The Allen valve toe is a rocking cam beneath a guided valve lifter. As the toe rocks, its contact with the lifter raises and lowers the valve rod. The drawing below follows this toe-and-lifter arrangement rather than Allan straight-link reversing gear.
Allen Valve Lift or Toe Interactive Calculator
Explore the rocking toe and guided lifter. The calculator separately compares projected eccentric and lift components.
Equation Used
The calculator adds two entered displacement projections: Te cos(theta_r) and Lt sin(theta_r). This is a separate comparison, not the contact-geometry solution for the illustrated toe. The angle is a projection angle, not a calibrated reverser or cutoff setting.
- The two entered displacement magnitudes are treated as orthogonal components for projection.
- theta_r is entered in degrees and converted to radians.
- Toe profile, lap, lead, port opening, contact force and steam dynamics are not calculated.
The Allen toe is a rocking valve lifter. It is distinct from Allan straight-link reversing gear. The projection calculator compares entered components; it does not solve a toe profile or steam timing.
A rocking toe beneath a guided lifter
The toe is a cam-shaped member carried by a rock shaft. As the shaft turns back and forth, the toe bears against a lifter attached to the valve rod. Guides constrain the rod’s motion while the toe changes the height of its supporting contact.
Hiscox describes the rock shaft as operated from a cam on the engine shaft. This toe-and-lifter arrangement is distinct from Allan straight-link reversing gear.
The illustration shows closed contact in a gravity-return arrangement. The lifter rises as the toe rocks beneath it and returns as the supporting surface lowers. The proportions are illustrative; the drawing does not specify a manufacturable cam profile.
Parts to follow
- Rock shaft: carries the rocking input.
- Toe: provides the changing contact surface.
- Lifter and valve rod: receive the rising and falling motion.
- Guides: constrain the rod’s direction of travel.
Studying valve-lifting motion
A toe mechanism illustrates how rocking motion can raise a guided follower. The shape of the toe, its axis location and the follower geometry determine the actual displacement and contact conditions.
For an engine, the driving cam and its phase must also be considered with the valve and ports. This page does not set locomotive cutoff, compare engine economy or prescribe overhaul dimensions. It separates the visible lifting principle from those engine-specific questions.
Adding projected components
The calculator uses Tv = Te cos θ + Lt sin θ. Te and Lt are entered displacement magnitudes; θ is the projection angle. Both lengths must use the same unit. The two terms and their sum are displayed separately.
The lift-share output is the second projected term divided by the total, expressed as a percentage. At θ = 0°, the second term is zero and the total equals Te.
This projection expression does not derive valve travel from a toe surface. It supplies no relationship between angle and steam cutoff, and it does not calculate port opening, dwell, lead, pressure or contact loading.
Worked projection example
Choose Te = 115 mm, Lt = 18 mm and θ = 30°. These are illustrative component inputs, not settings for a particular locomotive or valve mechanism.
- First projected component = 115 cos 30° = 99.593 mm.
- Second projected component = 18 sin 30° = 9.000 mm.
- Total = 99.593 + 9.000 = 108.593 mm.
- Second-component share = 9 / 108.593 × 100 = 8.29%.
At 0° with the same magnitudes, the total is 115 mm and the second-component share is zero. A change in these results describes the chosen projections; it does not establish a valve-event change.
Toe motion and complete valve gear
The illustrated toe and guided lifter form a contact mechanism. Complete reversing valve gear performs a broader task: coordinating valve motion with the engine cycle and its selected operating direction. Similar names do not make their geometry interchangeable.
Use the toe animation to follow contact and follower motion. Use the component calculator to examine a projection sum. A full valve-design analysis additionally needs the actual cam or linkage geometry, phase, ports, clearances and operating loads.
Valve-toe questions
Is this Allan straight-link valve gear?
No. The illustrated Allen toe is a rocking contact member beneath a guided valve lifter. A straight-link reversing mechanism has a different arrangement and purpose.
What keeps the illustrated lifter in contact?
The illustration uses a gravity-return arrangement with closed contact. It does not evaluate the forces or speed at which a real follower could lose contact.
Does the projection angle specify cutoff?
No. It is the angle used to resolve two entered displacement components. No mapping from this angle to a steam cutoff percentage is calculated.
Does the calculator generate a toe profile?
No. The projection sum does not solve cam contact geometry or synthesize a manufacturable toe. The displayed toe dimensions are illustrative.
Can these values be used to set a working engine?
No. Valve setting requires the drawings and event requirements of that engine. Port geometry, cam phase, lap, lead and operating conditions are outside this comparison.
What happens at zero projection angle?
The cosine term equals Te and the sine term is zero. The total is Te, with zero contribution from the second term.
Mechanism reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, entry “Allen Valve Lift or Toe,” describes the lifter and valve rod, and the toe on a cam-driven rock shaft.
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