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