In the ideal model, a journal box centered on the crank pin slides in a vertical cross-head slot while the cross-head translates horizontally. For θ measured from the positive stroke axis, x=r cosθ, v=−rω sinθ, a=−rω² cosθ and stroke=2r.
Slotted Cross-Head with Journal Box · Ideal Kinematics
Explore exact ideal harmonic motion of a guided cross-head driven by a captured sliding journal box.
Equation Used
- The crank pin and ideal journal-box center are coincident.
- The journal box remains captured in a finite vertical slot and the cross-head translates horizontally.
- Angular speed is constant and θ increases counterclockwise from the positive stroke axis.
- Clearance, friction, loads, inertia, wear, strength and safety are excluded.
The journal-box outline is illustrative; its center remains exactly coincident with the crank pin throughout the presentation.
Captured sliding journal box
The crank pin and finite journal block remain inside a transverse slot. The journal absorbs the pin's vertical component while its horizontal coordinate exactly drives the guided cross-head.
What the calculator determines
Select radius, crank angle and constant speed. The calculator reports exact ideal stroke, signed mid-stroke position, signed velocity and signed acceleration.
Ideal harmonic identities
ω=2πN/60; x=r cosθ; v=−rω sinθ; a=−rω² cosθ; stroke=2r.
Selected-input example
For r=25 mm, θ=0° and N=120 rpm, stroke is 50 mm, position is +25 mm, velocity is zero and acceleration is about −3947.8 mm/s².
Ideal kinematics only
Journal dimensions in the drawing are illustrative. Clearance, lubrication, friction, contact pressure, force, torque, inertia, balancing, wear, fatigue, strength and safe speed are excluded.
Questions
Does the journal box alter the ideal motion law?
No. With its center coincident with the crank pin and an ideal transverse slot, the cross-head follows the pin's axial projection.
Can acceleration size the journal?
No. Mass, loads, contact area, material and lubrication are absent.
References & Further Reading
- Wikipedia contributors. Slider-crank linkage. Wikipedia
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