A Watt linkage can make a selected coupler point follow an approximately straight path through part of its motion. This calculator evaluates an explicitly declared cubic small-motion proxy from entered arm length and half-stroke.
Watt's Linkage Interactive Calculator
Enter arm-length reference, half-stroke and an allowable deviation. The cubic result is a comparison proxy—not solved linkage closure, an optimized tracing point or certified path error.
Equation Used
- L is a positive entered scale reference.
- y is a nonnegative entered half-stroke.
- The cubic formula is a declared proxy, not a general Watt-link closure equation.
- Allowable deviation is independently entered and used only as a ratio denominator.
- The cubic calculation omits user-defined ground-pivot spacing, central-link dimensions, assembly mode, actual path, singularities, clearances, loads and dynamics.
Approximate Straight-Line Context
U.S. Patent 4,545,266 describes the conventional Watt linkage point as a close approximation to a straight line over the center of its travel. U.S. Patent 2,483,668 likewise states that Watt motion is approximate. Neither source makes this page's cubic expression a complete linkage solution.
What This Calculator Represents
The tool evaluates one declared cubic proxy and compares it with an independently entered allowable deviation.
Declared Proxy Calculation
stroke=2y
ratio=100y/L
use=100delta/limit
The drawing solves its fixed four-bar geometry. The cubic calculation does not solve custom linkage closure.
Worked Screening Example
For L=400 mm and y=100 mm, the declared proxy is 0.781 mm, full-stroke reference is 200 mm and y/L is 25%. Against a 1 mm entered allowance, proxy use is 78.1%.
Assumptions and Limits
- Calculated: the stated cubic proxy and entered-value ratios.
- Illustrated: a fixed four-bar with a green curve sampled from its actual coupler-midpoint positions.
- Not calculated: custom entered-geometry closure, actual path error, assembly limits, forces or dynamics.
Frequently Asked Questions
Is delta exact path error?
No.
Does the tool solve linkage geometry?
The animation solves a fixed illustrative four-bar. The numeric outputs use a separate cubic comparison and do not solve a linkage defined by the entered dimensions.
Is Watt motion perfectly straight?
No; it is approximate.
Is the allowable value a standard?
No; it is entered by the user.
Are singularities checked?
No.
Can this design a linkage?
No.
References
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