The historical dog-power machine illustrated by Hiscox uses a circular track wheel inclined about 20°. Its underside bears on a friction pulley, which drives a shaft, flywheel and crank for a churn. The animal walks on the upper tread while the wheel turns beneath it. This is a treadwheel construction, distinct from an endless-belt treadmill.
Dog-power Machine Interactive Calculator
Inspect the historical inclined circular treadwheel and friction drive. Explore a stated steady-motion power estimate, no-slip speed ratio and output torque.
Equation Used
- Steady mean body position at the uphill-tangent side of the wheel.
- Outer contact radius equals 1.25 times walking radius.
- Rigid wheel and friction pulley, with no slip.
- Illustrative gait and slider-crank proportions; animation slowed fourfold.
Walking tangent aligned with the uphill direction. Ideal no-slip contact. Efficiency is an entered assumption or measurement, not inferred.
From inclined treadwheel to churn
The wooden annular tread rotates about an inclined central spindle. The walking position is at the side of the wheel where its local tangent runs uphill. A small pulley bears against the underside near the outer edge. With no slip, the contacting surfaces have equal tangential speeds, so the smaller pulley and its shaft turn faster than the track wheel.
The illustration includes the central support, inclined wheel, animal silhouette, underside friction pulley, output shaft, flywheel and a crank-driven churn dasher. The dog remains near its walking position while the tread passes underneath. Leg motion is illustrative, not a biomechanical model.
The source establishes the wheel, friction drive, flywheel and churn arrangement but gives no dimensions. The animation therefore uses an explicit reconstruction: the outer friction-contact radius is 1.25 times the entered walking radius. The crank and connecting rod form a vertical slider-crank; that detail explains the reciprocating output rather than claiming undocumented historical dimensions.
Explore the power and speed relationships
Enter mass, wheel inclination, walking speed, walking radius, pulley radius and a measured or assumed drive efficiency. The outputs compare tangential weight component, estimated mechanical power, treadwheel speed, output-shaft speed and output torque.
These are idealized mechanical relationships, not an assessment of an animal’s endurance or a recommended working regimen. The calculator does not predict butter-making time, animal comfort, traction, permissible harness loads or a machine’s safe capacity.
Power, radius ratio and shaft torque
At the illustrated side position, the walking tangent is aligned with the steepest direction of the inclined plane. The tangential component of weight is F=m g sin θ. For a stationary mean body position and steady walking at tread speed v, the simplified available mechanical power is P=F v η. Efficiency η is entered as a percentage and converted to a fraction.
This is not free energy from gravity: the animal supplies metabolic work while remaining at approximately constant average height. The force model omits gait dynamics and any tangential force supplied by restraints. A different walking position around the wheel requires its own force projection.
With walking radius r, wheel angular speed is ω=v/r. The friction contact is at R=1.25 r, so the no-slip pulley angular speed is Ω=ω R/ρ. Rotational speed in rpm is 60 times angular speed divided by 2π. Output torque is T=P/Ω. Millimeter radii are converted to meters where required.
The underside pulley is placed one pulley radius along the wheel’s downward normal, which makes its rim tangent to the tread underside. Pulley rotation is synchronized with the outer tread speed. The churn crank has a fixed illustrative throw of r/6 and connecting-rod length 2r/3; its stroke is r/3. These proportions do not affect the reported power estimate.
Example with a 600 mm walking radius
For 18 kg, a 20° inclination, walking speed 0.60 m/s and 70% assumed drive efficiency, the tangential component is about 60.39 N and the output power about 25.37 W.
A 600 mm walking radius gives 9.55 rpm at the treadwheel. The outer contact radius is 750 mm. With a 75 mm pulley, the speed ratio is 10:1, giving about 95.49 rpm and 2.54 N·m at the output shaft. Reducing the pulley radius raises shaft speed and lowers shaft torque while preserving the stated output power.
What the model leaves out
The wheel and pulley are rigid and roll without slip. Bearing and transmission losses enter only through the specified efficiency; the model does not derive that efficiency from materials or lubrication. Contact pressure, wheel inertia, flywheel smoothing, starting torque and fluctuating churn loads are not solved.
The animation runs at one-quarter of the calculated speed so the contact and crank can be followed. Geometry follows the entered inclination and radius ratio, while the animal, stand and barrel are explanatory outlines. The old unverified animal-performance limits, historical price tables and churning-time estimates have been removed.
Dog-power machine questions
Why does this machine have a circular wheel?
Hiscox figure 1535 explicitly identifies an inclined track wheel resting on a friction pulley. Endless-belt animal treadmills are a different construction.
Does mass alone power the machine indefinitely?
No. The animal does work walking against the moving tread. Its average height can remain steady while energy passes through the wheel to the load.
Why is shaft speed higher than wheel speed?
The outer wheel contact radius is larger than the friction-pulley radius. Equal surface speeds require the smaller pulley to turn faster.
Why can changing wheel radius leave shaft speed unchanged?
The model fixes the outer-to-walking radius ratio at 1.25. At a fixed walking speed, a larger wheel rotates more slowly, but its larger contact radius offsets that reduction at the pulley.
Can the outputs be used to specify animal workloads?
No. They describe the stated mechanical model only, not an animal’s sustainable output or suitable use.
Historical construction reference
Gardner D. Hiscox, Mechanical Movements, Powers and Devices, printed page 372, figure 1535, identifies the inclined track wheel, underside friction pulley, shaft, flywheel and churn crank. The animation follows that arrangement with explicitly stated illustrative dimensions.
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