KEVOS® MAKEOS · Mechanics
Resultant of Non-Concurrent and Parallel Forces
What single force and line of action replaces these forces acting at different points?
Resultant magnitude, direction, moment about the origin and line of action of up to four coplanar forces acting at different points, including parallel forces.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Force 1 | ||
| Magnitude | N | Magnitude of force 1 (0 if not used). |
| Direction from +X | ° | Direction of force 1 anticlockwise from +X (−90° is straight down). |
| X of a point on its line | mm | X coordinate of any point on force 1’s line of action. |
| Y of that point | mm | Y coordinate of that point. |
| Force 2 | ||
| Magnitude | N | Magnitude of force 2 (0 if not used). |
| Direction from +X | ° | Direction of force 2 anticlockwise from +X (−90° is straight down). |
| X of a point on its line | mm | X coordinate of any point on force 2’s line of action. |
| Y of that point | mm | Y coordinate of that point. |
| Force 3 | ||
| Magnitude | N | Magnitude of force 3 (0 if not used). |
| Direction from +X | ° | Direction of force 3 anticlockwise from +X (−90° is straight down). |
| X of a point on its line | mm | X coordinate of any point on force 3’s line of action. |
| Y of that point | mm | Y coordinate of that point. |
| Force 4 | ||
| Magnitude | N | Magnitude of force 4 (0 if not used). |
| Direction from +X | ° | Direction of force 4 anticlockwise from +X (−90° is straight down). |
| X of a point on its line | mm | X coordinate of any point on force 4’s line of action. |
| Y of that point | mm | Y coordinate of that point. |
Method and formulas
- Rx = Σ F cos θ; Ry = Σ F sin θ.
- Moment about the origin M = Σ (x Fy − y Fx).
- Line of action crosses the X axis at x₀ = M ÷ Ry (or the Y axis at −M ÷ Rx); if R = 0 the system reduces to a couple M.
- Example: the default downward loads total 3,000 N acting at x = 366.67 mm.
Limitations
- Coplanar forces only; 3D systems need a wrench reduction.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find where the resultant of several loads acts on a beam or frame
- Find the centre of loads on a foundation
- Check equilibrium of a free body
Who it is for
- Design engineers
- Structural engineers
- Engineering students
What you get
- Resultant components and magnitude
- Moment about the origin
- Line of action of the resultant
- Couple when the resultant is zero
Interpreting the result
- For parallel loads, x₀ is the load centre: put a support or lifting point there to avoid tipping.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 153–163. Topic reference; no source tables or recommended settings are reproduced.
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