Haven’s planetary crank gear uses an orbiting external gear held by a sliding block in a rocking cross. The orbiting gear meshes with the gear on the sprocket shaft. Hiscox describes this as a bicycle mechanism for varying the motion through a crank revolution: with equal gears, the sprocket shaft makes two turns for each crank turn.
Haven’s Planetary Crank Gear Interactive Calculator
Change crank radius, the distance to the cross pivot, crank angle and input speed. Gear C stays aligned with the sliding block and cross; gear B turns on the central output shaft. The tiles describe the selected crank angle, while the animation continues from that position.
Equation Used
a is the crank radius and gear-centre distance. e is the distance from output shaft O to fixed cross pivot E above it. Both gears have the same pitch radius a/2 and 30 teeth in the drawing. θ is the crank angle measured clockwise from the right in this view. φ is the cross angle; the displayed rocker angle is φ−90°. The block slides at distance d from E. Dimensions are illustrative. The display runs at one fifth of input speed and fits the drawing to the available space; changing a changes physical dimensions without changing the proportions. Ideal rigid gears are assumed; loads, backlash and efficiency are not calculated.
A sliding block controls the planet’s orientation
The input crank A turns around the sprocket shaft O and carries the centre of gear C. Gear C is fastened to a block that slides along the straight slot in cross D. The cross pivots about fixed point E, so it rocks as the crank carries the block around O.
The curved arms of the cross have a slot centred on E. The output shaft passes through that curved slot, allowing the cross to swing past it. Gear B is fixed to the sprocket shaft and meshes externally with gear C. C therefore both orbits and changes its angle as the cross rocks.
The animation keeps the crank, sliding block, straight slot and curved clearance slot connected. Gears, cross and crank are shown in separate axial layers; an overlap in the front view does not join those parts. The outer circle gives a visual reference for the sprocket shaft and is not an internal gear.
Why equal gears give two turns per crank revolution
Let θ be the angle of the crank OC, and φ the angle of the cross EC. Because gear C is fixed to its block, its absolute angular motion follows φ. For equal external gears, the rolling relation is β=2θ−φ+constant, where β is the output angle of B.
The cross rocks back and forth and returns to its starting orientation after one complete crank revolution. Its net angular change is zero, so B advances through two complete turns. Its instantaneous speed still varies: dβ/dθ=2−dφ/dθ.
With O=(0,0), E=(0,−e) and C=(a cos θ,a sin θ), the block distance is d=√(a²+e²+2ae sin θ), and dφ/dθ=(a²+ae sin θ)/d². These equations use downward-positive drawing coordinates. The pivot remains outside the crank circle, e>a, over the whole input range.
An illustrative 60 mm crank
At a=60 mm and e/a=1.8, pivot spacing is 108 mm. At the selected angle θ=210°, the block is approximately 93.7 mm from E and the cross is about 33.7 degrees from the downward vertical. The instantaneous output/input speed ratio is about 1.959.
At 30 input rpm, the mean output speed is 60 rpm. It is not a constant 60 rpm throughout the turn: the cross motion makes the output accelerate and decelerate. Closer spacing between E and the crank circle gives a larger speed variation.
Haven’s bicycle-crank arrangement
Hiscox’s figure 870 identifies the mechanism as A. F. Haven’s planetary crank gear, adapted for bicycles to vary the proportion of motion. The crank and sprocket shaft are its rotating input and output.
The model is useful for examining the difference between average transmission ratio and angle-dependent speed. It does not establish a particular rider-power benefit, efficiency or historical production volume. Those questions require information about a complete bicycle drive and its load.
Moving gears and sliding guidance
The arrangement combines circular gears with a rocking and sliding constraint. It obtains a variable speed profile while retaining the equal-gear average ratio of two to one.
The sliding block, cross slots, shafts and gear teeth all need suitable support and clearance. The drawing separates their axial layers to show the relationships. Tooth proportions, bearing fits, loads, lubrication and slot contact stresses need their own design work; they cannot be obtained from the speed ratio alone.
Frequently asked questions
Is there a fixed internal ring gear?
No. The illustrated Haven mechanism uses two externally meshing gears, a crank and a rocking slotted cross. The circle around them is a visual shaft reference.
Why does the output make two turns?
The equal external gears give output angle 2θ−φ plus a constant. The cross returns to its starting angle each crank turn, leaving two output turns.
Is output speed constant?
No. Its instantaneous ratio is 2 minus the cross’s angular-speed ratio. The average remains two to one.
What does the curved slot do?
It lets the cross pass around the output shaft while rocking about pivot E. Its centre is E, not the output shaft.
Why must the cross pivot be outside the crank circle?
The illustrated rocking-cross motion requires e greater than a. If the pivot lies on or inside the crank orbit, the motion and its average gearing relation change.
What happens at zero input speed?
The animation stops and mean output rpm is zero. The selected-angle geometry and speed ratio remain available for inspection.
Mechanism references
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