The angle between a coupler and output rocker determines how an assumed coupler force divides into tangential and radial components. Change that angle to explore the two components at their shared joint.
Four-Bar Transmission-Angle Component Calculator
Vary transmission angle and a user-selected comparison band. The outputs are normalized components of an assumed axial coupler force; they are not efficiency, useful power, bearing load, torque or capacity.
Equation Used
- The coupler is an ideal two-force member in slow motion.
- Pins are frictionless and links are rigid for the component diagram.
- The low/high entries define only a user-selected comparison band.
The tangential component acts perpendicular to the rocker and contributes to its turning moment. The radial component acts along the rocker. The percentages describe force direction; they do not give an actual force or torque.
Coupler force at the output rocker
A planar four-bar has ground, input, coupler and output links joined by pins. The transmission angle is measured between the coupler and output rocker at their shared joint. In an ideal slow-motion force diagram, the coupler is treated as a two-force member, so its joint force acts along the coupler.
The animation focuses on that joint and the directions of the coupler and rocker. A complete moving four-bar cannot be drawn without four link lengths, ground-pivot placement, input angle and an assembly branch.
Use as a geometry diagnostic
The diagram helps explain how an assumed coupler-force direction relates to output-rocker moment. It does not select a linkage or predict a machine. Position analysis, mobility, interference, link stress, pins, bearings and dynamics must be checked from the actual geometry and load case.
Normalized force components
F_t is perpendicular to the output rocker and therefore has a moment arm about its fixed pivot. F_r lies along the rocker. These are vector components of an assumed axial force, not efficiency or bearing-load percentages. The third result is only angular distance outside the selected comparison band.
Angle example
At mu=90 degrees the normalized tangential component is 100% and the radial component is 0%. At mu=45 degrees both magnitudes are about 70.7%. No actual newtons or torque follow until a coupler force and rocker length are specified.
What angle alone cannot tell you
Transmission angle is a useful geometric diagnostic, but it is not a complete measure of transmission ratio, mechanical advantage, efficiency, bearing load or robustness. Real results depend on the complete linkage, assembly branch, input position, external load, speed, inertia, friction, clearances and stiffness.
Transmission-angle questions
Is the tangential percentage an efficiency?
No. It is a normalized vector component.
Is the radial percentage a bearing-load prediction?
No. Actual joint reaction requires a full force analysis.
Why does the diagram omit the input crank?
This diagram isolates the coupler-to-rocker joint. A complete four-bar model also needs the input link length, fixed-pivot positions and assembly configuration.
Kinematics references
- Rothenhofer et al., Precision Engineering: definition and design role of transmission angle.
- Carnegie Mellon, Planar Linkages: two-force-member assumption and output torque relation.
- Cornell Reuleaux Collection, Four-bar Linkage: four-link, four-joint topology.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
