# Wedge Angle Force Calculator Calculate the force-amplification ratio and self-locking condition of a wedge mechanism. Ideal M = 1/tan(α), with friction M = 1/tan(α+ρ) where ρ = arctan(μ). Self-locking when α ≤ ρ (i.e. tan(α) ≤ μ). > Canonical page: https://elysiatools.com/en/tools/wedge-angle-force-calculator - **Category:** Math & Numbers - **Keywords:** wedge mechanism, force amplification, self-locking, friction angle, wedge angle, tan(α), machine design, mechanical engineering ## Overview The Wedge Angle Force Calculator helps mechanical engineers and machine designers determine the force-amplification ratio and self-locking conditions of a wedge mechanism. By entering the wedge angle, friction coefficient, and friction model, you can quickly evaluate mechanical advantage and verify if the system will remain locked under load. ## Inputs - **Wedge Angle α (°)** (number): e.g. 10 - **Friction Coefficient μ** (number): e.g. 0.15 - **Friction Model** (select) - **Input Force F_in (N)** (number): Optional. If provided, the output force F_out = F_in × force ratio. - **Decimal Places** (number) ## When to use - Designing mechanical clamps, fixtures, or wedge jacks that require high force amplification. - Verifying if a wedge mechanism will self-lock under friction to prevent slipping. - Calculating the output force of a wedge system given a specific input force and friction coefficient. ## How it works - Enter the wedge angle (α) in degrees and the friction coefficient (μ) between the contacting surfaces. - Select the friction model, choosing either 'Ideal (no friction)' or 'With friction', and optionally input the applied force. - The calculator computes the force-amplification ratio, the friction angle (ρ), and checks the self-locking condition (α ≤ ρ). ## Use cases - Analyzing wedge-clamp designs in manufacturing fixtures to ensure they hold parts securely without slipping. - Calculating the mechanical advantage of wedge jacks used for lifting heavy machinery. - Determining the optimal wedge angle for self-locking fasteners and taper joints. ## Frequently asked questions ### What is the self-locking condition for a wedge? A wedge is self-locking when the wedge angle (α) is less than or equal to the friction angle (ρ), meaning tan(α) ≤ μ. ### How does friction affect the force-amplification ratio? Friction reduces the force-amplification ratio. The ideal ratio is 1/tan(α), whereas with friction it becomes 1/tan(α+ρ). ### Can I calculate the actual output force? Yes, by entering an optional input force (F_in), the calculator will output the resulting force (F_out) based on the calculated ratio. ### What is the friction angle (ρ)? The friction angle is the angle whose tangent is the friction coefficient, calculated as ρ = arctan(μ). ### What happens if the wedge is not self-locking? If the wedge is not self-locking, it is reversible, meaning the wedge may slip back out when the input force is removed. ## Related tools - [Cam Follower Displacement Calculator](https://elysiatools.com/en/tools/cam-follower-displacement): Calculate the follower displacement, velocity coefficient, acceleration coefficient and pressure angle during the cam rise phase. 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