This double-cam motion uses two perpendicular contact faces on one sliding follower. A rotating cam moves the follower sideways and up and down. Its horizontal arm slides through a box attached to a vertically guided output shaft, separating the two motion components.
The historical arrangement is shown in Hiscox figure 1105. The example uses an eccentric elliptical cam to calculate the contact positions and two equal strokes shifted by a quarter cycle. Its profile is illustrative; the historical drawing does not specify the exact contour.
Double Cam Motion Interactive Calculator
Explore an eccentric elliptical cam driving two perpendicular follower faces. The horizontal arm slides through a box on the vertically guided shaft. Both strokes come from solved tangent contacts.
Equation Used
- Rigid eccentric ellipse and perpendicular flat follower faces.
- Frictionless maintained contact; spring preload not solved.
- Horizontal arm translates through a box attached to the vertically guided output shaft.
- No torque, stress, wear or speed rating.
Hiscox figure 1105 arrangement; the ellipse profile and dimensions are illustrative assumptions. Maintained contact is assumed, not a dynamic prediction.
One cam, two contact faces
The blue follower has a horizontal underside resting against the top of the gold cam and a vertical inside face resting against its right side. As the cam rotates, those two tangent contacts set the follower’s vertical and horizontal position. The follower translates without rotating.
The horizontal arm passes through the blue sliding box. That box travels with the gray vertical output shaft, which is constrained by two stationary bearings. The arm can slide left and right through the box while lifting and lowering the shaft. A spring pulls the follower down and left to maintain the two ideal contacts.
Gold and blue contact dots mark the solved tangency points. The cam outline rotates as a rigid ellipse about its offset input shaft. A dot marks the ellipse center separately from the shaft. Housing, bearings and spring are explanatory outlines, not manufacturing details.
Studying coordinated perpendicular motion
The arrangement demonstrates how a single rotating profile can prescribe two translation components. Changing the ellipse ratio changes the lift waveform. Moving the shaft off the ellipse center changes the relative prominence of the two lobes in each revolution.
When the cam is circular and centered, both support distances are constant and there is no output stroke. A circular eccentric cam produces sinusoidal components. A centered noncircular ellipse produces two repeated lift events per shaft revolution. These distinctions remain visible in the animation and calculator.
Exact support geometry for the chosen ellipse
Let A and B be the cam’s major and minor semiaxes, e the input shaft’s offset from the ellipse center along the major axis, and θ the shaft angle. The origin is the input shaft. The cam center rotates at (e cosθ,e sinθ).
X=e cosθ+√(A²cos²θ+B²sin²θ)
Y=e sinθ+√(A²sin²θ+B²cos²θ)
X locates the vertical right-hand follower face. Y locates the horizontal upper face and the vertical output shaft. Since Y(θ)=X(θ−90°), the two motions have equal total stroke and a quarter-revolution phase shift.
For D=A²−B², the maximum support is A+e. If D>0 and e<D/A, the minimum is B√(1−e²/D); otherwise it is A−e. Stroke is maximum minus minimum. Stroke depends on both ellipse shape and shaft eccentricity, using the minimum and maximum support distances above.
One shaft revolution takes 60/N seconds. Playback is slowed for inspection; zero input speed stops automatic motion. Scrubbing still permits geometric inspection.
Example and limiting cases
With A=40 mm, B/A=0.8 and e/A=0.2, the minor radius is 32 mm and eccentricity is 8 mm. Each output ranges from about 30.17 mm to 48 mm from the shaft, giving 17.83 mm total stroke. At 60 rpm one shaft revolution takes one second.
Set B/A to one and eccentricity to zero to obtain a concentric circle: its orientation changes but neither follower moves. Keeping a circular cam and adding eccentricity gives a stroke of 2e. Setting eccentricity to zero with B/A below one gives a stroke of A−B.
Contact and model boundaries
The model uses frictionless flat followers on a convex elliptical cam and assumes enough spring preload to maintain contact. It solves position, not spring force, inertia, contact stress, wear, shaft torque or a maximum operating speed. The spring shown is schematic and is not sized by the calculator.
The historical source supplies the arrangement, but does not supply the exact cam law or dimensions. The adjustable ellipse supplies a defined example profile. Both follower positions come from tangent support distances of the same rotating ellipse.
A working assembly also requires contact-force, guide, spring and material data. The horizontal and vertical faces each follow their corresponding tangent contact on the cam.
Double-cam motion questions
Are there two separate cams?
Not in the historical arrangement shown here. One cam bears on two perpendicular faces of a translating follower.
Why do the two strokes match?
For the specified ellipse and offset, the horizontal support waveform becomes the vertical one after a 90° phase shift. Their minimum and maximum are therefore identical.
Why does a centered ellipse have two lift events?
Its outline repeats after a half-turn. The shaft still completes one full revolution per displayed cycle.
Does the spring guarantee real contact at any speed?
No. Contact is assumed for this geometric model; preload, follower mass and dynamic separation require a separate analysis.
Historical construction reference
Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 272, figure 1105, shows the perpendicular-faced follower, sliding horizontal arm, box on the guided vertical shaft and contact-maintaining spring. The ellipse and all adjustable dimensions are explicit modeling choices.
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