For the ideal transverse-slot cross-head shown here, the crank pin remains captured in a vertical slot while the yoke translates horizontally. With angle θ measured from the positive stroke axis, x=r cosθ, v=−ωr sinθ, stroke=2r and transverse pin offset=r sinθ.
How actuator stroke affects Slotted Cross-head Mechanism
With slotted cross-head mechanism, the motion profile matters. A linear actuator gives direct extension and retraction, but the output linkage may still create non-linear speed, changing mechanical advantage, and end-of-travel loads.
For structural members, the actuator load should be applied through brackets that do not introduce unintended bending. Check both static load and the extra load created when the mechanism starts, stops, or binds.
The mechanism may also change speed as the linkage angle changes. A constant actuator extension speed does not always create constant output speed, so timing should be checked at the actual output point.
- Map actuator stroke to the actual output travel before choosing a model.
- Check for binding, changing leverage, and peak load near the ends of travel.
- Decide whether timed motion is acceptable or position feedback is required.
For a FIRGELLI design review, calculate the load case with the FIRGELLI actuator force calculator and plan the switching or controller arrangement with the linear actuator wiring diagram generator. If an actuator or cylinder is already installed, the linear actuator replacement finder helps keep the comparison tied to real dimensions.
Slotted Cross-Head · Ideal Scotch-Yoke Kinematics
Explore exact ideal transverse-slot cross-head velocity, stroke and pin offset at a selected endpoint angle.
Equation Used
- The crank radius is fixed and the crank pin remains captured in a finite vertical slot.
- The cross-head translates only on a horizontal guide.
- Angular speed is constant and θ increases counterclockwise from the positive stroke axis.
- Clearance, friction, loads, inertia, wear, strength and safety are excluded.
With x=r cosθ and counterclockwise-positive angle, axial velocity is v=−ωr sinθ.
Closed crank-pin and slot geometry
The crank pin has fixed radius and its horizontal coordinate is exactly the cross-head coordinate. Its vertical coordinate is absorbed by a finite transverse slot, giving exact simple harmonic translation.
What the calculator determines
Select constant crank speed, radius and endpoint angle. The calculator reports signed axial velocity, peak speed magnitude, stroke and signed transverse pin offset.
Ideal Scotch-yoke identities
ω=2πN/60; x=r cosθ; v=−ωr sinθ; |v|max=ωr; stroke=2r; yslot=r sinθ.
Selected-input example
For N=250 rpm, r=40 mm and θ=90°, signed axial velocity is about −1.047 m/s, peak speed magnitude is 1.047 m/s, stroke is 80 mm and slot offset is 40 mm.
Ideal kinematics only
The reference does not size the pin, slot, guides, piston or structure. Clearance, friction, lubrication, contact pressure, force, torque, inertia, balancing, wear, fatigue, strength and safe speed are excluded.
Questions
Why is velocity negative at 90°?
With θ increasing counterclockwise from the positive stroke axis and x=r cosθ, dx/dt=−ωr sinθ.
Is this different from a Scotch yoke?
The modeled transverse-slot cross-head has the same ideal kinematic topology.
References & Further Reading
- Wikipedia contributors. Scotch yoke. Wikipedia
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