Clover-leaf Cam: Three-Lobe Opposed-Roller Motion and Travel Calculator

One bar, two rollers and a positive drive

Hiscox figure 1096 shows a three-lobe cam between rollers mounted on one rectilinear bar. The Scientific American description likewise explains that the cam fills the space between the rollers throughout its rotation. The followers are constrained mechanically in both directions, so this arrangement does not depend on a return spring.

The animation places the bar behind the cam so the shaft and roller pins remain visible. Fixed guides constrain the bar horizontally. Contact dots lie on the derived cam edge, offset from each roller center by the roller radius along the contact normal.

What makes this a clover-leaf drive?

The opposed rollers on one bar give positive drive in both directions. The three projections in the historical example produce three reciprocations per shaft revolution. The illustrated harmonic family extends the same constant-separation geometry to other odd lobe counts.

Derived harmonic geometry

For stroke s, let a = s/2. The bar displacement is x = −a cos(Nφ). N is an odd lobe count and φ is shaft angle. The roller-center pitch curve is r(θ) = B − a cos(Nθ). For odd N, r(θ) + r(θ+π) = 2B, so the two roller centers remain a fixed distance apart.

The actual cam surface is the inward normal offset of that pitch curve by the roller radius. Subtracting a radius only in the radial direction would not preserve tangency on the sloping flanks. The displayed family uses B = (0.6N+1)a + 2 mm and roller radius max(1 mm, 0.35a). These define an illustrative compatible geometry, not a manufacturing specification.

Each revolution gives N reciprocating cycles. For c = N × turns and f its fractional part, cumulative positive travel is s × [floor(c) + (1−cos(2πf))/2] when f is below one-half, and s × [floor(c)+1] otherwise. This counts only motion to the right, starting at the left-hand limit.

Worked cycle and travel example

For three lobes, one shaft revolution and a 10 mm stroke, the output completes three reciprocations. Lobe spacing is 120°. Total positive travel is 30 mm, and total travel including the return strokes is 60 mm.

For only one-quarter of a shaft revolution, the motion covers 0.75 cycle: one complete rise and half of the return. Cumulative positive travel is therefore 10 mm, not 7.5 mm. The cycle-equivalent count and travelled distance describe different quantities.

Reading the model

Increasing lobe count increases reciprocations per shaft revolution. Increasing stroke increases bar travel and the dimensions of the generated cam family. Shaft turns set the calculation interval and the span of the scrub control. Playback is an illustrative constant-speed demonstration, not an entered motor speed.

The model covers geometry and displacement. An actual machine also needs contact, bearing, lubrication, stiffness and dynamic analysis for its operating conditions.

Clover-leaf cam questions

Why are even lobe counts unavailable?

In this harmonic family, diametrically opposed roller-center radii add to a constant only for odd counts. An even count would change the required distance between rollers on the rigid bar.

Why does the historical example have three cycles per revolution?

Its three lobes repeat the rise-and-return motion three times in one full shaft turn.

Why is no return spring shown?

The two opposed rollers constrain the bar in both directions. This is a positive mechanical drive.

Does cumulative rise include the return stroke?

No. It adds only rightward movement from the left-hand starting position. A full reciprocation has twice that stroke distance when both directions are counted.