For a selected radial seating load R acting along the bisector of an ideal symmetric V-groove with included angle α, each flank normal is N = R/[2 sin(α/2)]. With selected friction coefficient μ, the ideal combined limiting friction is 2μN = μR/sin(α/2).
Ideal Symmetric V-Groove Wedge Model
Resolve a selected radial seating load into ideal symmetric V-groove flank normals and limiting friction.
Equation Used
- The groove is symmetric with straight flanks.
- The selected radial load acts along the groove bisector.
- Friction coefficient is constant and represents limiting static contact.
- Positive entered clearance means flank seating is assumed; deformation, wear, wrap and dynamics are excluded.
Clearance is an assumption flag, not a geometry check derived from rope and groove dimensions.
Ideal symmetric wedge cross-section
A circular rope cross-section is shown tangent to both straight groove flanks. The selected radial seating load is resolved into equal flank-normal forces by symmetry.
Positive entered bottom clearance is treated only as an assumption that flank seating exists. The calculator does not derive clearance from rope diameter, groove-root geometry, deformation or wear.
What the calculator determines
Select groove angle, friction coefficient, radial seating load and an assumed bottom-gap input. The calculator reports wedge factor, effective friction coefficient, ideal combined limiting friction and normal force per flank.
It does not determine tight- and slack-side rope tensions, wrap-angle capacity, torque, power, speed, centrifugal load, creep, slip, heat, wear, service life or a safe working rating.
Bounded static wedge identities
For positive assumed clearance, M = 1/sin(α/2), Nflank = R/[2 sin(α/2)], μeff = μM and Ffriction = μR/sin(α/2). If the entered clearance is zero, this model disables wedge amplification: M = 1, Nflank = R/2 and F = μR.
R is a selected radial resultant into the groove, not longitudinal rope tension. Applying the wedge coefficient to a drive requires a separate wrap-contact and tension model.
Selected-input example
At a 40° included angle, μ = 0.30, selected radial seating load R = 1,000 N and positive assumed clearance, M ≈ 2.924, μeff ≈ 0.877, ideal combined limiting friction is about 877 N and each flank normal is about 1,462 N.
These are ideal static cross-section quantities, not transmitted drive force or power.
Scope and correction boundary
The former calculator labeled R as rope tension and presented μR/sin(α/2) as drive grip without a wrap-angle or tight/slack-tension model. The input is corrected to radial seating load and the output is bounded to ideal cross-section friction capacity.
Unsupported power, speed, materials, groove, clearance, service-life, failure, maintenance and product claims plus the fabricated mill example and unrelated actuator section are removed.
Questions
Is radial seating load the tight-side rope tension?
No. It is the selected resultant pressing the rope cross-section into the groove.
Does a positive gap prove correct seating?
No. It is an assumption flag. Real seating requires rope and groove dimensions plus deformation and wear information.
Does friction capacity equal transmitted drive force?
No. Drive traction also depends on wrap angle and the tight/slack tension relationship.
Can this model size a rope drive?
No. It omits speed, centrifugal effects, fatigue, temperature, creep, materials, hardware and ratings.
Technical references
- OpenStax University Physics, Friction — limiting static friction and normal-force relationships.
- NIST Special Publication 811 — SI units and coherent quantity notation.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
