Two rigid coupling rods can connect two parallel shafts through two pairs of equal cranks. Within each pair, the input and output cranks stay parallel. The second pair is phased relative to the first, allowing one rod to provide leverage when the other pair passes through dead centre.
Continuous Rotary via Two Paired Link Cranks Interactive Calculator
Explore two parallel shafts connected by two separate crank pairs. Change the phase between the pairs or pause at a rotation angle. The rigid rods stay connected while the calculator compares their normalized torque contributions.
Equation Used
- Equal crank radii on two parallel shafts, with two rigid rods each equal in length to the fixed shaft spacing.
- Each pair remains on the parallel-crank assembly branch. The second pair is offset by φ on both shafts.
- Equal force magnitude in each rod; force signs chosen to assist rotation. No actual force, radius, stiffness or motor torque is entered.
- Prescribed rotation continues through singular positions for illustration. At phase 0° or 180° both pairs share dead centres; the animation is not a demonstration of self-starting there.
- No friction, bearing clearance, rod buckling, load-sharing stiffness or inertia calculation.
Each rod joins two cranks at the same angle. The phase offset belongs between the front and rear pairs on each shaft. Torque percentages assume equal rod-force magnitudes, with force direction chosen to assist rotation.
Four cranks and two rods
The front pair has one crank on each shaft and one blue rod between their pins. The rear pair has another crank on each shaft and a gold rod. Both cranks within a colored pair have the same angle, so their rod remains parallel to the line between the shaft axes.
Both rods have a constant length equal to the shaft spacing. Phase changes the relative angle between the front and rear pairs on each shaft; it does not offset the two ends of a single rod. The shaft bearings and the separate crank planes are shown to make that distinction visible.
Why quartering helps
The historical parallel-shaft coupling uses a second crank pair at 90° to the first to separate their dead-centre positions. Equal parallel cranks and rods give a 1:1 angular relationship between shafts on the selected assembly branch.
This calculator explores that geometry. It does not prescribe forces for a specific locomotive, engine or machine, nor establish a universal rod size, clearance or operating speed.
Normalized torque comparison
For a horizontal rod force F acting at crank radius r, the moment-arm magnitude is r|sin θ|. Torque magnitude divided by Fr is therefore |sin θ|. The second pair has angle θ+φ, giving |sin(θ+φ)|.
The displayed percentages are 100 times those values, and the combined curve is their sum. It is a comparison under equal available force magnitudes, with each force direction selected to assist rotation. It is not an automatically determined load split between two redundant rods.
For 0≤φ≤180°, the smallest sum is 100 sin φ. The calculation samples at 0.25° increments; each selectable 0.5° phase setting includes the minimizing positions. At 90°, the minimum is 100% and the maximum is approximately 141.4%.
Compare phases
At θ=0° and φ=90°, pair A has zero moment arm while pair B has its maximum. Their equal-force sum is 100%. At θ=45°, each contributes approximately 70.7%, totaling 141.4%.
At φ=0°, both pairs reach dead centre together. Their minimum sum is 0%, despite the higher 200% sum at 90° rotation. At φ=30°, the minimum sum is 50%. These percentages are relative to one rod’s Fr, not an efficiency rating.
Motion versus available torque
Playback imposes rotation to expose the geometry through a complete turn. It continues through dead-centre positions so they can be inspected. That does not imply a real mechanism could start there under load.
Real forces in the two rods depend on stiffness, clearances, applied shaft torque and support behavior. The equal-force comparison is an explicit idealization. Bearing reactions, rod bending, buckling, fatigue and friction are outside this model.
Questions about the paired cranks
Why are there two rods?
Each rod connects one matched crank pair. The second pair can provide leverage when the first reaches dead centre.
Where is the phase angle measured?
Between the front and rear cranks on each shaft. The two crank ends of any one rod have matching angles.
Does either rod change length?
No. Each rod stays equal to the fixed distance between the shaft axes.
Can the combined result exceed 100%?
Yes. It adds two contributions, each normalized to one rod’s maximum Fr.
Does the animation prove the mechanism can start at dead centre?
No. Rotation is imposed for visualization. At 0° or 180° phase, both pairs share singular positions.
Are these actual torque values?
No. They are normalized equal-force comparisons. Actual force sharing and torque capacity are not solved.
References
1911 Encyclopædia Britannica, Applied Mechanics, section 62, describes coupling parallel shafts with equal cranks and a second pair at right angles.
David Allan Low, An Introduction to Machine Drawing and Design, chapter X, explains crank arms, pins, shafts and quartered axle construction. The drawing here is a generic two-rod coupling, not a reproduction of a particular machine.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
