A conventional cycloidal reducer uses an eccentric input to move a lobed disc inside a ring of fixed rollers. With one fewer disc lobe than ring rollers, the disc rotates slowly in the opposite direction. Pins in enlarged disc holes transfer that slow rotation to an output carrier centered on the main axis.
Cycloidal Drive Interactive Calculator
Explore a conventional one-lobe-difference cycloidal reducer. Adjust roller count, size, eccentricity and input speed; watch the output pins remove the disc’s orbital motion.
Equation Used
- Fixed ring with N equally spaced round rollers and one disc with N−1 lobes.
- Ideal conjugate profile, zero-clearance point tangency and rigid parts.
- Six output pins at half the ring pitch radius; pin radius is 0.07R.
- One disc displayed; no dynamic balancing, friction, elastic load sharing or manufacturing clearance.
One-lobe-difference reducer; disc lobe count follows the ring count. Negative output means opposite rotation. No load-sharing or torque-rating estimate.
Orbiting disc, concentric output
The input moves the disc center around a small circle of radius e. The bronze disc meshes with the housing rollers and turns backward by one lobe pitch per input revolution. Its highlighted marker makes that slow rotation visible.
The teal output pins rotate about the fixed main axis. Each oversized hole follows the disc’s offset center, while its pin remains on the concentric carrier. Giving the hole a radius equal to pin radius plus e accommodates the orbit.
Compare count, size and eccentricity
Changing ring roller count changes the reduction ratio. Changing pitch diameter scales the mechanism. The eccentricity ratio changes the orbit size; the roller fraction changes roller diameter and the generated disc profile.
Input speed changes signed output speed. Animation is slowed for inspection at higher speeds, while the results retain the entered rpm. Setting speed to zero stops the mechanism.
One-lobe-difference geometry
For N ring rollers, this model uses L=N−1 disc lobes. The signed speed ratio is −1/L, so n_out=−n_in/L. Independent incompatible lobe counts are not drawn as though they belong to this arrangement.
With ring pitch radius R, eccentricity e=λR/N. Ring roller diameter is f times the adjacent pin-center spacing, or 2fR sin(π/N).
The disc profile is generated from the pin-center envelope q(t)=[R cos t−e cos Nt, R sin t−e sin Nt], offset inward by the roller radius along its outward normal. It is not a decorative wave. The disc then moves by center offset e at input angle α and rotation −α/L.
Eleven ring rollers and ten lobes
With11 rollers and10 lobes, the reduction is10:1. A60rpm input gives−6rpm output, or one opposite output revolution for every ten input revolutions.
For200mm pitch diameter and λ=0.5, eccentricity is about4.545mm. Every output hole therefore needs an ideal diameter9.091mm larger than its pin diameter to accommodate the offset. Manufacturing clearance is additional and is not specified here.
Geometry does not establish torque capacity
The former fixed65% loaded-pin estimate has been removed. Actual load sharing depends on deformation, clearance, contact geometry, material and applied load; pin count alone cannot establish it.
This educational cutaway shows one disc and omits balance masses or an opposed companion disc. Bearing selection, stresses, profile modifications, lubrication and tolerances are outside the calculator. The displayed geometry is not a manufacturing drawing.
Cycloidal drive questions
Why does the disc have one fewer lobe?
That is the conventional arrangement modeled here, making the reduction equal to the disc lobe count.
Why are the output holes larger than the pins?
The extra radius e lets the disc orbit around pins whose carrier remains centered.
Do all touching pins carry equal load?
No. Geometric tangency is not a load-sharing calculation.
Why is the output speed negative?
It denotes rotation opposite to the input with the ring fixed.
Reference
US20230223815A1, background and figure1, conventional cycloidal reducer arrangement with fixed ring pins, eccentric disc and output-pin carrier. The model represents that conventional background arrangement, not the publication’s later modified embodiments. Profile and tangency relationships here are independently derived and checked numerically.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
