This page now limits the calculation to exact declared handle torque and ideal pinion-to-sector pitch-circle identities. The connected press view does not turn sector torque into ram force or tonnage because the complete rod geometry, force direction, losses and structure are not specified.
Ideal Sector-and-Pinion Transmission Explorer
Enter declared handle force and length, pinion and sector pitch radii, and pinion rotation. The connected view preserves tangent pitch circles and an exact constant-length rod while reporting only ideal gear torque and angle.
Equation Used
- Handle force is declared and perpendicular to the declared handle length.
- Pinion and sector radii are declared pitch radii.
- The external mesh is ideal, rigid and lossless with equal pitch-line displacement and equal/opposite tangential tooth force.
- The animation preserves pitch-circle tangency and exact angular ratio; its crank pin and connecting rod are illustrative fixed display geometry.
- The constant-length rod drives a vertical guide for connected context only; its force transmission is not solved.
- Tooth form and count, contact ratio, backlash, friction, bearings, shafts, sector support, crank radius and rod angle in physical units, ram load, tooling, workpiece, stiffness, buckling, strength, fatigue, rated capacity, guards, controls and safe operation are excluded.
Removes unsupported ram force, tonnage and fixed efficiency from an underspecified downstream linkage while retaining exact declared handle and ideal gear-pair identities.
A handle turns a pinion that rotates a toothed sector
At the ideal external gear mesh, pinion and sector pitch circles have equal and opposite tangential displacement. The sector can carry a crank pin and connecting rod to a guided ram, but that downstream geometry must be specified before ram force can be solved.
The animation keeps the pitch circles tangent, enforces the exact angular ratio and preserves one illustrative connecting-rod length.
Use this page to audit the ideal gear stage
The worksheet checks handle torque, ideal tangential tooth force, ideal sector torque and opposite sector rotation from declared pitch radii.
It cannot determine ram force, press tonnage, capacity, tooling load, strength or safe operation.
Stop the force ledger at the documented gear mesh
The negative sign indicates opposite rotation for an external mesh. Values shown use magnitudes except the directional animation.
A transparent ideal gear example
For F=500 N perpendicular to L=600 mm, handle torque is 300.0 N·m. With r_p=50 mm, ideal tangential tooth force is 6000.0 N. An R_s=800 mm sector therefore has 4800.0 N·m ideal torque, and 60 degrees pinion rotation gives 3.75 degrees opposite sector rotation.
No ram force or tonnage follows without the full downstream mechanism and losses.
Sector torque is not press tonnage
Real ram force varies with crank-pin radius, connecting-rod angle, ram position and load, plus gear and bearing friction, tooth contact, shaft and frame deflection, backlash, inertia and workpiece response. Strength and safety require complete machine-specific checks.
The former fixed efficiency, arbitrary rod-radius division, 5–50 ton claims, universal advantage, named deployments, maintenance rules and operating advice are removed because they were not supported for one documented press.
Sector-and-pinion ledger questions
Why is ram force not shown?
Sector torque alone is insufficient; the downstream crank and rod geometry, force direction and losses are required.
Does ideal sector torque include efficiency?
No.
Why does the sector rotate the opposite way?
External gear pitch circles roll with opposite angular directions.
Can this size a press?
No.
Toothed-sector press references
- MIT 2.14, Two-Port Elements: ideal gear pitch-line speed, tooth force and torque identities.
- UC San Diego MAE 3, Gear Ratios: pitch-radius angular and torque ratios.
- DE 10034182 A1: toothed segment driven by a pinion in a press.
- JP 2004-337897 A: hand-lever and pinion press drive context.
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